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authorLorry Tar Creator <lorry-tar-importer@baserock.org>2015-04-08 03:09:47 +0000
committer <>2015-05-05 14:37:32 +0000
commitf2541bb90af059680aa7036f315f052175999355 (patch)
treea5b214744b256f07e1dc2bd7273035a7808c659f /libs/math/doc
parented232fdd34968697a68783b3195b1da4226915b5 (diff)
downloadboost-tarball-master.tar.gz
Imported from /home/lorry/working-area/delta_boost-tarball/boost_1_58_0.tar.bz2.HEADboost_1_58_0master
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1095 files changed, 7485 insertions, 1879 deletions
diff --git a/libs/math/doc/background/implementation.qbk b/libs/math/doc/background/implementation.qbk
index ca07b2dd5..ae0ece2fc 100644
--- a/libs/math/doc/background/implementation.qbk
+++ b/libs/math/doc/background/implementation.qbk
@@ -526,7 +526,21 @@ or Using Cygwin, a command such as:
/cygdrive/c/progra~1/Inkscape/inkscape -d 120 -e $(cygpath -a -w $(basename $file .svg).png) $(cygpath -a -w $file);
done]
-Currently Inkscape seems to generate the better looking png's.
+Using BASH
+
+[pre # Convert single SVG to PNG file.
+# /c/progra~1/Inkscape/inkscape -d 120 -e a.png a.svg
+]
+
+or to convert All files in folder SVG to PNG.
+
+[pre
+for file in *.svg; do
+/c/progra~1/Inkscape/inkscape -d 120 -e $(basename $file .svg).png $file
+done
+]
+
+Currently Inkscape seems to generate the better looking PNGs.
The PDF is generated into \pdf\math.pdf
using a command from a shell or command window with current directory
diff --git a/libs/math/doc/distributions/arcsine.qbk b/libs/math/doc/distributions/arcsine.qbk
new file mode 100644
index 000000000..1053ffb45
--- /dev/null
+++ b/libs/math/doc/distributions/arcsine.qbk
@@ -0,0 +1,288 @@
+[section:arcine_dist Arcsine Distribution]
+
+[import ../../example/arcsine_example.cpp] [/ for arcsine snips below]
+
+
+``#include <boost/math/distributions/arcsine.hpp>``
+
+ namespace boost{ namespace math{
+
+ template <class RealType = double,
+ class ``__Policy`` = ``__policy_class`` >
+ class arcsine_distribution;
+
+ typedef arcsine_distribution<double> arcsine; // double precision standard arcsine distribution [0,1].
+
+ template <class RealType, class ``__Policy``>
+ class arcsine_distribution
+ {
+ public:
+ typedef RealType value_type;
+ typedef Policy policy_type;
+
+ // Constructor from two range parameters, x_min and x_max:
+ arcsine_distribution(RealType x_min, RealType x_max);
+
+ // Range Parameter accessors:
+ RealType x_min() const;
+ RealType x_max() const;
+ };
+ }} // namespaces
+
+The class type `arcsine_distribution` represents an
+[@http://en.wikipedia.org/wiki/arcsine_distribution arcsine]
+[@http://en.wikipedia.org/wiki/Probability_distribution probability distribution function].
+The arcsine distribution is named because its CDF uses the inverse sin[super -1] or arcsine.
+
+This is implemented as a generalized version with support from ['x_min] to ['x_max]
+providing the 'standard arcsine distribution' as default with ['x_min = 0] and ['x_max = 1].
+(A few make other choices for 'standard').
+
+The arcsine distribution is generalized to include any bounded support ['a <= x <= b] by
+[@http://reference.wolfram.com/language/ref/ArcSinDistribution.html Wolfram] and
+[@http://en.wikipedia.org/wiki/arcsine_distribution Wikipedia],
+but also using ['location] and ['scale] parameters by
+[@http://www.math.uah.edu/stat/index.html Virtual Laboratories in Probability and Statistics]
+[@http://www.math.uah.edu/stat/special/Arcsine.html Arcsine distribution].
+The end-point version is simpler and more obvious, so we implement that.
+If desired, [@http://en.wikipedia.org/wiki/arcsine_distribution this]
+outlines how the __beta_distrib can be used to add a shape factor.
+
+The [@http://en.wikipedia.org/wiki/Probability_density_function probability density function PDF]
+for the [@http://en.wikipedia.org/wiki/arcsine_distribution arcsine distribution]
+defined on the interval \[['x_min, x_max]\] is given by:
+
+[figspace] [figspace] f(x; x_min, x_max) = 1 /([pi][sdot][sqrt]((x - x_min)[sdot](x_max - x))
+
+For example, __WolframAlpha arcsine distribution, from input of
+
+ N[PDF[arcsinedistribution[0, 1], 0.5], 50]
+
+computes the PDF value
+
+ 0.63661977236758134307553505349005744813783858296183
+
+The Probability Density Functions (PDF) of generalized arcsine distributions are symmetric U-shaped curves,
+centered on ['(x_max - x_min)/2],
+highest (infinite) near the two extrema, and quite flat over the central region.
+
+If random variate ['x] is ['x_min] or ['x_max], then the PDF is infinity.
+If random variate ['x] is ['x_min] then the CDF is zero.
+If random variate ['x] is ['x_max] then the CDF is unity.
+
+The 'Standard' (0, 1) arcsine distribution is shown in blue
+and some generalized examples with other ['x] ranges.
+
+[graph arcsine_pdf]
+
+The Cumulative Distribution Function CDF is defined as
+
+[figspace] [figspace] F(x) = 2[sdot]arcsin([sqrt]((x-x_min)/(x_max - x))) / [pi]
+
+[graph arcsine_cdf]
+
+[h5 Constructor]
+
+ arcsine_distribution(RealType x_min, RealType x_max);
+
+constructs an arcsine distribution with range parameters ['x_min] and ['x_max].
+
+Requires ['x_min < x_max], otherwise __domain_error is called.
+
+For example:
+
+ arcsine_distribution<> myarcsine(-2, 4);
+
+constructs an arcsine distribution with ['x_min = -2] and ['x_max = 4].
+
+Default values of ['x_min = 0] and ['x_max = 1] and a ` typedef arcsine_distribution<double> arcsine;` mean that
+
+ arcsine as;
+
+constructs a 'Standard 01' arcsine distribution.
+
+[h5 Parameter Accessors]
+
+ RealType x_min() const;
+ RealType x_max() const;
+
+Return the parameter ['x_min] or ['x_max] from which this distribution was constructed.
+
+So, for example:
+
+[arcsine_snip_8]
+
+[h4 Non-member Accessor Functions]
+
+All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
+that are generic to all distributions are supported: __usual_accessors.
+
+The formulae for calculating these are shown in the table below, and at
+[@http://mathworld.wolfram.com/arcsineDistribution.html Wolfram Mathworld].
+
+[note There are always [*two] values for the [*mode], at ['x_min] and at ['x_max], default 0 and 1,
+so instead we raise the exception __domain_error.
+At these extrema, the PDFs are infinite, and the CDFs zero or unity.]
+
+[h4 Applications]
+
+The arcsine distribution is useful to describe
+[@http://en.wikipedia.org/wiki/Random_walk Random walks], (including drunken walks)
+[@http://en.wikipedia.org/wiki/Brownian_motion Brownian motion],
+[@http://en.wikipedia.org/wiki/Wiener_process Weiner processes],
+[@http://en.wikipedia.org/wiki/Bernoulli_trial Bernoulli trials],
+and their appplication to solve stock market and other
+[@http://en.wikipedia.org/wiki/Gambler%27s_ruin ruinous gambling games].
+
+The random variate ['x] is constrained to ['x_min] and ['x_max], (for our 'standard' distribution, 0 and 1),
+and is usually some fraction. For any other ['x_min] and ['x_max] a fraction can be obtained from ['x] using
+
+[sixemspace] fraction = (x - x_min) / (x_max - x_min)
+
+The simplest example is tossing heads and tails with a fair coin and modelling the risk of losing, or winning.
+Walkers (molecules, drunks...) moving left or right of a centre line are another common example.
+
+The random variate ['x] is the fraction of time spent on the 'winning' side.
+If half the time is spent on the 'winning' side (and so the other half on the 'losing' side) then ['x = 1/2].
+
+For large numbers of tosses, this is modelled by the (standard \[0,1\]) arcsine distribution,
+and the PDF can be calculated thus:
+
+[arcsine_snip_2]
+
+From the plot of PDF, it is clear that ['x] = [frac12] is the [*minimum] of the curve,
+so this is the [*least likely] scenario.
+(This is highly counter-intuitive, considering that fair tosses must [*eventually] become equal.
+It turns out that ['eventually] is not just very long, but [*infinite]!).
+
+The [*most likely] scenarios are towards the extrema where ['x] = 0 or ['x] = 1.
+
+If fraction of time on the left is a [frac14],
+it is only slightly more likely because the curve is quite flat bottomed.
+
+[arcsine_snip_3]
+
+If we consider fair coin-tossing games being played for 100 days
+(hypothetically continuously to be 'at-limit')
+the person winning after day 5 will not change in fraction 0.144 of the cases.
+
+We can easily compute this setting ['x] = 5./100 = 0.05
+
+[arcsine_snip_4]
+
+Similarly, we can compute from a fraction of 0.05 /2 = 0.025
+(halved because we are considering both winners and losers)
+corresponding to 1 - 0.025 or 97.5% of the gamblers, (walkers, particles...) on the [*same side] of the origin
+
+[arcsine_snip_5]
+
+(use of the complement gives a bit more clarity,
+and avoids potential loss of accuracy when ['x] is close to unity, see __why_complements).
+
+[arcsine_snip_6]
+
+or we can reverse the calculation by assuming a fraction of time on one side, say fraction 0.2,
+
+[arcsine_snip_7]
+
+[*Summary]: Every time we toss, the odds are equal,
+so on average we have the same change of winning and losing.
+
+But this is [*not true] for an an individual game where one will be [*mostly in a bad or good patch].
+
+This is quite counter-intuitive to most people, but the mathematics is clear,
+and gamblers continue to provide proof.
+
+[*Moral]: if you in a losing patch, leave the game.
+(Because the odds to recover to a good patch are poor).
+
+[*Corollary]: Quit while you are ahead?
+
+A working example is at [@../../example/arcsine_example.cpp arcsine_example.cpp]
+including sample output .
+
+[h4 Related distributions]
+
+The arcsine distribution with ['x_min = 0] and ['x_max = 1] is special case of the
+__beta_distrib with [alpha] = 1/2 and [beta] = 1/2.
+
+[h4 Accuracy]
+
+This distribution is implemented using sqrt, sine, cos and arc sine and cos trigonometric functions
+which are normally accurate to a few __epsilon.
+But all values suffer from [@http://en.wikipedia.org/wiki/Loss_of_significance loss of significance or cancellation error]
+for values of ['x] close to ['x_max].
+For example, for a standard [0, 1] arcsine distribution ['as], the pdf is symmetric about random variate ['x = 0.5]
+so that one would expect `pdf(as, 0.01) == pdf(as, 0.99)`. But as ['x] nears unity, there is increasing
+[@http://en.wikipedia.org/wiki/Loss_of_significance loss of significance].
+To counteract this, the complement versions of CDF and quantile
+are implemented with alternative expressions using ['cos[super -1]] instead of ['sin[super -1]].
+Users should see __why_complements for guidance on when to avoid loss of accuracy by using complements.
+
+[h4 Testing]
+The results were tested against a few accurate spot values computed by __WolframAlpha, for example:
+
+ N[PDF[arcsinedistribution[0, 1], 0.5], 50]
+ 0.63661977236758134307553505349005744813783858296183
+
+[h4 Implementation]
+
+In the following table ['a] and ['b] are the parameters ['x_min][space] and ['x_max],
+['x] is the random variable, ['p] is the probability and its complement ['q = 1-p].
+
+[table
+[[Function][Implementation Notes]]
+[[support] [x [isin] \[a, b\], default x [isin] \[0, 1\] ]]
+[[pdf] [f(x; a, b) = 1/([pi][sdot][sqrt](x - a)[sdot](b - x))]]
+[[cdf] [F(x) = 2/[pi][sdot]sin[super-1]([sqrt](x - a) / (b - a) ) ]]
+[[cdf of complement] [2/([pi][sdot]cos[super-1]([sqrt](x - a) / (b - a)))]]
+[[quantile] [-a[sdot]sin[super 2]([frac12][pi][sdot]p) + a + b[sdot]sin[super 2]([frac12][pi][sdot]p)]]
+[[quantile from the complement] [-a[sdot]cos[super 2]([frac12][pi][sdot]p) + a + b[sdot]cos[super 2]([frac12][pi][sdot]q)]]
+[[mean] [[frac12](a+b)]]
+[[median] [[frac12](a+b)]]
+[[mode] [ x [isin] \[a, b\], so raises domain_error (returning NaN).]]
+[[variance] [(b - a)[super 2] / 8]]
+[[skewness] [0]]
+[[kurtosis excess] [ -3/2 ]]
+[[kurtosis] [kurtosis_excess + 3]]
+]
+
+The quantile was calculated using an expression obtained by using __WolframAlpha
+to invert the formula for the CDF thus
+
+ solve [p - 2/pi sin^-1(sqrt((x-a)/(b-a))) = 0, x]
+
+which was interpreted as
+
+ Solve[p - (2 ArcSin[Sqrt[(-a + x)/(-a + b)]])/Pi == 0, x, MaxExtraConditions -> Automatic]
+
+and produced the resulting expression
+
+ x = -a sin^2((pi p)/2)+a+b sin^2((pi p)/2)
+
+Thanks to Wolfram for providing this facility.
+
+[h4 References]
+
+* [@http://en.wikipedia.org/wiki/arcsine_distribution Wikipedia arcsine distribution]
+* [@http://en.wikipedia.org/wiki/Beta_distribution Wikipedia Beta distribution]
+* [@http://mathworld.wolfram.com/BetaDistribution.html Wolfram MathWorld]
+* [@http://www.wolframalpha.com/ Wolfram Alpha]
+
+[h4 Sources]
+
+*[@http://estebanmoro.org/2009/04/the-probability-of-going-through-a-bad-patch The probability of going through a bad patch] Esteban Moro's Blog.
+*[@http://www.gotohaggstrom.com/What%20do%20schmucks%20and%20the%20arc%20sine%20law%20have%20in%20common.pdf What soschumcks and the arc sine have in common] Peter Haggstrom.
+*[@http://www.math.uah.edu/stat/special/Arcsine.html arcsine distribution].
+*[@http://reference.wolfram.com/language/ref/ArcSinDistribution.html Wolfram reference arcsine examples].
+*[@http://www.math.harvard.edu/library/sternberg/slides/1180908.pdf Shlomo Sternberg slides].
+
+
+[endsect] [/section:arcsine_dist arcsine]
+
+[/ arcsine.qbk
+ Copyright 2014 John Maddock and Paul A. Bristow.
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt).
+]
diff --git a/libs/math/doc/distributions/bernoulli.qbk b/libs/math/doc/distributions/bernoulli.qbk
index 987a2012c..ae9c577bf 100644
--- a/libs/math/doc/distributions/bernoulli.qbk
+++ b/libs/math/doc/distributions/bernoulli.qbk
@@ -3,10 +3,10 @@
``#include <boost/math/distributions/bernoulli.hpp>``
namespace boost{ namespace math{
- template <class RealType = double,
+ template <class RealType = double,
class ``__Policy`` = ``__policy_class`` >
class bernoulli_distribution;
-
+
typedef bernoulli_distribution<> bernoulli;
template <class RealType, class ``__Policy``>
@@ -20,16 +20,16 @@
// Accessor function.
RealType success_fraction() const
// Probability of success (as a fraction).
- };
+ };
}} // namespaces
-
+
The Bernoulli distribution is a discrete distribution of the outcome
of a single trial with only two results, 0 (failure) or 1 (success),
with a probability of success p.
The Bernoulli distribution is the simplest building block
on which other discrete distributions of
-sequences of independent Bernoulli trials can be based.
+sequences of independent Bernoulli trials can be based.
The Bernoulli is the binomial distribution (k = 1, p) with only one trial.
@@ -51,12 +51,12 @@ and the [@http://en.wikipedia.org/wiki/Cumulative_Distribution_Function Cumulati
[h4 Member Functions]
bernoulli_distribution(RealType p);
-
-Constructs a [@http://en.wikipedia.org/wiki/bernoulli_distribution
+
+Constructs a [@http://en.wikipedia.org/wiki/bernoulli_distribution
bernoulli distribution] with success_fraction /p/.
RealType success_fraction() const
-
+
Returns the /success_fraction/ parameter of this distribution.
[h4 Non-member Accessors]
@@ -107,9 +107,9 @@ the binomial distribution with a single trial should be used, for example:
* [@http://en.wikipedia.org/wiki/Bernoulli_distribution Wikpedia Bernoulli distribution]
* [@http://mathworld.wolfram.com/BernoulliDistribution.html Weisstein, Eric W. "Bernoulli Distribution." From MathWorld--A Wolfram Web Resource.]
-[endsect][/section:bernoulli_dist bernoulli]
+[endsect] [/section:bernoulli_dist bernoulli]
-[/
+[/
Copyright 2006 John Maddock and Paul A. Bristow.
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
diff --git a/libs/math/doc/distributions/dist_reference.qbk b/libs/math/doc/distributions/dist_reference.qbk
index d700d70a0..3d5d82fe8 100644
--- a/libs/math/doc/distributions/dist_reference.qbk
+++ b/libs/math/doc/distributions/dist_reference.qbk
@@ -4,6 +4,7 @@
[section:dists Distributions]
+[include arcsine.qbk]
[include bernoulli.qbk]
[include beta.qbk]
[include binomial.qbk]
@@ -129,7 +130,7 @@ opportunity to integrate the statistical tests with this framework at some later
// Extract the result:
double p = probability(acc);
-[endsect][/section:future Extras Future Directions]
+[endsect] [/section:future Extras Future Directions]
[/ dist_reference.qbk
Copyright 2006, 2010 John Maddock and Paul A. Bristow.
diff --git a/libs/math/doc/distributions/hyperexponential.qbk b/libs/math/doc/distributions/hyperexponential.qbk
index 1dfdb9076..d2b2a1d48 100644
--- a/libs/math/doc/distributions/hyperexponential.qbk
+++ b/libs/math/doc/distributions/hyperexponential.qbk
@@ -108,7 +108,7 @@ A /k/-phase hyperexponential distribution is frequently used in [@http://en.wiki
For instance, CPUs service-time distribution in a computing system has often been observed to possess such a distribution (Rosin,1965).
Also, the arrival of different types of customer to a single queueing station is often modeled as a hyperexponential distribution (Papadopolous et al.,1993).
-Similarly, if a product manufactured in several parallel assemply lines and the outputs are merged, the failure density of the overall product is likely to be hyperexponential (Trivedi,2002).
+Similarly, if a product manufactured in several parallel assembly lines and the outputs are merged, the failure density of the overall product is likely to be hyperexponential (Trivedi,2002).
Finally, since the hyperexponential distribution exhibits a high Coefficient of Variation (CoV), that is a CoV > 1, it is especially suited to fit empirical data with large CoV (Feitelson,2014; Wolski et al.,2013) and to approximate [@http://en.wikipedia.org/wiki/Long_tail long-tail probability distributions] (Feldmann et al.,1998).
@@ -286,7 +286,7 @@ given by the range defined by `prob_range`, and /rate vector/ parameter given by
[note As an implementation detail, this constructor uses Boost's
[@http://www.boost.org/doc/libs/release/libs/core/doc/html/core/enable_if.html enable_if/disable_if mechanism] to
-disambiguage between this and other 2-argument constructors. Refer to the source code for more details.]
+disambiguate between this and other 2-argument constructors. Refer to the source code for more details.]
[h5 Parameters]
@@ -302,7 +302,7 @@ that includes native C++ arrays, standard library containers, or a std::pair or
[hyperexponential_snip3]
-[h4 Construction with rates-iterators (and all phase probablities equal)]
+[h4 Construction with rates-iterators (and all phase probabilities equal)]
template <typename RateIterT, typename RateIterT2>
hyperexponential_distribution(RateIterT const& rate_first,
@@ -314,7 +314,7 @@ probabilities (i.e., to a vector of the same length `n` of the /rate vector/ and
[note As an implementation detail, this constructor uses Boost's
[@http://www.boost.org/doc/libs/release/libs/core/doc/html/core/enable_if.html enable_if/disable_if mechanism] to
-disambiguage between this and other 2-argument constructors. Refer to the source code for more details.]
+disambiguate between this and other 2-argument constructors. Refer to the source code for more details.]
[h5 Parameters]
diff --git a/libs/math/doc/distributions/hypergeometric.qbk b/libs/math/doc/distributions/hypergeometric.qbk
index 881a1fe25..f89418992 100644
--- a/libs/math/doc/distributions/hypergeometric.qbk
+++ b/libs/math/doc/distributions/hypergeometric.qbk
@@ -58,7 +58,7 @@ then we obtain basically the same graphs:
hypergeometric_distribution(unsigned r, unsigned n, unsigned N);
-Constructs a hypergeometric distribution with with a population of /N/ objects,
+Constructs a hypergeometric distribution with a population of /N/ objects,
of which /r/ are defective, and from which /n/ are sampled.
unsigned total()const;
@@ -125,7 +125,7 @@ up to 104729.
For `N > boost::math::prime(boost::math::max_prime)` then accuracy quickly
degrades, with 5 or 6 decimal digits being lost for N = 110000.
-In general for very large N, the user should expect to loose log[sub 10]N
+In general for very large N, the user should expect to lose log[sub 10]N
decimal digits of precision during the calculation, with the results
becoming meaningless for N >= 10[super 15].
@@ -195,7 +195,7 @@ either lgamma, or by directly combining lanczos approximations to avoid
calculating via logarithms. We use the latter method, as it is usually
1 or 2 decimal digits more accurate than computing via logarithms with
lgamma. However, in this area where N > 104729, the user should expect
-to loose around log[sub 10]N decimal digits during the calculation in
+to lose around log[sub 10]N decimal digits during the calculation in
the worst case.
The CDF and its complement is calculated by directly summing the PDF's.
diff --git a/libs/math/doc/distributions/normal.qbk b/libs/math/doc/distributions/normal.qbk
index c78cb6f2e..a3db989a5 100644
--- a/libs/math/doc/distributions/normal.qbk
+++ b/libs/math/doc/distributions/normal.qbk
@@ -2,14 +2,14 @@
``#include <boost/math/distributions/normal.hpp>``
- namespace boost{ namespace math{
-
- template <class RealType = double,
+ namespace boost{ namespace math{
+
+ template <class RealType = double,
class ``__Policy`` = ``__policy_class`` >
class normal_distribution;
-
+
typedef normal_distribution<> normal;
-
+
template <class RealType, class ``__Policy``>
class normal_distribution
{
@@ -25,10 +25,10 @@
RealType location()const;
RealType scale()const;
};
-
+
}} // namespaces
-
-The normal distribution is probably the most well known statistical
+
+The normal distribution is probably the most well known statistical
distribution: it is also known as the Gaussian Distribution.
A normal distribution with mean zero and standard deviation one
is known as the ['Standard Normal Distribution].
@@ -54,20 +54,20 @@ and illustrated by this graph
[h4 Member Functions]
normal_distribution(RealType mean = 0, RealType sd = 1);
-
-Constructs a normal distribution with mean /mean/ and
+
+Constructs a normal distribution with mean /mean/ and
standard deviation /sd/.
Requires sd > 0, otherwise __domain_error is called.
RealType mean()const;
- RealType location()const;
-
+ RealType location()const;
+
both return the /mean/ of this distribution.
-
+
RealType standard_deviation()const;
RealType scale()const;
-
+
both return the /standard deviation/ of this distribution.
(Redundant location and scale function are provided to match other similar distributions,
allowing the functions find_location and find_scale to be used generically).
@@ -85,8 +85,8 @@ if RealType permits.
[h4 Accuracy]
-The normal distribution is implemented in terms of the
-[link math_toolkit.sf_erf.error_function error function],
+The normal distribution is implemented in terms of the
+[link math_toolkit.sf_erf.error_function error function],
and as such should have very low error rates.
[h4 Implementation]
@@ -109,7 +109,7 @@ and /s/ is its standard deviation.
[[kurtosis excess][0]]
]
-[endsect][/section:normal_dist Normal]
+[endsect] [/section:normal_dist Normal]
[/ normal.qbk
Copyright 2006, 2007, 2012 John Maddock and Paul A. Bristow.
diff --git a/libs/math/doc/equations/acosh1.png b/libs/math/doc/equations/acosh1.png
index 71d7627d8..9c91d1d8f 100644
--- a/libs/math/doc/equations/acosh1.png
+++ b/libs/math/doc/equations/acosh1.png
Binary files differ
diff --git a/libs/math/doc/equations/acosh1.svg b/libs/math/doc/equations/acosh1.svg
index 4d1eba0f1..bfba6e85f 100644
--- a/libs/math/doc/equations/acosh1.svg
+++ b/libs/math/doc/equations/acosh1.svg
@@ -1,2 +1,2 @@
<?xml version="1.0" encoding="utf-8"?>
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diff --git a/libs/math/doc/equations/gamma_ratio1.svg b/libs/math/doc/equations/gamma_ratio1.svg
index e8b0acd78..b86e28fa8 100644
--- a/libs/math/doc/equations/gamma_ratio1.svg
+++ b/libs/math/doc/equations/gamma_ratio1.svg
@@ -1,2 +1,2 @@
<?xml version="1.0" encoding="utf-8"?>
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diff --git a/libs/math/doc/equations/generate.sh b/libs/math/doc/equations/generate.sh
index a06e0b020..8f9cd50a5 100755
--- a/libs/math/doc/equations/generate.sh
+++ b/libs/math/doc/equations/generate.sh
@@ -8,10 +8,10 @@
# Paths to tools come first, change these to match your system:
#
math2svg='m:\download\open\SVGMath-0.3.1\math2svg.py'
-python='/cygdrive/c/program files/Python27/python.exe'
-inkscape='/cygdrive/c/Program Files (x86)/Inkscape/inkscape.exe'
+python='/cygdrive/c/Python27/python.exe'
+inkscape='/cygdrive/c/Program Files/Inkscape/inkscape.exe'
# Image DPI:
-dpi=120
+dpi=90
for mmlfile in $*; do
svgfile=$(basename $mmlfile .mml).svg
diff --git a/libs/math/doc/equations/hankel1.png b/libs/math/doc/equations/hankel1.png
index 7ec65d9b6..aa317f02d 100644
--- a/libs/math/doc/equations/hankel1.png
+++ b/libs/math/doc/equations/hankel1.png
Binary files differ
diff --git a/libs/math/doc/equations/hankel1.svg b/libs/math/doc/equations/hankel1.svg
index e29216685..54cf9fe50 100644
--- a/libs/math/doc/equations/hankel1.svg
+++ b/libs/math/doc/equations/hankel1.svg
@@ -1,2 +1,2 @@
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diff --git a/libs/math/doc/equations/hankel2.png b/libs/math/doc/equations/hankel2.png
index 614f7efbd..b690aa64d 100644
--- a/libs/math/doc/equations/hankel2.png
+++ b/libs/math/doc/equations/hankel2.png
Binary files differ
diff --git a/libs/math/doc/equations/hankel2.svg b/libs/math/doc/equations/hankel2.svg
index 70f70ab69..3c30d1e61 100644
--- a/libs/math/doc/equations/hankel2.svg
+++ b/libs/math/doc/equations/hankel2.svg
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+<g id="title">
+<text x="375" y="40" text-anchor="middle" font-size="20" font-family="Lucida Sans Unicode">Arcsine Distribution PDF</text></g>
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diff --git a/libs/math/doc/graphs/dist_graphs.cpp b/libs/math/doc/graphs/dist_graphs.cpp
index 07f2f7316..515d392ef 100644
--- a/libs/math/doc/graphs/dist_graphs.cpp
+++ b/libs/math/doc/graphs/dist_graphs.cpp
@@ -79,33 +79,34 @@ public:
void add(const Dist& d, const std::string& name)
{
- //
- // Add to our list for later:
- //
+ // Add name of distribution to our list for later:
m_distributions.push_back(std::make_pair(name, d));
//
- // Get the extent:
- //
+ // Get the extent of the distribution from the support:
double a, b;
std::tr1::tie(a, b) = support(d);
//
- // PDF maximimum is at the mode:
- //
+ // PDF maximimum is at the mode (probably):
double mod;
try
{
mod = mode(d);
}
catch(const std::domain_error& )
- {
+ { // but if not use the lower limit of support.
mod = a;
}
if((mod <= a) && !is_discrete_distribution<Dist>::value)
- {
- if((a != 0) && (fabs(a) > 1e-2))
- mod = a * (1 + 1e-2);
+ { // Continuous distribution at or below lower limit of support.
+ double margin = 1e-2; // Margin of 1% (say) to get lowest off the 'end stop'.
+ if((a != 0) && (fabs(a) > margin))
+ {
+ mod = a * (1 + ((a > 0) ? margin : -margin));
+ }
else
- mod = 1e-2;
+ { // Case of mod near zero?
+ mod = margin;
+ }
}
double peek_y = pdf(d, mod);
double min_y = peek_y / 20;
@@ -266,6 +267,7 @@ public:
.line_color(colors[color_index])
.line_width(1.)
.shape(none);
+
//.bezier_on(true) // Bezier can't cope with badly behaved like uniform & triangular.
++color_index;
color_index = color_index % (sizeof(colors)/sizeof(colors[0]));
@@ -322,6 +324,9 @@ private:
int main()
{
+ try
+ {
+
distribution_plotter<boost::math::gamma_distribution<> >
gamma_plotter;
gamma_plotter.add(boost::math::gamma_distribution<>(0.75), "shape = 0.75");
@@ -653,6 +658,16 @@ int main()
hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(450, 50, 500), "N=500, r=50, n=450");
hypergeometric_plotter2.plot("Hypergeometric Distribution PDF", "hypergeometric_pdf_2.svg");
+ }
+ catch (std::exception ex)
+ {
+ std::cout << ex.what() << std::endl;
+ }
+
+
+
+ /* these graphs for hyperexponential distribution not used.
+
distribution_plotter<boost::math::hyperexponential_distribution<> >
hyperexponential_plotter;
{
@@ -695,11 +710,13 @@ int main()
hyperexponential_plotter3.add(boost::math::hyperexponential_distribution<>(probs1,rates1), "&#x3B1=(1.0), &#x3BB=(2.0)");
const double probs2[] = {0.5,0.5};
const double rates2[] = {0.3,1.5};
- hyperexponential_plotter3.add(boost::math::hyperexponential_distribution<>(probs2_1,rates2_1), "&#x3B1=(0.5,0.5), &#x3BB=(0.3,1.5)");
+ hyperexponential_plotter3.add(boost::math::hyperexponential_distribution<>(probs2,rates2), "&#x3B1=(0.5,0.5), &#x3BB=(0.3,1.5)");
const double probs3[] = {1.0/3.0,1.0/3.0,1.0/3.0};
const double rates3[] = {0.2,1.5,3.0};
- hyperexponential_plotter3.add(boost::math::hyperexponential_distribution<>(probs2_2,rates2_2), "&#x3B1=(1.0/3.0,1.0/3.0,1.0/3.0), &#x3BB=(0.2,1.5,3.0)");
+ hyperexponential_plotter3.add(boost::math::hyperexponential_distribution<>(probs2,rates2), "&#x3B1=(1.0/3.0,1.0/3.0,1.0/3.0), &#x3BB=(0.2,1.5,3.0)");
}
hyperexponential_plotter3.plot("Hyperexponential Distribution PDF (Different Number of Phases, Same Mean)", "hyperexponential_pdf_samemean.svg");
+ */
+
} // int main()
diff --git a/libs/math/doc/graphs/generate.sh b/libs/math/doc/graphs/generate.sh
index bff99777e..d9659141f 100755
--- a/libs/math/doc/graphs/generate.sh
+++ b/libs/math/doc/graphs/generate.sh
@@ -8,15 +8,15 @@
# Paths to tools come first, change these to match your system:
#
math2svg='m:\download\open\SVGMath-0.3.1\math2svg.py'
-python=/cygdrive/c/Python26/python.exe
-inkscape=/cygdrive/c/progra~1/Inkscape/inkscape
+python='/cygdrive/c/program files/Python27/python.exe'
+inkscape='/cygdrive/c/Program Files (x86)/Inkscape/inkscape.exe'
# Image DPI:
dpi=96
for svgfile in $*; do
pngfile=$(basename $svgfile .svg).png
echo Generating $pngfile
- $inkscape -d $dpi -e $(cygpath -a -w $pngfile) $(cygpath -a -w $svgfile)
+ "$inkscape" -d $dpi -e $(cygpath -a -w $pngfile) $(cygpath -a -w $svgfile)
done
diff --git a/libs/math/doc/graphs/polygamma2.png b/libs/math/doc/graphs/polygamma2.png
new file mode 100644
index 000000000..b292a7ee9
--- /dev/null
+++ b/libs/math/doc/graphs/polygamma2.png
Binary files differ
diff --git a/libs/math/doc/graphs/polygamma2.svg b/libs/math/doc/graphs/polygamma2.svg
new file mode 100644
index 000000000..733112c61
--- /dev/null
+++ b/libs/math/doc/graphs/polygamma2.svg
@@ -0,0 +1,70 @@
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+<svg width="600" height ="400" version="1.1"
+xmlns:svg ="http://www.w3.org/2000/svg"
+xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
+xmlns:cc="http://web.resource.org/cc/"
+xmlns:dc="http://purl.org/dc/elements/1.1/"
+xmlns ="http://www.w3.org/2000/svg"
+>
+<!-- SVG plot written using Boost.Plot program (Creator Jacob Voytko) -->
+<!-- Use, modification and distribution of Boost.Plot subject to the -->
+<!-- Boost Software License, Version 1.0.-->
+<!-- (See accompanying file LICENSE_1_0.txt -->
+<!-- or copy at http://www.boost.org/LICENSE_1_0.txt) -->
+
+<!-- SVG Plot Copyright John Maddock 2008 -->
+<meta name="copyright" content="John Maddock" />
+<meta name="date" content="2008" />
+<!-- Use, modification and distribution of this Scalable Vector Graphic file -->
+<!-- are subject to the Boost Software License, Version 1.0. -->
+<!-- (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
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diff --git a/libs/math/doc/graphs/sf_graphs.cpp b/libs/math/doc/graphs/sf_graphs.cpp
index 9bae8db8e..713665c60 100644
--- a/libs/math/doc/graphs/sf_graphs.cpp
+++ b/libs/math/doc/graphs/sf_graphs.cpp
@@ -220,10 +220,10 @@ double find_end_point(F f, double x0, double target, bool rising, double x_off =
{
boost::math::tools::eps_tolerance<double> tol(50);
boost::uintmax_t max_iter = 1000;
- return boost::math::tools::bracket_and_solve_root(
+ return x_off + boost::math::tools::bracket_and_solve_root(
location_finder<F>(f, target, x_off),
x0,
- double(1.5),
+ 1.5,
rising,
tol,
max_iter).first;
@@ -248,10 +248,11 @@ int main()
double (*f2i)(int, double);
double (*f3)(double, double, double);
double (*f4)(double, double, double, double);
+ double max_val;
f = boost::math::zeta;
- plot.add(f, 1 + find_end_point(f, 0.1, 40.0, false, 1.0), 10, "");
- plot.add(f, -20, 1 + find_end_point(f, -0.1, -40.0, false, 1.0), "");
+ plot.add(f, find_end_point(f, 0.1, 40.0, false, 1.0), 10, "");
+ plot.add(f, -20, find_end_point(f, -0.1, -40.0, false, 1.0), "");
plot.plot("Zeta Function Over [-20,10]", "zeta1.svg", "z", "zeta(z)");
plot.clear();
@@ -259,34 +260,34 @@ int main()
plot.plot("Zeta Function Over [-14,0]", "zeta2.svg", "z", "zeta(z)");
f = boost::math::tgamma;
- double max_val = f(6);
+ max_val = f(6);
plot.clear();
plot.add(f, find_end_point(f, 0.1, max_val, false), 6, "");
- plot.add(f, -1 + find_end_point(f, 0.1, -max_val, true, -1), find_end_point(f, -0.1, -max_val, false), "");
- plot.add(f, -2 + find_end_point(f, 0.1, max_val, false, -2), -1 + find_end_point(f, -0.1, max_val, true, -1), "");
- plot.add(f, -3 + find_end_point(f, 0.1, -max_val, true, -3), -2 + find_end_point(f, -0.1, -max_val, false, -2), "");
- plot.add(f, -4 + find_end_point(f, 0.1, max_val, false, -4), -3 + find_end_point(f, -0.1, max_val, true, -3), "");
+ plot.add(f, find_end_point(f, 0.1, -max_val, true, -1), find_end_point(f, -0.1, -max_val, false), "");
+ plot.add(f, find_end_point(f, 0.1, max_val, false, -2), find_end_point(f, -0.1, max_val, true, -1), "");
+ plot.add(f, find_end_point(f, 0.1, -max_val, true, -3), find_end_point(f, -0.1, -max_val, false, -2), "");
+ plot.add(f, find_end_point(f, 0.1, max_val, false, -4), find_end_point(f, -0.1, max_val, true, -3), "");
plot.plot("tgamma", "tgamma.svg", "z", "tgamma(z)");
f = boost::math::lgamma;
max_val = f(10);
plot.clear();
plot.add(f, find_end_point(f, 0.1, max_val, false), 10, "");
- plot.add(f, -1 + find_end_point(f, 0.1, max_val, false, -1), find_end_point(f, -0.1, max_val, true), "");
- plot.add(f, -2 + find_end_point(f, 0.1, max_val, false, -2), -1 + find_end_point(f, -0.1, max_val, true, -1), "");
- plot.add(f, -3 + find_end_point(f, 0.1, max_val, false, -3), -2 + find_end_point(f, -0.1, max_val, true, -2), "");
- plot.add(f, -4 + find_end_point(f, 0.1, max_val, false, -4), -3 + find_end_point(f, -0.1, max_val, true, -3), "");
- plot.add(f, -5 + find_end_point(f, 0.1, max_val, false, -5), -4 + find_end_point(f, -0.1, max_val, true, -4), "");
+ plot.add(f, find_end_point(f, 0.1, max_val, false, -1), find_end_point(f, -0.1, max_val, true), "");
+ plot.add(f, find_end_point(f, 0.1, max_val, false, -2), find_end_point(f, -0.1, max_val, true, -1), "");
+ plot.add(f, find_end_point(f, 0.1, max_val, false, -3), find_end_point(f, -0.1, max_val, true, -2), "");
+ plot.add(f, find_end_point(f, 0.1, max_val, false, -4), find_end_point(f, -0.1, max_val, true, -3), "");
+ plot.add(f, find_end_point(f, 0.1, max_val, false, -5), find_end_point(f, -0.1, max_val, true, -4), "");
plot.plot("lgamma", "lgamma.svg", "z", "lgamma(z)");
f = boost::math::digamma;
max_val = 10;
plot.clear();
plot.add(f, find_end_point(f, 0.1, -max_val, true), 10, "");
- plot.add(f, -1 + find_end_point(f, 0.1, -max_val, true, -1), find_end_point(f, -0.1, max_val, true), "");
- plot.add(f, -2 + find_end_point(f, 0.1, -max_val, true, -2), -1 + find_end_point(f, -0.1, max_val, true, -1), "");
- plot.add(f, -3 + find_end_point(f, 0.1, -max_val, true, -3), -2 + find_end_point(f, -0.1, max_val, true, -2), "");
- plot.add(f, -4 + find_end_point(f, 0.1, -max_val, true, -4), -3 + find_end_point(f, -0.1, max_val, true, -3), "");
+ plot.add(f, find_end_point(f, 0.1, -max_val, true, -1), find_end_point(f, -0.1, max_val, true), "");
+ plot.add(f, find_end_point(f, 0.1, -max_val, true, -2), find_end_point(f, -0.1, max_val, true, -1), "");
+ plot.add(f, find_end_point(f, 0.1, -max_val, true, -3), find_end_point(f, -0.1, max_val, true, -2), "");
+ plot.add(f, find_end_point(f, 0.1, -max_val, true, -4), find_end_point(f, -0.1, max_val, true, -3), "");
plot.plot("digamma", "digamma.svg", "z", "digamma(z)");
f = boost::math::erf;
@@ -300,16 +301,16 @@ int main()
f = boost::math::erf_inv;
plot.clear();
- plot.add(f, -1 + find_end_point(f, 0.1, -3, true, -1), 1 + find_end_point(f, -0.1, 3, true, 1), "");
+ plot.add(f, find_end_point(f, 0.1, -3, true, -1), find_end_point(f, -0.1, 3, true, 1), "");
plot.plot("erf_inv", "erf_inv.svg", "z", "erf_inv(z)");
f = boost::math::erfc_inv;
plot.clear();
- plot.add(f, find_end_point(f, 0.1, 3, false), 2 + find_end_point(f, -0.1, -3, false, 2), "");
+ plot.add(f, find_end_point(f, 0.1, 3, false), find_end_point(f, -0.1, -3, false, 2), "");
plot.plot("erfc_inv", "erfc_inv.svg", "z", "erfc_inv(z)");
f = boost::math::log1p;
plot.clear();
- plot.add(f, -1 + find_end_point(f, 0.1, -10, true, -1), 10, "");
+ plot.add(f, find_end_point(f, 0.1, -10, true, -1), 10, "");
plot.plot("log1p", "log1p.svg", "z", "log1p(z)");
f = boost::math::expm1;
@@ -324,7 +325,7 @@ int main()
f = sqrt1pm1;
plot.clear();
- plot.add(f, -1 + find_end_point(f, 0.1, -10, true, -1), 5, "");
+ plot.add(f, find_end_point(f, 0.1, -10, true, -1), 5, "");
plot.plot("sqrt1pm1", "sqrt1pm1.svg", "z", "sqrt1pm1(z)");
f2 = boost::math::powm1;
@@ -359,7 +360,7 @@ int main()
f = boost::math::atanh;
plot.clear();
- plot.add(f, -1 + find_end_point(f, 0.1, -5, true, -1), 1 + find_end_point(f, -0.1, 5, true, 1), "");
+ plot.add(f, find_end_point(f, 0.1, -5, true, -1), find_end_point(f, -0.1, 5, true, 1), "");
plot.plot("atanh", "atanh.svg", "z", "atanh(z)");
f2 = boost::math::tgamma_delta_ratio;
@@ -450,15 +451,15 @@ int main()
"n = 2");
plot.add(boost::bind(f2u, 3, _1),
find_end_point(boost::bind(f2u, 3, _1), -2, 20, false),
- 8 + find_end_point(boost::bind(f2u, 3, _1), 1, 20, false, 8),
+ find_end_point(boost::bind(f2u, 3, _1), 1, 20, false, 8),
"n = 3");
plot.add(boost::bind(f2u, 4, _1),
find_end_point(boost::bind(f2u, 4, _1), -2, 20, false),
- 8 + find_end_point(boost::bind(f2u, 4, _1), 1, 20, true, 8),
+ find_end_point(boost::bind(f2u, 4, _1), 1, 20, true, 8),
"n = 4");
plot.add(boost::bind(f2u, 5, _1),
find_end_point(boost::bind(f2u, 5, _1), -2, 20, false),
- 8 + find_end_point(boost::bind(f2u, 5, _1), 1, 20, true, 8),
+ find_end_point(boost::bind(f2u, 5, _1), 1, 20, true, 8),
"n = 5");
plot.plot("Laguerre Polynomials", "laguerre.svg", "x", "laguerre(n, x)");
@@ -555,17 +556,17 @@ int main()
plot.add(boost::bind(f3, _1, 0.25, boost::math::constants::pi<double>() / 2),
find_end_point(
boost::bind(f3, _1, 0.25, boost::math::constants::pi<double>() / 2),
- 0.5, 4, false, -1) - 1,
+ 0.5, 4, false, -1),
find_end_point(
boost::bind(f3, _1, 0.25, boost::math::constants::pi<double>() / 2),
- -0.5, 4, true, 1) + 1, "n=0.25 &#x3C6;=&#x3C0;/2");
+ -0.5, 4, true, 1), "n=0.25 &#x3C6;=&#x3C0;/2");
plot.add(boost::bind(f3, _1, 0.75, boost::math::constants::pi<double>() / 2),
find_end_point(
boost::bind(f3, _1, 0.75, boost::math::constants::pi<double>() / 2),
- 0.5, 4, false, -1) - 1,
+ 0.5, 4, false, -1),
find_end_point(
boost::bind(f3, _1, 0.75, boost::math::constants::pi<double>() / 2),
- -0.5, 4, true, 1) + 1, "n=0.75 &#x3C6;=&#x3C0;/2");
+ -0.5, 4, true, 1), "n=0.75 &#x3C6;=&#x3C0;/2");
plot.plot("Elliptic Of the Third Kind", "ellint_3.svg", "k", "ellint_3(k, n, phi)");
f2 = boost::math::jacobi_sn;
@@ -696,6 +697,39 @@ int main()
plot.add(f, -20, 3, "");
plot.plot("Bi'", "airy_bip.svg", "z", "airy_bi_prime(z)");
+ f = boost::math::trigamma;
+ max_val = 30;
+ plot.clear();
+ plot.add(f, find_end_point(f, 0.1, max_val, false), 5, "");
+ plot.add(f, find_end_point(f, 0.1, max_val, false, -1), find_end_point(f, -0.1, max_val, true), "");
+ plot.add(f, find_end_point(f, 0.1, max_val, false, -2), find_end_point(f, -0.1, max_val, true, -1), "");
+ plot.add(f, find_end_point(f, 0.1, max_val, false, -3), find_end_point(f, -0.1, max_val, true, -2), "");
+ plot.add(f, find_end_point(f, 0.1, max_val, false, -4), find_end_point(f, -0.1, max_val, true, -3), "");
+ plot.add(f, find_end_point(f, 0.1, max_val, false, -5), find_end_point(f, -0.1, max_val, true, -4), "");
+ plot.plot("Trigamma", "trigamma.svg", "x", "trigamma(x)");
+
+ f2i = boost::math::polygamma;
+ max_val = -50;
+ plot.clear();
+ plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true), 5, "");
+ plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -1), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true), "");
+ plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -2), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true, -1), "");
+ plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -3), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true, -2), "");
+ plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -4), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true, -3), "");
+ plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -5), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true, -4), "");
+ plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -6), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true, -5), "");
+ plot.plot("Polygamma", "polygamma2.svg", "x", "polygamma(2, x)");
+
+ max_val = 800;
+ plot.clear();
+ plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false), 5, "");
+ plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -1), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true), "");
+ plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -2), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true, -1), "");
+ plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -3), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true, -2), "");
+ plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -4), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true, -3), "");
+ plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -5), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true, -4), "");
+ plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -6), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true, -5), "");
+ plot.plot("Polygamma", "polygamma3.svg", "x", "polygamma(3, x)");
return 0;
}
diff --git a/libs/math/doc/graphs/trigamma.png b/libs/math/doc/graphs/trigamma.png
new file mode 100644
index 000000000..3c00ff602
--- /dev/null
+++ b/libs/math/doc/graphs/trigamma.png
Binary files differ
diff --git a/libs/math/doc/graphs/trigamma.svg b/libs/math/doc/graphs/trigamma.svg
new file mode 100644
index 000000000..faee953d0
--- /dev/null
+++ b/libs/math/doc/graphs/trigamma.svg
@@ -0,0 +1,70 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<svg width="600" height ="400" version="1.1"
+xmlns:svg ="http://www.w3.org/2000/svg"
+xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
+xmlns:cc="http://web.resource.org/cc/"
+xmlns:dc="http://purl.org/dc/elements/1.1/"
+xmlns ="http://www.w3.org/2000/svg"
+>
+<!-- SVG plot written using Boost.Plot program (Creator Jacob Voytko) -->
+<!-- Use, modification and distribution of Boost.Plot subject to the -->
+<!-- Boost Software License, Version 1.0.-->
+<!-- (See accompanying file LICENSE_1_0.txt -->
+<!-- or copy at http://www.boost.org/LICENSE_1_0.txt) -->
+
+<!-- SVG Plot Copyright John Maddock 2008 -->
+<meta name="copyright" content="John Maddock" />
+<meta name="date" content="2008" />
+<!-- Use, modification and distribution of this Scalable Vector Graphic file -->
+<!-- are subject to the Boost Software License, Version 1.0. -->
+<!-- (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
+
+<clipPath id="plot_window"><rect x="76.8" y="59" width="496.2" height="281"/></clipPath>
+<g id="imageBackground" stroke="rgb(119,136,153)" fill="rgb(255,255,255)" stroke-width="2"><rect x="0" y="0" width="600" height="400"/></g>
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+<g id="yMinorGrid" stroke="rgb(200,220,255)" stroke-width="0.5"></g>
+<g id="yMajorGrid" stroke="rgb(200,220,255)" stroke-width="1"></g>
+<g id="xMinorGrid" stroke="rgb(200,220,255)" stroke-width="0.5"></g>
+<g id="xMajorGrid" stroke="rgb(200,220,255)" stroke-width="1"></g>
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<p><b>Table of Contents</b></p>
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<dt><span class="section"><a href="math_toolkit/constants_intro.html">Introduction</a></span></dt>
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<div class="toc">
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<link rel="prev" href="math_toolkit/oct_todo.html" title="To Do">
<link rel="next" href="math_toolkit/introduction.html" title="Introduction">
</head>
@@ -27,7 +27,7 @@
<a name="gcd_lcm"></a>Chapter&#160;11.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
-<dl class="toc">
+<dl>
<dt><span class="section"><a href="math_toolkit/introduction.html">Introduction</a></span></dt>
<dt><span class="section"><a href="math_toolkit/synopsis.html">Synopsis</a></span></dt>
<dt><span class="section"><a href="math_toolkit/gcd_function_object.html">GCD Function Object</a></span></dt>
diff --git a/libs/math/doc/html/index.html b/libs/math/doc/html/index.html
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--- a/libs/math/doc/html/index.html
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<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
-<title>Math Toolkit 2.1.0</title>
+<title>Math Toolkit 2.2.0</title>
<link rel="stylesheet" href="math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="index.html" title="Math Toolkit 2.2.0">
<link rel="next" href="overview.html" title="Chapter&#160;1.&#160;Overview">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@@ -22,7 +22,7 @@
<div class="titlepage">
<div>
<div><h1 class="title">
-<a name="math_toolkit"></a>Math Toolkit 2.1.0</h1></div>
+<a name="math_toolkit"></a>Math Toolkit 2.2.0</h1></div>
<div><div class="authorgroup">
<div class="author"><h3 class="author">
<span class="firstname">Nikhar</span> <span class="surname">Agrawal</span>
@@ -86,7 +86,7 @@ This manual is also available in <a href="http://sourceforge.net/projects/boost/
</div>
<div class="toc">
<p><b>Table of Contents</b></p>
-<dl class="toc">
+<dl>
<dt><span class="chapter"><a href="overview.html">1. Overview</a></span></dt>
<dt><span class="chapter"><a href="utils.html">2. Floating Point Utilities</a></span></dt>
<dt><span class="chapter"><a href="cstdfloat.html">3. Specified-width floating-point typedefs</a></span></dt>
@@ -111,7 +111,7 @@ This manual is also available in <a href="http://sourceforge.net/projects/boost/
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
-<td align="left"><p><small>Last revised: October 30, 2014 at 11:29:37 GMT</small></p></td>
+<td align="left"><p><small>Last revised: February 23, 2015 at 18:40:43 GMT</small></p></td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
<hr>
diff --git a/libs/math/doc/html/indexes.html b/libs/math/doc/html/indexes.html
index cd62fdc8a..f866d6463 100644
--- a/libs/math/doc/html/indexes.html
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@@ -3,9 +3,9 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;18.&#160;Indexes</title>
<link rel="stylesheet" href="math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.1.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.2.0">
<link rel="prev" href="math_toolkit/credits.html" title="Credits and Acknowledgements">
<link rel="next" href="indexes/s01.html" title="Function Index">
</head>
@@ -27,7 +27,7 @@
<a name="indexes"></a>Chapter&#160;18.&#160;Indexes</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
-<dl class="toc">
+<dl>
<dt><span class="section"><a href="indexes/s01.html">Function Index</a></span></dt>
<dt><span class="section"><a href="indexes/s02.html">Class Index</a></span></dt>
<dt><span class="section"><a href="indexes/s03.html">Typedef Index</a></span></dt>
diff --git a/libs/math/doc/html/indexes/s01.html b/libs/math/doc/html/indexes/s01.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Function Index</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../indexes.html" title="Chapter&#160;18.&#160;Indexes">
<link rel="prev" href="../indexes.html" title="Chapter&#160;18.&#160;Indexes">
<link rel="next" href="s02.html" title="Class Index">
@@ -24,7 +24,7 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="idm1503608992"></a>Function Index</h2></div></div></div>
+<a name="id1493418"></a>Function Index</h2></div></div></div>
<p><a class="link" href="s01.html#idx_id_0">A</a> <a class="link" href="s01.html#idx_id_1">B</a> <a class="link" href="s01.html#idx_id_2">C</a> <a class="link" href="s01.html#idx_id_3">D</a> <a class="link" href="s01.html#idx_id_4">E</a> <a class="link" href="s01.html#idx_id_5">F</a> <a class="link" href="s01.html#idx_id_6">G</a> <a class="link" href="s01.html#idx_id_7">H</a> <a class="link" href="s01.html#idx_id_8">I</a> <a class="link" href="s01.html#idx_id_9">J</a> <a class="link" href="s01.html#idx_id_10">K</a> <a class="link" href="s01.html#idx_id_11">L</a> <a class="link" href="s01.html#idx_id_12">M</a> <a class="link" href="s01.html#idx_id_13">N</a> <a class="link" href="s01.html#idx_id_14">O</a> <a class="link" href="s01.html#idx_id_15">P</a> <a class="link" href="s01.html#idx_id_16">Q</a> <a class="link" href="s01.html#idx_id_17">R</a> <a class="link" href="s01.html#idx_id_18">S</a> <a class="link" href="s01.html#idx_id_19">T</a> <a class="link" href="s01.html#idx_id_20">U</a> <a class="link" href="s01.html#idx_id_21">V</a> <a class="link" href="s01.html#idx_id_23">Z</a></p>
<div class="variablelist"><dl class="variablelist">
<dt>
@@ -276,6 +276,7 @@
<p><span class="index-entry-level-0">cdf</span></p>
<div class="index"><ul class="index" style="list-style-type: none; ">
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">Additional Implementation Notes</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">Arcsine Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example"><span class="index-entry-level-1">Binomial Coin-Flipping Example</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies"><span class="index-entry-level-1">Discrete Quantile Policies</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/future.html" title="Extras/Future Directions"><span class="index-entry-level-1">Extras/Future Directions</span></a></p></li>
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/overview_tr1.html" title="C99 and C++ TR1 C-style Functions"><span class="index-entry-level-1">C99 and C++ TR1 C-style Functions</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_tr1.html" title="C99 and TR1 C Functions Overview"><span class="index-entry-level-1">C99 and TR1 C Functions Overview</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_d.html" title="Elliptic Integral D - Legendre Form"><span class="index-entry-level-1">Elliptic Integral D - Legendre Form</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form"><span class="index-entry-level-1">Elliptic Integrals of the Third Kind - Legendre Form</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/tr1_ref.html" title="TR1 C Functions Quick Reference"><span class="index-entry-level-1">TR1 C Functions Quick Reference</span></a></p></li>
</ul></div>
@@ -669,6 +671,10 @@
</ul></div>
</li>
<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">ellint_d</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_d.html" title="Elliptic Integral D - Legendre Form"><span class="index-entry-level-1">Elliptic Integral D - Legendre Form</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">ellint_rc</span></p>
<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form"><span class="index-entry-level-1">Elliptic Integrals - Carlson Form</span></a></p></li></ul></div>
</li>
@@ -681,6 +687,10 @@
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</li>
<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">ellint_rg</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form"><span class="index-entry-level-1">Elliptic Integrals - Carlson Form</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">ellint_rj</span></p>
<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form"><span class="index-entry-level-1">Elliptic Integrals - Carlson Form</span></a></p></li></ul></div>
</li>
@@ -1112,6 +1122,10 @@
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</li>
<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">heuman_lambda</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/heuman_lambda.html" title="Heuman Lambda Function"><span class="index-entry-level-1">Heuman Lambda Function</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">hyperg</span></p>
<div class="index"><ul class="index" style="list-style-type: none; ">
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/overview_tr1.html" title="C99 and C++ TR1 C-style Functions"><span class="index-entry-level-1">C99 and C++ TR1 C-style Functions</span></a></p></li>
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<p><span class="index-entry-level-0">jacobi_sn</span></p>
<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/jacobi/jacobi_sn.html" title="Jacobi Elliptic Function sn"><span class="index-entry-level-1">Jacobi Elliptic Function sn</span></a></p></li></ul></div>
</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">jacobi_zeta</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/jacobi_zeta.html" title="Jacobi Zeta Function"><span class="index-entry-level-1">Jacobi Zeta Function</span></a></p></li></ul></div>
+</li>
</ul></div></dd>
<dt>
<a name="idx_id_10"></a><span class="term">K</span>
@@ -1859,10 +1877,12 @@
<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">pdf</span></p>
<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">Arcsine Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/overview/generic.html" title="Generic operations common to all distributions are non-member functions"><span class="index-entry-level-1">Generic operations common to all distributions are non-member functions</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/nmp.html" title="Non-Member Properties"><span class="index-entry-level-1">Non-Member Properties</span></a></p></li>
</ul></div>
</li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_gamma/polygamma.html" title="Polygamma"><span class="index-entry-level-0">polygamma</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/powers/powm1.html" title="powm1"><span class="index-entry-level-0">powm1</span></a></p></li>
<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">prime</span></p>
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</ul></div>
</li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_gamma/trigamma.html" title="Trigamma"><span class="index-entry-level-0">trigamma</span></a></p></li>
<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">trunc</span></p>
<div class="index"><ul class="index" style="list-style-type: none; ">
diff --git a/libs/math/doc/html/indexes/s02.html b/libs/math/doc/html/indexes/s02.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Class Index</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../indexes.html" title="Chapter&#160;18.&#160;Indexes">
<link rel="prev" href="s01.html" title="Function Index">
<link rel="next" href="s03.html" title="Typedef Index">
@@ -24,10 +24,14 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="idm1501976736"></a>Class Index</h2></div></div></div>
-<p><a class="link" href="s02.html#idx_id_25">B</a> <a class="link" href="s02.html#idx_id_26">C</a> <a class="link" href="s02.html#idx_id_27">D</a> <a class="link" href="s02.html#idx_id_28">E</a> <a class="link" href="s02.html#idx_id_29">F</a> <a class="link" href="s02.html#idx_id_30">G</a> <a class="link" href="s02.html#idx_id_31">H</a> <a class="link" href="s02.html#idx_id_32">I</a> <a class="link" href="s02.html#idx_id_35">L</a> <a class="link" href="s02.html#idx_id_36">M</a> <a class="link" href="s02.html#idx_id_37">N</a> <a class="link" href="s02.html#idx_id_38">O</a> <a class="link" href="s02.html#idx_id_39">P</a> <a class="link" href="s02.html#idx_id_40">Q</a> <a class="link" href="s02.html#idx_id_41">R</a> <a class="link" href="s02.html#idx_id_42">S</a> <a class="link" href="s02.html#idx_id_43">T</a> <a class="link" href="s02.html#idx_id_44">U</a> <a class="link" href="s02.html#idx_id_46">W</a></p>
+<a name="id1511621"></a>Class Index</h2></div></div></div>
+<p><a class="link" href="s02.html#idx_id_24">A</a> <a class="link" href="s02.html#idx_id_25">B</a> <a class="link" href="s02.html#idx_id_26">C</a> <a class="link" href="s02.html#idx_id_27">D</a> <a class="link" href="s02.html#idx_id_28">E</a> <a class="link" href="s02.html#idx_id_29">F</a> <a class="link" href="s02.html#idx_id_30">G</a> <a class="link" href="s02.html#idx_id_31">H</a> <a class="link" href="s02.html#idx_id_32">I</a> <a class="link" href="s02.html#idx_id_35">L</a> <a class="link" href="s02.html#idx_id_36">M</a> <a class="link" href="s02.html#idx_id_37">N</a> <a class="link" href="s02.html#idx_id_38">O</a> <a class="link" href="s02.html#idx_id_39">P</a> <a class="link" href="s02.html#idx_id_40">Q</a> <a class="link" href="s02.html#idx_id_41">R</a> <a class="link" href="s02.html#idx_id_42">S</a> <a class="link" href="s02.html#idx_id_43">T</a> <a class="link" href="s02.html#idx_id_44">U</a> <a class="link" href="s02.html#idx_id_46">W</a></p>
<div class="variablelist"><dl class="variablelist">
<dt>
+<a name="idx_id_24"></a><span class="term">A</span>
+</dt>
+<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-0">arcsine_distribution</span></a></p></li></ul></div></dd>
+<dt>
<a name="idx_id_25"></a><span class="term">B</span>
</dt>
<dd><div class="index"><ul class="index" style="list-style-type: none; ">
diff --git a/libs/math/doc/html/indexes/s03.html b/libs/math/doc/html/indexes/s03.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Typedef Index</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../indexes.html" title="Chapter&#160;18.&#160;Indexes">
<link rel="prev" href="s02.html" title="Class Index">
<link rel="next" href="s04.html" title="Macro Index">
@@ -24,16 +24,22 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="idm1501665056"></a>Typedef Index</h2></div></div></div>
+<a name="id1515543"></a>Typedef Index</h2></div></div></div>
<p><a class="link" href="s03.html#idx_id_48">A</a> <a class="link" href="s03.html#idx_id_49">B</a> <a class="link" href="s03.html#idx_id_50">C</a> <a class="link" href="s03.html#idx_id_51">D</a> <a class="link" href="s03.html#idx_id_52">E</a> <a class="link" href="s03.html#idx_id_53">F</a> <a class="link" href="s03.html#idx_id_54">G</a> <a class="link" href="s03.html#idx_id_55">H</a> <a class="link" href="s03.html#idx_id_56">I</a> <a class="link" href="s03.html#idx_id_59">L</a> <a class="link" href="s03.html#idx_id_61">N</a> <a class="link" href="s03.html#idx_id_62">O</a> <a class="link" href="s03.html#idx_id_63">P</a> <a class="link" href="s03.html#idx_id_65">R</a> <a class="link" href="s03.html#idx_id_66">S</a> <a class="link" href="s03.html#idx_id_67">T</a> <a class="link" href="s03.html#idx_id_68">U</a> <a class="link" href="s03.html#idx_id_69">V</a> <a class="link" href="s03.html#idx_id_70">W</a></p>
<div class="variablelist"><dl class="variablelist">
<dt>
<a name="idx_id_48"></a><span class="term">A</span>
</dt>
-<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none">
+<dd><div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">arcsine</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">Arcsine Distribution</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">assert_undefined_type</span></p>
<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/pol_ref/pol_ref_ref.html" title="Policy Class Reference"><span class="index-entry-level-1">Policy Class Reference</span></a></p></li></ul></div>
-</li></ul></div></dd>
+</li>
+</ul></div></dd>
<dt>
<a name="idx_id_49"></a><span class="term">B</span>
</dt>
@@ -267,6 +273,7 @@
<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">policy_type</span></p>
<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">Arcsine Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution"><span class="index-entry-level-1">Bernoulli Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/beta_dist.html" title="Beta Distribution"><span class="index-entry-level-1">Beta Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/binomial_dist.html" title="Binomial Distribution"><span class="index-entry-level-1">Binomial Distribution</span></a></p></li>
@@ -368,6 +375,7 @@
<dd><div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">value_type</span></p>
<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">Arcsine Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution"><span class="index-entry-level-1">Bernoulli Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/beta_dist.html" title="Beta Distribution"><span class="index-entry-level-1">Beta Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/binomial_dist.html" title="Binomial Distribution"><span class="index-entry-level-1">Binomial Distribution</span></a></p></li>
diff --git a/libs/math/doc/html/indexes/s04.html b/libs/math/doc/html/indexes/s04.html
index 5f971ea77..2a8f34bc7 100644
--- a/libs/math/doc/html/indexes/s04.html
+++ b/libs/math/doc/html/indexes/s04.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Macro Index</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../indexes.html" title="Chapter&#160;18.&#160;Indexes">
<link rel="prev" href="s03.html" title="Typedef Index">
<link rel="next" href="s05.html" title="Index">
@@ -24,7 +24,7 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="idm1501290272"></a>Macro Index</h2></div></div></div>
+<a name="id1519449"></a>Macro Index</h2></div></div></div>
<p><a class="link" href="s04.html#idx_id_73">B</a> <a class="link" href="s04.html#idx_id_77">F</a></p>
<div class="variablelist"><dl class="variablelist">
<dt>
diff --git a/libs/math/doc/html/indexes/s05.html b/libs/math/doc/html/indexes/s05.html
index bea2fdf7c..6683f1cc8 100644
--- a/libs/math/doc/html/indexes/s05.html
+++ b/libs/math/doc/html/indexes/s05.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Index</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../indexes.html" title="Chapter&#160;18.&#160;Indexes">
<link rel="prev" href="s04.html" title="Macro Index">
</head>
@@ -23,7 +23,7 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="idm1501145632"></a>Index</h2></div></div></div>
+<a name="id1518555"></a>Index</h2></div></div></div>
<p><a class="link" href="s05.html#idx_id_96">A</a> <a class="link" href="s05.html#idx_id_97">B</a> <a class="link" href="s05.html#idx_id_98">C</a> <a class="link" href="s05.html#idx_id_99">D</a> <a class="link" href="s05.html#idx_id_100">E</a> <a class="link" href="s05.html#idx_id_101">F</a> <a class="link" href="s05.html#idx_id_102">G</a> <a class="link" href="s05.html#idx_id_103">H</a> <a class="link" href="s05.html#idx_id_104">I</a> <a class="link" href="s05.html#idx_id_105">J</a> <a class="link" href="s05.html#idx_id_106">K</a> <a class="link" href="s05.html#idx_id_107">L</a> <a class="link" href="s05.html#idx_id_108">M</a> <a class="link" href="s05.html#idx_id_109">N</a> <a class="link" href="s05.html#idx_id_110">O</a> <a class="link" href="s05.html#idx_id_111">P</a> <a class="link" href="s05.html#idx_id_112">Q</a> <a class="link" href="s05.html#idx_id_113">R</a> <a class="link" href="s05.html#idx_id_114">S</a> <a class="link" href="s05.html#idx_id_115">T</a> <a class="link" href="s05.html#idx_id_116">U</a> <a class="link" href="s05.html#idx_id_117">V</a> <a class="link" href="s05.html#idx_id_118">W</a> <a class="link" href="s05.html#idx_id_119">Z</a></p>
<div class="variablelist"><dl class="variablelist">
<dt>
@@ -99,6 +99,23 @@
<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">History and What's New</span></a></p></li></ul></div>
</li>
<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">arcsine</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">Arcsine Distribution</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">Arcsine Distribution</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">arcsine</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">arcsine_distribution</span></a></strong></span></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">cdf</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">expression</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">pdf</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">policy_type</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">value_type</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-0">arcsine_distribution</span></a></p></li>
+<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">asinh</span></p>
<div class="index"><ul class="index" style="list-style-type: none; ">
<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../math_toolkit/inv_hyper/asinh.html" title="asinh"><span class="index-entry-level-1">asinh</span></a></strong></span></p></li>
@@ -1164,6 +1181,7 @@
<p><span class="index-entry-level-0">cdf</span></p>
<div class="index"><ul class="index" style="list-style-type: none; ">
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_implementation.html" title="Additional Implementation Notes"><span class="index-entry-level-1">Additional Implementation Notes</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">Arcsine Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example"><span class="index-entry-level-1">Binomial Coin-Flipping Example</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies"><span class="index-entry-level-1">Discrete Quantile Policies</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/future.html" title="Extras/Future Directions"><span class="index-entry-level-1">Extras/Future Directions</span></a></p></li>
@@ -1780,6 +1798,7 @@
<div class="index"><ul class="index" style="list-style-type: none; ">
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/overview_tr1.html" title="C99 and C++ TR1 C-style Functions"><span class="index-entry-level-1">C99 and C++ TR1 C-style Functions</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/main_tr1.html" title="C99 and TR1 C Functions Overview"><span class="index-entry-level-1">C99 and TR1 C Functions Overview</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_d.html" title="Elliptic Integral D - Legendre Form"><span class="index-entry-level-1">Elliptic Integral D - Legendre Form</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form"><span class="index-entry-level-1">Elliptic Integrals of the Third Kind - Legendre Form</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/tr1_ref.html" title="TR1 C Functions Quick Reference"><span class="index-entry-level-1">TR1 C Functions Quick Reference</span></a></p></li>
</ul></div>
@@ -1801,6 +1820,10 @@
</ul></div>
</li>
<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">ellint_d</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_d.html" title="Elliptic Integral D - Legendre Form"><span class="index-entry-level-1">Elliptic Integral D - Legendre Form</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">ellint_rc</span></p>
<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form"><span class="index-entry-level-1">Elliptic Integrals - Carlson Form</span></a></p></li></ul></div>
</li>
@@ -1813,10 +1836,21 @@
<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form"><span class="index-entry-level-1">Elliptic Integrals - Carlson Form</span></a></p></li></ul></div>
</li>
<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">ellint_rg</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form"><span class="index-entry-level-1">Elliptic Integrals - Carlson Form</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">ellint_rj</span></p>
<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form"><span class="index-entry-level-1">Elliptic Integrals - Carlson Form</span></a></p></li></ul></div>
</li>
<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">Elliptic Integral D - Legendre Form</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_d.html" title="Elliptic Integral D - Legendre Form"><span class="index-entry-level-1">ellint_3</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_d.html" title="Elliptic Integral D - Legendre Form"><span class="index-entry-level-1">ellint_d</span></a></p></li>
+</ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">Elliptic Integral Overview</span></p>
<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_intro.html" title="Elliptic Integral Overview"><span class="index-entry-level-1">expression</span></a></p></li></ul></div>
</li>
@@ -1826,6 +1860,7 @@
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form"><span class="index-entry-level-1">ellint_rc</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form"><span class="index-entry-level-1">ellint_rd</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form"><span class="index-entry-level-1">ellint_rf</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form"><span class="index-entry-level-1">ellint_rg</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form"><span class="index-entry-level-1">ellint_rj</span></a></p></li>
</ul></div>
</li>
@@ -2173,6 +2208,7 @@
<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">expression</span></p>
<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">Arcsine Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/c99.html" title="C99 C Functions"><span class="index-entry-level-1">C99 C Functions</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/weg/st_eg/tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution"><span class="index-entry-level-1">Calculating confidence intervals on the mean with the Students-t distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/compile_time.html" title="Compile time GCD and LCM determination"><span class="index-entry-level-1">Compile time GCD and LCM determination</span></a></p></li>
@@ -2768,6 +2804,14 @@
<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_poly/hermite.html" title="Hermite Polynomials"><span class="index-entry-level-1">Hermite Polynomials</span></a></p></li></ul></div>
</li>
<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">Heuman Lambda Function</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/heuman_lambda.html" title="Heuman Lambda Function"><span class="index-entry-level-1">heuman_lambda</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">heuman_lambda</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/heuman_lambda.html" title="Heuman Lambda Function"><span class="index-entry-level-1">Heuman Lambda Function</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">History and What's New</span></p>
<div class="index"><ul class="index" style="list-style-type: none; ">
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/history1.html" title="History and What's New"><span class="index-entry-level-1">airy_bi_zero</span></a></p></li>
@@ -3206,6 +3250,10 @@
</ul></div>
</li>
<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">Jacobi Zeta Function</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/jacobi_zeta.html" title="Jacobi Zeta Function"><span class="index-entry-level-1">jacobi_zeta</span></a></p></li></ul></div>
+</li>
+<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">jacobi_cd</span></p>
<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/jacobi/jacobi_cd.html" title="Jacobi Elliptic Function cd"><span class="index-entry-level-1">Jacobi Elliptic Function cd</span></a></p></li></ul></div>
</li>
@@ -3257,6 +3305,10 @@
<p><span class="index-entry-level-0">jacobi_sn</span></p>
<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/jacobi/jacobi_sn.html" title="Jacobi Elliptic Function sn"><span class="index-entry-level-1">Jacobi Elliptic Function sn</span></a></p></li></ul></div>
</li>
+<li class="listitem" style="list-style-type: none">
+<p><span class="index-entry-level-0">jacobi_zeta</span></p>
+<div class="index"><ul class="index" style="list-style-type: none; "><li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/ellint/jacobi_zeta.html" title="Jacobi Zeta Function"><span class="index-entry-level-1">Jacobi Zeta Function</span></a></p></li></ul></div>
+</li>
</ul></div></dd>
<dt>
<a name="idx_id_106"></a><span class="term">K</span>
@@ -4167,6 +4219,7 @@
<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">pdf</span></p>
<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">Arcsine Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/overview/generic.html" title="Generic operations common to all distributions are non-member functions"><span class="index-entry-level-1">Generic operations common to all distributions are non-member functions</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/nmp.html" title="Non-Member Properties"><span class="index-entry-level-1">Non-Member Properties</span></a></p></li>
</ul></div>
@@ -4226,6 +4279,7 @@
<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">policy_type</span></p>
<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">Arcsine Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution"><span class="index-entry-level-1">Bernoulli Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/beta_dist.html" title="Beta Distribution"><span class="index-entry-level-1">Beta Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/binomial_dist.html" title="Binomial Distribution"><span class="index-entry-level-1">Binomial Distribution</span></a></p></li>
@@ -4256,6 +4310,8 @@
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/weibull_dist.html" title="Weibull Distribution"><span class="index-entry-level-1">Weibull Distribution</span></a></p></li>
</ul></div>
</li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_gamma/polygamma.html" title="Polygamma"><span class="index-entry-level-0">Polygamma</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_gamma/polygamma.html" title="Polygamma"><span class="index-entry-level-0">polygamma</span></a></p></li>
<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">Polynomial and Rational Function Evaluation</span></p>
<div class="index"><ul class="index" style="list-style-type: none; ">
@@ -5196,6 +5252,8 @@
<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../math_toolkit/dist_ref/dists/triangular_dist.html" title="Triangular Distribution"><span class="index-entry-level-1">Triangular Distribution</span></a></strong></span></p></li>
</ul></div>
</li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_gamma/trigamma.html" title="Trigamma"><span class="index-entry-level-0">Trigamma</span></a></p></li>
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_gamma/trigamma.html" title="Trigamma"><span class="index-entry-level-0">trigamma</span></a></p></li>
<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">trunc</span></p>
<div class="index"><ul class="index" style="list-style-type: none; ">
@@ -5422,6 +5480,7 @@
<li class="listitem" style="list-style-type: none">
<p><span class="index-entry-level-0">value_type</span></p>
<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/arcine_dist.html" title="Arcsine Distribution"><span class="index-entry-level-1">Arcsine Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution"><span class="index-entry-level-1">Bernoulli Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/beta_dist.html" title="Beta Distribution"><span class="index-entry-level-1">Beta Distribution</span></a></p></li>
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/binomial_dist.html" title="Binomial Distribution"><span class="index-entry-level-1">Binomial Distribution</span></a></p></li>
diff --git a/libs/math/doc/html/inverse_complex.html b/libs/math/doc/html/inverse_complex.html
index bfbce0f9b..06498d190 100644
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@@ -3,9 +3,9 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;8.&#160;Complex Number Functions</title>
<link rel="stylesheet" href="math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.1.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.2.0">
<link rel="prev" href="math_toolkit/tr1_ref.html" title="TR1 C Functions Quick Reference">
<link rel="next" href="math_toolkit/complex_implementation.html" title="Implementation and Accuracy">
</head>
@@ -27,7 +27,7 @@
<a name="inverse_complex"></a>Chapter&#160;8.&#160;Complex Number Functions</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
-<dl class="toc">
+<dl>
<dt><span class="section"><a href="math_toolkit/complex_implementation.html">Implementation and
Accuracy</a></span></dt>
<dt><span class="section"><a href="math_toolkit/asin.html">asin</a></span></dt>
diff --git a/libs/math/doc/html/math_toolkit/acknowledgement.html b/libs/math/doc/html/math_toolkit/acknowledgement.html
index e8ff556f8..204992e4d 100644
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+++ b/libs/math/doc/html/math_toolkit/acknowledgement.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Acknowledgements</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="exp.html" title="The Quaternionic Exponential">
<link rel="next" href="quat_history.html" title="History">
diff --git a/libs/math/doc/html/math_toolkit/acknowledgements.html b/libs/math/doc/html/math_toolkit/acknowledgements.html
index 491f0baf0..8e61408a9 100644
--- a/libs/math/doc/html/math_toolkit/acknowledgements.html
+++ b/libs/math/doc/html/math_toolkit/acknowledgements.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Acknowledgements</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../octonions.html" title="Chapter&#160;10.&#160;Octonions">
<link rel="prev" href="oct_tests.html" title="Test Program">
<link rel="next" href="oct_history.html" title="History">
diff --git a/libs/math/doc/html/math_toolkit/acos.html b/libs/math/doc/html/math_toolkit/acos.html
index 2c9363b49..9f88373d2 100644
--- a/libs/math/doc/html/math_toolkit/acos.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>acos</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../inverse_complex.html" title="Chapter&#160;8.&#160;Complex Number Functions">
<link rel="prev" href="asin.html" title="asin">
<link rel="next" href="atan.html" title="atan">
diff --git a/libs/math/doc/html/math_toolkit/acosh.html b/libs/math/doc/html/math_toolkit/acosh.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>acosh</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../inverse_complex.html" title="Chapter&#160;8.&#160;Complex Number Functions">
<link rel="prev" href="asinh.html" title="asinh">
<link rel="next" href="atanh.html" title="atanh">
diff --git a/libs/math/doc/html/math_toolkit/airy.html b/libs/math/doc/html/math_toolkit/airy.html
index 791ac42e7..38b21999e 100644
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Airy Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
<link rel="prev" href="hankel/sph_hankel.html" title="Spherical Hankel Functions">
<link rel="next" href="airy/ai.html" title="Airy Ai Function">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.airy"></a><a class="link" href="airy.html" title="Airy Functions">Airy Functions</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="airy/ai.html">Airy Ai Function</a></span></dt>
<dt><span class="section"><a href="airy/bi.html">Airy Bi Function</a></span></dt>
<dt><span class="section"><a href="airy/aip.html">Airy Ai' Function</a></span></dt>
diff --git a/libs/math/doc/html/math_toolkit/airy/ai.html b/libs/math/doc/html/math_toolkit/airy/ai.html
index f4555f164..499bbd78c 100644
--- a/libs/math/doc/html/math_toolkit/airy/ai.html
+++ b/libs/math/doc/html/math_toolkit/airy/ai.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Airy Ai Function</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
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<link rel="next" href="bi.html" title="Airy Bi Function">
@@ -51,7 +51,7 @@
the Airy function Ai which is the first solution to the differential equation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/airy.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/airy.svg"></span>
</p>
<p>
See Weisstein, Eric W. "Airy Functions." From MathWorld--A Wolfram
@@ -69,7 +69,7 @@
for positive <span class="emphasis"><em>x</em></span> the value tends to zero:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/airy_ai.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/airy_ai.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.airy.ai.h2"></a>
@@ -101,7 +101,7 @@
This function is implemented in terms of the Bessel functions using the relations:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/airy_ai.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/airy_ai.svg"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/airy/aip.html b/libs/math/doc/html/math_toolkit/airy/aip.html
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+++ b/libs/math/doc/html/math_toolkit/airy/aip.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Airy Ai' Function</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
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+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../airy.html" title="Airy Functions">
<link rel="prev" href="bi.html" title="Airy Bi Function">
<link rel="next" href="bip.html" title="Airy Bi' Function">
@@ -52,7 +52,7 @@
differential equation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/airy.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/airy.svg"></span>
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
@@ -66,7 +66,7 @@
for positive <span class="emphasis"><em>x</em></span> the value tends to zero:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/airy_aip.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/airy_aip.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.airy.aip.h2"></a>
@@ -97,7 +97,7 @@
This function is implemented in terms of the Bessel functions using the relations:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/airy_aip.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/airy_aip.svg"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/airy/bi.html b/libs/math/doc/html/math_toolkit/airy/bi.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Airy Bi Function</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
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<link rel="next" href="aip.html" title="Airy Ai' Function">
@@ -51,7 +51,7 @@
the Airy function Bi which is the second solution to the differential equation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/airy.png"></span>
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</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
@@ -65,7 +65,7 @@
for positive <span class="emphasis"><em>x</em></span> the value tends to infinity:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/airy_bi.png" align="middle"></span>
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<a name="math_toolkit.airy.bi.h2"></a>
@@ -96,7 +96,7 @@
This function is implemented in terms of the Bessel functions using the relations:
</p>
<p>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/airy/bip.html b/libs/math/doc/html/math_toolkit/airy/bip.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Airy Bi' Function</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
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-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
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<link rel="next" href="../ellint.html" title="Elliptic Integrals">
@@ -52,7 +52,7 @@
differential equation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/airy.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/airy.svg"></span>
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
@@ -66,7 +66,7 @@
for positive <span class="emphasis"><em>x</em></span> the value tends to infinity:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/airy_bi.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/airy_bi.svg" align="middle"></span>
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<a name="math_toolkit.airy.bip.h2"></a>
@@ -97,7 +97,7 @@
This function is implemented in terms of the Bessel functions using the relations:
</p>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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<link rel="prev" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">
<link rel="next" href="../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">
diff --git a/libs/math/doc/html/math_toolkit/asin.html b/libs/math/doc/html/math_toolkit/asin.html
index 60870a765..5b951b81b 100644
--- a/libs/math/doc/html/math_toolkit/asin.html
+++ b/libs/math/doc/html/math_toolkit/asin.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>asin</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../inverse_complex.html" title="Chapter&#160;8.&#160;Complex Number Functions">
<link rel="prev" href="complex_implementation.html" title="Implementation and Accuracy">
<link rel="next" href="acos.html" title="acos">
diff --git a/libs/math/doc/html/math_toolkit/asinh.html b/libs/math/doc/html/math_toolkit/asinh.html
index 3f749ed52..61c3a98e6 100644
--- a/libs/math/doc/html/math_toolkit/asinh.html
+++ b/libs/math/doc/html/math_toolkit/asinh.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>asinh</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../inverse_complex.html" title="Chapter&#160;8.&#160;Complex Number Functions">
<link rel="prev" href="atan.html" title="atan">
<link rel="next" href="acosh.html" title="acosh">
diff --git a/libs/math/doc/html/math_toolkit/atan.html b/libs/math/doc/html/math_toolkit/atan.html
index bffb3c85d..6007e80ce 100644
--- a/libs/math/doc/html/math_toolkit/atan.html
+++ b/libs/math/doc/html/math_toolkit/atan.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>atan</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../inverse_complex.html" title="Chapter&#160;8.&#160;Complex Number Functions">
<link rel="prev" href="acos.html" title="acos">
<link rel="next" href="asinh.html" title="asinh">
diff --git a/libs/math/doc/html/math_toolkit/atanh.html b/libs/math/doc/html/math_toolkit/atanh.html
index 4a48af8d3..eb9e83b1a 100644
--- a/libs/math/doc/html/math_toolkit/atanh.html
+++ b/libs/math/doc/html/math_toolkit/atanh.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>atanh</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../inverse_complex.html" title="Chapter&#160;8.&#160;Complex Number Functions">
<link rel="prev" href="acosh.html" title="acosh">
<link rel="next" href="complex_history.html" title="History">
diff --git a/libs/math/doc/html/math_toolkit/bessel.html b/libs/math/doc/html/math_toolkit/bessel.html
index 000e0f2b8..4e8e57f36 100644
--- a/libs/math/doc/html/math_toolkit/bessel.html
+++ b/libs/math/doc/html/math_toolkit/bessel.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Bessel Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
<link rel="prev" href="sf_poly/sph_harm.html" title="Spherical Harmonics">
<link rel="next" href="bessel/bessel_over.html" title="Bessel Function Overview">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.bessel"></a><a class="link" href="bessel.html" title="Bessel Functions">Bessel Functions</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="bessel/bessel_over.html">Bessel Function Overview</a></span></dt>
<dt><span class="section"><a href="bessel/bessel_first.html">Bessel Functions of
the First and Second Kinds</a></span></dt>
diff --git a/libs/math/doc/html/math_toolkit/bessel/bessel_derivatives.html b/libs/math/doc/html/math_toolkit/bessel/bessel_derivatives.html
index 16f0bdac4..3515bf781 100644
--- a/libs/math/doc/html/math_toolkit/bessel/bessel_derivatives.html
+++ b/libs/math/doc/html/math_toolkit/bessel/bessel_derivatives.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Derivatives of the Bessel Functions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../bessel.html" title="Bessel Functions">
<link rel="prev" href="sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">
<link rel="next" href="../hankel.html" title="Hankel Functions">
@@ -119,19 +119,19 @@
In the general case, the derivatives are calculated using the relations:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel_derivatives1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel_derivatives1.svg"></span>
</p>
<p>
There are also a number of special cases, for large x we have:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel_derivatives4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel_derivatives4.svg"></span>
</p>
<p>
And for small x:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel_derivatives5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel_derivatives5.svg"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/bessel/bessel_first.html b/libs/math/doc/html/math_toolkit/bessel/bessel_first.html
index 1d99d2199..31ad8bae6 100644
--- a/libs/math/doc/html/math_toolkit/bessel/bessel_first.html
+++ b/libs/math/doc/html/math_toolkit/bessel/bessel_first.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Bessel Functions of the First and Second Kinds</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../bessel.html" title="Bessel Functions">
<link rel="prev" href="bessel_over.html" title="Bessel Function Overview">
<link rel="next" href="bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds">
@@ -65,10 +65,10 @@
where:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel2.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel3.svg"></span>
</p>
<p>
The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
@@ -98,14 +98,14 @@
The following graph illustrates the cyclic nature of J<sub>v</sub>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/cyl_bessel_j.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/cyl_bessel_j.svg" align="middle"></span>
</p>
<p>
The following graph shows the behaviour of Y<sub>v</sub>: this is also cyclic for large
<span class="emphasis"><em>x</em></span>, but tends to -&#8734; &#160; for small <span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/cyl_neumann.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/cyl_neumann.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.bessel.bessel_first.h2"></a>
@@ -509,10 +509,10 @@
can be used to move to <span class="emphasis"><em>v &gt; 0</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel9.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel9.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel10.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel10.svg"></span>
</p>
<p>
Note that if the order is an integer, then these formulae reduce to:
@@ -566,16 +566,16 @@
and <a href="http://functions.wolfram.com/03.03.06.0040.01" target="_top">http://functions.wolfram.com/03.03.06.0040.01</a>):
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel_y0_small_z.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel_y0_small_z.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel_y1_small_z.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel_y1_small_z.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel_y2_small_z.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel_y2_small_z.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel_yn_small_z.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel_yn_small_z.svg"></span>
</p>
<p>
When <span class="emphasis"><em>x</em></span> is small compared to <span class="emphasis"><em>v</em></span> and
@@ -584,14 +584,14 @@
often too slow to converge to be used (see <a href="http://functions.wolfram.com/03.03.06.0034.01" target="_top">http://functions.wolfram.com/03.03.06.0034.01</a>):
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel_yv_small_z.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel_yv_small_z.svg"></span>
</p>
<p>
When <span class="emphasis"><em>x</em></span> is small compared to <span class="emphasis"><em>v</em></span>,
J<sub>v</sub>x &#160; is best computed directly from the series:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel2.svg"></span>
</p>
<p>
In the general case we compute J<sub>v</sub> &#160; and Y<sub>v</sub> &#160; simultaneously.
@@ -606,13 +606,13 @@
as well as the Wronskian:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel8.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel8.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel11.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel11.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel12.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel12.svg"></span>
</p>
<p>
See: F.S. Acton, <span class="emphasis"><em>Numerical Methods that Work</em></span>, The Mathematical
@@ -639,13 +639,13 @@
J<sub>&#956;</sub>, J<sub>&#956;+1</sub>, Y<sub>&#956;</sub>, Y<sub>&#956;+1</sub> can be calculated by
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel13.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel13.svg"></span>
</p>
<p>
where
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel14.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel14.svg"></span>
</p>
<p>
J<sub>&#957;</sub> and Y<sub>&#956;</sub> are then calculated using backward (Miller's algorithm) and forward
@@ -657,13 +657,13 @@
series:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel15.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel15.svg"></span>
</p>
<p>
where
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel16.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel16.svg"></span>
</p>
<p>
g<sub>k</sub> &#160; and h<sub>k</sub> &#160;
diff --git a/libs/math/doc/html/math_toolkit/bessel/bessel_over.html b/libs/math/doc/html/math_toolkit/bessel/bessel_over.html
index 8896253ff..a85b80769 100644
--- a/libs/math/doc/html/math_toolkit/bessel/bessel_over.html
+++ b/libs/math/doc/html/math_toolkit/bessel/bessel_over.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Bessel Function Overview</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../bessel.html" title="Bessel Functions">
<link rel="prev" href="../bessel.html" title="Bessel Functions">
<link rel="next" href="bessel_first.html" title="Bessel Functions of the First and Second Kinds">
@@ -35,7 +35,7 @@
Bessel Functions are solutions to Bessel's ordinary differential equation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel1.svg"></span>
</p>
<p>
where &#957; &#160; is the <span class="emphasis"><em>order</em></span> of the equation, and may be an arbitrary
@@ -51,7 +51,7 @@ and known as a Bessel
function of the first kind:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel2.svg"></span>
</p>
<p>
This function is implemented in this library as <a class="link" href="bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>.
@@ -62,7 +62,7 @@ and is known as either a Bessel
Function of the second kind, or as a Neumann function:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel3.svg"></span>
</p>
<p>
This function is implemented in this library as <a class="link" href="bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>.
@@ -71,34 +71,34 @@ and is known as either a Bessel
The Bessel functions satisfy the recurrence relations:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel4.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel5.svg"></span>
</p>
<p>
Have the derivatives:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel6.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel6.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel7.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel7.svg"></span>
</p>
<p>
Have the Wronskian relation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel8.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel8.svg"></span>
</p>
<p>
and the reflection formulae:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel9.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel9.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bessel10.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bessel10.svg"></span>
</p>
<h5>
<a name="math_toolkit.bessel.bessel_over.h1"></a>
@@ -112,7 +112,7 @@ and is known as either a Bessel
are the two linearly independent solutions to the modified Bessel equation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel1.svg"></span>
</p>
<p>
The solutions are known as the modified Bessel functions of the first and
@@ -121,10 +121,10 @@ and is known as either a Bessel
respectively:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel2.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel3.svg"></span>
</p>
<p>
These functions are implemented in this library as <a class="link" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_i</a>
@@ -134,34 +134,34 @@ respectively:
The modified Bessel functions satisfy the recurrence relations:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel4.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel5.svg"></span>
</p>
<p>
Have the derivatives:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel6.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel6.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel7.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel7.svg"></span>
</p>
<p>
Have the Wronskian relation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel8.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel8.svg"></span>
</p>
<p>
and the reflection formulae:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel9.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel9.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel10.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel10.svg"></span>
</p>
<h5>
<a name="math_toolkit.bessel.bessel_over.h2"></a>
@@ -173,7 +173,7 @@ respectively:
of variables, the radial equation has the form:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/sbessel1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/sbessel1.svg"></span>
</p>
<p>
The two linearly independent solutions to this equation are called the spherical
@@ -181,7 +181,7 @@ respectively:
J<sub>n</sub> &#160; and Y<sub>n</sub> &#160; by:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/sbessel2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/sbessel2.svg"></span>
</p>
<p>
The spherical Bessel function of the second kind y<sub>n</sub> &#160;
diff --git a/libs/math/doc/html/math_toolkit/bessel/bessel_root.html b/libs/math/doc/html/math_toolkit/bessel/bessel_root.html
index 63ac4464a..45babf62f 100644
--- a/libs/math/doc/html/math_toolkit/bessel/bessel_root.html
+++ b/libs/math/doc/html/math_toolkit/bessel/bessel_root.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Finding Zeros of Bessel Functions of the First and Second Kinds</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../bessel.html" title="Bessel Functions">
<link rel="prev" href="bessel_first.html" title="Bessel Functions of the First and Second Kinds">
<link rel="next" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">
@@ -159,10 +159,10 @@
nor NaN.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/bessel_j_zeros.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/bessel_j_zeros.svg" align="middle"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/neumann_y_zeros.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/neumann_y_zeros.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.bessel.bessel_root.h2"></a>
diff --git a/libs/math/doc/html/math_toolkit/bessel/mbessel.html b/libs/math/doc/html/math_toolkit/bessel/mbessel.html
index ad62070e8..23c042376 100644
--- a/libs/math/doc/html/math_toolkit/bessel/mbessel.html
+++ b/libs/math/doc/html/math_toolkit/bessel/mbessel.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Modified Bessel Functions of the First and Second Kinds</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../bessel.html" title="Bessel Functions">
<link rel="prev" href="bessel_root.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds">
<link rel="next" href="sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">
@@ -66,10 +66,10 @@
where:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel2.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel3.svg"></span>
</p>
<p>
The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
@@ -99,13 +99,13 @@
The following graph illustrates the exponential behaviour of I<sub>v</sub>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/cyl_bessel_i.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/cyl_bessel_i.svg" align="middle"></span>
</p>
<p>
The following graph illustrates the exponential decay of K<sub>v</sub>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/cyl_bessel_k.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/cyl_bessel_k.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.bessel.mbessel.h2"></a>
@@ -365,7 +365,7 @@
the recurrence relation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel5.svg"></span>
</p>
<p>
starting from K<sub>0</sub> &#160; and K<sub>1</sub> &#160; which are calculated using rational the approximations
@@ -377,17 +377,17 @@
I<sub>v</sub>x &#160; is best computed directly from the series:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel17.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel17.svg"></span>
</p>
<p>
In the general case, we first normalize &#957; &#160; to [<code class="literal">0, [inf]</code>)
with the help of the reflection formulae:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel9.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel9.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel10.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel10.svg"></span>
</p>
<p>
Let &#956; &#160; = &#957; - floor(&#957; + 1/2), then &#956; &#160; is the fractional part of &#957; &#160; such that |&#956;| &lt;= 1/2
@@ -401,13 +401,13 @@
fractions as well as the Wronskian:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel11.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel11.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel12.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel12.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel8.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel8.svg"></span>
</p>
<p>
The continued fractions are computed using the modified Lentz's method (W.J.
@@ -431,13 +431,13 @@
can be calculated by
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel13.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel13.svg"></span>
</p>
<p>
where
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel14.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel14.svg"></span>
</p>
<p>
<span class="emphasis"><em>S</em></span> is also a series that is summed along with CF2, see
@@ -451,13 +451,13 @@ can be calculated by
series:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel15.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel15.svg"></span>
</p>
<p>
where
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/mbessel16.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/mbessel16.svg"></span>
</p>
<p>
f<sub>k</sub> &#160; and h<sub>k</sub> &#160;
diff --git a/libs/math/doc/html/math_toolkit/bessel/sph_bessel.html b/libs/math/doc/html/math_toolkit/bessel/sph_bessel.html
index 482154504..9d36025a2 100644
--- a/libs/math/doc/html/math_toolkit/bessel/sph_bessel.html
+++ b/libs/math/doc/html/math_toolkit/bessel/sph_bessel.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Spherical Bessel Functions of the First and Second Kinds</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../bessel.html" title="Bessel Functions">
<link rel="prev" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">
<link rel="next" href="bessel_derivatives.html" title="Derivatives of the Bessel Functions">
@@ -66,7 +66,7 @@
where:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/sbessel2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/sbessel2.svg"></span>
</p>
<p>
The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
@@ -86,14 +86,14 @@
The j<sub>v</sub> &#160; function is cyclic like J<sub>v</sub> &#160; but differs in its behaviour at the origin:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/sph_bessel.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/sph_bessel.svg" align="middle"></span>
</p>
<p>
Likewise y<sub>v</sub> &#160; is also cyclic for large x, but tends to -&#8734; &#160;
for small <span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/sph_neumann.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/sph_neumann.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.bessel.sph_bessel.h2"></a>
@@ -123,7 +123,7 @@ for small <span class="emphasis"><em>x</em></span>:
implemented directly in terms of their definitions:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/sbessel2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/sbessel2.svg"></span>
</p>
<p>
The special cases occur for:
@@ -136,7 +136,7 @@ for small <span class="emphasis"><em>x</em></span>:
and for small <span class="emphasis"><em>x &lt; 1</em></span>, we can use the series:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/sbessel5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/sbessel5.svg"></span>
</p>
<p>
which neatly avoids the problem of calculating 0/0 that can occur with the
diff --git a/libs/math/doc/html/math_toolkit/building.html b/libs/math/doc/html/math_toolkit/building.html
index acf424985..403a8581f 100644
--- a/libs/math/doc/html/math_toolkit/building.html
+++ b/libs/math/doc/html/math_toolkit/building.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>If and How to Build a Boost.Math Library, and its Examples and Tests</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="perf_over1.html" title="Performance">
<link rel="next" href="history1.html" title="History and What's New">
diff --git a/libs/math/doc/html/math_toolkit/c99.html b/libs/math/doc/html/math_toolkit/c99.html
index 7edf366a2..13a920cb5 100644
--- a/libs/math/doc/html/math_toolkit/c99.html
+++ b/libs/math/doc/html/math_toolkit/c99.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>C99 C Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../extern_c.html" title='Chapter&#160;7.&#160;TR1 and C99 external "C" Functions'>
<link rel="prev" href="main_tr1.html" title="C99 and TR1 C Functions Overview">
<link rel="next" href="tr1_ref.html" title="TR1 C Functions Quick Reference">
@@ -291,7 +291,7 @@
Returns the error function of <span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/erf1.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/erf1.svg"></span>
</p>
<p>
See also <a class="link" href="sf_erf/error_function.html" title="Error Functions">erf</a> for
@@ -356,7 +356,7 @@
Returns the log of the gamma function of <span class="emphasis"><em>x</em></span>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/lgamm1.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/lgamm1.svg"></span>
</p>
<p>
See also <a class="link" href="sf_gamma/lgamma.html" title="Log Gamma">lgamma</a> for the
@@ -436,7 +436,7 @@
Returns the gamma function of <span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/gamm1.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/gamm1.svg"></span>
</p>
<p>
See also <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a> for the
diff --git a/libs/math/doc/html/math_toolkit/comp_compilers.html b/libs/math/doc/html/math_toolkit/comp_compilers.html
index 1fb0cd3a2..a3fe374bd 100644
--- a/libs/math/doc/html/math_toolkit/comp_compilers.html
+++ b/libs/math/doc/html/math_toolkit/comp_compilers.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Comparing Compilers</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../perf.html" title="Chapter&#160;15.&#160;Performance">
<link rel="prev" href="getting_best.html" title="Getting the Best Performance from this Library">
<link rel="next" href="tuning.html" title="Performance Tuning Macros">
diff --git a/libs/math/doc/html/math_toolkit/comparisons.html b/libs/math/doc/html/math_toolkit/comparisons.html
index 86ca487af..e607a2f3a 100644
--- a/libs/math/doc/html/math_toolkit/comparisons.html
+++ b/libs/math/doc/html/math_toolkit/comparisons.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Comparisons to Other Open Source Libraries</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../perf.html" title="Chapter&#160;15.&#160;Performance">
<link rel="prev" href="tuning.html" title="Performance Tuning Macros">
<link rel="next" href="perf_test_app.html" title="The Performance Test Application">
@@ -344,7 +344,7 @@
</td>
<td>
<p>
- +INF <a href="#ftn.math_toolkit.comparisons.f0" class="footnote" name="math_toolkit.comparisons.f0"><sup class="footnote">[1]</sup></a>
+ +INF <a href="#ftn.math_toolkit.comparisons.f0" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f0"></a>[1]</sup></a>
</p>
</td>
</tr>
@@ -423,7 +423,7 @@
<td>
<p>
</p>
-<p>17.89<a href="#ftn.math_toolkit.comparisons.f1" class="footnote" name="math_toolkit.comparisons.f1"><sup class="footnote">[2]</sup></a></p>
+<p>17.89<a href="#ftn.math_toolkit.comparisons.f1" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f1"></a>[2]</sup></a></p>
<p> </p>
<p>(4.248e-005s)</p>
<p>
@@ -659,7 +659,7 @@
<td>
<p>
</p>
-<p>67.66<a href="#ftn.math_toolkit.comparisons.f2" class="footnote" name="math_toolkit.comparisons.f2"><sup class="footnote">[1]</sup></a></p>
+<p>67.66<a href="#ftn.math_toolkit.comparisons.f2" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f2"></a>[1]</sup></a></p>
<p> </p>
<p>(3.366e-004s)</p>
<p>
@@ -1089,7 +1089,7 @@
<td>
<p>
</p>
-<p>3.60<a href="#ftn.math_toolkit.comparisons.f3" class="footnote" name="math_toolkit.comparisons.f3"><sup class="footnote">[2]</sup></a></p>
+<p>3.60<a href="#ftn.math_toolkit.comparisons.f3" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f3"></a>[2]</sup></a></p>
<p> </p>
<p>(5.987e-007s)</p>
<p>
@@ -1319,7 +1319,7 @@
<td>
<p>
</p>
-<p>43.43<a href="#ftn.math_toolkit.comparisons.f4" class="footnote" name="math_toolkit.comparisons.f4"><sup class="footnote">[3]</sup></a></p>
+<p>43.43<a href="#ftn.math_toolkit.comparisons.f4" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f4"></a>[3]</sup></a></p>
<p> </p>
<p>(3.732e-004s)</p>
<p>
@@ -1389,7 +1389,7 @@
<td>
<p>
</p>
-<p>393.90<a href="#ftn.math_toolkit.comparisons.f5" class="footnote" name="math_toolkit.comparisons.f5"><sup class="footnote">[4]</sup></a></p>
+<p>393.90<a href="#ftn.math_toolkit.comparisons.f5" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f5"></a>[4]</sup></a></p>
<p> </p>
<p>(2.673e-002s)</p>
<p>
@@ -1525,7 +1525,7 @@
<td>
<p>
</p>
-<p><span class="bold"><strong>1.00</strong></span><a href="#ftn.math_toolkit.comparisons.f6" class="footnote" name="math_toolkit.comparisons.f6"><sup class="footnote">[5]</sup></a></p>
+<p><span class="bold"><strong>1.00</strong></span><a href="#ftn.math_toolkit.comparisons.f6" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f6"></a>[5]</sup></a></p>
<p> </p>
<p>(4.411e-004s)</p>
<p>
@@ -1936,7 +1936,7 @@
<td>
<p>
</p>
-<p>30.51<a href="#ftn.math_toolkit.comparisons.f7" class="footnote" name="math_toolkit.comparisons.f7"><sup class="footnote">[1]</sup></a></p>
+<p>30.51<a href="#ftn.math_toolkit.comparisons.f7" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f7"></a>[1]</sup></a></p>
<p> </p>
<p>(3.616e-004s)</p>
<p>
@@ -2366,7 +2366,7 @@
<td>
<p>
</p>
-<p>2.20<a href="#ftn.math_toolkit.comparisons.f8" class="footnote" name="math_toolkit.comparisons.f8"><sup class="footnote">[2]</sup></a></p>
+<p>2.20<a href="#ftn.math_toolkit.comparisons.f8" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f8"></a>[2]</sup></a></p>
<p> </p>
<p>(3.522e-007s)</p>
<p>
@@ -2596,7 +2596,7 @@
<td>
<p>
</p>
-<p>25.92<a href="#ftn.math_toolkit.comparisons.f9" class="footnote" name="math_toolkit.comparisons.f9"><sup class="footnote">[3]</sup></a></p>
+<p>25.92<a href="#ftn.math_toolkit.comparisons.f9" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f9"></a>[3]</sup></a></p>
<p> </p>
<p>(4.407e-004s)</p>
<p>
@@ -2666,7 +2666,7 @@
<td>
<p>
</p>
-<p>144.91<a href="#ftn.math_toolkit.comparisons.f10" class="footnote" name="math_toolkit.comparisons.f10"><sup class="footnote">[4]</sup></a></p>
+<p>144.91<a href="#ftn.math_toolkit.comparisons.f10" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f10"></a>[4]</sup></a></p>
<p> </p>
<p>(3.214e-002s)</p>
<p>
@@ -2802,7 +2802,7 @@
<td>
<p>
</p>
-<p><span class="bold"><strong>1.00</strong></span><a href="#ftn.math_toolkit.comparisons.f11" class="footnote" name="math_toolkit.comparisons.f11"><sup class="footnote">[5]</sup></a></p>
+<p><span class="bold"><strong>1.00</strong></span><a href="#ftn.math_toolkit.comparisons.f11" class="footnote"><sup class="footnote"><a name="math_toolkit.comparisons.f11"></a>[5]</sup></a></p>
<p> </p>
<p>(5.916e-004s)</p>
<p>
diff --git a/libs/math/doc/html/math_toolkit/compile_time.html b/libs/math/doc/html/math_toolkit/compile_time.html
index d3e8cb29c..42ed13cc4 100644
--- a/libs/math/doc/html/math_toolkit/compile_time.html
+++ b/libs/math/doc/html/math_toolkit/compile_time.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Compile time GCD and LCM determination</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../gcd_lcm.html" title="Chapter&#160;11.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)">
<link rel="prev" href="run_time.html" title="Run-time GCD &amp; LCM Determination">
<link rel="next" href="gcd_header.html" title="Header &lt;boost/math/common_factor.hpp&gt;">
diff --git a/libs/math/doc/html/math_toolkit/compilers_overview.html b/libs/math/doc/html/math_toolkit/compilers_overview.html
index 3ec87c325..155edeb17 100644
--- a/libs/math/doc/html/math_toolkit/compilers_overview.html
+++ b/libs/math/doc/html/math_toolkit/compilers_overview.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Compilers</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="error_handling.html" title="Error Handling">
<link rel="next" href="config_macros.html" title="Configuration Macros">
diff --git a/libs/math/doc/html/math_toolkit/complex_history.html b/libs/math/doc/html/math_toolkit/complex_history.html
index eeaba48e3..dfbba0d8c 100644
--- a/libs/math/doc/html/math_toolkit/complex_history.html
+++ b/libs/math/doc/html/math_toolkit/complex_history.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>History</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../inverse_complex.html" title="Chapter&#160;8.&#160;Complex Number Functions">
<link rel="prev" href="atanh.html" title="atanh">
<link rel="next" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
diff --git a/libs/math/doc/html/math_toolkit/complex_implementation.html b/libs/math/doc/html/math_toolkit/complex_implementation.html
index d4c59ffbc..13295b19e 100644
--- a/libs/math/doc/html/math_toolkit/complex_implementation.html
+++ b/libs/math/doc/html/math_toolkit/complex_implementation.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Implementation and Accuracy</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../inverse_complex.html" title="Chapter&#160;8.&#160;Complex Number Functions">
<link rel="prev" href="../inverse_complex.html" title="Chapter&#160;8.&#160;Complex Number Functions">
<link rel="next" href="asin.html" title="asin">
diff --git a/libs/math/doc/html/math_toolkit/concepts.html b/libs/math/doc/html/math_toolkit/concepts.html
index bbc7e5460..93db31780 100644
--- a/libs/math/doc/html/math_toolkit/concepts.html
+++ b/libs/math/doc/html/math_toolkit/concepts.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Conceptual Requirements for Real Number Types</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../using_udt.html" title="Chapter&#160;13.&#160;Use with User-Defined Floating-Point Types - Boost.Multiprecision and others">
<link rel="prev" href="high_precision/using_test.html" title="Using without expression templates for Boost.Test and others">
<link rel="next" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">
diff --git a/libs/math/doc/html/math_toolkit/config_macros.html b/libs/math/doc/html/math_toolkit/config_macros.html
index 73440e7b9..757d0c12f 100644
--- a/libs/math/doc/html/math_toolkit/config_macros.html
+++ b/libs/math/doc/html/math_toolkit/config_macros.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Configuration Macros</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="compilers_overview.html" title="Compilers">
<link rel="next" href="intro_pol_overview.html" title="Policies">
diff --git a/libs/math/doc/html/math_toolkit/constants.html b/libs/math/doc/html/math_toolkit/constants.html
index 35a1a552e..f1e1a0254 100644
--- a/libs/math/doc/html/math_toolkit/constants.html
+++ b/libs/math/doc/html/math_toolkit/constants.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>The Mathematical Constants</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../constants.html" title="Chapter&#160;4.&#160;Mathematical Constants">
<link rel="prev" href="tutorial/user_def.html" title="Use With User-Defined Types">
<link rel="next" href="new_const.html" title="Defining New Constants">
diff --git a/libs/math/doc/html/math_toolkit/constants_faq.html b/libs/math/doc/html/math_toolkit/constants_faq.html
index 1b079611c..1eaaa66ed 100644
--- a/libs/math/doc/html/math_toolkit/constants_faq.html
+++ b/libs/math/doc/html/math_toolkit/constants_faq.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>FAQs</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../constants.html" title="Chapter&#160;4.&#160;Mathematical Constants">
<link rel="prev" href="new_const.html" title="Defining New Constants">
<link rel="next" href="../dist.html" title="Chapter&#160;5.&#160;Statistical Distributions and Functions">
diff --git a/libs/math/doc/html/math_toolkit/constants_intro.html b/libs/math/doc/html/math_toolkit/constants_intro.html
index 743f333d9..1d5ae5381 100644
--- a/libs/math/doc/html/math_toolkit/constants_intro.html
+++ b/libs/math/doc/html/math_toolkit/constants_intro.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Introduction</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../constants.html" title="Chapter&#160;4.&#160;Mathematical Constants">
<link rel="prev" href="../constants.html" title="Chapter&#160;4.&#160;Mathematical Constants">
<link rel="next" href="tutorial.html" title="Tutorial">
diff --git a/libs/math/doc/html/math_toolkit/contact.html b/libs/math/doc/html/math_toolkit/contact.html
index e9f553aa8..0b372096c 100644
--- a/libs/math/doc/html/math_toolkit/contact.html
+++ b/libs/math/doc/html/math_toolkit/contact.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Contact Info and Support</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="main_faq.html" title="Frequently Asked Questions FAQ">
<link rel="next" href="../utils.html" title="Chapter&#160;2.&#160;Floating Point Utilities">
diff --git a/libs/math/doc/html/math_toolkit/conventions.html b/libs/math/doc/html/math_toolkit/conventions.html
index e6a10ae56..2266ebc22 100644
--- a/libs/math/doc/html/math_toolkit/conventions.html
+++ b/libs/math/doc/html/math_toolkit/conventions.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Document Conventions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="navigation.html" title="Navigation">
<link rel="next" href="hints.html" title="Other Hints and tips">
@@ -27,7 +27,7 @@
<a name="math_toolkit.conventions"></a><a class="link" href="conventions.html" title="Document Conventions">Document Conventions</a>
</h2></div></div></div>
<p>
- <a class="indexterm" name="idm1567449536"></a>
+ <a class="indexterm" name="id845521"></a>
</p>
<p>
This documentation aims to use of the following naming and formatting conventions.
diff --git a/libs/math/doc/html/math_toolkit/create.html b/libs/math/doc/html/math_toolkit/create.html
index 2e081e715..03baf28fd 100644
--- a/libs/math/doc/html/math_toolkit/create.html
+++ b/libs/math/doc/html/math_toolkit/create.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Quaternion Creation Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="value_op.html" title="Quaternion Value Operations">
<link rel="next" href="trans.html" title="Quaternion Transcendentals">
diff --git a/libs/math/doc/html/math_toolkit/credits.html b/libs/math/doc/html/math_toolkit/credits.html
index 8ced0a110..98881705f 100644
--- a/libs/math/doc/html/math_toolkit/credits.html
+++ b/libs/math/doc/html/math_toolkit/credits.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Credits and Acknowledgements</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../status.html" title="Chapter&#160;17.&#160;Library Status">
<link rel="prev" href="issues.html" title="Known Issues, and TODO List">
<link rel="next" href="../indexes.html" title="Chapter&#160;18.&#160;Indexes">
@@ -143,6 +143,13 @@
Christopher Kormanyos wrote some examples for using <a href="http://www.boost.org/doc/libs/1_53_0_beta1/libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>,
and added methods for finding zeros of Bessel Functions.
</p>
+<p>
+ Marco Guazzone provided the hyper-geometric distribution.
+ </p>
+<p>
+ Rocco Romeo has found numerous small bugs and generally stress tested the special
+ functions code to near destruction!
+ </p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
diff --git a/libs/math/doc/html/math_toolkit/demo.html b/libs/math/doc/html/math_toolkit/demo.html
index 7f0e456a9..acf831de2 100644
--- a/libs/math/doc/html/math_toolkit/demo.html
+++ b/libs/math/doc/html/math_toolkit/demo.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Demonstration Program</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../gcd_lcm.html" title="Chapter&#160;11.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)">
<link rel="prev" href="gcd_header.html" title="Header &lt;boost/math/common_factor.hpp&gt;">
<link rel="next" href="rationale0.html" title="Rationale">
diff --git a/libs/math/doc/html/math_toolkit/directories.html b/libs/math/doc/html/math_toolkit/directories.html
index a3ef4dcdc..4a0b79809 100644
--- a/libs/math/doc/html/math_toolkit/directories.html
+++ b/libs/math/doc/html/math_toolkit/directories.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Directory and File Structure</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="hints.html" title="Other Hints and tips">
<link rel="next" href="namespaces.html" title="Namespaces">
diff --git a/libs/math/doc/html/math_toolkit/dist_concept.html b/libs/math/doc/html/math_toolkit/dist_concept.html
index c7db5c7ee..4604aa563 100644
--- a/libs/math/doc/html/math_toolkit/dist_concept.html
+++ b/libs/math/doc/html/math_toolkit/dist_concept.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Conceptual Requirements for Distribution Types</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../using_udt.html" title="Chapter&#160;13.&#160;Use with User-Defined Floating-Point Types - Boost.Multiprecision and others">
<link rel="prev" href="concepts.html" title="Conceptual Requirements for Real Number Types">
<link rel="next" href="archetypes.html" title="Conceptual Archetypes for Reals and Distributions">
diff --git a/libs/math/doc/html/math_toolkit/dist_ref.html b/libs/math/doc/html/math_toolkit/dist_ref.html
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--- a/libs/math/doc/html/math_toolkit/dist_ref.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Statistical Distributions Reference</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dist.html" title="Chapter&#160;5.&#160;Statistical Distributions and Functions">
<link rel="prev" href="stat_tut/dist_params.html" title="Discrete Probability Distributions">
<link rel="next" href="dist_ref/nmp.html" title="Non-Member Properties">
@@ -26,10 +26,11 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.dist_ref"></a><a class="link" href="dist_ref.html" title="Statistical Distributions Reference">Statistical Distributions Reference</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="dist_ref/nmp.html">Non-Member Properties</a></span></dt>
<dt><span class="section"><a href="dist_ref/dists.html">Distributions</a></span></dt>
<dd><dl>
+<dt><span class="section"><a href="dist_ref/dists/arcine_dist.html">Arcsine Distribution</a></span></dt>
<dt><span class="section"><a href="dist_ref/dists/bernoulli_dist.html">Bernoulli
Distribution</a></span></dt>
<dt><span class="section"><a href="dist_ref/dists/beta_dist.html">Beta Distribution</a></span></dt>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dist_algorithms.html b/libs/math/doc/html/math_toolkit/dist_ref/dist_algorithms.html
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--- a/libs/math/doc/html/math_toolkit/dist_ref/dist_algorithms.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dist_algorithms.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Distribution Algorithms</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dist_ref.html" title="Statistical Distributions Reference">
<link rel="prev" href="dists/weibull_dist.html" title="Weibull Distribution">
<link rel="next" href="../future.html" title="Extras/Future Directions">
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists.html b/libs/math/doc/html/math_toolkit/dist_ref/dists.html
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--- a/libs/math/doc/html/math_toolkit/dist_ref/dists.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists.html
@@ -3,11 +3,11 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Distributions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dist_ref.html" title="Statistical Distributions Reference">
<link rel="prev" href="nmp.html" title="Non-Member Properties">
-<link rel="next" href="dists/bernoulli_dist.html" title="Bernoulli Distribution">
+<link rel="next" href="dists/arcine_dist.html" title="Arcsine Distribution">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
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</tr></table>
<hr>
<div class="spirit-nav">
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+<a accesskey="p" href="nmp.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="dists/arcine_dist.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.dist_ref.dists"></a><a class="link" href="dists.html" title="Distributions">Distributions</a>
</h3></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
+<dt><span class="section"><a href="dists/arcine_dist.html">Arcsine Distribution</a></span></dt>
<dt><span class="section"><a href="dists/bernoulli_dist.html">Bernoulli
Distribution</a></span></dt>
<dt><span class="section"><a href="dists/beta_dist.html">Beta Distribution</a></span></dt>
@@ -97,7 +98,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="nmp.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="dists/bernoulli_dist.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+<a accesskey="p" href="nmp.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="dists/arcine_dist.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/arcine_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/arcine_dist.html
new file mode 100644
index 000000000..21f27354d
--- /dev/null
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/arcine_dist.html
@@ -0,0 +1,642 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Arcsine Distribution</title>
+<link rel="stylesheet" href="../../../math.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="../dists.html" title="Distributions">
+<link rel="prev" href="../dists.html" title="Distributions">
+<link rel="next" href="bernoulli_dist.html" title="Bernoulli Distribution">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
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+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.dist_ref.dists.arcine_dist"></a><a class="link" href="arcine_dist.html" title="Arcsine Distribution">Arcsine Distribution</a>
+</h4></div></div></div>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">arcsine</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+ <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+ <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> <span class="special">=</span> <a class="link" href="../../pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">arcsine_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">arcsine_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">arcsine</span><span class="special">;</span> <span class="comment">// double precision standard arcsine distribution [0,1].</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">arcsine_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+ <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+ <span class="keyword">typedef</span> <span class="identifier">Policy</span> <span class="identifier">policy_type</span><span class="special">;</span>
+
+ <span class="comment">// Constructor from two range parameters, x_min and x_max:</span>
+ <span class="identifier">arcsine_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">x_min</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">x_max</span><span class="special">);</span>
+
+ <span class="comment">// Range Parameter accessors:</span>
+ <span class="identifier">RealType</span> <span class="identifier">x_min</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
+ <span class="identifier">RealType</span> <span class="identifier">x_max</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+<span class="special">}}</span> <span class="comment">// namespaces</span>
+</pre>
+<p>
+ The class type <code class="computeroutput"><span class="identifier">arcsine_distribution</span></code>
+ represents an <a href="http://en.wikipedia.org/wiki/arcsine_distribution" target="_top">arcsine</a>
+ <a href="http://en.wikipedia.org/wiki/Probability_distribution" target="_top">probability
+ distribution function</a>. The arcsine distribution is named because
+ its CDF uses the inverse sin<sup>-1</sup> or arcsine.
+ </p>
+<p>
+ This is implemented as a generalized version with support from <span class="emphasis"><em>x_min</em></span>
+ to <span class="emphasis"><em>x_max</em></span> providing the 'standard arcsine distribution'
+ as default with <span class="emphasis"><em>x_min = 0</em></span> and <span class="emphasis"><em>x_max = 1</em></span>.
+ (A few make other choices for 'standard').
+ </p>
+<p>
+ The arcsine distribution is generalized to include any bounded support
+ <span class="emphasis"><em>a &lt;= x &lt;= b</em></span> by <a href="http://reference.wolfram.com/language/ref/ArcSinDistribution.html" target="_top">Wolfram</a>
+ and <a href="http://en.wikipedia.org/wiki/arcsine_distribution" target="_top">Wikipedia</a>,
+ but also using <span class="emphasis"><em>location</em></span> and <span class="emphasis"><em>scale</em></span>
+ parameters by <a href="http://www.math.uah.edu/stat/index.html" target="_top">Virtual
+ Laboratories in Probability and Statistics</a> <a href="http://www.math.uah.edu/stat/special/Arcsine.html" target="_top">Arcsine
+ distribution</a>. The end-point version is simpler and more obvious,
+ so we implement that. If desired, <a href="http://en.wikipedia.org/wiki/arcsine_distribution" target="_top">this</a>
+ outlines how the <a class="link" href="beta_dist.html" title="Beta Distribution">Beta
+ Distribution</a> can be used to add a shape factor.
+ </p>
+<p>
+ The <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">probability
+ density function PDF</a> for the <a href="http://en.wikipedia.org/wiki/arcsine_distribution" target="_top">arcsine
+ distribution</a> defined on the interval [<span class="emphasis"><em>x_min, x_max</em></span>]
+ is given by:
+ </p>
+<p>
+ &#8199; &#8199; f(x; x_min, x_max) = 1 /(&#960;&#8901;&#8730;((x - x_min)&#8901;(x_max - x))
+ </p>
+<p>
+ For example, <a href="http://www.wolframalpha.com/" target="_top">Wolfram Alpha</a>
+ arcsine distribution, from input of
+ </p>
+<pre class="programlisting"><span class="identifier">N</span><span class="special">[</span><span class="identifier">PDF</span><span class="special">[</span><span class="identifier">arcsinedistribution</span><span class="special">[</span><span class="number">0</span><span class="special">,</span> <span class="number">1</span><span class="special">],</span> <span class="number">0.5</span><span class="special">],</span> <span class="number">50</span><span class="special">]</span>
+</pre>
+<p>
+ computes the PDF value
+ </p>
+<pre class="programlisting"><span class="number">0.63661977236758134307553505349005744813783858296183</span>
+</pre>
+<p>
+ The Probability Density Functions (PDF) of generalized arcsine distributions
+ are symmetric U-shaped curves, centered on <span class="emphasis"><em>(x_max - x_min)/2</em></span>,
+ highest (infinite) near the two extrema, and quite flat over the central
+ region.
+ </p>
+<p>
+ If random variate <span class="emphasis"><em>x</em></span> is <span class="emphasis"><em>x_min</em></span>
+ or <span class="emphasis"><em>x_max</em></span>, then the PDF is infinity. If random variate
+ <span class="emphasis"><em>x</em></span> is <span class="emphasis"><em>x_min</em></span> then the CDF is zero.
+ If random variate <span class="emphasis"><em>x</em></span> is <span class="emphasis"><em>x_max</em></span>
+ then the CDF is unity.
+ </p>
+<p>
+ The 'Standard' (0, 1) arcsine distribution is shown in blue and some generalized
+ examples with other <span class="emphasis"><em>x</em></span> ranges.
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/arcsine_pdf.svg" align="middle"></span>
+ </p>
+<p>
+ The Cumulative Distribution Function CDF is defined as
+ </p>
+<p>
+ &#8199; &#8199; F(x) = 2&#8901;arcsin(&#8730;((x-x_min)/(x_max - x))) / &#960;
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/arcsine_cdf.svg" align="middle"></span>
+ </p>
+<h6>
+<a name="math_toolkit.dist_ref.dists.arcine_dist.h0"></a>
+ <span class="phrase"><a name="math_toolkit.dist_ref.dists.arcine_dist.constructor"></a></span><a class="link" href="arcine_dist.html#math_toolkit.dist_ref.dists.arcine_dist.constructor">Constructor</a>
+ </h6>
+<pre class="programlisting"><span class="identifier">arcsine_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">x_min</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">x_max</span><span class="special">);</span>
+</pre>
+<p>
+ constructs an arcsine distribution with range parameters <span class="emphasis"><em>x_min</em></span>
+ and <span class="emphasis"><em>x_max</em></span>.
+ </p>
+<p>
+ Requires <span class="emphasis"><em>x_min &lt; x_max</em></span>, otherwise <a class="link" href="../../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
+ is called.
+ </p>
+<p>
+ For example:
+ </p>
+<pre class="programlisting"><span class="identifier">arcsine_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">myarcsine</span><span class="special">(-</span><span class="number">2</span><span class="special">,</span> <span class="number">4</span><span class="special">);</span>
+</pre>
+<p>
+ constructs an arcsine distribution with <span class="emphasis"><em>x_min = -2</em></span>
+ and <span class="emphasis"><em>x_max = 4</em></span>.
+ </p>
+<p>
+ Default values of <span class="emphasis"><em>x_min = 0</em></span> and <span class="emphasis"><em>x_max =
+ 1</em></span> and a <code class="computeroutput"> <span class="keyword">typedef</span> <span class="identifier">arcsine_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">arcsine</span><span class="special">;</span></code>
+ mean that
+ </p>
+<pre class="programlisting"><span class="identifier">arcsine</span> <span class="identifier">as</span><span class="special">;</span>
+</pre>
+<p>
+ constructs a 'Standard 01' arcsine distribution.
+ </p>
+<h6>
+<a name="math_toolkit.dist_ref.dists.arcine_dist.h1"></a>
+ <span class="phrase"><a name="math_toolkit.dist_ref.dists.arcine_dist.parameter_accessors"></a></span><a class="link" href="arcine_dist.html#math_toolkit.dist_ref.dists.arcine_dist.parameter_accessors">Parameter
+ Accessors</a>
+ </h6>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">x_min</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
+<span class="identifier">RealType</span> <span class="identifier">x_max</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+ Return the parameter <span class="emphasis"><em>x_min</em></span> or <span class="emphasis"><em>x_max</em></span>
+ from which this distribution was constructed.
+ </p>
+<p>
+ So, for example:
+ </p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">arcsine_distribution</span><span class="special">;</span>
+
+<span class="identifier">arcsine_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">as</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">5</span><span class="special">);</span> <span class="comment">// Cconstructs a double arcsine distribution.</span>
+<span class="identifier">assert</span><span class="special">(</span><span class="identifier">as</span><span class="special">.</span><span class="identifier">x_min</span><span class="special">()</span> <span class="special">==</span> <span class="number">2.</span><span class="special">);</span> <span class="comment">// as.x_min() returns 2.</span>
+<span class="identifier">assert</span><span class="special">(</span><span class="identifier">as</span><span class="special">.</span><span class="identifier">x_max</span><span class="special">()</span> <span class="special">==</span> <span class="number">5.</span><span class="special">);</span> <span class="comment">// as.x_max() returns 5.</span>
+</pre>
+<h5>
+<a name="math_toolkit.dist_ref.dists.arcine_dist.h2"></a>
+ <span class="phrase"><a name="math_toolkit.dist_ref.dists.arcine_dist.non_member_accessor_functions"></a></span><a class="link" href="arcine_dist.html#math_toolkit.dist_ref.dists.arcine_dist.non_member_accessor_functions">Non-member
+ Accessor Functions</a>
+ </h5>
+<p>
+ All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member accessor
+ functions</a> that are generic to all distributions are supported:
+ <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.cdf">Cumulative Distribution Function</a>,
+ <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.pdf">Probability Density Function</a>,
+ <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.quantile">Quantile</a>, <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.hazard">Hazard Function</a>, <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.chf">Cumulative Hazard Function</a>,
+ <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.mean">mean</a>, <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.median">median</a>,
+ <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.mode">mode</a>, <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.variance">variance</a>,
+ <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.sd">standard deviation</a>,
+ <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.skewness">skewness</a>, <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.kurtosis_excess">kurtosis_excess</a>,
+ <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.range">range</a> and <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.support">support</a>.
+ </p>
+<p>
+ The formulae for calculating these are shown in the table below, and at
+ <a href="http://mathworld.wolfram.com/arcsineDistribution.html" target="_top">Wolfram
+ Mathworld</a>.
+ </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+ There are always <span class="bold"><strong>two</strong></span> values for the
+ <span class="bold"><strong>mode</strong></span>, at <span class="emphasis"><em>x_min</em></span>
+ and at <span class="emphasis"><em>x_max</em></span>, default 0 and 1, so instead we raise
+ the exception <a class="link" href="../../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
+ At these extrema, the PDFs are infinite, and the CDFs zero or unity.
+ </p></td></tr>
+</table></div>
+<h5>
+<a name="math_toolkit.dist_ref.dists.arcine_dist.h3"></a>
+ <span class="phrase"><a name="math_toolkit.dist_ref.dists.arcine_dist.applications"></a></span><a class="link" href="arcine_dist.html#math_toolkit.dist_ref.dists.arcine_dist.applications">Applications</a>
+ </h5>
+<p>
+ The arcsine distribution is useful to describe <a href="http://en.wikipedia.org/wiki/Random_walk" target="_top">Random
+ walks</a>, (including drunken walks) <a href="http://en.wikipedia.org/wiki/Brownian_motion" target="_top">Brownian
+ motion</a>, <a href="http://en.wikipedia.org/wiki/Wiener_process" target="_top">Weiner
+ processes</a>, <a href="http://en.wikipedia.org/wiki/Bernoulli_trial" target="_top">Bernoulli
+ trials</a>, and their appplication to solve stock market and other
+ <a href="http://en.wikipedia.org/wiki/Gambler%27s_ruin" target="_top">ruinous gambling
+ games</a>.
+ </p>
+<p>
+ The random variate <span class="emphasis"><em>x</em></span> is constrained to <span class="emphasis"><em>x_min</em></span>
+ and <span class="emphasis"><em>x_max</em></span>, (for our 'standard' distribution, 0 and
+ 1), and is usually some fraction. For any other <span class="emphasis"><em>x_min</em></span>
+ and <span class="emphasis"><em>x_max</em></span> a fraction can be obtained from <span class="emphasis"><em>x</em></span>
+ using
+ </p>
+<p>
+ &#8198; fraction = (x - x_min) / (x_max - x_min)
+ </p>
+<p>
+ The simplest example is tossing heads and tails with a fair coin and modelling
+ the risk of losing, or winning. Walkers (molecules, drunks...) moving left
+ or right of a centre line are another common example.
+ </p>
+<p>
+ The random variate <span class="emphasis"><em>x</em></span> is the fraction of time spent
+ on the 'winning' side. If half the time is spent on the 'winning' side
+ (and so the other half on the 'losing' side) then <span class="emphasis"><em>x = 1/2</em></span>.
+ </p>
+<p>
+ For large numbers of tosses, this is modelled by the (standard [0,1]) arcsine
+ distribution, and the PDF can be calculated thus:
+ </p>
+<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">as</span><span class="special">,</span> <span class="number">1.</span> <span class="special">/</span> <span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.637</span>
+<span class="comment">// pdf has a minimum at x = 0.5</span>
+</pre>
+<p>
+ From the plot of PDF, it is clear that <span class="emphasis"><em>x</em></span> = &#189; is the
+ <span class="bold"><strong>minimum</strong></span> of the curve, so this is the
+ <span class="bold"><strong>least likely</strong></span> scenario. (This is highly
+ counter-intuitive, considering that fair tosses must <span class="bold"><strong>eventually</strong></span>
+ become equal. It turns out that <span class="emphasis"><em>eventually</em></span> is not
+ just very long, but <span class="bold"><strong>infinite</strong></span>!).
+ </p>
+<p>
+ The <span class="bold"><strong>most likely</strong></span> scenarios are towards
+ the extrema where <span class="emphasis"><em>x</em></span> = 0 or <span class="emphasis"><em>x</em></span>
+ = 1.
+ </p>
+<p>
+ If fraction of time on the left is a &#188;, it is only slightly more likely
+ because the curve is quite flat bottomed.
+ </p>
+<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">as</span><span class="special">,</span> <span class="number">1.</span> <span class="special">/</span> <span class="number">4</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.735</span>
+</pre>
+<p>
+ If we consider fair coin-tossing games being played for 100 days (hypothetically
+ continuously to be 'at-limit') the person winning after day 5 will not
+ change in fraction 0.144 of the cases.
+ </p>
+<p>
+ We can easily compute this setting <span class="emphasis"><em>x</em></span> = 5./100 = 0.05
+ </p>
+<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">as</span><span class="special">,</span> <span class="number">0.05</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.144</span>
+</pre>
+<p>
+ Similarly, we can compute from a fraction of 0.05 /2 = 0.025 (halved because
+ we are considering both winners and losers) corresponding to 1 - 0.025
+ or 97.5% of the gamblers, (walkers, particles...) on the <span class="bold"><strong>same
+ side</strong></span> of the origin
+ </p>
+<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="number">2</span> <span class="special">*</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">as</span><span class="special">,</span> <span class="number">1</span> <span class="special">-</span> <span class="number">0.975</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.202</span>
+</pre>
+<p>
+ (use of the complement gives a bit more clarity, and avoids potential loss
+ of accuracy when <span class="emphasis"><em>x</em></span> is close to unity, see <a class="link" href="../../stat_tut/overview/complements.html#why_complements">why
+ complements?</a>).
+ </p>
+<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="number">2</span> <span class="special">*</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">as</span><span class="special">,</span> <span class="number">0.975</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.202</span>
+</pre>
+<p>
+ or we can reverse the calculation by assuming a fraction of time on one
+ side, say fraction 0.2,
+ </p>
+<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">as</span><span class="special">,</span> <span class="number">1</span> <span class="special">-</span> <span class="number">0.2</span> <span class="special">/</span> <span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.976</span>
+
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">as</span><span class="special">,</span> <span class="number">0.2</span> <span class="special">/</span> <span class="number">2</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.976</span>
+</pre>
+<p>
+ <span class="bold"><strong>Summary</strong></span>: Every time we toss, the odds
+ are equal, so on average we have the same change of winning and losing.
+ </p>
+<p>
+ But this is <span class="bold"><strong>not true</strong></span> for an an individual
+ game where one will be <span class="bold"><strong>mostly in a bad or good patch</strong></span>.
+ </p>
+<p>
+ This is quite counter-intuitive to most people, but the mathematics is
+ clear, and gamblers continue to provide proof.
+ </p>
+<p>
+ <span class="bold"><strong>Moral</strong></span>: if you in a losing patch, leave
+ the game. (Because the odds to recover to a good patch are poor).
+ </p>
+<p>
+ <span class="bold"><strong>Corollary</strong></span>: Quit while you are ahead?
+ </p>
+<p>
+ A working example is at <a href="../../../../../example/arcsine_example.cpp" target="_top">arcsine_example.cpp</a>
+ including sample output .
+ </p>
+<h5>
+<a name="math_toolkit.dist_ref.dists.arcine_dist.h4"></a>
+ <span class="phrase"><a name="math_toolkit.dist_ref.dists.arcine_dist.related_distributions"></a></span><a class="link" href="arcine_dist.html#math_toolkit.dist_ref.dists.arcine_dist.related_distributions">Related
+ distributions</a>
+ </h5>
+<p>
+ The arcsine distribution with <span class="emphasis"><em>x_min = 0</em></span> and <span class="emphasis"><em>x_max
+ = 1</em></span> is special case of the <a class="link" href="beta_dist.html" title="Beta Distribution">Beta
+ Distribution</a> with &#945; = 1/2 and &#946; = 1/2.
+ </p>
+<h5>
+<a name="math_toolkit.dist_ref.dists.arcine_dist.h5"></a>
+ <span class="phrase"><a name="math_toolkit.dist_ref.dists.arcine_dist.accuracy"></a></span><a class="link" href="arcine_dist.html#math_toolkit.dist_ref.dists.arcine_dist.accuracy">Accuracy</a>
+ </h5>
+<p>
+ This distribution is implemented using sqrt, sine, cos and arc sine and
+ cos trigonometric functions which are normally accurate to a few <a href="http://en.wikipedia.org/wiki/Machine_epsilon" target="_top">machine epsilon</a>.
+ But all values suffer from <a href="http://en.wikipedia.org/wiki/Loss_of_significance" target="_top">loss
+ of significance or cancellation error</a> for values of <span class="emphasis"><em>x</em></span>
+ close to <span class="emphasis"><em>x_max</em></span>. For example, for a standard [0, 1]
+ arcsine distribution <span class="emphasis"><em>as</em></span>, the pdf is symmetric about
+ random variate <span class="emphasis"><em>x = 0.5</em></span> so that one would expect <code class="computeroutput"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">as</span><span class="special">,</span> <span class="number">0.01</span><span class="special">)</span> <span class="special">==</span>
+ <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">as</span><span class="special">,</span> <span class="number">0.99</span><span class="special">)</span></code>. But
+ as <span class="emphasis"><em>x</em></span> nears unity, there is increasing <a href="http://en.wikipedia.org/wiki/Loss_of_significance" target="_top">loss
+ of significance</a>. To counteract this, the complement versions of
+ CDF and quantile are implemented with alternative expressions using <span class="emphasis"><em>cos<sup>-1</sup></em></span>
+ instead of <span class="emphasis"><em>sin<sup>-1</sup></em></span>. Users should see <a class="link" href="../../stat_tut/overview/complements.html#why_complements">why
+ complements?</a> for guidance on when to avoid loss of accuracy by using
+ complements.
+ </p>
+<h5>
+<a name="math_toolkit.dist_ref.dists.arcine_dist.h6"></a>
+ <span class="phrase"><a name="math_toolkit.dist_ref.dists.arcine_dist.testing"></a></span><a class="link" href="arcine_dist.html#math_toolkit.dist_ref.dists.arcine_dist.testing">Testing</a>
+ </h5>
+<p>
+ The results were tested against a few accurate spot values computed by
+ <a href="http://www.wolframalpha.com/" target="_top">Wolfram Alpha</a>, for example:
+ </p>
+<pre class="programlisting"><span class="identifier">N</span><span class="special">[</span><span class="identifier">PDF</span><span class="special">[</span><span class="identifier">arcsinedistribution</span><span class="special">[</span><span class="number">0</span><span class="special">,</span> <span class="number">1</span><span class="special">],</span> <span class="number">0.5</span><span class="special">],</span> <span class="number">50</span><span class="special">]</span>
+ <span class="number">0.63661977236758134307553505349005744813783858296183</span>
+</pre>
+<h5>
+<a name="math_toolkit.dist_ref.dists.arcine_dist.h7"></a>
+ <span class="phrase"><a name="math_toolkit.dist_ref.dists.arcine_dist.implementation"></a></span><a class="link" href="arcine_dist.html#math_toolkit.dist_ref.dists.arcine_dist.implementation">Implementation</a>
+ </h5>
+<p>
+ In the following table <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>
+ are the parameters <span class="emphasis"><em>x_min</em></span> &#160; and <span class="emphasis"><em>x_max</em></span>,
+ <span class="emphasis"><em>x</em></span> is the random variable, <span class="emphasis"><em>p</em></span> is
+ the probability and its complement <span class="emphasis"><em>q = 1-p</em></span>.
+ </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+ <p>
+ Function
+ </p>
+ </th>
+<th>
+ <p>
+ Implementation Notes
+ </p>
+ </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+ <p>
+ support
+ </p>
+ </td>
+<td>
+ <p>
+ x &#8712; [a, b], default x &#8712; [0, 1]
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ pdf
+ </p>
+ </td>
+<td>
+ <p>
+ f(x; a, b) = 1/(&#960;&#8901;&#8730;(x - a)&#8901;(b - x))
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ cdf
+ </p>
+ </td>
+<td>
+ <p>
+ F(x) = 2/&#960;&#8901;sin<sup>-1</sup>(&#8730;(x - a) / (b - a) )
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ cdf of complement
+ </p>
+ </td>
+<td>
+ <p>
+ 2/(&#960;&#8901;cos<sup>-1</sup>(&#8730;(x - a) / (b - a)))
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ quantile
+ </p>
+ </td>
+<td>
+ <p>
+ -a&#8901;sin<sup>2</sup>(&#189;&#960;&#8901;p) + a + b&#8901;sin<sup>2</sup>(&#189;&#960;&#8901;p)
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ quantile from the complement
+ </p>
+ </td>
+<td>
+ <p>
+ -a&#8901;cos<sup>2</sup>(&#189;&#960;&#8901;p) + a + b&#8901;cos<sup>2</sup>(&#189;&#960;&#8901;q)
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ mean
+ </p>
+ </td>
+<td>
+ <p>
+ &#189;(a+b)
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ median
+ </p>
+ </td>
+<td>
+ <p>
+ &#189;(a+b)
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ mode
+ </p>
+ </td>
+<td>
+ <p>
+ x &#8712; [a, b], so raises domain_error (returning NaN).
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ variance
+ </p>
+ </td>
+<td>
+ <p>
+ (b - a)<sup>2</sup> / 8
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ skewness
+ </p>
+ </td>
+<td>
+ <p>
+ 0
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ kurtosis excess
+ </p>
+ </td>
+<td>
+ <p>
+ -3/2
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ kurtosis
+ </p>
+ </td>
+<td>
+ <p>
+ kurtosis_excess + 3
+ </p>
+ </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+ The quantile was calculated using an expression obtained by using <a href="http://www.wolframalpha.com/" target="_top">Wolfram Alpha</a> to invert the
+ formula for the CDF thus
+ </p>
+<pre class="programlisting"><span class="identifier">solve</span> <span class="special">[</span><span class="identifier">p</span> <span class="special">-</span> <span class="number">2</span><span class="special">/</span><span class="identifier">pi</span> <span class="identifier">sin</span><span class="special">^-</span><span class="number">1</span><span class="special">(</span><span class="identifier">sqrt</span><span class="special">((</span><span class="identifier">x</span><span class="special">-</span><span class="identifier">a</span><span class="special">)/(</span><span class="identifier">b</span><span class="special">-</span><span class="identifier">a</span><span class="special">)))</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">x</span><span class="special">]</span>
+</pre>
+<p>
+ which was interpreted as
+ </p>
+<pre class="programlisting"><span class="identifier">Solve</span><span class="special">[</span><span class="identifier">p</span> <span class="special">-</span> <span class="special">(</span><span class="number">2</span> <span class="identifier">ArcSin</span><span class="special">[</span><span class="identifier">Sqrt</span><span class="special">[(-</span><span class="identifier">a</span> <span class="special">+</span> <span class="identifier">x</span><span class="special">)/(-</span><span class="identifier">a</span> <span class="special">+</span> <span class="identifier">b</span><span class="special">)]])/</span><span class="identifier">Pi</span> <span class="special">==</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">MaxExtraConditions</span> <span class="special">-&gt;</span> <span class="identifier">Automatic</span><span class="special">]</span>
+</pre>
+<p>
+ and produced the resulting expression
+ </p>
+<pre class="programlisting"><span class="identifier">x</span> <span class="special">=</span> <span class="special">-</span><span class="identifier">a</span> <span class="identifier">sin</span><span class="special">^</span><span class="number">2</span><span class="special">((</span><span class="identifier">pi</span> <span class="identifier">p</span><span class="special">)/</span><span class="number">2</span><span class="special">)+</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span> <span class="identifier">sin</span><span class="special">^</span><span class="number">2</span><span class="special">((</span><span class="identifier">pi</span> <span class="identifier">p</span><span class="special">)/</span><span class="number">2</span><span class="special">)</span>
+</pre>
+<p>
+ Thanks to Wolfram for providing this facility.
+ </p>
+<h5>
+<a name="math_toolkit.dist_ref.dists.arcine_dist.h8"></a>
+ <span class="phrase"><a name="math_toolkit.dist_ref.dists.arcine_dist.references"></a></span><a class="link" href="arcine_dist.html#math_toolkit.dist_ref.dists.arcine_dist.references">References</a>
+ </h5>
+<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
+<li class="listitem">
+ <a href="http://en.wikipedia.org/wiki/arcsine_distribution" target="_top">Wikipedia
+ arcsine distribution</a>
+ </li>
+<li class="listitem">
+ <a href="http://en.wikipedia.org/wiki/Beta_distribution" target="_top">Wikipedia
+ Beta distribution</a>
+ </li>
+<li class="listitem">
+ <a href="http://mathworld.wolfram.com/BetaDistribution.html" target="_top">Wolfram
+ MathWorld</a>
+ </li>
+<li class="listitem">
+ <a href="http://www.wolframalpha.com/" target="_top">Wolfram Alpha</a>
+ </li>
+</ul></div>
+<h5>
+<a name="math_toolkit.dist_ref.dists.arcine_dist.h9"></a>
+ <span class="phrase"><a name="math_toolkit.dist_ref.dists.arcine_dist.sources"></a></span><a class="link" href="arcine_dist.html#math_toolkit.dist_ref.dists.arcine_dist.sources">Sources</a>
+ </h5>
+<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
+<li class="listitem">
+ <a href="http://estebanmoro.org/2009/04/the-probability-of-going-through-a-bad-patch" target="_top">The
+ probability of going through a bad patch</a> Esteban Moro's Blog.
+ </li>
+<li class="listitem">
+ <a href="http://www.gotohaggstrom.com/What%20do%20schmucks%20and%20the%20arc%20sine%20law%20have%20in%20common.pdf" target="_top">What
+ soschumcks and the arc sine have in common</a> Peter Haggstrom.
+ </li>
+<li class="listitem">
+ <a href="http://www.math.uah.edu/stat/special/Arcsine.html" target="_top">arcsine
+ distribution</a>.
+ </li>
+<li class="listitem">
+ <a href="http://reference.wolfram.com/language/ref/ArcSinDistribution.html" target="_top">Wolfram
+ reference arcsine examples</a>.
+ </li>
+<li class="listitem">
+ <a href="http://www.math.harvard.edu/library/sternberg/slides/1180908.pdf" target="_top">Shlomo
+ Sternberg slides</a>.
+ </li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
+ Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
+ Holin, Bruno Lalande, John Maddock, Johan R&#229;de, Gautam Sewani, Benjamin Sobotta,
+ Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+ </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../dists.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="bernoulli_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/bernoulli_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/bernoulli_dist.html
index d8bc0819e..76cdafb06 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/bernoulli_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/bernoulli_dist.html
@@ -3,10 +3,10 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Bernoulli Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
-<link rel="prev" href="../dists.html" title="Distributions">
+<link rel="prev" href="arcine_dist.html" title="Arcsine Distribution">
<link rel="next" href="beta_dist.html" title="Beta Distribution">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@@ -20,7 +20,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="../dists.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="beta_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
+<a accesskey="p" href="arcine_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="beta_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
@@ -72,14 +72,14 @@
density function pdf</a> varies with the outcome of the single trial:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/bernoulli_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/bernoulli_pdf.svg" align="middle"></span>
</p>
<p>
and the <a href="http://en.wikipedia.org/wiki/Cumulative_Distribution_Function" target="_top">Cumulative
distribution function</a>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/bernoulli_cdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/bernoulli_cdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.bernoulli_dist.h0"></a>
@@ -350,7 +350,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="../dists.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="beta_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
+<a accesskey="p" href="arcine_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="beta_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/beta_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/beta_dist.html
index 7ca1ca0d5..3459c6265 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/beta_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/beta_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Beta Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="bernoulli_dist.html" title="Bernoulli Distribution">
<link rel="next" href="binomial_dist.html" title="Binomial Distribution">
@@ -116,7 +116,7 @@
might be approximated by a symmetrical triangular distribution.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/beta_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/beta_pdf.svg" align="middle"></span>
</p>
<p>
If &#945; = &#946; = 1, then it is a __space <a href="http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29" target="_top">uniform
@@ -466,7 +466,7 @@
</td>
<td>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/beta_dist_kurtosis.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/beta_dist_kurtosis.svg"></span>
</p>
</td>
</tr>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html
index f2e7020ea..57ac34667 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Binomial Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="beta_dist.html" title="Beta Distribution">
<link rel="next" href="cauchy_dist.html" title="Cauchy-Lorentz Distribution">
@@ -105,7 +105,7 @@
The PDF for the binomial distribution is given by:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/binomial_ref2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/binomial_ref2.svg"></span>
</p>
<p>
The following two graphs illustrate how the PDF changes depending upon
@@ -113,14 +113,14 @@
fixed at 0.5, and vary the sample size:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/binomial_pdf_1.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/binomial_pdf_1.svg" align="middle"></span>
</p>
<p>
Alternatively, we can keep the sample size fixed at N=20 and vary the success
fraction <span class="emphasis"><em>p</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/binomial_pdf_2.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/binomial_pdf_2.svg" align="middle"></span>
</p>
<div class="caution"><table border="0" summary="Caution">
<tr>
@@ -673,7 +673,7 @@
if <sub>n</sub>C<sub>k </sub> is the binomial coefficient of a and b, then we have:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/binomial_ref1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/binomial_ref1.svg"></span>
</p>
<p>
Which can be evaluated as <code class="computeroutput"><span class="identifier">ibeta_derivative</span><span class="special">(</span><span class="identifier">k</span><span class="special">+</span><span class="number">1</span><span class="special">,</span> <span class="identifier">n</span><span class="special">-</span><span class="identifier">k</span><span class="special">+</span><span class="number">1</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html
index f17f3bc43..3088e031a 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Cauchy-Lorentz Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="binomial_dist.html" title="Binomial Distribution">
<link rel="next" href="chi_squared_dist.html" title="Chi Squared Distribution">
@@ -55,7 +55,7 @@
distribution function PDF</a> given by:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/cauchy_ref1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/cauchy_ref1.svg"></span>
</p>
<p>
The location parameter x<sub>0</sub> &#160; is the location of the peak of the distribution
@@ -73,14 +73,14 @@
changes:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/cauchy_pdf1.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/cauchy_pdf1.svg" align="middle"></span>
</p>
<p>
While the following graph shows how the shape (scale) parameter alters
the distribution:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/cauchy_pdf2.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/cauchy_pdf2.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.cauchy_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/chi_squared_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/chi_squared_dist.html
index e5a22af4d..97dd33791 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/chi_squared_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/chi_squared_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chi Squared Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="cauchy_dist.html" title="Cauchy-Lorentz Distribution">
<link rel="next" href="exp_dist.html" title="Exponential Distribution">
@@ -67,7 +67,7 @@ independent, normally distributed random
variables with means &#956;<sub>i</sub> &#160; and variances &#963;<sub>i</sub><sup>2</sup>, then the random variable:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/chi_squ_ref1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/chi_squ_ref1.svg"></span>
</p>
<p>
is distributed according to the Chi-Squared distribution.
@@ -79,7 +79,7 @@ independent, normally distributed random
values of &#957;:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/chi_squared_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/chi_squared_pdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.chi_squared_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/exp_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/exp_dist.html
index 885c507a9..b1abb014d 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/exp_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/exp_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Exponential Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="chi_squared_dist.html" title="Chi Squared Distribution">
<link rel="next" href="extreme_dist.html" title="Extreme Value Distribution">
@@ -51,7 +51,7 @@
probability distribution</a> with PDF:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/exponential_dist_ref1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/exponential_dist_ref1.svg"></span>
</p>
<p>
It is often used to model the time between independent events that happen
@@ -62,7 +62,7 @@
of the rate parameter lambda:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/exponential_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/exponential_pdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.exp_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/extreme_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/extreme_dist.html
index 10d8d7754..199c75f15 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/extreme_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/extreme_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Extreme Value Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="exp_dist.html" title="Exponential Distribution">
<link rel="next" href="f_dist.html" title="F Distribution">
@@ -85,13 +85,13 @@
The following graph illustrates how the PDF varies with the location parameter:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/extreme_value_pdf1.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/extreme_value_pdf1.svg" align="middle"></span>
</p>
<p>
And this graph illustrates how the PDF varies with the shape parameter:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/extreme_value_pdf2.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/extreme_value_pdf2.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.extreme_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/f_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/f_dist.html
index b9f2a989a..7cfe73954 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/f_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/f_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>F Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="extreme_dist.html" title="Extreme Value Distribution">
<link rel="next" href="gamma_dist.html" title="Gamma (and Erlang) Distribution">
@@ -65,14 +65,14 @@
PDF:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/fisher_pdf.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/fisher_pdf.svg"></span>
</p>
<p>
The following graph illustrates how the PDF varies depending on the two
degrees of freedom parameters.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/fisher_f_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/fisher_f_pdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.f_dist.h0"></a>
@@ -175,7 +175,7 @@
The usual form of the PDF is given by:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/fisher_pdf.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/fisher_pdf.svg"></span>
</p>
<p>
However, that form is hard to evaluate directly without incurring
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/gamma_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/gamma_dist.html
index 4b5e90583..77d91b4e2 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/gamma_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/gamma_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Gamma (and Erlang) Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="f_dist.html" title="F Distribution">
<link rel="next" href="geometric_dist.html" title="Geometric Distribution">
@@ -79,14 +79,14 @@
by the probability density function:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/gamma_dist_ref1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/gamma_dist_ref1.svg"></span>
</p>
<p>
Sometimes an alternative formulation is used: given parameters &#945; &#160;= k and
&#946; &#160;= 1 / &#952;, then the distribution can be defined by the PDF:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/gamma_dist_ref2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/gamma_dist_ref2.svg"></span>
</p>
<p>
In this form the inverse scale parameter is called a <span class="emphasis"><em>rate parameter</em></span>.
@@ -102,10 +102,10 @@
varies as the parameters vary:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/gamma1_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/gamma1_pdf.svg" align="middle"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/gamma2_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/gamma2_pdf.svg" align="middle"></span>
</p>
<p>
The <span class="bold"><strong>Erlang Distribution</strong></span> is the same as
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/geometric_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/geometric_dist.html
index 25d49a877..f782bfe80 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/geometric_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/geometric_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Geometric Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="gamma_dist.html" title="Gamma (and Erlang) Distribution">
<link rel="next" href="hyperexponential_dist.html" title="Hyperexponential Distribution">
@@ -125,19 +125,19 @@
distribution as a continuous function),
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/geometric_pdf_2.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/geometric_pdf_2.svg" align="middle"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/geometric_cdf_2.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/geometric_cdf_2.svg" align="middle"></span>
</p>
<p>
and as discrete.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/geometric_pdf_discrete.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/geometric_pdf_discrete.svg" align="middle"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/geometric_cdf_discrete.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/geometric_cdf_discrete.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.geometric_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/hyperexponential_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/hyperexponential_dist.html
index b17a9ae46..86f53b8ad 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/hyperexponential_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/hyperexponential_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Hyperexponential Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="geometric_dist.html" title="Geometric Distribution">
<link rel="next" href="hypergeometric_dist.html" title="Hypergeometric Distribution">
@@ -111,7 +111,7 @@
hyperexponential distribution is given by:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_pdf.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_pdf.svg"></span>
</p>
<p>
The following graph illustrates the PDF of the hyperexponential distribution
@@ -140,7 +140,7 @@
</li>
</ol></div>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/hyperexponential_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/hyperexponential_pdf.svg" align="middle"></span>
</p>
<p>
Also, the following graph illustrates the PDF of the hyperexponential distribution
@@ -180,7 +180,7 @@
nears the exponential distribution with parameter <span class="emphasis"><em>&#955;=1.5</em></span>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/hyperexponential_pdf_samerate.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/hyperexponential_pdf_samerate.svg" align="middle"></span>
</p>
<p>
Finally, the following graph compares the PDF of the hyperexponential distribution
@@ -202,7 +202,7 @@
</li>
</ol></div>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/hyperexponential_pdf_samemean.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/hyperexponential_pdf_samemean.svg" align="middle"></span>
</p>
<p>
As can be noted, even if the three distributions have the same mean value,
@@ -232,7 +232,7 @@
often been observed to possess such a distribution (Rosin,1965). Also,
the arrival of different types of customer to a single queueing station
is often modeled as a hyperexponential distribution (Papadopolous et al.,1993).
- Similarly, if a product manufactured in several parallel assemply lines
+ Similarly, if a product manufactured in several parallel assembly lines
and the outputs are merged, the failure density of the overall product
is likely to be hyperexponential (Trivedi,2002).
</p>
@@ -866,7 +866,7 @@
</tr>
<tr><td align="left" valign="top"><p>
As an implementation detail, this constructor uses Boost's <a href="http://www.boost.org/doc/libs/release/libs/core/doc/html/core/enable_if.html" target="_top">enable_if/disable_if
- mechanism</a> to disambiguage between this and other 2-argument constructors.
+ mechanism</a> to disambiguate between this and other 2-argument constructors.
Refer to the source code for more details.
</p></td></tr>
</table></div>
@@ -914,7 +914,7 @@
<h5>
<a name="math_toolkit.dist_ref.dists.hyperexponential_dist.h15"></a>
<span class="phrase"><a name="math_toolkit.dist_ref.dists.hyperexponential_dist.construction_with_rates_iterator"></a></span><a class="link" href="hyperexponential_dist.html#math_toolkit.dist_ref.dists.hyperexponential_dist.construction_with_rates_iterator">Construction
- with rates-iterators (and all phase probablities equal)</a>
+ with rates-iterators (and all phase probabilities equal)</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">RateIterT</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">RateIterT2</span><span class="special">&gt;</span>
<span class="identifier">hyperexponential_distribution</span><span class="special">(</span><span class="identifier">RateIterT</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">rate_first</span><span class="special">,</span>
@@ -935,7 +935,7 @@
</tr>
<tr><td align="left" valign="top"><p>
As an implementation detail, this constructor uses Boost's <a href="http://www.boost.org/doc/libs/release/libs/core/doc/html/core/enable_if.html" target="_top">enable_if/disable_if
- mechanism</a> to disambiguage between this and other 2-argument constructors.
+ mechanism</a> to disambiguate between this and other 2-argument constructors.
Refer to the source code for more details.
</p></td></tr>
</table></div>
@@ -1264,7 +1264,7 @@
</td>
<td>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_pdf.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_pdf.svg"></span>
</p>
</td>
</tr>
@@ -1276,7 +1276,7 @@
</td>
<td>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_cdf.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_cdf.svg"></span>
</p>
</td>
</tr>
@@ -1288,7 +1288,7 @@
</td>
<td>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_ccdf.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_ccdf.svg"></span>
</p>
</td>
</tr>
@@ -1324,7 +1324,7 @@
</td>
<td>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_mean.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_mean.svg"></span>
</p>
</td>
</tr>
@@ -1336,7 +1336,7 @@
</td>
<td>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_variance.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_variance.svg"></span>
</p>
</td>
</tr>
@@ -1360,7 +1360,7 @@
</td>
<td>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_skewness.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_skewness.svg"></span>
</p>
</td>
</tr>
@@ -1372,7 +1372,7 @@
</td>
<td>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_kurtosis.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/hyperexponential_kurtosis.svg"></span>
</p>
</td>
</tr>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/hypergeometric_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/hypergeometric_dist.html
index 99c2470d1..9adfc46e5 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/hypergeometric_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/hypergeometric_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Hypergeometric Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="hyperexponential_dist.html" title="Hyperexponential Distribution">
<link rel="next" href="inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution">
@@ -86,7 +86,7 @@
sample sizes constant:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/hypergeometric_pdf_1.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/hypergeometric_pdf_1.svg" align="middle"></span>
</p>
<p>
Note that since the distribution is symmetrical in parameters <span class="emphasis"><em>n</em></span>
@@ -95,7 +95,7 @@
the same graphs:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/hypergeometric_pdf_2.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/hypergeometric_pdf_2.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.hypergeometric_dist.h0"></a>
@@ -105,7 +105,7 @@
<pre class="programlisting"><span class="identifier">hypergeometric_distribution</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">r</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">N</span><span class="special">);</span>
</pre>
<p>
- Constructs a hypergeometric distribution with with a population of <span class="emphasis"><em>N</em></span>
+ Constructs a hypergeometric distribution with a population of <span class="emphasis"><em>N</em></span>
objects, of which <span class="emphasis"><em>r</em></span> are defective, and from which
<span class="emphasis"><em>n</em></span> are sampled.
</p>
@@ -202,7 +202,7 @@
N = 110000.
</p>
<p>
- In general for very large N, the user should expect to loose log<sub>10</sub>N decimal
+ In general for very large N, the user should expect to lose log<sub>10</sub>N decimal
digits of precision during the calculation, with the results becoming meaningless
for N &gt;= 10<sup>15</sup>.
</p>
@@ -226,7 +226,7 @@
The PDF can be calculated directly using the formula:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/hypergeometric1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/hypergeometric1.svg"></span>
</p>
<p>
However, this can only be used directly when the largest of the factorials
@@ -244,21 +244,21 @@
method for factorising a factorial into the product of prime numbers:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/hypergeometric2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/hypergeometric2.svg"></span>
</p>
<p>
Where p<sub>i</sub> is the i'th prime number, and e<sub>i</sub> is a small positive integer or
zero, which can be calculated via:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/hypergeometric3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/hypergeometric3.svg"></span>
</p>
<p>
Further we can combine the factorials in the expression for the PDF to
yield the PDF directly as the product of prime numbers:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/hypergeometric4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/hypergeometric4.svg"></span>
</p>
<p>
With this time the exponents e<sub>i</sub> being either positive, negative or zero.
@@ -289,7 +289,7 @@
lgamma, or by directly combining lanczos approximations to avoid calculating
via logarithms. We use the latter method, as it is usually 1 or 2 decimal
digits more accurate than computing via logarithms with lgamma. However,
- in this area where N &gt; 104729, the user should expect to loose around
+ in this area where N &gt; 104729, the user should expect to lose around
log<sub>10</sub>N decimal digits during the calculation in the worst case.
</p>
<p>
@@ -300,7 +300,7 @@
successive PDF values via the recurrence relations:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/hypergeometric5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/hypergeometric5.svg"></span>
</p>
<p>
Until we either reach the end of the distributions domain, or the next
@@ -317,7 +317,7 @@
are calculated via:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/hypergeometric6.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/hypergeometric6.svg"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html
index 20a9a604e..c636e97c8 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Inverse Chi Squared Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="hypergeometric_dist.html" title="Hypergeometric Distribution">
<link rel="next" href="inverse_gamma_dist.html" title="Inverse Gamma Distribution">
@@ -177,10 +177,10 @@
distribution varies for a few values of parameters &#957; and &#958;:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/inverse_chi_squared_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/inverse_chi_squared_pdf.svg" align="middle"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/inverse_chi_squared_cdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/inverse_chi_squared_cdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.inverse_chi_squared_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/inverse_gamma_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/inverse_gamma_dist.html
index 8fd13512a..e28a3e7b8 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/inverse_gamma_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/inverse_gamma_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Inverse Gamma Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution">
<link rel="next" href="inverse_gaussian_dist.html" title="Inverse Gaussian (or Inverse Normal) Distribution">
@@ -108,10 +108,10 @@
distribution varies as the parameters vary:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/inverse_gamma_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/inverse_gamma_pdf.svg" align="middle"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/inverse_gamma_cdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/inverse_gamma_cdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.inverse_gamma_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/inverse_gaussian_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/inverse_gaussian_dist.html
index 2db348156..053911f0f 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/inverse_gaussian_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/inverse_gaussian_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Inverse Gaussian (or Inverse Normal) Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="inverse_gamma_dist.html" title="Inverse Gamma Distribution">
<link rel="next" href="laplace_dist.html" title="Laplace Distribution">
@@ -123,10 +123,10 @@
distribution varies for a few values of parameters &#956; and &#955;:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/inverse_gaussian_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/inverse_gaussian_pdf.svg" align="middle"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/inverse_gaussian_cdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/inverse_gaussian_cdf.svg" align="middle"></span>
</p>
<p>
Tweedie also provided 3 other parameterisations where (&#956; and &#955;) are replaced
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/laplace_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/laplace_dist.html
index e72302de0..571e61eaa 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/laplace_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/laplace_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Laplace Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="inverse_gaussian_dist.html" title="Inverse Gaussian (or Inverse Normal) Distribution">
<link rel="next" href="logistic_dist.html" title="Logistic Distribution">
@@ -60,7 +60,7 @@
density function:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/laplace_pdf.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/laplace_pdf.svg"></span>
</p>
<p>
The location and scale parameters are equivalent to the mean and standard
@@ -72,7 +72,7 @@
of the value of the location parameter:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/laplace_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/laplace_pdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.laplace_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/logistic_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/logistic_dist.html
index cecda20f7..d2a9242ac 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/logistic_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/logistic_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Logistic Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="laplace_dist.html" title="Laplace Distribution">
<link rel="next" href="lognormal_dist.html" title="Log Normal Distribution">
@@ -64,7 +64,7 @@
change:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/logistic_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/logistic_pdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.logistic_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/lognormal_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/lognormal_dist.html
index abb83592c..0e2be8ff6 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/lognormal_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/lognormal_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Log Normal Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="logistic_dist.html" title="Logistic Distribution">
<link rel="next" href="negative_binomial_dist.html" title="Negative Binomial Distribution">
@@ -62,7 +62,7 @@
it is defined by the probability density function:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/lognormal_ref.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/lognormal_ref.svg"></span>
</p>
<p>
The location and scale parameters are equivalent to the mean and standard
@@ -74,13 +74,13 @@
of the value of the location parameter:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/lognormal_pdf1.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/lognormal_pdf1.svg" align="middle"></span>
</p>
<p>
The next graph illustrates the effect of the scale parameter on the PDF:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/lognormal_pdf2.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/lognormal_pdf2.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.lognormal_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_beta_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_beta_dist.html
index 032d837f4..530942e9f 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_beta_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_beta_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Noncentral Beta Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="negative_binomial_dist.html" title="Negative Binomial Distribution">
<link rel="next" href="nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">
@@ -72,7 +72,7 @@ is
PDFs:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_beta_ref1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_beta_ref1.svg"></span>
</p>
<p>
where P(i;&#955;/2) is the discrete Poisson probablity at <span class="emphasis"><em>i</em></span>,
@@ -80,14 +80,14 @@ is
This leads to the usual form of the CDF as:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_beta_ref2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_beta_ref2.svg"></span>
</p>
<p>
The following graph illustrates how the distribution changes for different
values of &#955;:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/nc_beta_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/nc_beta_pdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.nc_beta_dist.h0"></a>
@@ -321,13 +321,13 @@ is
pp. 146-156.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_beta_ref3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_beta_ref3.svg"></span>
</p>
<p>
Then either the CDF or its complement is computed using the relations:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_beta_ref4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_beta_ref4.svg"></span>
</p>
<p>
The summation is performed by starting at i = &#955;/2, and then recursing in
@@ -384,7 +384,7 @@ is
and the relation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_beta_ref1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_beta_ref1.svg"></span>
</p>
<p>
Quantiles are computed using a specially modified version of <a class="link" href="../../internals1/roots2.html" title="Root Finding Without Derivatives: Bisection, Bracket and TOMS748">bracket_and_solve_root</a>,
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_chi_squared_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_chi_squared_dist.html
index c4d038859..3b727b392 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_chi_squared_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_chi_squared_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Noncentral Chi-Squared Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_beta_dist.html" title="Noncentral Beta Distribution">
<link rel="next" href="nc_f_dist.html" title="Noncentral F Distribution">
@@ -70,7 +70,7 @@
&#956;<sub>i</sub> and variances &#963;<sub>i</sub><sup>2</sup>, then the random variable
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref1.svg"></span>
</p>
<p>
is distributed according to the noncentral chi-squared distribution.
@@ -81,7 +81,7 @@
related to the mean of the random variables X<sub>i</sub> by:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref2.svg"></span>
</p>
<p>
(Note that some references define &#955; as one half of the above sum).
@@ -90,7 +90,7 @@
This leads to a PDF of:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref3.svg"></span>
</p>
<p>
where <span class="emphasis"><em>f(x;k)</em></span> is the central chi-squared distribution
@@ -102,7 +102,7 @@
values of &#955;:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/nccs_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/nccs_pdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.nc_chi_squared_dist.h0"></a>
@@ -390,7 +390,7 @@
41, No. 2. (1992), pp. 478-482). This uses the following series representation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref4.svg"></span>
</p>
<p>
which requires just one call to <a class="link" href="../../sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">gamma_p_derivative</a>
@@ -415,7 +415,7 @@
This method uses the well known sum:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref5.svg"></span>
</p>
<p>
Where P<sub>a</sub>(x) is the incomplete gamma function.
@@ -436,7 +436,7 @@
method, given that:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref6.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref6.svg"></span>
</p>
<p>
we can again start at the &#955;'th term and proceed in both directions from
@@ -449,7 +449,7 @@
The PDF is computed directly using the relation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref3.svg"></span>
</p>
<p>
Where <span class="emphasis"><em>f(x; v)</em></span> is the PDF of the central <a class="link" href="chi_squared_dist.html" title="Chi Squared Distribution">Chi
@@ -474,7 +474,7 @@
The remaining non-member functions use the following formulas:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref7.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_chi_squ_ref7.svg"></span>
</p>
<p>
Some analytic properties of noncentral distributions (particularly unimodality,
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_f_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_f_dist.html
index 08f5610bf..aec21e27c 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_f_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_f_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Noncentral F Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">
<link rel="next" href="nc_t_dist.html" title="Noncentral T Distribution">
@@ -72,20 +72,20 @@ random variable with <span class="emphasis"><em>v1</em></span> degrees
This gives the following PDF:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_f_ref1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_f_ref1.svg"></span>
</p>
<p>
where L<sub>a</sub><sup>b</sup>(c) is a generalised Laguerre polynomial and B(a,b) is the <a class="link" href="../../sf_beta/beta_function.html" title="Beta">beta</a> function, or
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_f_ref2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_f_ref2.svg"></span>
</p>
<p>
The following graph illustrates how the distribution changes for different
values of &#955;:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/nc_f_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/nc_f_pdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.nc_f_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_t_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_t_dist.html
index c6f521ba3..c9d9b43df 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_t_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_t_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Noncentral T Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_f_dist.html" title="Noncentral F Distribution">
<link rel="next" href="normal_dist.html" title="Normal (Gaussian) Distribution">
@@ -67,7 +67,7 @@
This gives the following PDF:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref1.svg"></span>
</p>
<p>
where <sub>1</sub>F<sub>1</sub>(a;b;x) is a confluent hypergeometric function.
@@ -77,8 +77,8 @@
values of &#957; and &#948;:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/nc_t_pdf.png" align="middle"></span>
- <span class="inlinemediaobject"><img src="../../../../graphs/nc_t_cdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/nc_t_pdf.svg" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/nc_t_cdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.nc_t_dist.h0"></a>
@@ -300,7 +300,7 @@ when the normal distribution
This uses the following formula for the CDF:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref2.svg"></span>
</p>
<p>
Where I<sub>x</sub>(a,b) is the incomplete beta function, and &#934;(x) is the normal CDF
@@ -316,13 +316,13 @@ when the normal distribution
therefore I<sub>x</sub>(a,b) = 1 and:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref3.svg"></span>
</p>
<p>
From this we can easily show that:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref4.svg"></span>
</p>
<p>
and therefore we have a means to compute either the probability or its
@@ -335,7 +335,7 @@ when the normal distribution
The PDF can be computed by a very similar method using:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/nc_t_ref5.svg"></span>
</p>
<p>
Where I<sub>x</sub><sup>'</sup>(a,b) is the derivative of the incomplete beta function.
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/negative_binomial_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/negative_binomial_dist.html
index 5a64924eb..3926a6cac 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/negative_binomial_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/negative_binomial_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Negative Binomial Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="lognormal_dist.html" title="Log Normal Distribution">
<link rel="next" href="nc_beta_dist.html" title="Noncentral Beta Distribution">
@@ -101,21 +101,21 @@
It has the PDF:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/neg_binomial_ref.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/neg_binomial_ref.svg"></span>
</p>
<p>
The following graph illustrate how the PDF varies as the success fraction
<span class="emphasis"><em>p</em></span> changes:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/negative_binomial_pdf_1.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/negative_binomial_pdf_1.svg" align="middle"></span>
</p>
<p>
Alternatively, this graph shows how the shape of the PDF varies as the
number of successes changes:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/negative_binomial_pdf_2.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/negative_binomial_pdf_2.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.negative_binomial_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/normal_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/normal_dist.html
index 877702c6a..38ee5a6d9 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/normal_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/normal_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Normal (Gaussian) Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_t_dist.html" title="Noncentral T Distribution">
<link rel="next" href="pareto.html" title="Pareto Distribution">
@@ -64,26 +64,26 @@
Given mean &#956; &#160;and standard deviation &#963; &#160;it has the PDF:
</p>
<p>
- &#160; <span class="inlinemediaobject"><img src="../../../../equations/normal_ref1.png"></span>
+ &#160; <span class="inlinemediaobject"><img src="../../../../equations/normal_ref1.svg"></span>
</p>
<p>
The variation the PDF with its parameters is illustrated in the following
graph:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/normal_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/normal_pdf.svg" align="middle"></span>
</p>
<p>
The cumulative distribution function is given by
</p>
<p>
- &#160; <span class="inlinemediaobject"><img src="../../../../equations/normal_cdf.png"></span>
+ &#160; <span class="inlinemediaobject"><img src="../../../../equations/normal_cdf.svg"></span>
</p>
<p>
and illustrated by this graph
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/normal_cdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/normal_cdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.normal_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/pareto.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/pareto.html
index 4b993f461..266599927 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/pareto.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/pareto.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Pareto Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="normal_dist.html" title="Normal (Gaussian) Distribution">
<link rel="next" href="poisson_dist.html" title="Poisson Distribution">
@@ -71,14 +71,14 @@
&#946;:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/pareto_pdf1.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/pareto_pdf1.svg" align="middle"></span>
</p>
<p>
And this graph illustrates how the PDF varies with the shape parameter
&#945;:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/pareto_pdf2.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/pareto_pdf2.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.pareto.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/poisson_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/poisson_dist.html
index f053b2d1b..0c82de5f7 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/poisson_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/poisson_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Poisson Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="pareto.html" title="Pareto Distribution">
<link rel="next" href="rayleigh.html" title="Rayleigh Distribution">
@@ -64,7 +64,7 @@
It has the Probability Mass Function:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/poisson_ref1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/poisson_ref1.svg"></span>
</p>
<p>
for k events, with an expected number of events &#955;.
@@ -73,7 +73,7 @@
The following graph illustrates how the PDF varies with the parameter &#955;:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/poisson_pdf_1.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/poisson_pdf_1.svg" align="middle"></span>
</p>
<div class="caution"><table border="0" summary="Caution">
<tr>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/rayleigh.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/rayleigh.html
index d891caa11..4f5b04fc6 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/rayleigh.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/rayleigh.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Rayleigh Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="poisson_dist.html" title="Poisson Distribution">
<link rel="next" href="skew_normal_dist.html" title="Skew Normal Distribution">
@@ -71,13 +71,13 @@
varies with the shape parameter &#963;:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/rayleigh_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/rayleigh_pdf.svg" align="middle"></span>
</p>
<p>
and the Cumulative Distribution Function (cdf)
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/rayleigh_cdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/rayleigh_cdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.rayleigh.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/skew_normal_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/skew_normal_dist.html
index f030c0572..eb4982442 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/skew_normal_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/skew_normal_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Skew Normal Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="rayleigh.html" title="Rayleigh Distribution">
<link rel="next" href="students_t_dist.html" title="Students t Distribution">
@@ -67,13 +67,13 @@
function is
</p>
<p>
- &#160; &#160; <span class="inlinemediaobject"><img src="../../../../equations/normal01_pdf.png"></span>
+ &#160; &#160; <span class="inlinemediaobject"><img src="../../../../equations/normal01_pdf.svg"></span>
</p>
<p>
and the cumulative distribution function
</p>
<p>
- &#160; &#160; <span class="inlinemediaobject"><img src="../../../../equations/normal01_cdf.png"></span>
+ &#160; &#160; <span class="inlinemediaobject"><img src="../../../../equations/normal01_cdf.svg"></span>
</p>
<p>
then the <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">PDF</a>
@@ -82,7 +82,7 @@
Leonhard (1976) is
</p>
<p>
- &#160; &#160; <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_pdf0.png"></span>
+ &#160; &#160; <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_pdf0.svg"></span>
</p>
<p>
Given <a href="http://en.wikipedia.org/wiki/Location_parameter" target="_top">location</a>
@@ -92,13 +92,13 @@
to the form:
</p>
<p>
- &#160; &#160; <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_pdf.png"></span>
+ &#160; &#160; <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_pdf.svg"></span>
</p>
<p>
and <a href="http://en.wikipedia.org/wiki/Cumulative_distribution_function" target="_top">CDF</a>:
</p>
<p>
- &#160; &#160; <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_cdf.png"></span>
+ &#160; &#160; <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_cdf.svg"></span>
</p>
<p>
where <span class="emphasis"><em>T(h,a)</em></span> is Owen's T function, and <span class="emphasis"><em>&#934;(x)</em></span>
@@ -109,8 +109,8 @@
following graphs:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/skew_normal_pdf.png" align="middle"></span>
- <span class="inlinemediaobject"><img src="../../../../graphs/skew_normal_cdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/skew_normal_pdf.svg" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/skew_normal_cdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.skew_normal_dist.h0"></a>
@@ -160,7 +160,7 @@
</p>
<p>
A parameter &#948; is related to the shape &#945; by &#948; = &#945; / (1 + &#945;&#178;), and used in the expression
- for skewness <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_skewness.png"></span>
+ for skewness <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_skewness.svg"></span>
</p>
</td></tr>
@@ -302,7 +302,7 @@
</td>
<td>
<p>
- Using: <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_pdf.png"></span>
+ Using: <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_pdf.svg"></span>
</p>
</td>
</tr>
@@ -314,7 +314,7 @@
</td>
<td>
<p>
- Using: <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_cdf.png"></span><br> where <span class="emphasis"><em>T(h,a)</em></span>
+ Using: <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_cdf.svg"></span><br> where <span class="emphasis"><em>T(h,a)</em></span>
is Owen's T function, and <span class="emphasis"><em>&#934;(x)</em></span> is the normal
distribution.
</p>
@@ -412,7 +412,7 @@
</td>
<td>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_mean.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_mean.svg"></span>
</p>
</td>
</tr>
@@ -436,7 +436,7 @@
</td>
<td>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_variance.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_variance.svg"></span>
</p>
</td>
</tr>
@@ -448,7 +448,7 @@
</td>
<td>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_skewness.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_skewness.svg"></span>
</p>
</td>
</tr>
@@ -472,7 +472,7 @@
</td>
<td>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_kurt_ex.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_kurt_ex.svg"></span>
</p>
</td>
</tr>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/students_t_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/students_t_dist.html
index 751b33b42..b0567f767 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/students_t_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/students_t_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Students t Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="skew_normal_dist.html" title="Skew Normal Distribution">
<link rel="next" href="triangular_dist.html" title="Triangular Distribution">
@@ -66,7 +66,7 @@
Given N independent measurements, let
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/students_t_dist.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/students_t_dist.svg"></span>
</p>
<p>
where <span class="emphasis"><em>M</em></span> is the population mean,<span class="emphasis"><em>&#956;</em></span>
@@ -78,7 +78,7 @@
the true standard deviation of the sample. It has the PDF:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../equations/students_t_ref1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../equations/students_t_ref1.svg"></span>
</p>
<p>
The Student's t-distribution takes a single parameter: the number of degrees
@@ -89,7 +89,7 @@
with the degrees of freedom &#957;:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/students_t_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/students_t_pdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.students_t_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/triangular_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/triangular_dist.html
index 01da61fdd..6b74caf06 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/triangular_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/triangular_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Triangular Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="students_t_dist.html" title="Students t Distribution">
<link rel="next" href="uniform_dist.html" title="Uniform Distribution">
@@ -113,13 +113,13 @@
density function PDF</a> varies with the various parameters:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/triangular_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/triangular_pdf.svg" align="middle"></span>
</p>
<p>
and cumulative distribution function
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/triangular_cdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/triangular_cdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.triangular_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/uniform_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/uniform_dist.html
index aac50b5c4..0b3a4a072 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/uniform_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/uniform_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Uniform Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="triangular_dist.html" title="Triangular Distribution">
<link rel="next" href="weibull_dist.html" title="Weibull Distribution">
@@ -102,13 +102,13 @@
density function PDF</a> varies with the shape parameter:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/uniform_pdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/uniform_pdf.svg" align="middle"></span>
</p>
<p>
Likewise for the CDF:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/uniform_cdf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/uniform_cdf.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.uniform_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/dists/weibull_dist.html b/libs/math/doc/html/math_toolkit/dist_ref/dists/weibull_dist.html
index a26907460..25cefdd39 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/dists/weibull_dist.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/dists/weibull_dist.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Weibull Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="uniform_dist.html" title="Uniform Distribution">
<link rel="next" href="../dist_algorithms.html" title="Distribution Algorithms">
@@ -84,14 +84,14 @@
&#945;:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/weibull_pdf1.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/weibull_pdf1.svg" align="middle"></span>
</p>
<p>
While this graph illustrates how the PDF varies with the scale parameter
&#946;:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/weibull_pdf2.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/weibull_pdf2.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.dist_ref.dists.weibull_dist.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/dist_ref/nmp.html b/libs/math/doc/html/math_toolkit/dist_ref/nmp.html
index 669bb8ad0..5ac329426 100644
--- a/libs/math/doc/html/math_toolkit/dist_ref/nmp.html
+++ b/libs/math/doc/html/math_toolkit/dist_ref/nmp.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Non-Member Properties</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../dist_ref.html" title="Statistical Distributions Reference">
<link rel="prev" href="../dist_ref.html" title="Statistical Distributions Reference">
<link rel="next" href="dists.html" title="Distributions">
@@ -273,7 +273,7 @@
if the random variable is outside the defined range for the distribution.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/hazard.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/hazard.svg"></span>
</p>
<div class="caution"><table border="0" summary="Caution">
<tr>
@@ -302,7 +302,7 @@
if the random variable is outside the defined range for the distribution.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/chf.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/chf.svg"></span>
</p>
<div class="caution"><table border="0" summary="Caution">
<tr>
diff --git a/libs/math/doc/html/math_toolkit/ellint.html b/libs/math/doc/html/math_toolkit/ellint.html
index 47677269c..637285948 100644
--- a/libs/math/doc/html/math_toolkit/ellint.html
+++ b/libs/math/doc/html/math_toolkit/ellint.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Elliptic Integrals</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
<link rel="prev" href="airy/bip.html" title="Airy Bi' Function">
<link rel="next" href="ellint/ellint_intro.html" title="Elliptic Integral Overview">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.ellint"></a><a class="link" href="ellint.html" title="Elliptic Integrals">Elliptic Integrals</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="ellint/ellint_intro.html">Elliptic Integral Overview</a></span></dt>
<dt><span class="section"><a href="ellint/ellint_carlson.html">Elliptic Integrals
- Carlson Form</a></span></dt>
@@ -36,6 +36,10 @@
Second Kind - Legendre Form</a></span></dt>
<dt><span class="section"><a href="ellint/ellint_3.html">Elliptic Integrals of the
Third Kind - Legendre Form</a></span></dt>
+<dt><span class="section"><a href="ellint/ellint_d.html">Elliptic Integral D - Legendre
+ Form</a></span></dt>
+<dt><span class="section"><a href="ellint/jacobi_zeta.html">Jacobi Zeta Function</a></span></dt>
+<dt><span class="section"><a href="ellint/heuman_lambda.html">Heuman Lambda Function</a></span></dt>
</dl></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/ellint/ellint_1.html b/libs/math/doc/html/math_toolkit/ellint/ellint_1.html
index aad7b996e..a741c516d 100644
--- a/libs/math/doc/html/math_toolkit/ellint/ellint_1.html
+++ b/libs/math/doc/html/math_toolkit/ellint/ellint_1.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Elliptic Integrals of the First Kind - Legendre Form</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../ellint.html" title="Elliptic Integrals">
<link rel="prev" href="ellint_carlson.html" title="Elliptic Integrals - Carlson Form">
<link rel="next" href="ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">
@@ -59,7 +59,7 @@
= F(&#960;/2, k)</em></span>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/ellint_1.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/ellint_1.svg" align="middle"></span>
</p>
<p>
The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
@@ -77,7 +77,7 @@
k)</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint2.svg"></span>
</p>
<p>
Requires -1 &lt;= k &lt;= 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
@@ -98,7 +98,7 @@
Returns the complete elliptic integral of the first kind <span class="emphasis"><em>K(k)</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint6.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint6.svg"></span>
</p>
<p>
Requires -1 &lt;= k &lt;= 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
@@ -240,13 +240,13 @@
relations:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint19.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint19.svg"></span>
</p>
<p>
and
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint20.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint20.svg"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/ellint/ellint_2.html b/libs/math/doc/html/math_toolkit/ellint/ellint_2.html
index 80a42e359..8d43bc71d 100644
--- a/libs/math/doc/html/math_toolkit/ellint/ellint_2.html
+++ b/libs/math/doc/html/math_toolkit/ellint/ellint_2.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Elliptic Integrals of the Second Kind - Legendre Form</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../ellint.html" title="Elliptic Integrals">
<link rel="prev" href="ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">
<link rel="next" href="ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">
@@ -59,7 +59,7 @@
= E(&#960;/2, k)</em></span>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/ellint_2.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/ellint_2.svg" align="middle"></span>
</p>
<p>
The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
@@ -77,7 +77,7 @@
k)</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint3.svg"></span>
</p>
<p>
Requires -1 &lt;= k &lt;= 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
@@ -98,7 +98,7 @@
Returns the complete elliptic integral of the second kind <span class="emphasis"><em>E(k)</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint7.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint7.svg"></span>
</p>
<p>
Requires -1 &lt;= k &lt;= 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
@@ -240,13 +240,13 @@
relations:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint21.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint21.svg"></span>
</p>
<p>
and
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint22.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint22.svg"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/ellint/ellint_3.html b/libs/math/doc/html/math_toolkit/ellint/ellint_3.html
index fc706d8c6..7ba079056 100644
--- a/libs/math/doc/html/math_toolkit/ellint/ellint_3.html
+++ b/libs/math/doc/html/math_toolkit/ellint/ellint_3.html
@@ -3,11 +3,11 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Elliptic Integrals of the Third Kind - Legendre Form</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../ellint.html" title="Elliptic Integrals">
<link rel="prev" href="ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">
-<link rel="next" href="../jacobi.html" title="Jacobi Elliptic Functions">
+<link rel="next" href="ellint_d.html" title="Elliptic Integral D - Legendre Form">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
@@ -20,7 +20,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="ellint_2.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../jacobi.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+<a accesskey="p" href="ellint_2.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="ellint_d.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
@@ -59,7 +59,7 @@
k) = E(n, &#960;/2, k)</em></span>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/ellint_3.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/ellint_3.svg" align="middle"></span>
</p>
<p>
The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
@@ -78,7 +78,7 @@
&#966;, k)</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint4.svg"></span>
</p>
<p>
Requires <span class="emphasis"><em>-1 &lt;= k &lt;= 1</em></span> and <span class="emphasis"><em>n &lt; 1/sin<sup>2</sup>(&#966;)</em></span>,
@@ -101,7 +101,7 @@
Returns the complete elliptic integral of the first kind <span class="emphasis"><em>&#928;(n, k)</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint8.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint8.svg"></span>
</p>
<p>
Requires <span class="emphasis"><em>-1 &lt;= k &lt;= 1</em></span> and <span class="emphasis"><em>n &lt; 1</em></span>,
@@ -253,13 +253,13 @@
and
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint23.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint23.svg"></span>
</p>
<p>
Then if n &lt; 0 the relations (A&amp;S 17.7.15/16):
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint24.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint24.svg"></span>
</p>
<p>
are used to shift <span class="emphasis"><em>n</em></span> to the range [0, 1].
@@ -274,7 +274,7 @@
<span class="emphasis"><em>&#928;(n, &#966;+m&#960;, k) = &#928;(n, &#966;, k) + 2m&#928;(n, k) ; n &lt;= 1</em></span>
</p>
<p>
- <span class="emphasis"><em>&#928;(n, &#966;+m&#960;, k) = &#928;(n, &#966;, k) ; n &gt; 1</em></span> <a href="#ftn.math_toolkit.ellint.ellint_3.f0" class="footnote" name="math_toolkit.ellint.ellint_3.f0"><sup class="footnote">[1]</sup></a>
+ <span class="emphasis"><em>&#928;(n, &#966;+m&#960;, k) = &#928;(n, &#966;, k) ; n &gt; 1</em></span> <a href="#ftn.math_toolkit.ellint.ellint_3.f0" class="footnote"><sup class="footnote"><a name="math_toolkit.ellint.ellint_3.f0"></a>[1]</sup></a>
</p>
<p>
are used to move &#966; &#160; to the range [0, &#960;/2].
@@ -284,16 +284,16 @@
the relations:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint25.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint25.svg"></span>
</p>
<p>
and
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint26.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint26.svg"></span>
</p>
<div class="footnotes">
-<br><hr style="width:100; text-align:left;margin-left: 0">
+<br><hr style="width:100; align:left;">
<div id="ftn.math_toolkit.ellint.ellint_3.f0" class="footnote"><p><a href="#math_toolkit.ellint.ellint_3.f0" class="para"><sup class="para">[1] </sup></a>
I haven't been able to find a literature reference for this relation, but
it appears to be the convention used by Mathematica. Intuitively the first
@@ -315,7 +315,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="ellint_2.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../jacobi.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+<a accesskey="p" href="ellint_2.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="ellint_d.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>
diff --git a/libs/math/doc/html/math_toolkit/ellint/ellint_carlson.html b/libs/math/doc/html/math_toolkit/ellint/ellint_carlson.html
index 8b5465148..429802b76 100644
--- a/libs/math/doc/html/math_toolkit/ellint/ellint_carlson.html
+++ b/libs/math/doc/html/math_toolkit/ellint/ellint_carlson.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Elliptic Integrals - Carlson Form</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../ellint.html" title="Elliptic Integrals">
<link rel="prev" href="ellint_intro.html" title="Elliptic Integral Overview">
<link rel="next" href="ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">
@@ -79,6 +79,18 @@
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">ellint_rg</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rg</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">)</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rg</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;)</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces</span>
+</pre>
<h5>
<a name="math_toolkit.ellint.ellint_carlson.h1"></a>
<span class="phrase"><a name="math_toolkit.ellint.ellint_carlson.description"></a></span><a class="link" href="ellint_carlson.html#math_toolkit.ellint.ellint_carlson.description">Description</a>
@@ -89,7 +101,7 @@
graph gives an idea of their behavior:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/ellint_carlson.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/ellint_carlson.svg" align="middle"></span>
</p>
<p>
The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
@@ -106,7 +118,7 @@
Returns Carlson's Elliptic Integral R<sub>F</sub>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint9.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint9.svg"></span>
</p>
<p>
Requires that all of the arguments are non-negative, and at most one may
@@ -128,7 +140,7 @@
Returns Carlson's elliptic integral R<sub>D</sub>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint10.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint10.svg"></span>
</p>
<p>
Requires that x and y are non-negative, with at most one of them zero, and
@@ -150,7 +162,7 @@
Returns Carlson's elliptic integral R<sub>J</sub>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint11.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint11.svg"></span>
</p>
<p>
Requires that x, y and z are non-negative, with at most one of them zero,
@@ -167,7 +179,7 @@
principal value</a> using the relation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint17.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint17.svg"></span>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rc</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">)</span>
@@ -179,7 +191,7 @@
Returns Carlson's elliptic integral R<sub>C</sub>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint12.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint12.svg"></span>
</p>
<p>
Requires that <span class="emphasis"><em>x &gt; 0</em></span> and that <span class="emphasis"><em>y != 0</em></span>.
@@ -196,7 +208,29 @@
principal value</a> using the relation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint18.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint18.svg"></span>
+ </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rg</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">)</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rg</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;)</span>
+</pre>
+<p>
+ Returns Carlson's elliptic integral R<sub>G</sub>:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint27.svg"></span>
+ </p>
+<p>
+ Requires that x and y are non-negative, otherwise returns the result of
+ <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
+ </p>
+<p>
+ The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
+ be used to control the behaviour of the function: how it handles errors,
+ what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">policy
+ documentation for more details</a>.
</p>
<h5>
<a name="math_toolkit.ellint.ellint_carlson.h2"></a>
@@ -384,7 +418,7 @@
is the duplication theorem:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint13.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint13.svg"></span>
</p>
<p>
By applying it repeatedly, <span class="emphasis"><em>x</em></span>, <span class="emphasis"><em>y</em></span>,
@@ -392,12 +426,13 @@
the special case equation
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint16.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint16.svg"></span>
</p>
<p>
is used. More specifically, <span class="emphasis"><em>[R F]</em></span> is evaluated from
a Taylor series expansion to the fifth order. The calculations of the other
- three integrals are analogous.
+ three integrals are analogous, except for R<sub>C</sub> which can be computed from elementary
+ functions.
</p>
<p>
For <span class="emphasis"><em>p &lt; 0</em></span> in <span class="emphasis"><em>R<sub>J</sub>(x, y, z, p)</em></span>
@@ -406,10 +441,10 @@
principal values</a> are returned via the relations:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint17.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint17.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint18.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint18.svg"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/ellint/ellint_d.html b/libs/math/doc/html/math_toolkit/ellint/ellint_d.html
new file mode 100644
index 000000000..5ded1ea3b
--- /dev/null
+++ b/libs/math/doc/html/math_toolkit/ellint/ellint_d.html
@@ -0,0 +1,175 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Elliptic Integral D - Legendre Form</title>
+<link rel="stylesheet" href="../../math.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="../ellint.html" title="Elliptic Integrals">
+<link rel="prev" href="ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">
+<link rel="next" href="jacobi_zeta.html" title="Jacobi Zeta Function">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center"><a href="../../../../../../index.html">Home</a></td>
+<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
+<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
+<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
+<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ellint_3.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="jacobi_zeta.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.ellint.ellint_d"></a><a class="link" href="ellint_d.html" title="Elliptic Integral D - Legendre Form">Elliptic Integral D - Legendre
+ Form</a>
+</h3></div></div></div>
+<h5>
+<a name="math_toolkit.ellint.ellint_d.h0"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.ellint_d.synopsis"></a></span><a class="link" href="ellint_d.html#math_toolkit.ellint.ellint_d.synopsis">Synopsis</a>
+ </h5>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">ellint_d</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces</span>
+</pre>
+<h5>
+<a name="math_toolkit.ellint.ellint_d.h1"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.ellint_d.description"></a></span><a class="link" href="ellint_d.html#math_toolkit.ellint.ellint_d.description">Description</a>
+ </h5>
+<p>
+ These two functions evaluate the incomplete elliptic integral <span class="emphasis"><em>D(&#966;,
+ k)</em></span> and its complete counterpart <span class="emphasis"><em>D(k) = D(&#960;/2, k)</em></span>.
+ </p>
+<p>
+ The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+ type calculation rules</em></span></a> when the arguments are of different
+ types: when they are the same type then the result is the same type as the
+ arguments.
+ </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_3</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+ Returns the incomplete elliptic integral:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint_d.svg"></span>
+ </p>
+<p>
+ Requires <span class="emphasis"><em>-1 &lt;= k &lt;= 1</em></span>, otherwise returns the result
+ of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
+ (outside this range the result would be complex).
+ </p>
+<p>
+ The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
+ be used to control the behaviour of the function: how it handles errors,
+ what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">policy
+ documentation for more details</a>.
+ </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_d</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+ Returns the complete elliptic integral <span class="emphasis"><em>D(k) = D(&#960;/2, k)</em></span>
+ </p>
+<p>
+ Requires <span class="emphasis"><em>-1 &lt;= k &lt;= 1</em></span> otherwise returns the result
+ of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
+ (outside this range the result would be complex).
+ </p>
+<p>
+ The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
+ be used to control the behaviour of the function: how it handles errors,
+ what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">policy
+ documentation for more details</a>.
+ </p>
+<h5>
+<a name="math_toolkit.ellint.ellint_d.h2"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.ellint_d.accuracy"></a></span><a class="link" href="ellint_d.html#math_toolkit.ellint.ellint_d.accuracy">Accuracy</a>
+ </h5>
+<p>
+ These functions are trivially computed in terms of other elliptic integrals
+ and generally have very low error rates (a few epsilon) unless parameter
+ &#966;
+is very large, in which case the usual trigonometric function argument-reduction
+ issues apply.
+ </p>
+<h5>
+<a name="math_toolkit.ellint.ellint_d.h3"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.ellint_d.testing"></a></span><a class="link" href="ellint_d.html#math_toolkit.ellint.ellint_d.testing">Testing</a>
+ </h5>
+<p>
+ The tests use a mixture of spot test values calculated using values calculated
+ at wolframalpha.com, and random test data generated using MPFR at 1000-bit
+ precision and a deliberately naive implementation in terms of the Legendre
+ integrals.
+ </p>
+<h5>
+<a name="math_toolkit.ellint.ellint_d.h4"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.ellint_d.implementation"></a></span><a class="link" href="ellint_d.html#math_toolkit.ellint.ellint_d.implementation">Implementation</a>
+ </h5>
+<p>
+ The implementation for D(&#966;, k) first performs argument reduction using the
+ relations:
+ </p>
+<p>
+ <span class="emphasis"><em>D(-&#966;, k) = -D(&#966;, k)</em></span>
+ </p>
+<p>
+ and
+ </p>
+<p>
+ <span class="emphasis"><em>D(n&#960;+&#966;, k) = 2nD(k) + D(&#966;, k)</em></span>
+ </p>
+<p>
+ to move &#966; &#160; to the range [0, &#960;/2].
+ </p>
+<p>
+ The functions are then implemented in terms of Carlson's integral R<sub>D</sub>
+using
+ the relation:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint_d.svg"></span>
+ </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
+ Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
+ Holin, Bruno Lalande, John Maddock, Johan R&#229;de, Gautam Sewani, Benjamin Sobotta,
+ Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+ </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ellint_3.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="jacobi_zeta.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>
diff --git a/libs/math/doc/html/math_toolkit/ellint/ellint_intro.html b/libs/math/doc/html/math_toolkit/ellint/ellint_intro.html
index 61ea6f381..839f1fc0e 100644
--- a/libs/math/doc/html/math_toolkit/ellint/ellint_intro.html
+++ b/libs/math/doc/html/math_toolkit/ellint/ellint_intro.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Elliptic Integral Overview</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../ellint.html" title="Elliptic Integrals">
<link rel="prev" href="../ellint.html" title="Elliptic Integrals">
<link rel="next" href="ellint_carlson.html" title="Elliptic Integrals - Carlson Form">
@@ -58,7 +58,7 @@
<span class="phrase"><a name="math_toolkit.ellint.ellint_intro.definition"></a></span><a class="link" href="ellint_intro.html#math_toolkit.ellint.ellint_intro.definition">Definition</a>
</h5>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint1.svg"></span>
</p>
<p>
is called elliptic integral if <span class="emphasis"><em>R(t, s)</em></span> is a rational
@@ -74,25 +74,25 @@
Elliptic Integral of the First Kind (Legendre form)
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint2.svg"></span>
</p>
<p>
Elliptic Integral of the Second Kind (Legendre form)
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint3.svg"></span>
</p>
<p>
Elliptic Integral of the Third Kind (Legendre form)
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint4.svg"></span>
</p>
<p>
where
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint5.svg"></span>
</p>
<div class="note"><table border="0" summary="Note">
<tr>
@@ -168,21 +168,37 @@
Complete Elliptic Integral of the First Kind (Legendre form)
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint6.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint6.svg"></span>
</p>
<p>
Complete Elliptic Integral of the Second Kind (Legendre form)
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint7.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint7.svg"></span>
</p>
<p>
Complete Elliptic Integral of the Third Kind (Legendre form)
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint8.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint8.svg"></span>
</p>
<p>
+ Legendre also defined a forth integral D(&#966;,k) which is a combination of the
+ other three:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint_d.svg"></span>
+ </p>
+<p>
+ Like the other Legendre integrals this comes in both complete and incomplete
+ forms.
+ </p>
+<h5>
+<a name="math_toolkit.ellint.ellint_intro.h2"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.ellint_intro.carlson_elliptic_integrals"></a></span><a class="link" href="ellint_intro.html#math_toolkit.ellint.ellint_intro.carlson_elliptic_integrals">Carlson
+ Elliptic Integrals</a>
+ </h5>
+<p>
Carlson [<a class="link" href="ellint_intro.html#ellint_ref_carlson77">Carlson77</a>] [<a class="link" href="ellint_intro.html#ellint_ref_carlson78">Carlson78</a>]
gives an alternative definition of elliptic integral's canonical forms:
</p>
@@ -190,7 +206,7 @@
Carlson's Elliptic Integral of the First Kind
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint9.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint9.svg"></span>
</p>
<p>
where <span class="emphasis"><em>x</em></span>, <span class="emphasis"><em>y</em></span>, <span class="emphasis"><em>z</em></span>
@@ -200,7 +216,7 @@
Carlson's Elliptic Integral of the Second Kind
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint10.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint10.svg"></span>
</p>
<p>
where <span class="emphasis"><em>x</em></span>, <span class="emphasis"><em>y</em></span> are nonnegative, at
@@ -210,7 +226,7 @@
Carlson's Elliptic Integral of the Third Kind
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint11.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint11.svg"></span>
</p>
<p>
where <span class="emphasis"><em>x</em></span>, <span class="emphasis"><em>y</em></span>, <span class="emphasis"><em>z</em></span>
@@ -221,7 +237,7 @@
Carlson's Degenerate Elliptic Integral
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint12.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint12.svg"></span>
</p>
<p>
where <span class="emphasis"><em>x</em></span> is nonnegative and <span class="emphasis"><em>y</em></span> is
@@ -241,8 +257,14 @@
</p>
</td></tr>
</table></div>
+<p>
+ Carlson's Symmetric Integral
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint27.svg"></span>
+ </p>
<h5>
-<a name="math_toolkit.ellint.ellint_intro.h2"></a>
+<a name="math_toolkit.ellint.ellint_intro.h3"></a>
<span class="phrase"><a name="math_toolkit.ellint.ellint_intro.duplication_theorem"></a></span><a class="link" href="ellint_intro.html#math_toolkit.ellint.ellint_intro.duplication_theorem">Duplication
Theorem</a>
</h5>
@@ -251,10 +273,10 @@
that
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint13.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint13.svg"></span>
</p>
<h5>
-<a name="math_toolkit.ellint.ellint_intro.h3"></a>
+<a name="math_toolkit.ellint.ellint_intro.h4"></a>
<span class="phrase"><a name="math_toolkit.ellint.ellint_intro.carlson_s_formulas"></a></span><a class="link" href="ellint_intro.html#math_toolkit.ellint.ellint_intro.carlson_s_formulas">Carlson's
Formulas</a>
</h5>
@@ -262,16 +284,39 @@
The Legendre form and Carlson form of elliptic integrals are related by equations:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint14.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint14.svg"></span>
</p>
<p>
In particular,
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ellint15.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ellint15.svg"></span>
</p>
<h5>
-<a name="math_toolkit.ellint.ellint_intro.h4"></a>
+<a name="math_toolkit.ellint.ellint_intro.h5"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.ellint_intro.miscellaneous_elliptic_integrals"></a></span><a class="link" href="ellint_intro.html#math_toolkit.ellint.ellint_intro.miscellaneous_elliptic_integrals">Miscellaneous
+ Elliptic Integrals</a>
+ </h5>
+<p>
+ There are two functions related to the elliptic integrals which otherwise
+ defy categorisation, these are the Jacobi Zeta function:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/jacobi_zeta.svg"></span>
+ </p>
+<p>
+ and the Heuman Lambda function:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/heuman_lambda.svg"></span>
+ </p>
+<p>
+ Both of these functions are easily implemented in terms of Carlson's integrals,
+ and are provided in this library as <a class="link" href="jacobi_zeta.html" title="Jacobi Zeta Function">jacobi_zeta</a>
+ and <a class="link" href="heuman_lambda.html" title="Heuman Lambda Function">heuman_lambda</a>.
+ </p>
+<h5>
+<a name="math_toolkit.ellint.ellint_intro.h6"></a>
<span class="phrase"><a name="math_toolkit.ellint.ellint_intro.numerical_algorithms"></a></span><a class="link" href="ellint_intro.html#math_toolkit.ellint.ellint_intro.numerical_algorithms">Numerical
Algorithms</a>
</h5>
@@ -285,7 +330,7 @@
precisions.
</p>
<h5>
-<a name="math_toolkit.ellint.ellint_intro.h5"></a>
+<a name="math_toolkit.ellint.ellint_intro.h7"></a>
<span class="phrase"><a name="math_toolkit.ellint.ellint_intro.references"></a></span><a class="link" href="ellint_intro.html#math_toolkit.ellint.ellint_intro.references">References</a>
</h5>
<p>
diff --git a/libs/math/doc/html/math_toolkit/ellint/heuman_lambda.html b/libs/math/doc/html/math_toolkit/ellint/heuman_lambda.html
new file mode 100644
index 000000000..96fce53b1
--- /dev/null
+++ b/libs/math/doc/html/math_toolkit/ellint/heuman_lambda.html
@@ -0,0 +1,130 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Heuman Lambda Function</title>
+<link rel="stylesheet" href="../../math.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="../ellint.html" title="Elliptic Integrals">
+<link rel="prev" href="jacobi_zeta.html" title="Jacobi Zeta Function">
+<link rel="next" href="../jacobi.html" title="Jacobi Elliptic Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center"><a href="../../../../../../index.html">Home</a></td>
+<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
+<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
+<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
+<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="jacobi_zeta.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../jacobi.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.ellint.heuman_lambda"></a><a class="link" href="heuman_lambda.html" title="Heuman Lambda Function">Heuman Lambda Function</a>
+</h3></div></div></div>
+<h5>
+<a name="math_toolkit.ellint.heuman_lambda.h0"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.heuman_lambda.synopsis"></a></span><a class="link" href="heuman_lambda.html#math_toolkit.ellint.heuman_lambda.synopsis">Synopsis</a>
+ </h5>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">heuman_lambda</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">heuman_lambda</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">heuman_lambda</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces</span>
+</pre>
+<h5>
+<a name="math_toolkit.ellint.heuman_lambda.h1"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.heuman_lambda.description"></a></span><a class="link" href="heuman_lambda.html#math_toolkit.ellint.heuman_lambda.description">Description</a>
+ </h5>
+<p>
+ This function evaluates the Heuman Lambda Function <span class="emphasis"><em>&#923;<sub>0</sub>(&#966;, k)</em></span>
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/heuman_lambda.svg"></span>
+ </p>
+<p>
+ The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+ type calculation rules</em></span></a> when the arguments are of different
+ types: when they are the same type then the result is the same type as the
+ arguments.
+ </p>
+<p>
+ Requires <span class="emphasis"><em>-1 &lt;= k &lt;= 1</em></span>, otherwise returns the result
+ of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
+ (outside this range the result would be complex).
+ </p>
+<p>
+ The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
+ be used to control the behaviour of the function: how it handles errors,
+ what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">policy
+ documentation for more details</a>.
+ </p>
+<p>
+ Note that there is no complete analogue of this function (where &#966; = &#960; / 2) as
+ this takes the value 1 for all <span class="emphasis"><em>k</em></span>.
+ </p>
+<h5>
+<a name="math_toolkit.ellint.heuman_lambda.h2"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.heuman_lambda.accuracy"></a></span><a class="link" href="heuman_lambda.html#math_toolkit.ellint.heuman_lambda.accuracy">Accuracy</a>
+ </h5>
+<p>
+ These functions are trivially computed in terms of other elliptic integrals
+ and generally have very low error rates (a few epsilon) unless parameter
+ &#966;
+is very large, in which case the usual trigonometric function argument-reduction
+ issues apply.
+ </p>
+<h5>
+<a name="math_toolkit.ellint.heuman_lambda.h3"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.heuman_lambda.testing"></a></span><a class="link" href="heuman_lambda.html#math_toolkit.ellint.heuman_lambda.testing">Testing</a>
+ </h5>
+<p>
+ The tests use a mixture of spot test values calculated using values calculated
+ at wolframalpha.com, and random test data generated using MPFR at 1000-bit
+ precision and a deliberately naive implementation in terms of the Legendre
+ integrals.
+ </p>
+<h5>
+<a name="math_toolkit.ellint.heuman_lambda.h4"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.heuman_lambda.implementation"></a></span><a class="link" href="heuman_lambda.html#math_toolkit.ellint.heuman_lambda.implementation">Implementation</a>
+ </h5>
+<p>
+ The function is then implemented in terms of Carlson's integrals R<sub>J</sub> and R<sub>F</sub>
+using
+ the relation:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/heuman_lambda.svg"></span>
+ </p>
+<p>
+ This relation fails for <span class="emphasis"><em>|&#966;| &gt;= &#960;/2</em></span> in which case the
+ definition in terms of the Jacobi Zeta is used.
+ </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
+ Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
+ Holin, Bruno Lalande, John Maddock, Johan R&#229;de, Gautam Sewani, Benjamin Sobotta,
+ Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+ </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="jacobi_zeta.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../jacobi.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>
diff --git a/libs/math/doc/html/math_toolkit/ellint/jacobi_zeta.html b/libs/math/doc/html/math_toolkit/ellint/jacobi_zeta.html
new file mode 100644
index 000000000..945ace297
--- /dev/null
+++ b/libs/math/doc/html/math_toolkit/ellint/jacobi_zeta.html
@@ -0,0 +1,139 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Jacobi Zeta Function</title>
+<link rel="stylesheet" href="../../math.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="../ellint.html" title="Elliptic Integrals">
+<link rel="prev" href="ellint_d.html" title="Elliptic Integral D - Legendre Form">
+<link rel="next" href="heuman_lambda.html" title="Heuman Lambda Function">
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+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center"><a href="../../../../../../index.html">Home</a></td>
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+<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
+<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
+<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ellint_d.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="heuman_lambda.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.ellint.jacobi_zeta"></a><a class="link" href="jacobi_zeta.html" title="Jacobi Zeta Function">Jacobi Zeta Function</a>
+</h3></div></div></div>
+<h5>
+<a name="math_toolkit.ellint.jacobi_zeta.h0"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.jacobi_zeta.synopsis"></a></span><a class="link" href="jacobi_zeta.html#math_toolkit.ellint.jacobi_zeta.synopsis">Synopsis</a>
+ </h5>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">jacobi_zeta</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">jacobi_zeta</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">jacobi_zeta</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces</span>
+</pre>
+<h5>
+<a name="math_toolkit.ellint.jacobi_zeta.h1"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.jacobi_zeta.description"></a></span><a class="link" href="jacobi_zeta.html#math_toolkit.ellint.jacobi_zeta.description">Description</a>
+ </h5>
+<p>
+ This function evaluates the Jacobi Zeta Function <span class="emphasis"><em>Z(&#966;, k)</em></span>
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/jacobi_zeta.svg"></span>
+ </p>
+<p>
+ The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+ type calculation rules</em></span></a> when the arguments are of different
+ types: when they are the same type then the result is the same type as the
+ arguments.
+ </p>
+<p>
+ Requires <span class="emphasis"><em>-1 &lt;= k &lt;= 1</em></span>, otherwise returns the result
+ of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
+ (outside this range the result would be complex).
+ </p>
+<p>
+ The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
+ be used to control the behaviour of the function: how it handles errors,
+ what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">policy
+ documentation for more details</a>.
+ </p>
+<p>
+ Note that there is no complete analogue of this function (where &#966; = &#960; / 2) as
+ this takes the value 0 for all <span class="emphasis"><em>k</em></span>.
+ </p>
+<h5>
+<a name="math_toolkit.ellint.jacobi_zeta.h2"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.jacobi_zeta.accuracy"></a></span><a class="link" href="jacobi_zeta.html#math_toolkit.ellint.jacobi_zeta.accuracy">Accuracy</a>
+ </h5>
+<p>
+ These functions are trivially computed in terms of other elliptic integrals
+ and generally have very low error rates (a few epsilon) unless parameter
+ &#966;
+is very large, in which case the usual trigonometric function argument-reduction
+ issues apply.
+ </p>
+<h5>
+<a name="math_toolkit.ellint.jacobi_zeta.h3"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.jacobi_zeta.testing"></a></span><a class="link" href="jacobi_zeta.html#math_toolkit.ellint.jacobi_zeta.testing">Testing</a>
+ </h5>
+<p>
+ The tests use a mixture of spot test values calculated using values calculated
+ at wolframalpha.com, and random test data generated using MPFR at 1000-bit
+ precision and a deliberately naive implementation in terms of the Legendre
+ integrals.
+ </p>
+<h5>
+<a name="math_toolkit.ellint.jacobi_zeta.h4"></a>
+ <span class="phrase"><a name="math_toolkit.ellint.jacobi_zeta.implementation"></a></span><a class="link" href="jacobi_zeta.html#math_toolkit.ellint.jacobi_zeta.implementation">Implementation</a>
+ </h5>
+<p>
+ The implementation for Z(&#966;, k) first makes the argument &#966; positive using:
+ </p>
+<p>
+ <span class="emphasis"><em>Z(-&#966;, k) = -Z(&#966;, k)</em></span>
+ </p>
+<p>
+ The function is then implemented in terms of Carlson's integral R<sub>J</sub>
+using the
+ relation:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/jacobi_zeta.svg"></span>
+ </p>
+<p>
+ There is one special case where the above relation fails: when <span class="emphasis"><em>k
+ = 1</em></span>, in that case the function simplifies to
+ </p>
+<p>
+ <span class="emphasis"><em>Z(&#966;, 1) = sign(cos(&#966;)) sin(&#966;)</em></span>
+ </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
+ Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
+ Holin, Bruno Lalande, John Maddock, Johan R&#229;de, Gautam Sewani, Benjamin Sobotta,
+ Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+ </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ellint_d.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="heuman_lambda.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>
diff --git a/libs/math/doc/html/math_toolkit/error_handling.html b/libs/math/doc/html/math_toolkit/error_handling.html
index eefe39045..79f113586 100644
--- a/libs/math/doc/html/math_toolkit/error_handling.html
+++ b/libs/math/doc/html/math_toolkit/error_handling.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Error Handling</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="result_type.html" title="Calculation of the Type of the Result">
<link rel="next" href="compilers_overview.html" title="Compilers">
diff --git a/libs/math/doc/html/math_toolkit/exact_typdefs.html b/libs/math/doc/html/math_toolkit/exact_typdefs.html
index f5a457160..6523b7cae 100644
--- a/libs/math/doc/html/math_toolkit/exact_typdefs.html
+++ b/libs/math/doc/html/math_toolkit/exact_typdefs.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Exact-Width Floating-Point typedefs</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../cstdfloat.html" title="Chapter&#160;3.&#160;Specified-width floating-point typedefs">
<link rel="prev" href="rationale.html" title="Rationale">
<link rel="next" href="minimum_typdefs.html" title="Minimum-width floating-point typedefs">
diff --git a/libs/math/doc/html/math_toolkit/examples.html b/libs/math/doc/html/math_toolkit/examples.html
index 620c1c027..8c1d9b0a0 100644
--- a/libs/math/doc/html/math_toolkit/examples.html
+++ b/libs/math/doc/html/math_toolkit/examples.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Examples</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../cstdfloat.html" title="Chapter&#160;3.&#160;Specified-width floating-point typedefs">
<link rel="prev" href="macros.html" title="Floating-Point Constant Macros">
<link rel="next" href="float128.html" title="Implementation of Float128 type">
diff --git a/libs/math/doc/html/math_toolkit/exp.html b/libs/math/doc/html/math_toolkit/exp.html
index 225b669a4..ced723bf8 100644
--- a/libs/math/doc/html/math_toolkit/exp.html
+++ b/libs/math/doc/html/math_toolkit/exp.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>The Quaternionic Exponential</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="quat_tests.html" title="Test Program">
<link rel="next" href="acknowledgement.html" title="Acknowledgements">
diff --git a/libs/math/doc/html/math_toolkit/expint.html b/libs/math/doc/html/math_toolkit/expint.html
index 1e089f6a1..3afd1c1f0 100644
--- a/libs/math/doc/html/math_toolkit/expint.html
+++ b/libs/math/doc/html/math_toolkit/expint.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Exponential Integrals</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
<link rel="prev" href="zetas/zeta.html" title="Riemann Zeta Function">
<link rel="next" href="expint/expint_n.html" title="Exponential Integral En">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.expint"></a><a class="link" href="expint.html" title="Exponential Integrals">Exponential Integrals</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="expint/expint_n.html">Exponential Integral En</a></span></dt>
<dt><span class="section"><a href="expint/expint_i.html">Exponential Integral Ei</a></span></dt>
</dl></div>
diff --git a/libs/math/doc/html/math_toolkit/expint/expint_i.html b/libs/math/doc/html/math_toolkit/expint/expint_i.html
index deaeb7975..1513422ff 100644
--- a/libs/math/doc/html/math_toolkit/expint/expint_i.html
+++ b/libs/math/doc/html/math_toolkit/expint/expint_i.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Exponential Integral Ei</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../expint.html" title="Exponential Integrals">
<link rel="prev" href="expint_n.html" title="Exponential Integral En">
<link rel="next" href="../powers.html" title="Basic Functions">
@@ -67,10 +67,10 @@
integral</a> of z:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/expint_i_1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/expint_i_1.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/expint_i.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/expint_i.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.expint.expint_i.h2"></a>
@@ -223,7 +223,7 @@
For x &gt; 0 the generic version is implemented using the infinte series:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/expint_i_2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/expint_i_2.svg"></span>
</p>
<p>
However, when the precision of the argument type is known at compile time
@@ -234,14 +234,14 @@
For 0 &lt; z &lt; 6 a root-preserving approximation of the form:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/expint_i_3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/expint_i_3.svg"></span>
</p>
<p>
is used, where z<sub>0</sub> is the positive root of the function, and R(z/3 - 1) is
a minimax rational approximation rescaled so that it is evaluated over [-1,1].
Note that while the rational approximation over [0,6] converges rapidly to
the minimax solution it is rather ill-conditioned in practice. Cody and Thacher
- <a href="#ftn.math_toolkit.expint.expint_i.f0" class="footnote" name="math_toolkit.expint.expint_i.f0"><sup class="footnote">[5]</sup></a> experienced the same issue and converted the polynomials into
+ <a href="#ftn.math_toolkit.expint.expint_i.f0" class="footnote"><sup class="footnote"><a name="math_toolkit.expint.expint_i.f0"></a>[5]</sup></a> experienced the same issue and converted the polynomials into
Chebeshev form to ensure stable computation. By experiment we found that
the polynomials are just as stable in polynomial as Chebyshev form, <span class="emphasis"><em>provided</em></span>
they are computed over the interval [-1,1].
@@ -251,7 +251,7 @@
takes the form:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/expint_i_4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/expint_i_4.svg"></span>
</p>
<p>
where <span class="emphasis"><em>c</em></span> is a constant, and R(t) is a minimax solution
@@ -268,7 +268,7 @@
involved.
</p>
<div class="footnotes">
-<br><hr style="width:100; text-align:left;margin-left: 0">
+<br><hr style="width:100; align:left;">
<div id="ftn.math_toolkit.expint.expint_i.f0" class="footnote"><p><a href="#math_toolkit.expint.expint_i.f0" class="para"><sup class="para">[5] </sup></a>
W. J. Cody and H. C. Thacher, Jr., Rational Chebyshev approximations for
the exponential integral E<sub>1</sub>(x), Math. Comp. 22 (1968), 641-649, and W.
diff --git a/libs/math/doc/html/math_toolkit/expint/expint_n.html b/libs/math/doc/html/math_toolkit/expint/expint_n.html
index 032c473da..3e5411322 100644
--- a/libs/math/doc/html/math_toolkit/expint/expint_n.html
+++ b/libs/math/doc/html/math_toolkit/expint/expint_n.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Exponential Integral En</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../expint.html" title="Exponential Integrals">
<link rel="prev" href="../expint.html" title="Exponential Integrals">
<link rel="next" href="expint_i.html" title="Exponential Integral Ei">
@@ -67,10 +67,10 @@
integral En</a> of z:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/expint_n_1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/expint_n_1.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/expint2.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/expint2.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.expint.expint_n.h2"></a>
@@ -237,13 +237,13 @@
The generic version of this function uses the continued fraction:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/expint_n_3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/expint_n_3.svg"></span>
</p>
<p>
for large <span class="emphasis"><em>x</em></span> and the infinite series:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/expint_n_2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/expint_n_2.svg"></span>
</p>
<p>
for small <span class="emphasis"><em>x</em></span>.
@@ -261,7 +261,7 @@
approximation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/expint_n_4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/expint_n_4.svg"></span>
</p>
<p>
and for <code class="computeroutput"><span class="identifier">x</span> <span class="special">&gt;</span>
@@ -269,7 +269,7 @@
of the form:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/expint_n_5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/expint_n_5.svg"></span>
</p>
<p>
is used.
diff --git a/libs/math/doc/html/math_toolkit/factorials.html b/libs/math/doc/html/math_toolkit/factorials.html
index 2252c8715..99569689d 100644
--- a/libs/math/doc/html/math_toolkit/factorials.html
+++ b/libs/math/doc/html/math_toolkit/factorials.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Factorials and Binomial Coefficients</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
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<link rel="up" href="../factorials.html" title="Factorials and Binomial Coefficients">
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diff --git a/libs/math/doc/html/math_toolkit/factorials/sf_falling_factorial.html b/libs/math/doc/html/math_toolkit/factorials/sf_falling_factorial.html
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<link rel="next" href="sf_binomial.html" title="Binomial Coefficients">
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<link rel="next" href="../../constants.html" title="Chapter&#160;4.&#160;Mathematical Constants">
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-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
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+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../gcd_lcm.html" title="Chapter&#160;11.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)">
<link rel="prev" href="synopsis.html" title="Synopsis">
<link rel="next" href="lcm_function_object.html" title="LCM Function Object">
diff --git a/libs/math/doc/html/math_toolkit/gcd_header.html b/libs/math/doc/html/math_toolkit/gcd_header.html
index b1b0d7cbd..523e9c75a 100644
--- a/libs/math/doc/html/math_toolkit/gcd_header.html
+++ b/libs/math/doc/html/math_toolkit/gcd_header.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Header &lt;boost/math/common_factor.hpp&gt;</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../gcd_lcm.html" title="Chapter&#160;11.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)">
<link rel="prev" href="compile_time.html" title="Compile time GCD and LCM determination">
<link rel="next" href="demo.html" title="Demonstration Program">
diff --git a/libs/math/doc/html/math_toolkit/gcd_history.html b/libs/math/doc/html/math_toolkit/gcd_history.html
index 180d38b0d..5b1bf062b 100644
--- a/libs/math/doc/html/math_toolkit/gcd_history.html
+++ b/libs/math/doc/html/math_toolkit/gcd_history.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>History</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../gcd_lcm.html" title="Chapter&#160;11.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)">
<link rel="prev" href="rationale0.html" title="Rationale">
<link rel="next" href="gcd_credits.html" title="Credits">
diff --git a/libs/math/doc/html/math_toolkit/getting_best.html b/libs/math/doc/html/math_toolkit/getting_best.html
index 9c7b27e5b..53be9c2f0 100644
--- a/libs/math/doc/html/math_toolkit/getting_best.html
+++ b/libs/math/doc/html/math_toolkit/getting_best.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Getting the Best Performance from this Library</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../perf.html" title="Chapter&#160;15.&#160;Performance">
<link rel="prev" href="interp.html" title="Interpreting these Results">
<link rel="next" href="comp_compilers.html" title="Comparing Compilers">
diff --git a/libs/math/doc/html/math_toolkit/greatest_typdefs.html b/libs/math/doc/html/math_toolkit/greatest_typdefs.html
index 34e37abde..6690a9fe9 100644
--- a/libs/math/doc/html/math_toolkit/greatest_typdefs.html
+++ b/libs/math/doc/html/math_toolkit/greatest_typdefs.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Greatest-width floating-point typedef</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../cstdfloat.html" title="Chapter&#160;3.&#160;Specified-width floating-point typedefs">
<link rel="prev" href="fastest_typdefs.html" title="Fastest floating-point typedefs">
<link rel="next" href="macros.html" title="Floating-Point Constant Macros">
diff --git a/libs/math/doc/html/math_toolkit/hankel.html b/libs/math/doc/html/math_toolkit/hankel.html
index 7f028e419..8af1edc54 100644
--- a/libs/math/doc/html/math_toolkit/hankel.html
+++ b/libs/math/doc/html/math_toolkit/hankel.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Hankel Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
<link rel="prev" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">
<link rel="next" href="hankel/cyl_hankel.html" title="Cyclic Hankel Functions">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.hankel"></a><a class="link" href="hankel.html" title="Hankel Functions">Hankel Functions</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="hankel/cyl_hankel.html">Cyclic Hankel Functions</a></span></dt>
<dt><span class="section"><a href="hankel/sph_hankel.html">Spherical Hankel Functions</a></span></dt>
</dl></div>
diff --git a/libs/math/doc/html/math_toolkit/hankel/cyl_hankel.html b/libs/math/doc/html/math_toolkit/hankel/cyl_hankel.html
index c823c01da..de8110944 100644
--- a/libs/math/doc/html/math_toolkit/hankel/cyl_hankel.html
+++ b/libs/math/doc/html/math_toolkit/hankel/cyl_hankel.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Cyclic Hankel Functions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../hankel.html" title="Hankel Functions">
<link rel="prev" href="../hankel.html" title="Hankel Functions">
<link rel="next" href="sph_hankel.html" title="Spherical Hankel Functions">
@@ -121,15 +121,15 @@
</p>
<p>
<a href="http://functions.wolfram.com/Bessel-TypeFunctions/BesselJ/16/01/01/" target="_top">
- <span class="inlinemediaobject"><img src="../../../equations/hankel1.png"></span></a>
+ <span class="inlinemediaobject"><img src="../../../equations/hankel1.svg"></span></a>
</p>
<p>
<a href="http://functions.wolfram.com/Bessel-TypeFunctions/BesselY/16/01/01/" target="_top">
- <span class="inlinemediaobject"><img src="../../../equations/hankel2.png"></span></a>
+ <span class="inlinemediaobject"><img src="../../../equations/hankel2.svg"></span></a>
</p>
<p>
<a href="http://functions.wolfram.com/Bessel-TypeFunctions/BesselY/16/01/01/" target="_top">
- <span class="inlinemediaobject"><img src="../../../equations/hankel3.png"></span></a>
+ <span class="inlinemediaobject"><img src="../../../equations/hankel3.svg"></span></a>
</p>
<p>
Otherwise the implementation is trivially in terms of the Bessel J and Y
diff --git a/libs/math/doc/html/math_toolkit/hankel/sph_hankel.html b/libs/math/doc/html/math_toolkit/hankel/sph_hankel.html
index fcb8893a3..0b02ec8aa 100644
--- a/libs/math/doc/html/math_toolkit/hankel/sph_hankel.html
+++ b/libs/math/doc/html/math_toolkit/hankel/sph_hankel.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Spherical Hankel Functions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../hankel.html" title="Hankel Functions">
<link rel="prev" href="cyl_hankel.html" title="Cyclic Hankel Functions">
<link rel="next" href="../airy.html" title="Airy Functions">
@@ -53,10 +53,10 @@
functions</a> of the first and second kind respectively:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/hankel4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/hankel4.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/hankel5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/hankel5.svg"></span>
</p>
<p>
The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
diff --git a/libs/math/doc/html/math_toolkit/high_precision.html b/libs/math/doc/html/math_toolkit/high_precision.html
index ff66608ae..e8fb5ddb7 100644
--- a/libs/math/doc/html/math_toolkit/high_precision.html
+++ b/libs/math/doc/html/math_toolkit/high_precision.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Using Boost.Math with High-Precision Floating-Point Libraries</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../using_udt.html" title="Chapter&#160;13.&#160;Use with User-Defined Floating-Point Types - Boost.Multiprecision and others">
<link rel="prev" href="../using_udt.html" title="Chapter&#160;13.&#160;Use with User-Defined Floating-Point Types - Boost.Multiprecision and others">
<link rel="next" href="high_precision/why_high_precision.html" title="Why use a high-precision library rather than built-in floating-point types?">
@@ -27,7 +27,7 @@
<a name="math_toolkit.high_precision"></a><a class="link" href="high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">Using Boost.Math with High-Precision
Floating-Point Libraries</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="high_precision/why_high_precision.html">Why use
a high-precision library rather than built-in floating-point types?</a></span></dt>
<dt><span class="section"><a href="high_precision/use_multiprecision.html">Using
diff --git a/libs/math/doc/html/math_toolkit/high_precision/e_float.html b/libs/math/doc/html/math_toolkit/high_precision/e_float.html
index 6ffbfc12d..5da550c4a 100644
--- a/libs/math/doc/html/math_toolkit/high_precision/e_float.html
+++ b/libs/math/doc/html/math_toolkit/high_precision/e_float.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Using e_float Library</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
<link rel="prev" href="use_mpfr.html" title="Using With MPFR or GMP - High-Precision Floating-Point Library">
<link rel="next" href="use_ntl.html" title="Using NTL Library">
diff --git a/libs/math/doc/html/math_toolkit/high_precision/float128.html b/libs/math/doc/html/math_toolkit/high_precision/float128.html
index 952419f76..962537e42 100644
--- a/libs/math/doc/html/math_toolkit/high_precision/float128.html
+++ b/libs/math/doc/html/math_toolkit/high_precision/float128.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Using with GCC's __float128 datatype</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
<link rel="prev" href="use_multiprecision.html" title="Using Boost.Multiprecision">
<link rel="next" href="use_mpfr.html" title="Using With MPFR or GMP - High-Precision Floating-Point Library">
diff --git a/libs/math/doc/html/math_toolkit/high_precision/use_mpfr.html b/libs/math/doc/html/math_toolkit/high_precision/use_mpfr.html
index 8efc2e8da..a537dc909 100644
--- a/libs/math/doc/html/math_toolkit/high_precision/use_mpfr.html
+++ b/libs/math/doc/html/math_toolkit/high_precision/use_mpfr.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Using With MPFR or GMP - High-Precision Floating-Point Library</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
<link rel="prev" href="float128.html" title="Using with GCC's __float128 datatype">
<link rel="next" href="e_float.html" title="Using e_float Library">
diff --git a/libs/math/doc/html/math_toolkit/high_precision/use_multiprecision.html b/libs/math/doc/html/math_toolkit/high_precision/use_multiprecision.html
index c464c0765..0f7789942 100644
--- a/libs/math/doc/html/math_toolkit/high_precision/use_multiprecision.html
+++ b/libs/math/doc/html/math_toolkit/high_precision/use_multiprecision.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Using Boost.Multiprecision</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
<link rel="prev" href="why_high_precision.html" title="Why use a high-precision library rather than built-in floating-point types?">
<link rel="next" href="float128.html" title="Using with GCC's __float128 datatype">
diff --git a/libs/math/doc/html/math_toolkit/high_precision/use_ntl.html b/libs/math/doc/html/math_toolkit/high_precision/use_ntl.html
index f1b05a1ce..4f113a815 100644
--- a/libs/math/doc/html/math_toolkit/high_precision/use_ntl.html
+++ b/libs/math/doc/html/math_toolkit/high_precision/use_ntl.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Using NTL Library</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
<link rel="prev" href="e_float.html" title="Using e_float Library">
<link rel="next" href="using_test.html" title="Using without expression templates for Boost.Test and others">
diff --git a/libs/math/doc/html/math_toolkit/high_precision/using_test.html b/libs/math/doc/html/math_toolkit/high_precision/using_test.html
index 521a7ba3f..e47cbfd25 100644
--- a/libs/math/doc/html/math_toolkit/high_precision/using_test.html
+++ b/libs/math/doc/html/math_toolkit/high_precision/using_test.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Using without expression templates for Boost.Test and others</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
<link rel="prev" href="use_ntl.html" title="Using NTL Library">
<link rel="next" href="../concepts.html" title="Conceptual Requirements for Real Number Types">
diff --git a/libs/math/doc/html/math_toolkit/high_precision/why_high_precision.html b/libs/math/doc/html/math_toolkit/high_precision/why_high_precision.html
index 0166b3719..34ca566f0 100644
--- a/libs/math/doc/html/math_toolkit/high_precision/why_high_precision.html
+++ b/libs/math/doc/html/math_toolkit/high_precision/why_high_precision.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Why use a high-precision library rather than built-in floating-point types?</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
<link rel="prev" href="../high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
<link rel="next" href="use_multiprecision.html" title="Using Boost.Multiprecision">
diff --git a/libs/math/doc/html/math_toolkit/hints.html b/libs/math/doc/html/math_toolkit/hints.html
index 548a7317b..c50affaa1 100644
--- a/libs/math/doc/html/math_toolkit/hints.html
+++ b/libs/math/doc/html/math_toolkit/hints.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Other Hints and tips</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="conventions.html" title="Document Conventions">
<link rel="next" href="directories.html" title="Directory and File Structure">
diff --git a/libs/math/doc/html/math_toolkit/history1.html b/libs/math/doc/html/math_toolkit/history1.html
index 83f13c9b5..2a561c3af 100644
--- a/libs/math/doc/html/math_toolkit/history1.html
+++ b/libs/math/doc/html/math_toolkit/history1.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>History and What's New</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="building.html" title="If and How to Build a Boost.Math Library, and its Examples and Tests">
<link rel="next" href="overview_tr1.html" title="C99 and C++ TR1 C-style Functions">
@@ -34,6 +34,50 @@
</p>
<h5>
<a name="math_toolkit.history1.h0"></a>
+ <span class="phrase"><a name="math_toolkit.history1.math_2_2_0_boost_1_58_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_2_0_boost_1_58_0">Math-2.2.0
+ (boost-1.58.0)</a>
+ </h5>
+<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
+<li class="listitem">
+ Added two new special functions - <a class="link" href="sf_gamma/trigamma.html" title="Trigamma">trigamma</a>
+ and <a class="link" href="sf_gamma/polygamma.html" title="Polygamma">polygamma</a>.
+ </li>
+<li class="listitem">
+ Fixed namespace scope constants so they are constexpr on conforming compilers,
+ see https://svn.boost.org/trac/boost/ticket/10901.
+ </li>
+<li class="listitem">
+ Fixed various cases of spurious under/overflow in the incomplete beta and
+ gamma functions, plus the elliptic integrals, with thanks to Rocco Romeo.
+ </li>
+<li class="listitem">
+ Fix 3-arg <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a>
+ and <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_q</a> functions
+ to not call the policy based overload if the final argument is not actually
+ a policy.
+ </li>
+<li class="listitem">
+ Cleaned up some dead code in the incomplete beta function, see <a href="https://svn.boost.org/trac/boost/ticket/10985" target="_top">#10985</a>.
+ </li>
+<li class="listitem">
+ Fixed extreme-value pdf for large valued inputs, see <a href="https://svn.boost.org/trac/boost/ticket/10938" target="_top">#10938</a>.
+ </li>
+<li class="listitem">
+ Large update to the Elliptic integral code to use Carlson's latest algorithms
+ - these should be more stable, more accurate and slightly faster than before.
+ Also added support for Carlson's RG integral.
+ </li>
+<li class="listitem">
+ Added <a class="link" href="ellint/ellint_d.html" title="Elliptic Integral D - Legendre Form">ellint_d</a>, <a class="link" href="ellint/jacobi_zeta.html" title="Jacobi Zeta Function">jacobi_zeta</a> and <a class="link" href="ellint/heuman_lambda.html" title="Heuman Lambda Function">heuman_lambda</a> elliptic
+ integrals.
+ </li>
+<li class="listitem">
+ Switched documentation to use SVG rather than PNG graphs and equations
+ - browsers seem to have finally caught up!
+ </li>
+</ul></div>
+<h5>
+<a name="math_toolkit.history1.h1"></a>
<span class="phrase"><a name="math_toolkit.history1.math_2_1_0_boost_1_57_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_1_0_boost_1_57_0">Math-2.1.0
(boost-1.57.0)</a>
</h5>
@@ -59,7 +103,7 @@
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h1"></a>
+<a name="math_toolkit.history1.h2"></a>
<span class="phrase"><a name="math_toolkit.history1.math_2_0_0_boost_1_56_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_0_0_boost_1_56_0">Math-2.0.0
(Boost-1.56.0)</a>
</h5>
@@ -110,7 +154,7 @@
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h2"></a>
+<a name="math_toolkit.history1.h3"></a>
<span class="phrase"><a name="math_toolkit.history1.math_1_9_1"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_1_9_1">Math-1.9.1</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -125,7 +169,7 @@
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h3"></a>
+<a name="math_toolkit.history1.h4"></a>
<span class="phrase"><a name="math_toolkit.history1.math_1_9_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_1_9_0">Math-1.9.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -192,7 +236,7 @@
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h4"></a>
+<a name="math_toolkit.history1.h5"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_55"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_55">Boost-1.55</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -248,7 +292,7 @@
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h5"></a>
+<a name="math_toolkit.history1.h6"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_54"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_54">Boost-1.54</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -302,7 +346,7 @@
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h6"></a>
+<a name="math_toolkit.history1.h7"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_53"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_53">Boost-1.53</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -337,7 +381,7 @@
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h7"></a>
+<a name="math_toolkit.history1.h8"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_52"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_52">Boost-1.52</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -384,14 +428,14 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h8"></a>
+<a name="math_toolkit.history1.h9"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_51"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_51">Boost-1.51</a>
</h5>
<p>
See Boost-1.52 - some items were added but not listed in time for the release.
</p>
<h5>
-<a name="math_toolkit.history1.h9"></a>
+<a name="math_toolkit.history1.h10"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_50"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_50">Boost-1.50</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -428,7 +472,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h10"></a>
+<a name="math_toolkit.history1.h11"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_49"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_49">Boost-1.49</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -472,7 +516,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h11"></a>
+<a name="math_toolkit.history1.h12"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_48"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_48">Boost-1.48</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -523,7 +567,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h12"></a>
+<a name="math_toolkit.history1.h13"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_47"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_47">Boost-1.47</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -540,7 +584,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h13"></a>
+<a name="math_toolkit.history1.h14"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_46_1"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_46_1">Boost-1.46.1</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
@@ -548,7 +592,7 @@ by switching to use the Students t distribution (or Normal distribution
<a href="https://svn.boost.org/trac/boost/ticket/5095" target="_top">#5113</a>.
</li></ul></div>
<h5>
-<a name="math_toolkit.history1.h14"></a>
+<a name="math_toolkit.history1.h15"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_46_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_46_0">Boost-1.46.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -563,7 +607,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h15"></a>
+<a name="math_toolkit.history1.h16"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_45_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_45_0">Boost-1.45.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -580,7 +624,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h16"></a>
+<a name="math_toolkit.history1.h17"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_44_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_44_0">Boost-1.44.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -594,7 +638,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h17"></a>
+<a name="math_toolkit.history1.h18"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_41_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_41_0">Boost-1.41.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
@@ -602,7 +646,7 @@ by switching to use the Students t distribution (or Normal distribution
its inverse.
</li></ul></div>
<h5>
-<a name="math_toolkit.history1.h18"></a>
+<a name="math_toolkit.history1.h19"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_40_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_40_0">Boost-1.40.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -638,7 +682,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h19"></a>
+<a name="math_toolkit.history1.h20"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_38_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_38_0">Boost-1.38.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -650,14 +694,14 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h20"></a>
+<a name="math_toolkit.history1.h21"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_37_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_37_0">Boost-1.37.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
Improved accuracy and testing of the inverse hypergeometric functions.
</li></ul></div>
<h5>
-<a name="math_toolkit.history1.h21"></a>
+<a name="math_toolkit.history1.h22"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_36_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_36_0">Boost-1.36.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -690,7 +734,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h22"></a>
+<a name="math_toolkit.history1.h23"></a>
<span class="phrase"><a name="math_toolkit.history1.boost_1_35_0_post_review_first_o"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_35_0_post_review_first_o">Boost-1.35.0:
Post Review First Official Release</a>
</h5>
@@ -722,7 +766,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h23"></a>
+<a name="math_toolkit.history1.h24"></a>
<span class="phrase"><a name="math_toolkit.history1.milestone_4_second_review_candid"></a></span><a class="link" href="history1.html#math_toolkit.history1.milestone_4_second_review_candid">Milestone
4: Second Review Candidate (1st March 2007)</a>
</h5>
@@ -736,7 +780,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h24"></a>
+<a name="math_toolkit.history1.h25"></a>
<span class="phrase"><a name="math_toolkit.history1.milestone_3_first_review_candida"></a></span><a class="link" href="history1.html#math_toolkit.history1.milestone_3_first_review_candida">Milestone
3: First Review Candidate (31st Dec 2006)</a>
</h5>
@@ -764,7 +808,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h25"></a>
+<a name="math_toolkit.history1.h26"></a>
<span class="phrase"><a name="math_toolkit.history1.milestone_2_released_september_1"></a></span><a class="link" href="history1.html#math_toolkit.history1.milestone_2_released_september_1">Milestone
2: Released September 10th 2006</a>
</h5>
@@ -800,7 +844,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history1.h26"></a>
+<a name="math_toolkit.history1.h27"></a>
<span class="phrase"><a name="math_toolkit.history1.milestone_1_released_march_31st_"></a></span><a class="link" href="history1.html#math_toolkit.history1.milestone_1_released_march_31st_">Milestone
1: Released March 31st 2006</a>
</h5>
diff --git a/libs/math/doc/html/math_toolkit/history2.html b/libs/math/doc/html/math_toolkit/history2.html
index db207aadb..f8d21af44 100644
--- a/libs/math/doc/html/math_toolkit/history2.html
+++ b/libs/math/doc/html/math_toolkit/history2.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>History and What's New</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../status.html" title="Chapter&#160;17.&#160;Library Status">
<link rel="prev" href="../status.html" title="Chapter&#160;17.&#160;Library Status">
<link rel="next" href="issues.html" title="Known Issues, and TODO List">
@@ -34,6 +34,50 @@
</p>
<h5>
<a name="math_toolkit.history2.h0"></a>
+ <span class="phrase"><a name="math_toolkit.history2.math_2_2_0_boost_1_58_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_2_0_boost_1_58_0">Math-2.2.0
+ (boost-1.58.0)</a>
+ </h5>
+<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
+<li class="listitem">
+ Added two new special functions - <a class="link" href="sf_gamma/trigamma.html" title="Trigamma">trigamma</a>
+ and <a class="link" href="sf_gamma/polygamma.html" title="Polygamma">polygamma</a>.
+ </li>
+<li class="listitem">
+ Fixed namespace scope constants so they are constexpr on conforming compilers,
+ see https://svn.boost.org/trac/boost/ticket/10901.
+ </li>
+<li class="listitem">
+ Fixed various cases of spurious under/overflow in the incomplete beta and
+ gamma functions, plus the elliptic integrals, with thanks to Rocco Romeo.
+ </li>
+<li class="listitem">
+ Fix 3-arg <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a>
+ and <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_q</a> functions
+ to not call the policy based overload if the final argument is not actually
+ a policy.
+ </li>
+<li class="listitem">
+ Cleaned up some dead code in the incomplete beta function, see <a href="https://svn.boost.org/trac/boost/ticket/10985" target="_top">#10985</a>.
+ </li>
+<li class="listitem">
+ Fixed extreme-value pdf for large valued inputs, see <a href="https://svn.boost.org/trac/boost/ticket/10938" target="_top">#10938</a>.
+ </li>
+<li class="listitem">
+ Large update to the Elliptic integral code to use Carlson's latest algorithms
+ - these should be more stable, more accurate and slightly faster than before.
+ Also added support for Carlson's RG integral.
+ </li>
+<li class="listitem">
+ Added <a class="link" href="ellint/ellint_d.html" title="Elliptic Integral D - Legendre Form">ellint_d</a>, <a class="link" href="ellint/jacobi_zeta.html" title="Jacobi Zeta Function">jacobi_zeta</a> and <a class="link" href="ellint/heuman_lambda.html" title="Heuman Lambda Function">heuman_lambda</a> elliptic
+ integrals.
+ </li>
+<li class="listitem">
+ Switched documentation to use SVG rather than PNG graphs and equations
+ - browsers seem to have finally caught up!
+ </li>
+</ul></div>
+<h5>
+<a name="math_toolkit.history2.h1"></a>
<span class="phrase"><a name="math_toolkit.history2.math_2_1_0_boost_1_57_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_1_0_boost_1_57_0">Math-2.1.0
(boost-1.57.0)</a>
</h5>
@@ -59,7 +103,7 @@
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h1"></a>
+<a name="math_toolkit.history2.h2"></a>
<span class="phrase"><a name="math_toolkit.history2.math_2_0_0_boost_1_56_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_0_0_boost_1_56_0">Math-2.0.0
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</h5>
@@ -110,7 +154,7 @@
</li>
</ul></div>
<h5>
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+<a name="math_toolkit.history2.h3"></a>
<span class="phrase"><a name="math_toolkit.history2.math_1_9_1"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_1_9_1">Math-1.9.1</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -125,7 +169,7 @@
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h3"></a>
+<a name="math_toolkit.history2.h4"></a>
<span class="phrase"><a name="math_toolkit.history2.math_1_9_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_1_9_0">Math-1.9.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -192,7 +236,7 @@
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h4"></a>
+<a name="math_toolkit.history2.h5"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_55"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_55">Boost-1.55</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -248,7 +292,7 @@
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h5"></a>
+<a name="math_toolkit.history2.h6"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_54"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_54">Boost-1.54</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -302,7 +346,7 @@
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h6"></a>
+<a name="math_toolkit.history2.h7"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_53"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_53">Boost-1.53</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -337,7 +381,7 @@
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h7"></a>
+<a name="math_toolkit.history2.h8"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_52"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_52">Boost-1.52</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -384,14 +428,14 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h8"></a>
+<a name="math_toolkit.history2.h9"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_51"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_51">Boost-1.51</a>
</h5>
<p>
See Boost-1.52 - some items were added but not listed in time for the release.
</p>
<h5>
-<a name="math_toolkit.history2.h9"></a>
+<a name="math_toolkit.history2.h10"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_50"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_50">Boost-1.50</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -428,7 +472,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h10"></a>
+<a name="math_toolkit.history2.h11"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_49"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_49">Boost-1.49</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -472,7 +516,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h11"></a>
+<a name="math_toolkit.history2.h12"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_48"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_48">Boost-1.48</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -523,7 +567,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h12"></a>
+<a name="math_toolkit.history2.h13"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_47"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_47">Boost-1.47</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -540,7 +584,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h13"></a>
+<a name="math_toolkit.history2.h14"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_46_1"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_46_1">Boost-1.46.1</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
@@ -548,7 +592,7 @@ by switching to use the Students t distribution (or Normal distribution
<a href="https://svn.boost.org/trac/boost/ticket/5095" target="_top">#5113</a>.
</li></ul></div>
<h5>
-<a name="math_toolkit.history2.h14"></a>
+<a name="math_toolkit.history2.h15"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_46_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_46_0">Boost-1.46.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -563,7 +607,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h15"></a>
+<a name="math_toolkit.history2.h16"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_45_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_45_0">Boost-1.45.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -580,7 +624,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h16"></a>
+<a name="math_toolkit.history2.h17"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_44_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_44_0">Boost-1.44.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -594,7 +638,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h17"></a>
+<a name="math_toolkit.history2.h18"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_41_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_41_0">Boost-1.41.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
@@ -602,7 +646,7 @@ by switching to use the Students t distribution (or Normal distribution
its inverse.
</li></ul></div>
<h5>
-<a name="math_toolkit.history2.h18"></a>
+<a name="math_toolkit.history2.h19"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_40_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_40_0">Boost-1.40.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -638,7 +682,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h19"></a>
+<a name="math_toolkit.history2.h20"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_38_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_38_0">Boost-1.38.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -650,14 +694,14 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h20"></a>
+<a name="math_toolkit.history2.h21"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_37_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_37_0">Boost-1.37.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
Improved accuracy and testing of the inverse hypergeometric functions.
</li></ul></div>
<h5>
-<a name="math_toolkit.history2.h21"></a>
+<a name="math_toolkit.history2.h22"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_36_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_36_0">Boost-1.36.0</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
@@ -690,7 +734,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h22"></a>
+<a name="math_toolkit.history2.h23"></a>
<span class="phrase"><a name="math_toolkit.history2.boost_1_35_0_post_review_first_o"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_35_0_post_review_first_o">Boost-1.35.0:
Post Review First Official Release</a>
</h5>
@@ -722,7 +766,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h23"></a>
+<a name="math_toolkit.history2.h24"></a>
<span class="phrase"><a name="math_toolkit.history2.milestone_4_second_review_candid"></a></span><a class="link" href="history2.html#math_toolkit.history2.milestone_4_second_review_candid">Milestone
4: Second Review Candidate (1st March 2007)</a>
</h5>
@@ -736,7 +780,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h24"></a>
+<a name="math_toolkit.history2.h25"></a>
<span class="phrase"><a name="math_toolkit.history2.milestone_3_first_review_candida"></a></span><a class="link" href="history2.html#math_toolkit.history2.milestone_3_first_review_candida">Milestone
3: First Review Candidate (31st Dec 2006)</a>
</h5>
@@ -764,7 +808,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h25"></a>
+<a name="math_toolkit.history2.h26"></a>
<span class="phrase"><a name="math_toolkit.history2.milestone_2_released_september_1"></a></span><a class="link" href="history2.html#math_toolkit.history2.milestone_2_released_september_1">Milestone
2: Released September 10th 2006</a>
</h5>
@@ -800,7 +844,7 @@ by switching to use the Students t distribution (or Normal distribution
</li>
</ul></div>
<h5>
-<a name="math_toolkit.history2.h26"></a>
+<a name="math_toolkit.history2.h27"></a>
<span class="phrase"><a name="math_toolkit.history2.milestone_1_released_march_31st_"></a></span><a class="link" href="history2.html#math_toolkit.history2.milestone_1_released_march_31st_">Milestone
1: Released March 31st 2006</a>
</h5>
diff --git a/libs/math/doc/html/math_toolkit/internals1.html b/libs/math/doc/html/math_toolkit/internals1.html
index 78976444e..8df5c7048 100644
--- a/libs/math/doc/html/math_toolkit/internals1.html
+++ b/libs/math/doc/html/math_toolkit/internals1.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Utilities &amp; internals</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../toolkit.html" title="Chapter&#160;12.&#160;Internals (Series, Rationals and Continued Fractions, Root Finding, Function Minimization, Testing and Development Tools)">
<link rel="prev" href="internals_overview.html" title="Overview">
<link rel="next" href="internals1/series_evaluation.html" title="Series Evaluation">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.internals1"></a><a class="link" href="internals1.html" title="Utilities &amp; internals">Utilities &amp; internals</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="internals1/series_evaluation.html">Series Evaluation</a></span></dt>
<dt><span class="section"><a href="internals1/cf.html">Continued Fraction Evaluation</a></span></dt>
<dt><span class="section"><a href="internals1/rational.html">Polynomial and Rational
diff --git a/libs/math/doc/html/math_toolkit/internals1/cf.html b/libs/math/doc/html/math_toolkit/internals1/cf.html
index 524ca673d..fdbfd1084 100644
--- a/libs/math/doc/html/math_toolkit/internals1/cf.html
+++ b/libs/math/doc/html/math_toolkit/internals1/cf.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Continued Fraction Evaluation</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../internals1.html" title="Utilities &amp; internals">
<link rel="prev" href="series_evaluation.html" title="Series Evaluation">
<link rel="next" href="rational.html" title="Polynomial and Rational Function Evaluation">
@@ -82,13 +82,13 @@
argument. The functions with an "_a" suffix evaluate the fraction:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/fraction2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/fraction2.svg"></span>
</p>
<p>
and those with a "_b" suffix evaluate the fraction:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/fraction1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/fraction1.svg"></span>
</p>
<p>
This latter form is somewhat more natural in that it corresponds with the
@@ -190,7 +190,7 @@
of all:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/fraction3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/fraction3.svg"></span>
</p>
<p>
We begin by defining a generator function:
@@ -219,7 +219,7 @@
fractions, for example the tan function is defined by:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/fraction4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/fraction4.svg"></span>
</p>
<p>
So its generator object would look like:
diff --git a/libs/math/doc/html/math_toolkit/internals1/minima.html b/libs/math/doc/html/math_toolkit/internals1/minima.html
index 8929c04c3..b6cd3f7d8 100644
--- a/libs/math/doc/html/math_toolkit/internals1/minima.html
+++ b/libs/math/doc/html/math_toolkit/internals1/minima.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Locating Function Minima: Brent's algorithm</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../internals1.html" title="Utilities &amp; internals">
<link rel="prev" href="roots2.html" title="Root Finding Without Derivatives: Bisection, Bracket and TOMS748">
<link rel="next" href="tuples.html" title="Tuples">
diff --git a/libs/math/doc/html/math_toolkit/internals1/rational.html b/libs/math/doc/html/math_toolkit/internals1/rational.html
index 866626ef3..0643955b3 100644
--- a/libs/math/doc/html/math_toolkit/internals1/rational.html
+++ b/libs/math/doc/html/math_toolkit/internals1/rational.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Polynomial and Rational Function Evaluation</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../internals1.html" title="Utilities &amp; internals">
<link rel="prev" href="cf.html" title="Continued Fraction Evaluation">
<link rel="next" href="roots.html" title="Root Finding With Derivatives: Newton-Raphson, Halley &amp; Schroeder">
diff --git a/libs/math/doc/html/math_toolkit/internals1/roots.html b/libs/math/doc/html/math_toolkit/internals1/roots.html
index a3c66cae3..00efbc180 100644
--- a/libs/math/doc/html/math_toolkit/internals1/roots.html
+++ b/libs/math/doc/html/math_toolkit/internals1/roots.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Root Finding With Derivatives: Newton-Raphson, Halley &amp; Schroeder</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../internals1.html" title="Utilities &amp; internals">
<link rel="prev" href="rational.html" title="Polynomial and Rational Function Evaluation">
<link rel="next" href="roots2.html" title="Root Finding Without Derivatives: Bisection, Bracket and TOMS748">
@@ -211,7 +211,7 @@
Given an initial guess x0 the subsequent values are computed using:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/roots1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/roots1.svg"></span>
</p>
<p>
Out of bounds steps revert to bisection of the current bounds.
@@ -228,7 +228,7 @@
Given an initial guess x0 the subsequent values are computed using:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/roots2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/roots2.svg"></span>
</p>
<p>
Over-compensation by the second derivative (one which would proceed in the
@@ -249,7 +249,7 @@
Given an initial guess x0 the subsequent values are computed using:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/roots3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/roots3.svg"></span>
</p>
<p>
Over-compensation by the second derivative (one which would proceed in the
@@ -272,7 +272,7 @@
want to solve along with its derivatives are:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/roots4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/roots4.svg"></span>
</p>
<p>
To begin with lets solve the problem using Newton-Raphson iterations, we'll
diff --git a/libs/math/doc/html/math_toolkit/internals1/roots2.html b/libs/math/doc/html/math_toolkit/internals1/roots2.html
index ff5f33d40..b07b6bf45 100644
--- a/libs/math/doc/html/math_toolkit/internals1/roots2.html
+++ b/libs/math/doc/html/math_toolkit/internals1/roots2.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Root Finding Without Derivatives: Bisection, Bracket and TOMS748</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../internals1.html" title="Utilities &amp; internals">
<link rel="prev" href="roots.html" title="Root Finding With Derivatives: Newton-Raphson, Halley &amp; Schroeder">
<link rel="next" href="minima.html" title="Locating Function Minima: Brent's algorithm">
diff --git a/libs/math/doc/html/math_toolkit/internals1/series_evaluation.html b/libs/math/doc/html/math_toolkit/internals1/series_evaluation.html
index ebb01eba1..0f9c251aa 100644
--- a/libs/math/doc/html/math_toolkit/internals1/series_evaluation.html
+++ b/libs/math/doc/html/math_toolkit/internals1/series_evaluation.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Series Evaluation</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../internals1.html" title="Utilities &amp; internals">
<link rel="prev" href="../internals1.html" title="Utilities &amp; internals">
<link rel="next" href="cf.html" title="Continued Fraction Evaluation">
@@ -129,7 +129,7 @@
infinite series,
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/log1pseries.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/log1pseries.svg"></span>
</p>
<p>
We begin by writing a small function object to return successive terms of
diff --git a/libs/math/doc/html/math_toolkit/internals1/tuples.html b/libs/math/doc/html/math_toolkit/internals1/tuples.html
index 106fcca45..89465d210 100644
--- a/libs/math/doc/html/math_toolkit/internals1/tuples.html
+++ b/libs/math/doc/html/math_toolkit/internals1/tuples.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Tuples</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../internals1.html" title="Utilities &amp; internals">
<link rel="prev" href="minima.html" title="Locating Function Minima: Brent's algorithm">
<link rel="next" href="../internals2.html" title="Testing and Development">
diff --git a/libs/math/doc/html/math_toolkit/internals2.html b/libs/math/doc/html/math_toolkit/internals2.html
index bb087aeab..499889e16 100644
--- a/libs/math/doc/html/math_toolkit/internals2.html
+++ b/libs/math/doc/html/math_toolkit/internals2.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Testing and Development</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../toolkit.html" title="Chapter&#160;12.&#160;Internals (Series, Rationals and Continued Fractions, Root Finding, Function Minimization, Testing and Development Tools)">
<link rel="prev" href="internals1/tuples.html" title="Tuples">
<link rel="next" href="internals2/polynomials.html" title="Polynomials">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.internals2"></a><a class="link" href="internals2.html" title="Testing and Development">Testing and Development</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="internals2/polynomials.html">Polynomials</a></span></dt>
<dt><span class="section"><a href="internals2/minimax.html">Minimax Approximations
and the Remez Algorithm</a></span></dt>
diff --git a/libs/math/doc/html/math_toolkit/internals2/error_test.html b/libs/math/doc/html/math_toolkit/internals2/error_test.html
index 864c1de2d..c5cd8a329 100644
--- a/libs/math/doc/html/math_toolkit/internals2/error_test.html
+++ b/libs/math/doc/html/math_toolkit/internals2/error_test.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Relative Error and Testing</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../internals2.html" title="Testing and Development">
<link rel="prev" href="minimax.html" title="Minimax Approximations and the Remez Algorithm">
<link rel="next" href="test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">
@@ -63,7 +63,7 @@
using the usual formula:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/error1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/error1.svg"></span>
</p>
<p>
In addition the value returned is zero if:
diff --git a/libs/math/doc/html/math_toolkit/internals2/minimax.html b/libs/math/doc/html/math_toolkit/internals2/minimax.html
index 7d8bc6157..be9319cc3 100644
--- a/libs/math/doc/html/math_toolkit/internals2/minimax.html
+++ b/libs/math/doc/html/math_toolkit/internals2/minimax.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Minimax Approximations and the Remez Algorithm</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../internals2.html" title="Testing and Development">
<link rel="prev" href="polynomials.html" title="Polynomials">
<link rel="next" href="error_test.html" title="Relative Error and Testing">
diff --git a/libs/math/doc/html/math_toolkit/internals2/polynomials.html b/libs/math/doc/html/math_toolkit/internals2/polynomials.html
index 81dd34c3d..62b3a9610 100644
--- a/libs/math/doc/html/math_toolkit/internals2/polynomials.html
+++ b/libs/math/doc/html/math_toolkit/internals2/polynomials.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Polynomials</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../internals2.html" title="Testing and Development">
<link rel="prev" href="../internals2.html" title="Testing and Development">
<link rel="next" href="minimax.html" title="Minimax Approximations and the Remez Algorithm">
diff --git a/libs/math/doc/html/math_toolkit/internals2/test_data.html b/libs/math/doc/html/math_toolkit/internals2/test_data.html
index 89530be15..649b6d743 100644
--- a/libs/math/doc/html/math_toolkit/internals2/test_data.html
+++ b/libs/math/doc/html/math_toolkit/internals2/test_data.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Graphing, Profiling, and Generating Test Data for Special Functions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../internals2.html" title="Testing and Development">
<link rel="prev" href="error_test.html" title="Relative Error and Testing">
<link rel="next" href="../../using_udt.html" title="Chapter&#160;13.&#160;Use with User-Defined Floating-Point Types - Boost.Multiprecision and others">
@@ -221,7 +221,7 @@
Which, when plotted, results in:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/lgamma.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/lgamma.svg" align="middle"></span>
</p>
<h6>
<a name="math_toolkit.internals2.test_data.h3"></a>
diff --git a/libs/math/doc/html/math_toolkit/internals_overview.html b/libs/math/doc/html/math_toolkit/internals_overview.html
index a302e508e..23d1ad839 100644
--- a/libs/math/doc/html/math_toolkit/internals_overview.html
+++ b/libs/math/doc/html/math_toolkit/internals_overview.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Overview</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../toolkit.html" title="Chapter&#160;12.&#160;Internals (Series, Rationals and Continued Fractions, Root Finding, Function Minimization, Testing and Development Tools)">
<link rel="prev" href="../toolkit.html" title="Chapter&#160;12.&#160;Internals (Series, Rationals and Continued Fractions, Root Finding, Function Minimization, Testing and Development Tools)">
<link rel="next" href="internals1.html" title="Utilities &amp; internals">
diff --git a/libs/math/doc/html/math_toolkit/interp.html b/libs/math/doc/html/math_toolkit/interp.html
index 865343dc9..f443b0e83 100644
--- a/libs/math/doc/html/math_toolkit/interp.html
+++ b/libs/math/doc/html/math_toolkit/interp.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Interpreting these Results</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../perf.html" title="Chapter&#160;15.&#160;Performance">
<link rel="prev" href="perf_over2.html" title="Performance Overview">
<link rel="next" href="getting_best.html" title="Getting the Best Performance from this Library">
diff --git a/libs/math/doc/html/math_toolkit/intro_pol_overview.html b/libs/math/doc/html/math_toolkit/intro_pol_overview.html
index 66df55bb7..0561a081e 100644
--- a/libs/math/doc/html/math_toolkit/intro_pol_overview.html
+++ b/libs/math/doc/html/math_toolkit/intro_pol_overview.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Policies</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="config_macros.html" title="Configuration Macros">
<link rel="next" href="threads.html" title="Thread Safety">
diff --git a/libs/math/doc/html/math_toolkit/introduction.html b/libs/math/doc/html/math_toolkit/introduction.html
index 875a1f383..34d56c753 100644
--- a/libs/math/doc/html/math_toolkit/introduction.html
+++ b/libs/math/doc/html/math_toolkit/introduction.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Introduction</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../gcd_lcm.html" title="Chapter&#160;11.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)">
<link rel="prev" href="../gcd_lcm.html" title="Chapter&#160;11.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)">
<link rel="next" href="synopsis.html" title="Synopsis">
diff --git a/libs/math/doc/html/math_toolkit/inv_hyper.html b/libs/math/doc/html/math_toolkit/inv_hyper.html
index df77a4265..306a93dda 100644
--- a/libs/math/doc/html/math_toolkit/inv_hyper.html
+++ b/libs/math/doc/html/math_toolkit/inv_hyper.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Inverse Hyperbolic Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
<link rel="prev" href="sinc/sinhc_pi.html" title="sinhc_pi">
<link rel="next" href="inv_hyper/inv_hyper_over.html" title="Inverse Hyperbolic Functions Overview">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.inv_hyper"></a><a class="link" href="inv_hyper.html" title="Inverse Hyperbolic Functions">Inverse Hyperbolic Functions</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="inv_hyper/inv_hyper_over.html">Inverse Hyperbolic
Functions Overview</a></span></dt>
<dt><span class="section"><a href="inv_hyper/acosh.html">acosh</a></span></dt>
diff --git a/libs/math/doc/html/math_toolkit/inv_hyper/acosh.html b/libs/math/doc/html/math_toolkit/inv_hyper/acosh.html
index 07dd0a0ab..a4838e2f6 100644
--- a/libs/math/doc/html/math_toolkit/inv_hyper/acosh.html
+++ b/libs/math/doc/html/math_toolkit/inv_hyper/acosh.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>acosh</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../inv_hyper.html" title="Inverse Hyperbolic Functions">
<link rel="prev" href="inv_hyper_over.html" title="Inverse Hyperbolic Functions Overview">
<link rel="next" href="asinh.html" title="asinh">
@@ -54,7 +54,7 @@
documentation for more details</a>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/acosh.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/acosh.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.inv_hyper.acosh.h0"></a>
@@ -73,7 +73,7 @@
formula:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/acosh1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/acosh1.svg"></span>
</p>
<p>
along with a selection of sanity check values computed using functions.wolfram.com
@@ -87,27 +87,27 @@
For sufficiently large x, we can use the <a href="http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/06/01/0001/" target="_top">approximation</a>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/acosh2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/acosh2.svg"></span>
</p>
<p>
For x sufficiently close to 1 we can use the <a href="http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/" target="_top">approximation</a>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/acosh4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/acosh4.svg"></span>
</p>
<p>
Otherwise for x close to 1 we can use the following rearrangement of the
primary definition to preserve accuracy:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/acosh3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/acosh3.svg"></span>
</p>
<p>
Otherwise the <a href="http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/" target="_top">primary
definition</a> is used:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/acosh1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/acosh1.svg"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/inv_hyper/asinh.html b/libs/math/doc/html/math_toolkit/inv_hyper/asinh.html
index be777c85b..a2e2d035d 100644
--- a/libs/math/doc/html/math_toolkit/inv_hyper/asinh.html
+++ b/libs/math/doc/html/math_toolkit/inv_hyper/asinh.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>asinh</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../inv_hyper.html" title="Inverse Hyperbolic Functions">
<link rel="prev" href="acosh.html" title="acosh">
<link rel="next" href="atanh.html" title="atanh">
@@ -43,7 +43,7 @@
type calculation rules</em></span></a>: the return type is <code class="computeroutput"><span class="keyword">double</span></code> when T is an integer type, and T otherwise.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/asinh.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/asinh.svg" align="middle"></span>
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
@@ -68,7 +68,7 @@
formula:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/asinh1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/asinh1.svg"></span>
</p>
<p>
along with a selection of sanity check values computed using functions.wolfram.com
@@ -82,27 +82,27 @@
For sufficiently large x we can use the <a href="http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/06/01/0001/" target="_top">approximation</a>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/asinh2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/asinh2.svg"></span>
</p>
<p>
While for very small x we can use the <a href="http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/03/01/0001/" target="_top">approximation</a>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/asinh3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/asinh3.svg"></span>
</p>
<p>
For 0.5 &gt; x &gt; &#949; the following rearrangement of the primary definition
is used:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/asinh4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/asinh4.svg"></span>
</p>
<p>
Otherwise evalution is via the <a href="http://functions.wolfram.com/ElementaryFunctions/ArcSinh/02/" target="_top">primary
definition</a>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/asinh4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/asinh4.svg"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/inv_hyper/atanh.html b/libs/math/doc/html/math_toolkit/inv_hyper/atanh.html
index 46bc5fe5b..c1532d7c6 100644
--- a/libs/math/doc/html/math_toolkit/inv_hyper/atanh.html
+++ b/libs/math/doc/html/math_toolkit/inv_hyper/atanh.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>atanh</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../inv_hyper.html" title="Inverse Hyperbolic Functions">
<link rel="prev" href="asinh.html" title="asinh">
<link rel="next" href="../owens_t.html" title="Owen's T function">
@@ -63,7 +63,7 @@ denoting numeric_limits&lt;T&gt;::epsilon().
type calculation rules</em></span></a>: the return type is <code class="computeroutput"><span class="keyword">double</span></code> when T is an integer type, and T otherwise.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/atanh.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/atanh.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.inv_hyper.atanh.h0"></a>
@@ -82,7 +82,7 @@ denoting numeric_limits&lt;T&gt;::epsilon().
formula:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/atanh1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/atanh1.svg"></span>
</p>
<p>
along with a selection of sanity check values computed using functions.wolfram.com
@@ -96,20 +96,20 @@ denoting numeric_limits&lt;T&gt;::epsilon().
For sufficiently small x we can use the <a href="http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/" target="_top">approximation</a>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/atanh2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/atanh2.svg"></span>
</p>
<p>
Otherwise the <a href="http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/" target="_top">primary
definition</a>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/atanh1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/atanh1.svg"></span>
</p>
<p>
or its equivalent form:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/atanh3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/atanh3.svg"></span>
</p>
<p>
is used.
diff --git a/libs/math/doc/html/math_toolkit/inv_hyper/inv_hyper_over.html b/libs/math/doc/html/math_toolkit/inv_hyper/inv_hyper_over.html
index cac9b7594..725cf2167 100644
--- a/libs/math/doc/html/math_toolkit/inv_hyper/inv_hyper_over.html
+++ b/libs/math/doc/html/math_toolkit/inv_hyper/inv_hyper_over.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Inverse Hyperbolic Functions Overview</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../inv_hyper.html" title="Inverse Hyperbolic Functions">
<link rel="prev" href="../inv_hyper.html" title="Inverse Hyperbolic Functions">
<link rel="next" href="acosh.html" title="acosh">
@@ -29,7 +29,7 @@
</h3></div></div></div>
<p>
The exponential funtion is defined, for all objects for which this makes
- sense, as the power series <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb1.png"></span>,
+ sense, as the power series <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb1.svg"></span>,
with <span class="emphasis"><em><code class="literal">n! = 1x2x3x4x5...xn</code></em></span> (and <span class="emphasis"><em><code class="literal">0!
= 1</code></em></span> by definition) being the factorial of <span class="emphasis"><em><code class="literal">n</code></em></span>.
In particular, the exponential function is well defined for real numbers,
@@ -53,13 +53,13 @@
(for reals, complex, quaternions and octonions) as:
</p>
<p>
- Hyperbolic cosine: <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb5.png"></span>
+ Hyperbolic cosine: <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb5.svg"></span>
</p>
<p>
- Hyperbolic sine: <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb6.png"></span>
+ Hyperbolic sine: <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb6.svg"></span>
</p>
<p>
- Hyperbolic tangent: <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb7.png"></span>
+ Hyperbolic tangent: <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb7.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="emphasis"><em><span class="bold"><strong>Trigonometric functions on R (cos: purple;
@@ -86,15 +86,15 @@
</p>
<p>
The inverse of the hyperbolic tangent is called the Argument hyperbolic tangent,
- and can be computed as <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb15.png"></span>.
+ and can be computed as <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb15.svg"></span>.
</p>
<p>
The inverse of the hyperbolic sine is called the Argument hyperbolic sine,
- and can be computed (for <code class="literal">[-1;-1+&#949;[</code>) as <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb17.png"></span>.
+ and can be computed (for <code class="literal">[-1;-1+&#949;[</code>) as <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb17.svg"></span>.
</p>
<p>
The inverse of the hyperbolic cosine is called the Argument hyperbolic cosine,
- and can be computed as <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb18.png"></span>.
+ and can be computed as <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb18.svg"></span>.
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/issues.html b/libs/math/doc/html/math_toolkit/issues.html
index 37185f1b9..2534a18fe 100644
--- a/libs/math/doc/html/math_toolkit/issues.html
+++ b/libs/math/doc/html/math_toolkit/issues.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Known Issues, and TODO List</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../status.html" title="Chapter&#160;17.&#160;Library Status">
<link rel="prev" href="history2.html" title="History and What's New">
<link rel="next" href="credits.html" title="Credits and Acknowledgements">
@@ -97,13 +97,6 @@
</h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
- Carlson's algorithms are essentially unchanged from Xiaogang Zhang's Google
- Summer of Code student project, and are based on Carlson's original papers.
- However, Carlson has revised his algorithms since then (refer to the references
- in the elliptic integral docs for a list), to improve performance and accuracy,
- we may be able to take advantage of these improvements too (Low Priority).
- </li>
-<li class="listitem">
[para Carlson's algorithms (mainly R<sub>J</sub>) are somewhat prone to internal overflow/underflow
when the arguments are very large or small. The homogeneity relations:]
[para R<sub>F</sub>(ka, kb, kc) = k<sup>-1/2</sup> R<sub>F</sub>(a, b, c)] [para and] [para R<sub>J</sub>(ka, kb, kc,
@@ -111,31 +104,14 @@
provided the problem domains can be accurately identified. (Medium Priority).]
</li>
<li class="listitem">
- Carlson's R<sub>C</sub> can be reduced to elementary funtions (asin and log), would
- it be more efficient evaluated this way, rather than by Carlson's algorithms?
- (Low Priority).
- </li>
-<li class="listitem">
- Should we add an implementation of Carlson's R<sub>G</sub>? It's not required for
- the Legendre form integrals, but some people may find it useful (Low Priority).
- </li>
-<li class="listitem">
- There are a several other integrals: D(&#966;, k), Z(&#946;, k), &#923;<sub>0</sub>(&#946;, k) and Bulirsch's
- <span class="emphasis"><em>el</em></span> functions that could be implemented using Carlson's
- integrals (Low Priority).
+ There are a several other integrals: Bulirsch's <span class="emphasis"><em>el</em></span>
+ functions that could be implemented using Carlson's integrals (Low Priority).
</li>
<li class="listitem">
The integrals K(k) and E(k) could be implemented using rational approximations
(both for efficiency and accuracy), assuming we can find them. (Medium
Priority).
</li>
-<li class="listitem">
- There is a sub-domain of <a class="link" href="ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">ellint_3</a>
- that is unimplemented (see the docs for details), currently it's not clear
- how to solve this issue, or if it's ever likely to be an real problem in
- practice - especially as most other implementations don't support this
- domain either (Medium Priority).
- </li>
</ul></div>
<h5>
<a name="math_toolkit.issues.h6"></a>
@@ -177,6 +153,9 @@
Requests</a>
</h5>
<p>
+ We have a request for the Lambert W function, see <a href="https://svn.boost.org/trac/boost/ticket/11027" target="_top">#11027</a>.
+ </p>
+<p>
The following table lists distributions that are found in other packages but
which are not yet present here, the more frequently the distribution is found,
the higher the priority for implementing it:
diff --git a/libs/math/doc/html/math_toolkit/jacobi.html b/libs/math/doc/html/math_toolkit/jacobi.html
index d593262c3..1bd7b82b6 100644
--- a/libs/math/doc/html/math_toolkit/jacobi.html
+++ b/libs/math/doc/html/math_toolkit/jacobi.html
@@ -3,10 +3,10 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
-<link rel="prev" href="ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">
+<link rel="prev" href="ellint/heuman_lambda.html" title="Heuman Lambda Function">
<link rel="next" href="jacobi/jac_over.html" title="Overvew of the Jacobi Elliptic Functions">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@@ -20,13 +20,13 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="ellint/ellint_3.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="jacobi/jac_over.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
+<a accesskey="p" href="ellint/heuman_lambda.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="jacobi/jac_over.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.jacobi"></a><a class="link" href="jacobi.html" title="Jacobi Elliptic Functions">Jacobi Elliptic Functions</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="jacobi/jac_over.html">Overvew of the Jacobi Elliptic
Functions</a></span></dt>
<dt><span class="section"><a href="jacobi/jacobi_elliptic.html">Jacobi Elliptic
@@ -70,7 +70,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="ellint/ellint_3.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="jacobi/jac_over.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
+<a accesskey="p" href="ellint/heuman_lambda.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="jacobi/jac_over.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>
diff --git a/libs/math/doc/html/math_toolkit/jacobi/jac_over.html b/libs/math/doc/html/math_toolkit/jacobi/jac_over.html
index 09f973067..69caa1f8c 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jac_over.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jac_over.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Overvew of the Jacobi Elliptic Functions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="next" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">
@@ -31,7 +31,7 @@
There are twelve Jacobi Elliptic functions, of which the three copolar functions
<span class="emphasis"><em>sn</em></span>, <span class="emphasis"><em>cn</em></span> and <span class="emphasis"><em>dn</em></span>
are the most important as the other nine can be computed from these three
- <a href="#ftn.math_toolkit.jacobi.jac_over.f0" class="footnote" name="math_toolkit.jacobi.jac_over.f0"><sup class="footnote">[2]</sup></a> <a href="#ftn.math_toolkit.jacobi.jac_over.f1" class="footnote" name="math_toolkit.jacobi.jac_over.f1"><sup class="footnote">[3]</sup></a> <a href="#ftn.math_toolkit.jacobi.jac_over.f2" class="footnote" name="math_toolkit.jacobi.jac_over.f2"><sup class="footnote">[4]</sup></a>.
+ <a href="#ftn.math_toolkit.jacobi.jac_over.f0" class="footnote"><sup class="footnote"><a name="math_toolkit.jacobi.jac_over.f0"></a>[2]</sup></a> <a href="#ftn.math_toolkit.jacobi.jac_over.f1" class="footnote"><sup class="footnote"><a name="math_toolkit.jacobi.jac_over.f1"></a>[3]</sup></a> <a href="#ftn.math_toolkit.jacobi.jac_over.f2" class="footnote"><sup class="footnote"><a name="math_toolkit.jacobi.jac_over.f2"></a>[4]</sup></a>.
</p>
<p>
These functions each take two arguments: a parameter, and a variable as described
@@ -88,7 +88,7 @@
to use <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>.
</p>
<div class="footnotes">
-<br><hr style="width:100; text-align:left;margin-left: 0">
+<br><hr style="width:100; align:left;">
<div id="ftn.math_toolkit.jacobi.jac_over.f0" class="footnote"><p><a href="#math_toolkit.jacobi.jac_over.f0" class="para"><sup class="para">[2] </sup></a>
<a href="http://en.wikipedia.org/wiki/Jacobi_elliptic_functions" target="_top">Wikipedia:
Jacobi elliptic functions</a>
diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_cd.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_cd.html
index 9a10b1c7a..3aad57895 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_cd.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_cd.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function cd</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">
<link rel="next" href="jacobi_cn.html" title="Jacobi Elliptic Function cn">
@@ -64,7 +64,7 @@
<span class="emphasis"><em>cd(u, k) = cn(u, k) / dn(u, k)</em></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/jacobi_cd.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/jacobi_cd.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_cn.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_cn.html
index f0910ef91..ac4b8158f 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_cn.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_cn.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function cn</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_cd.html" title="Jacobi Elliptic Function cd">
<link rel="next" href="jacobi_cs.html" title="Jacobi Elliptic Function cs">
@@ -60,7 +60,7 @@
This function is a trivial wrapper around <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/jacobi_cn.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/jacobi_cn.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_cs.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_cs.html
index d2a9812b9..e4bd827c6 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_cs.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_cs.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function cs</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_cn.html" title="Jacobi Elliptic Function cn">
<link rel="next" href="jacobi_dc.html" title="Jacobi Elliptic Function dc">
@@ -64,7 +64,7 @@
<span class="emphasis"><em>cs(u, k) = cn(u, k) / sn(u, k)</em></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/jacobi_cs.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/jacobi_cs.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_dc.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_dc.html
index 28cfe6626..41e1646e9 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_dc.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_dc.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function dc</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_cs.html" title="Jacobi Elliptic Function cs">
<link rel="next" href="jacobi_dn.html" title="Jacobi Elliptic Function dn">
@@ -64,7 +64,7 @@
<span class="emphasis"><em>dc(u, k) = dn(u, k) / cn(u, k)</em></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/jacobi_dc.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/jacobi_dc.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_dn.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_dn.html
index 6f55ca71e..d53ceb12c 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_dn.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_dn.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function dn</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_dc.html" title="Jacobi Elliptic Function dc">
<link rel="next" href="jacobi_ds.html" title="Jacobi Elliptic Function ds">
@@ -60,7 +60,7 @@
This function is a trivial wrapper around <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/jacobi_dn.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/jacobi_dn.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_ds.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_ds.html
index a393fd4ca..311791299 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_ds.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_ds.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function ds</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_dn.html" title="Jacobi Elliptic Function dn">
<link rel="next" href="jacobi_nc.html" title="Jacobi Elliptic Function nc">
@@ -64,7 +64,7 @@
<span class="emphasis"><em>ds(u, k) = dn(u, k) / sn(u, k)</em></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/jacobi_ds.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/jacobi_ds.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_elliptic.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_elliptic.html
index a39a9b172..9caa6c77f 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_elliptic.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_elliptic.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic SN, CN and DN</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jac_over.html" title="Overvew of the Jacobi Elliptic Functions">
<link rel="next" href="jacobi_cd.html" title="Jacobi Elliptic Function cd">
@@ -59,13 +59,13 @@
The functions are defined as follows, given:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/jacobi1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/jacobi1.svg"></span>
</p>
<p>
The the angle &#966; is called the <span class="emphasis"><em>amplitude</em></span> and:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/jacobi2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/jacobi2.svg"></span>
</p>
<div class="note"><table border="0" summary="Note">
<tr>
@@ -140,13 +140,13 @@
<span class="emphasis"><em>k</em></span> tends to 1 they become hyperbolic functions:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/jacobi_sn.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/jacobi_sn.svg" align="middle"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/jacobi_cn.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/jacobi_cn.svg" align="middle"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/jacobi_dn.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/jacobi_dn.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.jacobi.jacobi_elliptic.h2"></a>
@@ -258,7 +258,7 @@
For <span class="emphasis"><em>k &gt; 1</em></span> we apply the relations:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/jacobi3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/jacobi3.svg"></span>
</p>
<p>
Then filter off the special cases:
@@ -276,7 +276,7 @@
And for <span class="emphasis"><em>k<sup>4</sup> &lt; &#949;</em></span> we have:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/jacobi4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/jacobi4.svg"></span>
</p>
<p>
Otherwise the values are calculated using the method of <a href="http://dlmf.nist.gov/22.20#SS2" target="_top">arithmetic
diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_nc.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_nc.html
index f213ed4ae..b729adae5 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_nc.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_nc.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function nc</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_ds.html" title="Jacobi Elliptic Function ds">
<link rel="next" href="jacobi_nd.html" title="Jacobi Elliptic Function nd">
@@ -64,7 +64,7 @@
<span class="emphasis"><em>nc(u, k) = 1 / cn(u, k)</em></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/jacobi_nc.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/jacobi_nc.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_nd.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_nd.html
index 2b00a44b2..446f17927 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_nd.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_nd.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function nd</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_nc.html" title="Jacobi Elliptic Function nc">
<link rel="next" href="jacobi_ns.html" title="Jacobi Elliptic Function ns">
@@ -64,7 +64,7 @@
<span class="emphasis"><em>nd(u, k) = 1 / dn(u, k)</em></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/jacobi_nd.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/jacobi_nd.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_ns.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_ns.html
index 605b4ecb5..f803dce27 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_ns.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_ns.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function ns</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_nd.html" title="Jacobi Elliptic Function nd">
<link rel="next" href="jacobi_sc.html" title="Jacobi Elliptic Function sc">
@@ -64,7 +64,7 @@
<span class="emphasis"><em>ns(u, k) = 1 / sn(u, k)</em></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/jacobi_ns.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/jacobi_ns.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_sc.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_sc.html
index b02d9a287..58f2e8456 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_sc.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_sc.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function sc</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_ns.html" title="Jacobi Elliptic Function ns">
<link rel="next" href="jacobi_sd.html" title="Jacobi Elliptic Function sd">
@@ -64,7 +64,7 @@
<span class="emphasis"><em>sc(u, k) = sn(u, k) / cn(u, k)</em></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/jacobi_sc.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/jacobi_sc.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_sd.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_sd.html
index 0b230864f..5d44b60f0 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_sd.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_sd.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function sd</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_sc.html" title="Jacobi Elliptic Function sc">
<link rel="next" href="jacobi_sn.html" title="Jacobi Elliptic Function sn">
@@ -64,7 +64,7 @@
<span class="emphasis"><em>sd(u, k) = sn(u, k) / dn(u, k)</em></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/jacobi_sd.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/jacobi_sd.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/jacobi/jacobi_sn.html b/libs/math/doc/html/math_toolkit/jacobi/jacobi_sn.html
index 49e05222c..d6cf6ddc4 100644
--- a/libs/math/doc/html/math_toolkit/jacobi/jacobi_sn.html
+++ b/libs/math/doc/html/math_toolkit/jacobi/jacobi_sn.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function sn</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_sd.html" title="Jacobi Elliptic Function sd">
<link rel="next" href="../zetas.html" title="Zeta Functions">
@@ -60,7 +60,7 @@
This function is a trivial wrapper around <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/jacobi_sn.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/jacobi_sn.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/lanczos.html b/libs/math/doc/html/math_toolkit/lanczos.html
index e178ba6f2..daa6cb855 100644
--- a/libs/math/doc/html/math_toolkit/lanczos.html
+++ b/libs/math/doc/html/math_toolkit/lanczos.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>The Lanczos Approximation</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../backgrounders.html" title="Chapter&#160;16.&#160;Backgrounders">
<link rel="prev" href="relative_error.html" title="Relative Error">
<link rel="next" href="remez.html" title="The Remez Method">
@@ -106,7 +106,7 @@
The Lanczos Approximation to the Gamma Function is given by:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/lanczos0.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/lanczos0.svg"></span>
</p>
<p>
Where S<sub>g</sub>(z) is an infinite sum, that is convergent for all z &gt; 0, and <span class="emphasis"><em>g</em></span>
@@ -114,13 +114,13 @@
in the sum which is given by:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/lanczos0a.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/lanczos0a.svg"></span>
</p>
<p>
With individual coefficients defined in closed form by:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/lanczos0b.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/lanczos0b.svg"></span>
</p>
<p>
However, evaluation of the sum in that form can lead to numerical instability
@@ -133,13 +133,13 @@
with the leading constants absorbed by the coefficients in the sum:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/lanczos1.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/lanczos1.svg"></span>
</p>
<p>
where:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/lanczos2.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/lanczos2.svg"></span>
</p>
<p>
Again parameter <span class="emphasis"><em>g</em></span> is an arbitrarily chosen constant, and
@@ -178,25 +178,25 @@
where B is an NxN matrix:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/lanczos4.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/lanczos4.svg"></span>
</p>
<p>
D is an NxN matrix:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/lanczos3.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/lanczos3.svg"></span>
</p>
<p>
C is an NxN matrix:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/lanczos5.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/lanczos5.svg"></span>
</p>
<p>
and F is an N element column vector:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/lanczos6.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/lanczos6.svg"></span>
</p>
<p>
Note than the matrices B, D and C contain all integer terms and depend only
@@ -526,7 +526,7 @@
by exp(g):
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/lanczos7.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/lanczos7.svg"></span>
</p>
<p>
This form is more convenient for calculating lgamma, but for the gamma function
diff --git a/libs/math/doc/html/math_toolkit/lcm_function_object.html b/libs/math/doc/html/math_toolkit/lcm_function_object.html
index 78e0a3ff6..98a358d30 100644
--- a/libs/math/doc/html/math_toolkit/lcm_function_object.html
+++ b/libs/math/doc/html/math_toolkit/lcm_function_object.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>LCM Function Object</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../gcd_lcm.html" title="Chapter&#160;11.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)">
<link rel="prev" href="gcd_function_object.html" title="GCD Function Object">
<link rel="next" href="run_time.html" title="Run-time GCD &amp; LCM Determination">
diff --git a/libs/math/doc/html/math_toolkit/macros.html b/libs/math/doc/html/math_toolkit/macros.html
index 103db5621..8992a220a 100644
--- a/libs/math/doc/html/math_toolkit/macros.html
+++ b/libs/math/doc/html/math_toolkit/macros.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Floating-Point Constant Macros</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../cstdfloat.html" title="Chapter&#160;3.&#160;Specified-width floating-point typedefs">
<link rel="prev" href="greatest_typdefs.html" title="Greatest-width floating-point typedef">
<link rel="next" href="examples.html" title="Examples">
diff --git a/libs/math/doc/html/math_toolkit/main_faq.html b/libs/math/doc/html/math_toolkit/main_faq.html
index 2a3ac0e54..88306905d 100644
--- a/libs/math/doc/html/math_toolkit/main_faq.html
+++ b/libs/math/doc/html/math_toolkit/main_faq.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Frequently Asked Questions FAQ</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="overview_tr1.html" title="C99 and C++ TR1 C-style Functions">
<link rel="next" href="contact.html" title="Contact Info and Support">
diff --git a/libs/math/doc/html/math_toolkit/main_intro.html b/libs/math/doc/html/math_toolkit/main_intro.html
index 69e6ba300..d551b856c 100644
--- a/libs/math/doc/html/math_toolkit/main_intro.html
+++ b/libs/math/doc/html/math_toolkit/main_intro.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>About the Math Toolkit</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="next" href="navigation.html" title="Navigation">
diff --git a/libs/math/doc/html/math_toolkit/main_tr1.html b/libs/math/doc/html/math_toolkit/main_tr1.html
index 3fe1afb83..772759569 100644
--- a/libs/math/doc/html/math_toolkit/main_tr1.html
+++ b/libs/math/doc/html/math_toolkit/main_tr1.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>C99 and TR1 C Functions Overview</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../extern_c.html" title='Chapter&#160;7.&#160;TR1 and C99 external "C" Functions'>
<link rel="prev" href="../extern_c.html" title='Chapter&#160;7.&#160;TR1 and C99 external "C" Functions'>
<link rel="next" href="c99.html" title="C99 C Functions">
diff --git a/libs/math/doc/html/math_toolkit/mem_typedef.html b/libs/math/doc/html/math_toolkit/mem_typedef.html
index 877fe7495..f87c86fb8 100644
--- a/libs/math/doc/html/math_toolkit/mem_typedef.html
+++ b/libs/math/doc/html/math_toolkit/mem_typedef.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Quaternion Member Typedefs</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="spec.html" title="Quaternion Specializations">
<link rel="next" href="quat_mem_fun.html" title="Quaternion Member Functions">
diff --git a/libs/math/doc/html/math_toolkit/minimum_typdefs.html b/libs/math/doc/html/math_toolkit/minimum_typdefs.html
index 6b9140f8e..73dae4111 100644
--- a/libs/math/doc/html/math_toolkit/minimum_typdefs.html
+++ b/libs/math/doc/html/math_toolkit/minimum_typdefs.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Minimum-width floating-point typedefs</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../cstdfloat.html" title="Chapter&#160;3.&#160;Specified-width floating-point typedefs">
<link rel="prev" href="exact_typdefs.html" title="Exact-Width Floating-Point typedefs">
<link rel="next" href="fastest_typdefs.html" title="Fastest floating-point typedefs">
diff --git a/libs/math/doc/html/math_toolkit/namespaces.html b/libs/math/doc/html/math_toolkit/namespaces.html
index 5a7325357..e8c6c3140 100644
--- a/libs/math/doc/html/math_toolkit/namespaces.html
+++ b/libs/math/doc/html/math_toolkit/namespaces.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Namespaces</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="directories.html" title="Directory and File Structure">
<link rel="next" href="result_type.html" title="Calculation of the Type of the Result">
diff --git a/libs/math/doc/html/math_toolkit/navigation.html b/libs/math/doc/html/math_toolkit/navigation.html
index d65ceabdb..fee3399b2 100644
--- a/libs/math/doc/html/math_toolkit/navigation.html
+++ b/libs/math/doc/html/math_toolkit/navigation.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Navigation</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="main_intro.html" title="About the Math Toolkit">
<link rel="next" href="conventions.html" title="Document Conventions">
@@ -27,7 +27,7 @@
<a name="math_toolkit.navigation"></a><a class="link" href="navigation.html" title="Navigation">Navigation</a>
</h2></div></div></div>
<p>
- <a class="indexterm" name="idm1567463232"></a>
+ <a class="indexterm" name="id845442"></a>
</p>
<p>
Boost.Math documentation is provided in both HTML and PDF formats.
diff --git a/libs/math/doc/html/math_toolkit/new_const.html b/libs/math/doc/html/math_toolkit/new_const.html
index db0f9490c..0b86a7eae 100644
--- a/libs/math/doc/html/math_toolkit/new_const.html
+++ b/libs/math/doc/html/math_toolkit/new_const.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Defining New Constants</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../constants.html" title="Chapter&#160;4.&#160;Mathematical Constants">
<link rel="prev" href="constants.html" title="The Mathematical Constants">
<link rel="next" href="constants_faq.html" title="FAQs">
diff --git a/libs/math/doc/html/math_toolkit/next_float.html b/libs/math/doc/html/math_toolkit/next_float.html
index bd06fa0da..3460c19f8 100644
--- a/libs/math/doc/html/math_toolkit/next_float.html
+++ b/libs/math/doc/html/math_toolkit/next_float.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../utils.html" title="Chapter&#160;2.&#160;Floating Point Utilities">
<link rel="prev" href="fp_facets/rationale.html" title="Design Rationale">
<link rel="next" href="next_float/nextafter.html" title="Finding the Next Representable Value in a Specific Direction (nextafter)">
@@ -27,7 +27,7 @@
<a name="math_toolkit.next_float"></a><a class="link" href="next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">Floating-Point Representation
Distance (ULP), and Finding Adjacent Floating-Point Values</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="next_float/nextafter.html">Finding the Next Representable
Value in a Specific Direction (nextafter)</a></span></dt>
<dt><span class="section"><a href="next_float/float_next.html">Finding the Next
diff --git a/libs/math/doc/html/math_toolkit/next_float/float_advance.html b/libs/math/doc/html/math_toolkit/next_float/float_advance.html
index 2c7b55cdf..78990d003 100644
--- a/libs/math/doc/html/math_toolkit/next_float/float_advance.html
+++ b/libs/math/doc/html/math_toolkit/next_float/float_advance.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">
<link rel="prev" href="float_distance.html" title="Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance">
<link rel="next" href="../../cstdfloat.html" title="Chapter&#160;3.&#160;Specified-width floating-point typedefs">
diff --git a/libs/math/doc/html/math_toolkit/next_float/float_distance.html b/libs/math/doc/html/math_toolkit/next_float/float_distance.html
index f8d533349..8bfde34f0 100644
--- a/libs/math/doc/html/math_toolkit/next_float/float_distance.html
+++ b/libs/math/doc/html/math_toolkit/next_float/float_distance.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">
<link rel="prev" href="float_prior.html" title="Finding the Next Smaller Representable Value (float_prior)">
<link rel="next" href="float_advance.html" title="Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance">
diff --git a/libs/math/doc/html/math_toolkit/next_float/float_next.html b/libs/math/doc/html/math_toolkit/next_float/float_next.html
index 09ffbb0f5..5e17917f6 100644
--- a/libs/math/doc/html/math_toolkit/next_float/float_next.html
+++ b/libs/math/doc/html/math_toolkit/next_float/float_next.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Finding the Next Greater Representable Value (float_next)</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">
<link rel="prev" href="nextafter.html" title="Finding the Next Representable Value in a Specific Direction (nextafter)">
<link rel="next" href="float_prior.html" title="Finding the Next Smaller Representable Value (float_prior)">
diff --git a/libs/math/doc/html/math_toolkit/next_float/float_prior.html b/libs/math/doc/html/math_toolkit/next_float/float_prior.html
index f93b00430..8fc09791b 100644
--- a/libs/math/doc/html/math_toolkit/next_float/float_prior.html
+++ b/libs/math/doc/html/math_toolkit/next_float/float_prior.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Finding the Next Smaller Representable Value (float_prior)</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">
<link rel="prev" href="float_next.html" title="Finding the Next Greater Representable Value (float_next)">
<link rel="next" href="float_distance.html" title="Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance">
diff --git a/libs/math/doc/html/math_toolkit/next_float/nextafter.html b/libs/math/doc/html/math_toolkit/next_float/nextafter.html
index 02dec32b1..3f53be871 100644
--- a/libs/math/doc/html/math_toolkit/next_float/nextafter.html
+++ b/libs/math/doc/html/math_toolkit/next_float/nextafter.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Finding the Next Representable Value in a Specific Direction (nextafter)</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">
<link rel="prev" href="../next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">
<link rel="next" href="float_next.html" title="Finding the Next Greater Representable Value (float_next)">
diff --git a/libs/math/doc/html/math_toolkit/number_series.html b/libs/math/doc/html/math_toolkit/number_series.html
index 5bc8b535d..6664d9cba 100644
--- a/libs/math/doc/html/math_toolkit/number_series.html
+++ b/libs/math/doc/html/math_toolkit/number_series.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Number Series</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
<link rel="prev" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
<link rel="next" href="number_series/bernoulli_numbers.html" title="Bernoulli Numbers">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.number_series"></a><a class="link" href="number_series.html" title="Number Series">Number Series</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="number_series/bernoulli_numbers.html">Bernoulli
Numbers</a></span></dt>
<dt><span class="section"><a href="number_series/tangent_numbers.html">Tangent Numbers</a></span></dt>
diff --git a/libs/math/doc/html/math_toolkit/number_series/bernoulli_numbers.html b/libs/math/doc/html/math_toolkit/number_series/bernoulli_numbers.html
index 2e909502f..ce80d0f9d 100644
--- a/libs/math/doc/html/math_toolkit/number_series/bernoulli_numbers.html
+++ b/libs/math/doc/html/math_toolkit/number_series/bernoulli_numbers.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Bernoulli Numbers</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../number_series.html" title="Number Series">
<link rel="prev" href="../number_series.html" title="Number Series">
<link rel="next" href="tangent_numbers.html" title="Tangent Numbers">
@@ -135,7 +135,7 @@ and also obtain much
<code class="computeroutput"><span class="identifier">unchecked_bernoulli_b2n</span></code> provides
access to Bernoulli numbers <span class="bold"><strong>without any checks for
overflow or invalid parameters</strong></span>. It is implemented as a direct
- (and very fast) table lookup, and while not recomended for general use it
+ (and very fast) table lookup, and while not recommended for general use it
can be useful inside inner loops where the ultimate performance is required,
and error checking is moved outside the loop.
</p>
@@ -153,7 +153,7 @@ and also obtain much
types, it's the largest value for which the result can be represented as
the ratio of two 64-bit integers, for example <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">max_bernoulli_b2n</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float_50</span><span class="special">&gt;::</span><span class="identifier">value</span></code>
is just 17. Of course larger indexes can be passed to <code class="computeroutput"><span class="identifier">bernoulli_b2n</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">n</span><span class="special">)</span></code>, but
- then then you loose fast table lookup (i.e. values may need to be calculated).
+ then you lose fast table lookup (i.e. values may need to be calculated).
</p>
<pre class="programlisting"><span class="comment">/*For example:
*/</span>
@@ -328,14 +328,14 @@ and also obtain much
is given by Brent and Harvey's equation 14:
</p>
<p>
- &#8192;&#8192; <span class="inlinemediaobject"><img src="../../../equations/tangent_numbers.png"></span>
+ &#8192;&#8192; <span class="inlinemediaobject"><img src="../../../equations/tangent_numbers.svg"></span>
</p>
<p>
Their relation with Bernoulli numbers <span class="emphasis"><em>B<sub>i</sub></em></span> are defined
by
</p>
<p>
- if i &gt; 0 and i is even then &#8192;&#8192; <span class="inlinemediaobject"><img src="../../../equations/bernoulli_numbers.png"></span> <br> elseif
+ if i &gt; 0 and i is even then &#8192;&#8192; <span class="inlinemediaobject"><img src="../../../equations/bernoulli_numbers.svg"></span> <br> elseif
i == 0 then <span class="emphasis"><em>B<sub>i</sub></em></span> = 1 <br> elseif i == 1 then <span class="emphasis"><em>B<sub>i</sub></em></span>
= -1/2 <br> elseif i &lt; 0 or i is odd then <span class="emphasis"><em>B<sub>i</sub></em></span> =
0
@@ -343,15 +343,15 @@ and also obtain much
<p>
Note that computed values are stored in a fixed-size table, access is thread
safe via atomic operations (i.e. lock free programming), this imparts a much
- lower overhead on access to cached values than might overwise be expected
+ lower overhead on access to cached values than might otherwise be expected
- typically for multiprecision types the cost of thread synchronisation is
- negligable, while for built in types this code is not normally executed anyway.
+ negligible, while for built in types this code is not normally executed anyway.
For very large arguments which cannot be reasonably computed or stored in
our cache, an asymptotic expansion <a href="http://www.luschny.de/math/primes/bernincl.html" target="_top">due
to Luschny</a> is used:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/bernoulli_numbers2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/bernoulli_numbers2.svg"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/number_series/primes.html b/libs/math/doc/html/math_toolkit/number_series/primes.html
index 539e5e0ef..2bf0d999f 100644
--- a/libs/math/doc/html/math_toolkit/number_series/primes.html
+++ b/libs/math/doc/html/math_toolkit/number_series/primes.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Prime Numbers</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../number_series.html" title="Number Series">
<link rel="prev" href="tangent_numbers.html" title="Tangent Numbers">
<link rel="next" href="../sf_gamma.html" title="Gamma Functions">
diff --git a/libs/math/doc/html/math_toolkit/number_series/tangent_numbers.html b/libs/math/doc/html/math_toolkit/number_series/tangent_numbers.html
index 3d49ca46e..860661d00 100644
--- a/libs/math/doc/html/math_toolkit/number_series/tangent_numbers.html
+++ b/libs/math/doc/html/math_toolkit/number_series/tangent_numbers.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Tangent Numbers</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../number_series.html" title="Number Series">
<link rel="prev" href="bernoulli_numbers.html" title="Bernoulli Numbers">
<link rel="next" href="primes.html" title="Prime Numbers">
@@ -43,13 +43,13 @@
or odd numbered values as non-zero), we use:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/tangent_number_def.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/tangent_number_def.svg"></span>
</p>
<p>
Which gives:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/tangent_number_def2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/tangent_number_def2.svg"></span>
</p>
<p>
Tangent numbers are used in the computation of Bernoulli numbers, but are
diff --git a/libs/math/doc/html/math_toolkit/oct_create.html b/libs/math/doc/html/math_toolkit/oct_create.html
index 8161046f9..f1dd3d3d8 100644
--- a/libs/math/doc/html/math_toolkit/oct_create.html
+++ b/libs/math/doc/html/math_toolkit/oct_create.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Octonion Creation Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../octonions.html" title="Chapter&#160;10.&#160;Octonions">
<link rel="prev" href="oct_value_ops.html" title="Octonion Value Operations">
<link rel="next" href="oct_trans.html" title="Octonions Transcendentals">
diff --git a/libs/math/doc/html/math_toolkit/oct_header.html b/libs/math/doc/html/math_toolkit/oct_header.html
index 268262f49..c202721f4 100644
--- a/libs/math/doc/html/math_toolkit/oct_header.html
+++ b/libs/math/doc/html/math_toolkit/oct_header.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Header File</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../octonions.html" title="Chapter&#160;10.&#160;Octonions">
<link rel="prev" href="oct_overview.html" title="Overview">
<link rel="next" href="oct_synopsis.html" title="Synopsis">
diff --git a/libs/math/doc/html/math_toolkit/oct_history.html b/libs/math/doc/html/math_toolkit/oct_history.html
index 7004e64b2..c7ccef05f 100644
--- a/libs/math/doc/html/math_toolkit/oct_history.html
+++ b/libs/math/doc/html/math_toolkit/oct_history.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>History</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../octonions.html" title="Chapter&#160;10.&#160;Octonions">
<link rel="prev" href="acknowledgements.html" title="Acknowledgements">
<link rel="next" href="oct_todo.html" title="To Do">
diff --git a/libs/math/doc/html/math_toolkit/oct_mem_fun.html b/libs/math/doc/html/math_toolkit/oct_mem_fun.html
index 9ec11f238..055d54f36 100644
--- a/libs/math/doc/html/math_toolkit/oct_mem_fun.html
+++ b/libs/math/doc/html/math_toolkit/oct_mem_fun.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Octonion Member Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../octonions.html" title="Chapter&#160;10.&#160;Octonions">
<link rel="prev" href="oct_typedefs.html" title="Octonion Member Typedefs">
<link rel="next" href="oct_non_mem.html" title="Octonion Non-Member Operators">
diff --git a/libs/math/doc/html/math_toolkit/oct_non_mem.html b/libs/math/doc/html/math_toolkit/oct_non_mem.html
index 97682d0d1..5dae4e8d5 100644
--- a/libs/math/doc/html/math_toolkit/oct_non_mem.html
+++ b/libs/math/doc/html/math_toolkit/oct_non_mem.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Octonion Non-Member Operators</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../octonions.html" title="Chapter&#160;10.&#160;Octonions">
<link rel="prev" href="oct_mem_fun.html" title="Octonion Member Functions">
<link rel="next" href="oct_value_ops.html" title="Octonion Value Operations">
diff --git a/libs/math/doc/html/math_toolkit/oct_overview.html b/libs/math/doc/html/math_toolkit/oct_overview.html
index 48247b97f..ef4dd1f6f 100644
--- a/libs/math/doc/html/math_toolkit/oct_overview.html
+++ b/libs/math/doc/html/math_toolkit/oct_overview.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Overview</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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<link rel="next" href="acknowledgements.html" title="Acknowledgements">
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<link rel="next" href="../gcd_lcm.html" title="Chapter&#160;11.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)">
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Octonions Transcendentals</title>
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<link rel="next" href="oct_tests.html" title="Test Program">
diff --git a/libs/math/doc/html/math_toolkit/oct_typedefs.html b/libs/math/doc/html/math_toolkit/oct_typedefs.html
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Octonion Member Typedefs</title>
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<link rel="up" href="../octonions.html" title="Chapter&#160;10.&#160;Octonions">
<link rel="prev" href="oct_specialization.html" title="Octonion Specializations">
<link rel="next" href="oct_mem_fun.html" title="Octonion Member Functions">
diff --git a/libs/math/doc/html/math_toolkit/oct_value_ops.html b/libs/math/doc/html/math_toolkit/oct_value_ops.html
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<title>Octonion Value Operations</title>
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<link rel="next" href="oct_create.html" title="Octonion Creation Functions">
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<link rel="next" href="oct_specialization.html" title="Octonion Specializations">
diff --git a/libs/math/doc/html/math_toolkit/overview.html b/libs/math/doc/html/math_toolkit/overview.html
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<link rel="prev" href="../cstdfloat.html" title="Chapter&#160;3.&#160;Specified-width floating-point typedefs">
<link rel="next" href="rationale.html" title="Rationale">
diff --git a/libs/math/doc/html/math_toolkit/overview_tr1.html b/libs/math/doc/html/math_toolkit/overview_tr1.html
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for more details</a>.
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That is the area shaded in the figure below (Owens 1956).
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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+++ b/libs/math/doc/html/math_toolkit/pol_ref/iteration_pol.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Iteration Limits Policies</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../pol_ref.html" title="Policy Reference">
<link rel="prev" href="precision_pol.html" title="Precision Policies">
<link rel="next" href="policy_defaults.html" title="Using Macros to Change the Policy Defaults">
diff --git a/libs/math/doc/html/math_toolkit/pol_ref/namespace_pol.html b/libs/math/doc/html/math_toolkit/pol_ref/namespace_pol.html
index 396dec0fc..71c25d003 100644
--- a/libs/math/doc/html/math_toolkit/pol_ref/namespace_pol.html
+++ b/libs/math/doc/html/math_toolkit/pol_ref/namespace_pol.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Setting Polices at Namespace Scope</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../pol_ref.html" title="Policy Reference">
<link rel="prev" href="policy_defaults.html" title="Using Macros to Change the Policy Defaults">
<link rel="next" href="pol_ref_ref.html" title="Policy Class Reference">
diff --git a/libs/math/doc/html/math_toolkit/pol_ref/pol_ref_ref.html b/libs/math/doc/html/math_toolkit/pol_ref/pol_ref_ref.html
index 8c5d60f31..a76d9e2f8 100644
--- a/libs/math/doc/html/math_toolkit/pol_ref/pol_ref_ref.html
+++ b/libs/math/doc/html/math_toolkit/pol_ref/pol_ref_ref.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Policy Class Reference</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../pol_ref.html" title="Policy Reference">
<link rel="prev" href="namespace_pol.html" title="Setting Polices at Namespace Scope">
<link rel="next" href="../../perf.html" title="Chapter&#160;15.&#160;Performance">
diff --git a/libs/math/doc/html/math_toolkit/pol_ref/policy_defaults.html b/libs/math/doc/html/math_toolkit/pol_ref/policy_defaults.html
index 9f30b97e7..268297d3d 100644
--- a/libs/math/doc/html/math_toolkit/pol_ref/policy_defaults.html
+++ b/libs/math/doc/html/math_toolkit/pol_ref/policy_defaults.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Using Macros to Change the Policy Defaults</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../pol_ref.html" title="Policy Reference">
<link rel="prev" href="iteration_pol.html" title="Iteration Limits Policies">
<link rel="next" href="namespace_pol.html" title="Setting Polices at Namespace Scope">
diff --git a/libs/math/doc/html/math_toolkit/pol_ref/precision_pol.html b/libs/math/doc/html/math_toolkit/pol_ref/precision_pol.html
index dbcf73f91..e71334add 100644
--- a/libs/math/doc/html/math_toolkit/pol_ref/precision_pol.html
+++ b/libs/math/doc/html/math_toolkit/pol_ref/precision_pol.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Precision Policies</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../pol_ref.html" title="Policy Reference">
<link rel="prev" href="discrete_quant_ref.html" title="Discrete Quantile Policies">
<link rel="next" href="iteration_pol.html" title="Iteration Limits Policies">
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial.html b/libs/math/doc/html/math_toolkit/pol_tutorial.html
index 1e3383beb..60b1a4e5d 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Policy Tutorial</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">
<link rel="prev" href="pol_overview.html" title="Policy Overview">
<link rel="next" href="pol_tutorial/what_is_a_policy.html" title="So Just What is a Policy Anyway?">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.pol_tutorial"></a><a class="link" href="pol_tutorial.html" title="Policy Tutorial">Policy Tutorial</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="pol_tutorial/what_is_a_policy.html">So Just What
is a Policy Anyway?</a></span></dt>
<dt><span class="section"><a href="pol_tutorial/policy_tut_defaults.html">Policies
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_dist_policies.html b/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_dist_policies.html
index 120697835..743a3b469 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_dist_policies.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_dist_policies.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Setting Policies for Distributions on an Ad Hoc Basis</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
<link rel="prev" href="changing_policy_defaults.html" title="Changing the Policy Defaults">
<link rel="next" href="ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_sf_policies.html b/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_sf_policies.html
index 7cd3ee2e6..a23d0931f 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_sf_policies.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/ad_hoc_sf_policies.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Changing the Policy on an Ad Hoc Basis for the Special Functions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
<link rel="prev" href="ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">
<link rel="next" href="namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/changing_policy_defaults.html b/libs/math/doc/html/math_toolkit/pol_tutorial/changing_policy_defaults.html
index 229a7b122..bf905d7d3 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/changing_policy_defaults.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/changing_policy_defaults.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Changing the Policy Defaults</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
<link rel="prev" href="policy_usage.html" title="So How are Policies Used Anyway?">
<link rel="next" href="ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/namespace_policies.html b/libs/math/doc/html/math_toolkit/pol_tutorial/namespace_policies.html
index e981e0e53..9b0ff6fb6 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/namespace_policies.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/namespace_policies.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Setting Policies at Namespace or Translation Unit Scope</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
<link rel="prev" href="ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">
<link rel="next" href="user_def_err_pol.html" title="Calling User Defined Error Handlers">
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/policy_tut_defaults.html b/libs/math/doc/html/math_toolkit/pol_tutorial/policy_tut_defaults.html
index c5d337cbd..35739f3ad 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/policy_tut_defaults.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/policy_tut_defaults.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Policies Have Sensible Defaults</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
<link rel="prev" href="what_is_a_policy.html" title="So Just What is a Policy Anyway?">
<link rel="next" href="policy_usage.html" title="So How are Policies Used Anyway?">
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/policy_usage.html b/libs/math/doc/html/math_toolkit/pol_tutorial/policy_usage.html
index 54f232656..b5a632039 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/policy_usage.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/policy_usage.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>So How are Policies Used Anyway?</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
<link rel="prev" href="policy_tut_defaults.html" title="Policies Have Sensible Defaults">
<link rel="next" href="changing_policy_defaults.html" title="Changing the Policy Defaults">
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/understand_dis_quant.html b/libs/math/doc/html/math_toolkit/pol_tutorial/understand_dis_quant.html
index a008b31fc..702333421 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/understand_dis_quant.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/understand_dis_quant.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Understanding Quantiles of Discrete Distributions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
<link rel="prev" href="user_def_err_pol.html" title="Calling User Defined Error Handlers">
<link rel="next" href="../pol_ref.html" title="Policy Reference">
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/user_def_err_pol.html b/libs/math/doc/html/math_toolkit/pol_tutorial/user_def_err_pol.html
index 7616021ce..1e95f012c 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/user_def_err_pol.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/user_def_err_pol.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Calling User Defined Error Handlers</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
<link rel="prev" href="namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">
<link rel="next" href="understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">
diff --git a/libs/math/doc/html/math_toolkit/pol_tutorial/what_is_a_policy.html b/libs/math/doc/html/math_toolkit/pol_tutorial/what_is_a_policy.html
index 70bf221cf..7fa9a268f 100644
--- a/libs/math/doc/html/math_toolkit/pol_tutorial/what_is_a_policy.html
+++ b/libs/math/doc/html/math_toolkit/pol_tutorial/what_is_a_policy.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>So Just What is a Policy Anyway?</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
<link rel="prev" href="../pol_tutorial.html" title="Policy Tutorial">
<link rel="next" href="policy_tut_defaults.html" title="Policies Have Sensible Defaults">
diff --git a/libs/math/doc/html/math_toolkit/powers.html b/libs/math/doc/html/math_toolkit/powers.html
index b31a43398..a5720a978 100644
--- a/libs/math/doc/html/math_toolkit/powers.html
+++ b/libs/math/doc/html/math_toolkit/powers.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Basic Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
<link rel="prev" href="expint/expint_i.html" title="Exponential Integral Ei">
<link rel="next" href="powers/sin_pi.html" title="sin_pi">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.powers"></a><a class="link" href="powers.html" title="Basic Functions">Basic Functions</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="powers/sin_pi.html">sin_pi</a></span></dt>
<dt><span class="section"><a href="powers/cos_pi.html">cos_pi</a></span></dt>
<dt><span class="section"><a href="powers/log1p.html">log1p</a></span></dt>
diff --git a/libs/math/doc/html/math_toolkit/powers/cbrt.html b/libs/math/doc/html/math_toolkit/powers/cbrt.html
index 197e1da3a..ed685d877 100644
--- a/libs/math/doc/html/math_toolkit/powers/cbrt.html
+++ b/libs/math/doc/html/math_toolkit/powers/cbrt.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>cbrt</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../powers.html" title="Basic Functions">
<link rel="prev" href="expm1.html" title="expm1">
<link rel="next" href="sqrt1pm1.html" title="sqrt1pm1">
@@ -59,7 +59,7 @@
The following graph illustrates the behaviour of cbrt:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/cbrt.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/cbrt.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.powers.cbrt.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/powers/cos_pi.html b/libs/math/doc/html/math_toolkit/powers/cos_pi.html
index b26292c4f..8d4fc8e1c 100644
--- a/libs/math/doc/html/math_toolkit/powers/cos_pi.html
+++ b/libs/math/doc/html/math_toolkit/powers/cos_pi.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>cos_pi</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../powers.html" title="Basic Functions">
<link rel="prev" href="sin_pi.html" title="sin_pi">
<link rel="next" href="log1p.html" title="log1p">
diff --git a/libs/math/doc/html/math_toolkit/powers/ct_pow.html b/libs/math/doc/html/math_toolkit/powers/ct_pow.html
index 579e385c1..b2a68f1a5 100644
--- a/libs/math/doc/html/math_toolkit/powers/ct_pow.html
+++ b/libs/math/doc/html/math_toolkit/powers/ct_pow.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Compile Time Power of a Runtime Base</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../powers.html" title="Basic Functions">
<link rel="prev" href="hypot.html" title="hypot">
<link rel="next" href="../sinc.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions">
diff --git a/libs/math/doc/html/math_toolkit/powers/expm1.html b/libs/math/doc/html/math_toolkit/powers/expm1.html
index 952154adf..f73f8b146 100644
--- a/libs/math/doc/html/math_toolkit/powers/expm1.html
+++ b/libs/math/doc/html/math_toolkit/powers/expm1.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>expm1</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../powers.html" title="Basic Functions">
<link rel="prev" href="log1p.html" title="log1p">
<link rel="next" href="cbrt.html" title="cbrt">
@@ -68,7 +68,7 @@
The following graph illustrates the behaviour of expm1:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/expm1.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/expm1.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.powers.expm1.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/powers/hypot.html b/libs/math/doc/html/math_toolkit/powers/hypot.html
index 4302e7a88..f90cbfc7e 100644
--- a/libs/math/doc/html/math_toolkit/powers/hypot.html
+++ b/libs/math/doc/html/math_toolkit/powers/hypot.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>hypot</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../powers.html" title="Basic Functions">
<link rel="prev" href="powm1.html" title="powm1">
<link rel="next" href="ct_pow.html" title="Compile Time Power of a Runtime Base">
@@ -33,7 +33,7 @@
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hypot</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
</pre>
<p>
- <span class="bold"><strong>Effects: </strong></span> computes <span class="inlinemediaobject"><img src="../../../equations/hypot.png"></span>
+ <span class="bold"><strong>Effects: </strong></span> computes <span class="inlinemediaobject"><img src="../../../equations/hypot.svg"></span>
in such a way
as to avoid undue underflow and overflow.
</p>
@@ -49,7 +49,7 @@ in such a way
documentation for more details</a>.
</p>
<p>
- When calculating <span class="inlinemediaobject"><img src="../../../equations/hypot.png"></span> it's quite easy for the intermediate terms to
+ When calculating <span class="inlinemediaobject"><img src="../../../equations/hypot.svg"></span> it's quite easy for the intermediate terms to
either overflow or underflow, even though the result is in fact perfectly
representable.
</p>
@@ -69,7 +69,7 @@ in such a way
Otherwise the result is given by:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/hypot2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/hypot2.svg"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/powers/log1p.html b/libs/math/doc/html/math_toolkit/powers/log1p.html
index 419802d2f..3f221bcf8 100644
--- a/libs/math/doc/html/math_toolkit/powers/log1p.html
+++ b/libs/math/doc/html/math_toolkit/powers/log1p.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>log1p</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../powers.html" title="Basic Functions">
<link rel="prev" href="cos_pi.html" title="cos_pi">
<link rel="next" href="expm1.html" title="expm1">
@@ -82,7 +82,7 @@
The following graph illustrates the behaviour of log1p:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/log1p.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/log1p.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.powers.log1p.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/powers/powm1.html b/libs/math/doc/html/math_toolkit/powers/powm1.html
index c125b4e19..6b2847d9b 100644
--- a/libs/math/doc/html/math_toolkit/powers/powm1.html
+++ b/libs/math/doc/html/math_toolkit/powers/powm1.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>powm1</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../powers.html" title="Basic Functions">
<link rel="prev" href="sqrt1pm1.html" title="sqrt1pm1">
<link rel="next" href="hypot.html" title="hypot">
@@ -62,7 +62,7 @@
The following graph illustrates the behaviour of powm1:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/powm1.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/powm1.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.powers.powm1.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/powers/sin_pi.html b/libs/math/doc/html/math_toolkit/powers/sin_pi.html
index 2f0f54d67..5d80ee3a4 100644
--- a/libs/math/doc/html/math_toolkit/powers/sin_pi.html
+++ b/libs/math/doc/html/math_toolkit/powers/sin_pi.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>sin_pi</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../powers.html" title="Basic Functions">
<link rel="prev" href="../powers.html" title="Basic Functions">
<link rel="next" href="cos_pi.html" title="cos_pi">
diff --git a/libs/math/doc/html/math_toolkit/powers/sqrt1pm1.html b/libs/math/doc/html/math_toolkit/powers/sqrt1pm1.html
index d8d50cbd6..df4f76dc5 100644
--- a/libs/math/doc/html/math_toolkit/powers/sqrt1pm1.html
+++ b/libs/math/doc/html/math_toolkit/powers/sqrt1pm1.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>sqrt1pm1</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../powers.html" title="Basic Functions">
<link rel="prev" href="cbrt.html" title="cbrt">
<link rel="next" href="powm1.html" title="powm1">
@@ -64,7 +64,7 @@
The following graph illustrates the behaviour of sqrt1pm1:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/sqrt1pm1.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/sqrt1pm1.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.powers.sqrt1pm1.h0"></a>
diff --git a/libs/math/doc/html/math_toolkit/quat.html b/libs/math/doc/html/math_toolkit/quat.html
index 691370a98..7361c61ba 100644
--- a/libs/math/doc/html/math_toolkit/quat.html
+++ b/libs/math/doc/html/math_toolkit/quat.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Template Class quaternion</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="quat_synopsis.html" title="Synopsis">
<link rel="next" href="spec.html" title="Quaternion Specializations">
diff --git a/libs/math/doc/html/math_toolkit/quat_header.html b/libs/math/doc/html/math_toolkit/quat_header.html
index 9e0b0a235..12632ef2a 100644
--- a/libs/math/doc/html/math_toolkit/quat_header.html
+++ b/libs/math/doc/html/math_toolkit/quat_header.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Header File</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="quat_overview.html" title="Overview">
<link rel="next" href="quat_synopsis.html" title="Synopsis">
diff --git a/libs/math/doc/html/math_toolkit/quat_history.html b/libs/math/doc/html/math_toolkit/quat_history.html
index ecdb337ca..fad63b10b 100644
--- a/libs/math/doc/html/math_toolkit/quat_history.html
+++ b/libs/math/doc/html/math_toolkit/quat_history.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>History</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="acknowledgement.html" title="Acknowledgements">
<link rel="next" href="quat_todo.html" title="To Do">
diff --git a/libs/math/doc/html/math_toolkit/quat_mem_fun.html b/libs/math/doc/html/math_toolkit/quat_mem_fun.html
index 50bfa344e..cf344163f 100644
--- a/libs/math/doc/html/math_toolkit/quat_mem_fun.html
+++ b/libs/math/doc/html/math_toolkit/quat_mem_fun.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Quaternion Member Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="mem_typedef.html" title="Quaternion Member Typedefs">
<link rel="next" href="quat_non_mem.html" title="Quaternion Non-Member Operators">
diff --git a/libs/math/doc/html/math_toolkit/quat_non_mem.html b/libs/math/doc/html/math_toolkit/quat_non_mem.html
index 2dda8a308..90eae823d 100644
--- a/libs/math/doc/html/math_toolkit/quat_non_mem.html
+++ b/libs/math/doc/html/math_toolkit/quat_non_mem.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Quaternion Non-Member Operators</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="quat_mem_fun.html" title="Quaternion Member Functions">
<link rel="next" href="value_op.html" title="Quaternion Value Operations">
diff --git a/libs/math/doc/html/math_toolkit/quat_overview.html b/libs/math/doc/html/math_toolkit/quat_overview.html
index 5559fbbd5..d7e99bffa 100644
--- a/libs/math/doc/html/math_toolkit/quat_overview.html
+++ b/libs/math/doc/html/math_toolkit/quat_overview.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Overview</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="next" href="quat_header.html" title="Header File">
diff --git a/libs/math/doc/html/math_toolkit/quat_synopsis.html b/libs/math/doc/html/math_toolkit/quat_synopsis.html
index 27f4e57db..1c9941f5c 100644
--- a/libs/math/doc/html/math_toolkit/quat_synopsis.html
+++ b/libs/math/doc/html/math_toolkit/quat_synopsis.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Synopsis</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="quat_header.html" title="Header File">
<link rel="next" href="quat.html" title="Template Class quaternion">
diff --git a/libs/math/doc/html/math_toolkit/quat_tests.html b/libs/math/doc/html/math_toolkit/quat_tests.html
index 61b45cfcb..49dc2ce52 100644
--- a/libs/math/doc/html/math_toolkit/quat_tests.html
+++ b/libs/math/doc/html/math_toolkit/quat_tests.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Test Program</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="trans.html" title="Quaternion Transcendentals">
<link rel="next" href="exp.html" title="The Quaternionic Exponential">
diff --git a/libs/math/doc/html/math_toolkit/quat_todo.html b/libs/math/doc/html/math_toolkit/quat_todo.html
index da88c16ed..eb4831c2d 100644
--- a/libs/math/doc/html/math_toolkit/quat_todo.html
+++ b/libs/math/doc/html/math_toolkit/quat_todo.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>To Do</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="quat_history.html" title="History">
<link rel="next" href="../octonions.html" title="Chapter&#160;10.&#160;Octonions">
diff --git a/libs/math/doc/html/math_toolkit/rationale.html b/libs/math/doc/html/math_toolkit/rationale.html
index 37fbefd92..99daf6336 100644
--- a/libs/math/doc/html/math_toolkit/rationale.html
+++ b/libs/math/doc/html/math_toolkit/rationale.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Rationale</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../cstdfloat.html" title="Chapter&#160;3.&#160;Specified-width floating-point typedefs">
<link rel="prev" href="overview.html" title="Overview">
<link rel="next" href="exact_typdefs.html" title="Exact-Width Floating-Point typedefs">
diff --git a/libs/math/doc/html/math_toolkit/rationale0.html b/libs/math/doc/html/math_toolkit/rationale0.html
index efe7e44fb..57ea86865 100644
--- a/libs/math/doc/html/math_toolkit/rationale0.html
+++ b/libs/math/doc/html/math_toolkit/rationale0.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Rationale</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../gcd_lcm.html" title="Chapter&#160;11.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)">
<link rel="prev" href="demo.html" title="Demonstration Program">
<link rel="next" href="gcd_history.html" title="History">
diff --git a/libs/math/doc/html/math_toolkit/refs.html b/libs/math/doc/html/math_toolkit/refs.html
index f57020d6c..d80e7c834 100644
--- a/libs/math/doc/html/math_toolkit/refs.html
+++ b/libs/math/doc/html/math_toolkit/refs.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>References</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../backgrounders.html" title="Chapter&#160;16.&#160;Backgrounders">
<link rel="prev" href="remez.html" title="The Remez Method">
<link rel="next" href="../status.html" title="Chapter&#160;17.&#160;Library Status">
diff --git a/libs/math/doc/html/math_toolkit/relative_error.html b/libs/math/doc/html/math_toolkit/relative_error.html
index a75d06b3e..38d39e14a 100644
--- a/libs/math/doc/html/math_toolkit/relative_error.html
+++ b/libs/math/doc/html/math_toolkit/relative_error.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Relative Error</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../backgrounders.html" title="Chapter&#160;16.&#160;Backgrounders">
<link rel="prev" href="special_tut/special_tut_test.html" title="Testing">
<link rel="next" href="lanczos.html" title="The Lanczos Approximation">
@@ -31,13 +31,13 @@
the relative error can be calculated from:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/error2.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/error2.svg"></span>
</p>
<p>
However the test programs in the library use the symmetrical form:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/error1.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/error1.svg"></span>
</p>
<p>
which measures <span class="emphasis"><em>relative difference</em></span> and happens to be less
diff --git a/libs/math/doc/html/math_toolkit/remez.html b/libs/math/doc/html/math_toolkit/remez.html
index 40e3aedd2..72ec521d9 100644
--- a/libs/math/doc/html/math_toolkit/remez.html
+++ b/libs/math/doc/html/math_toolkit/remez.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>The Remez Method</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../backgrounders.html" title="Chapter&#160;16.&#160;Backgrounders">
<link rel="prev" href="lanczos.html" title="The Lanczos Approximation">
<link rel="next" href="refs.html" title="References">
diff --git a/libs/math/doc/html/math_toolkit/result_type.html b/libs/math/doc/html/math_toolkit/result_type.html
index b176d3cea..c7e279e57 100644
--- a/libs/math/doc/html/math_toolkit/result_type.html
+++ b/libs/math/doc/html/math_toolkit/result_type.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Calculation of the Type of the Result</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="namespaces.html" title="Namespaces">
<link rel="next" href="error_handling.html" title="Error Handling">
diff --git a/libs/math/doc/html/math_toolkit/rounding.html b/libs/math/doc/html/math_toolkit/rounding.html
index f4344c5c1..9ef313289 100644
--- a/libs/math/doc/html/math_toolkit/rounding.html
+++ b/libs/math/doc/html/math_toolkit/rounding.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Rounding Truncation and Integer Conversion</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../utils.html" title="Chapter&#160;2.&#160;Floating Point Utilities">
<link rel="prev" href="../utils.html" title="Chapter&#160;2.&#160;Floating Point Utilities">
<link rel="next" href="rounding/round.html" title="Rounding Functions">
@@ -27,7 +27,7 @@
<a name="math_toolkit.rounding"></a><a class="link" href="rounding.html" title="Rounding Truncation and Integer Conversion">Rounding Truncation and Integer
Conversion</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="rounding/round.html">Rounding Functions</a></span></dt>
<dt><span class="section"><a href="rounding/trunc.html">Truncation Functions</a></span></dt>
<dt><span class="section"><a href="rounding/modf.html">Integer and Fractional Part
diff --git a/libs/math/doc/html/math_toolkit/rounding/modf.html b/libs/math/doc/html/math_toolkit/rounding/modf.html
index f637ef13d..60b2f57fd 100644
--- a/libs/math/doc/html/math_toolkit/rounding/modf.html
+++ b/libs/math/doc/html/math_toolkit/rounding/modf.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Integer and Fractional Part Splitting (modf)</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../rounding.html" title="Rounding Truncation and Integer Conversion">
<link rel="prev" href="trunc.html" title="Truncation Functions">
<link rel="next" href="../fpclass.html" title="Floating-Point Classification: Infinities and NaNs">
diff --git a/libs/math/doc/html/math_toolkit/rounding/round.html b/libs/math/doc/html/math_toolkit/rounding/round.html
index b21bb29ca..145af64c9 100644
--- a/libs/math/doc/html/math_toolkit/rounding/round.html
+++ b/libs/math/doc/html/math_toolkit/rounding/round.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Rounding Functions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../rounding.html" title="Rounding Truncation and Integer Conversion">
<link rel="prev" href="../rounding.html" title="Rounding Truncation and Integer Conversion">
<link rel="next" href="trunc.html" title="Truncation Functions">
diff --git a/libs/math/doc/html/math_toolkit/rounding/trunc.html b/libs/math/doc/html/math_toolkit/rounding/trunc.html
index 81892e9f8..691eb4ebd 100644
--- a/libs/math/doc/html/math_toolkit/rounding/trunc.html
+++ b/libs/math/doc/html/math_toolkit/rounding/trunc.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Truncation Functions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../rounding.html" title="Rounding Truncation and Integer Conversion">
<link rel="prev" href="round.html" title="Rounding Functions">
<link rel="next" href="modf.html" title="Integer and Fractional Part Splitting (modf)">
diff --git a/libs/math/doc/html/math_toolkit/run_time.html b/libs/math/doc/html/math_toolkit/run_time.html
index a68698a67..4bbb931c2 100644
--- a/libs/math/doc/html/math_toolkit/run_time.html
+++ b/libs/math/doc/html/math_toolkit/run_time.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Run-time GCD &amp; LCM Determination</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../gcd_lcm.html" title="Chapter&#160;11.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)">
<link rel="prev" href="lcm_function_object.html" title="LCM Function Object">
<link rel="next" href="compile_time.html" title="Compile time GCD and LCM determination">
diff --git a/libs/math/doc/html/math_toolkit/sf_beta.html b/libs/math/doc/html/math_toolkit/sf_beta.html
index 4d1e17d19..9a3e0e656 100644
--- a/libs/math/doc/html/math_toolkit/sf_beta.html
+++ b/libs/math/doc/html/math_toolkit/sf_beta.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Beta Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
<link rel="prev" href="factorials/sf_binomial.html" title="Binomial Coefficients">
<link rel="next" href="sf_beta/beta_function.html" title="Beta">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.sf_beta"></a><a class="link" href="sf_beta.html" title="Beta Functions">Beta Functions</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="sf_beta/beta_function.html">Beta</a></span></dt>
<dt><span class="section"><a href="sf_beta/ibeta_function.html">Incomplete Beta
Functions</a></span></dt>
diff --git a/libs/math/doc/html/math_toolkit/sf_beta/beta_derivative.html b/libs/math/doc/html/math_toolkit/sf_beta/beta_derivative.html
index 5b32df073..a323a47f4 100644
--- a/libs/math/doc/html/math_toolkit/sf_beta/beta_derivative.html
+++ b/libs/math/doc/html/math_toolkit/sf_beta/beta_derivative.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Derivative of the Incomplete Beta Function</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_beta.html" title="Beta Functions">
<link rel="prev" href="ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">
<link rel="next" href="../sf_erf.html" title="Error Functions">
@@ -53,7 +53,7 @@
beta function <a class="link" href="ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/derivative2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/derivative2.svg"></span>
</p>
<p>
The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
diff --git a/libs/math/doc/html/math_toolkit/sf_beta/beta_function.html b/libs/math/doc/html/math_toolkit/sf_beta/beta_function.html
index 9087ca33e..e8aedecd3 100644
--- a/libs/math/doc/html/math_toolkit/sf_beta/beta_function.html
+++ b/libs/math/doc/html/math_toolkit/sf_beta/beta_function.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Beta</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_beta.html" title="Beta Functions">
<link rel="prev" href="../sf_beta.html" title="Beta Functions">
<link rel="next" href="ibeta_function.html" title="Incomplete Beta Functions">
@@ -50,10 +50,10 @@
The beta function is defined by:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/beta1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/beta1.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/beta.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/beta.svg" align="middle"></span>
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
@@ -256,7 +256,7 @@
approximation</a>, then we can combine the power terms:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/beta2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/beta2.svg"></span>
</p>
<p>
which is almost the ideal solution, however almost all of the error occurs
@@ -266,7 +266,7 @@
which immediately cuts the maximum error in half:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/beta3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/beta3.svg"></span>
</p>
<p>
This may not be the final solution, but it is very competitive compared to
@@ -280,7 +280,7 @@
fraction parts are collected together into:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/beta8.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/beta8.svg"></span>
</p>
<p>
where la, lb and lc are the integration limits used for a, b, and a+b.
@@ -293,10 +293,10 @@
we can use the recurrence relations:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/beta4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/beta4.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/beta5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/beta5.svg"></span>
</p>
<p>
to move to a more favorable region where they are both greater than 1.
@@ -305,7 +305,7 @@
In addition:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/beta7.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/beta7.svg"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/sf_beta/ibeta_function.html b/libs/math/doc/html/math_toolkit/sf_beta/ibeta_function.html
index a050e4326..20a3340d5 100644
--- a/libs/math/doc/html/math_toolkit/sf_beta/ibeta_function.html
+++ b/libs/math/doc/html/math_toolkit/sf_beta/ibeta_function.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Incomplete Beta Functions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_beta.html" title="Beta Functions">
<link rel="prev" href="beta_function.html" title="Beta">
<link rel="next" href="ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">
@@ -109,10 +109,10 @@
Returns the normalised incomplete beta function of a, b and x:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta3.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/ibeta.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/ibeta.svg" align="middle"></span>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">);</span>
@@ -125,7 +125,7 @@
and x:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta4.svg"></span>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">beta</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">);</span>
@@ -137,7 +137,7 @@
Returns the full (non-normalised) incomplete beta function of a, b and x:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta1.svg"></span>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">betac</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">);</span>
@@ -150,7 +150,7 @@
of a, b and x:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta2.svg"></span>
</p>
<h5>
<a name="math_toolkit.sf_beta.ibeta_function.h2"></a>
@@ -891,7 +891,7 @@
both x and y, and can return either p or q where these are related by:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv5.svg"></span>
</p>
<p>
so at any point we can swap a for b, x for y and p for q if this results
@@ -905,7 +905,7 @@
than the alternatives - however it is used to generate test data:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta5.svg"></span>
</p>
<p>
The following continued fraction is due to <a href="http://portal.acm.org/citation.cfm?doid=131766.131776" target="_top">Didonato
@@ -913,13 +913,13 @@
greater than 1:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta6.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta6.svg"></span>
</p>
<p>
For smallish b and x then a series representation can be used:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta7.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta7.svg"></span>
</p>
<p>
When b &lt;&lt; a then the transition from 0 to 1 occurs very close to x
@@ -927,7 +927,7 @@
case the following series representation is used:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta8.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta8.svg"></span>
</p>
<p>
@@ -942,17 +942,17 @@
the following finite sum:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta12.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta12.svg"></span>
</p>
<p>
Finally we can sidestep difficult areas, or move to an area with a more efficient
means of computation, by using the duplication formulae:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta10.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta10.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta11.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta11.svg"></span>
</p>
<p>
The domains of a, b and x for which the various methods are used are identical
diff --git a/libs/math/doc/html/math_toolkit/sf_beta/ibeta_inv_function.html b/libs/math/doc/html/math_toolkit/sf_beta/ibeta_inv_function.html
index f3d78ad4e..f18f6513c 100644
--- a/libs/math/doc/html/math_toolkit/sf_beta/ibeta_inv_function.html
+++ b/libs/math/doc/html/math_toolkit/sf_beta/ibeta_inv_function.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>The Incomplete Beta Function Inverses</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_beta.html" title="Beta Functions">
<link rel="prev" href="ibeta_function.html" title="Incomplete Beta Functions">
<link rel="next" href="beta_derivative.html" title="Derivative of the Incomplete Beta Function">
@@ -337,7 +337,7 @@
Firstly recall that:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv5.svg"></span>
</p>
<p>
We may wish to start from either p or q, and to calculate either x or y.
@@ -356,7 +356,7 @@
The nearly symmetrical case (section 2 of the paper) is used for
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv2.svg"></span>
</p>
<p>
and involves solving the inverse error function first. The method is accurate
@@ -367,7 +367,7 @@
The general error function case (section 3 of the paper) is used for
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv3.svg"></span>
</p>
<p>
and again expresses the inverse incomplete beta in terms of the inverse of
@@ -378,7 +378,7 @@
it is better to use the following as an initial estimate:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv4.svg"></span>
</p>
<p>
Finally the for all other cases where <code class="computeroutput"><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span> <span class="special">&gt;</span>
@@ -394,7 +394,7 @@
(<code class="literal">q<sup>1/p</sup> &lt; 10<sup>-3</sup></code>) we use:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv6.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv6.svg"></span>
</p>
<p>
which is both cheaper to compute than the full method, and a more accurate
@@ -417,7 +417,7 @@
and on a convex curve. An initial estimate for x is made with:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv7.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv7.svg"></span>
</p>
<p>
which is provably below the true value for x: <a href="http://en.wikipedia.org/wiki/Newton%27s_method" target="_top">Newton
@@ -435,13 +435,13 @@
and on a concave curve. An initial estimate for x is made with:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv4.svg"></span>
</p>
<p>
which can be improved somewhat to:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv1.svg"></span>
</p>
<p>
when b and x are both small (I've used b &lt; a and x &lt; 0.2). This actually
@@ -456,7 +456,7 @@
points of inflection in [0,1]. For small p, x can be estimated using
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv4.svg"></span>
</p>
<p>
which under-estimates x, and drops us on the right side of the true value
@@ -470,7 +470,7 @@
quarter circle, and estimating y from:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv8.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/ibeta_inv8.svg"></span>
</p>
<p>
This doesn't guarantee that we will drop in on the right side of x for monotonic
diff --git a/libs/math/doc/html/math_toolkit/sf_erf.html b/libs/math/doc/html/math_toolkit/sf_erf.html
index 7edeca764..57e629e86 100644
--- a/libs/math/doc/html/math_toolkit/sf_erf.html
+++ b/libs/math/doc/html/math_toolkit/sf_erf.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Error Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
<link rel="prev" href="sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">
<link rel="next" href="sf_erf/error_function.html" title="Error Functions">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.sf_erf"></a><a class="link" href="sf_erf.html" title="Error Functions">Error Functions</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="sf_erf/error_function.html">Error Functions</a></span></dt>
<dt><span class="section"><a href="sf_erf/error_inv.html">Error Function Inverses</a></span></dt>
</dl></div>
diff --git a/libs/math/doc/html/math_toolkit/sf_erf/error_function.html b/libs/math/doc/html/math_toolkit/sf_erf/error_function.html
index 2582b373e..d71cf4704 100644
--- a/libs/math/doc/html/math_toolkit/sf_erf/error_function.html
+++ b/libs/math/doc/html/math_toolkit/sf_erf/error_function.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Error Functions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_erf.html" title="Error Functions">
<link rel="prev" href="../sf_erf.html" title="Error Functions">
<link rel="next" href="error_inv.html" title="Error Function Inverses">
@@ -74,10 +74,10 @@
of z:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/erf1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/erf1.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/erf.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/erf.svg" align="middle"></span>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erfc</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
@@ -90,10 +90,10 @@
function</a> of z:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/erf2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/erf2.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/erfc.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/erfc.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.sf_erf.error_function.h2"></a>
diff --git a/libs/math/doc/html/math_toolkit/sf_erf/error_inv.html b/libs/math/doc/html/math_toolkit/sf_erf/error_inv.html
index 5b61aae25..1848da903 100644
--- a/libs/math/doc/html/math_toolkit/sf_erf/error_inv.html
+++ b/libs/math/doc/html/math_toolkit/sf_erf/error_inv.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Error Function Inverses</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_erf.html" title="Error Functions">
<link rel="prev" href="error_function.html" title="Error Functions">
<link rel="next" href="../sf_poly.html" title="Polynomials">
@@ -75,7 +75,7 @@
<pre class="programlisting"><span class="identifier">p</span> <span class="special">=</span> <span class="identifier">erf</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span>
</pre>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/erf_inv.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/erf_inv.svg" align="middle"></span>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erfc_inv</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
@@ -90,7 +90,7 @@
<pre class="programlisting"><span class="identifier">p</span> <span class="special">=</span> <span class="identifier">erfc</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span>
</pre>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/erfc_inv.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/erfc_inv.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.sf_erf.error_inv.h2"></a>
diff --git a/libs/math/doc/html/math_toolkit/sf_gamma.html b/libs/math/doc/html/math_toolkit/sf_gamma.html
index 395d73769..705af156f 100644
--- a/libs/math/doc/html/math_toolkit/sf_gamma.html
+++ b/libs/math/doc/html/math_toolkit/sf_gamma.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Gamma Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
<link rel="prev" href="number_series/primes.html" title="Prime Numbers">
<link rel="next" href="sf_gamma/tgamma.html" title="Gamma">
@@ -26,10 +26,12 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.sf_gamma"></a><a class="link" href="sf_gamma.html" title="Gamma Functions">Gamma Functions</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="sf_gamma/tgamma.html">Gamma</a></span></dt>
<dt><span class="section"><a href="sf_gamma/lgamma.html">Log Gamma</a></span></dt>
<dt><span class="section"><a href="sf_gamma/digamma.html">Digamma</a></span></dt>
+<dt><span class="section"><a href="sf_gamma/trigamma.html">Trigamma</a></span></dt>
+<dt><span class="section"><a href="sf_gamma/polygamma.html">Polygamma</a></span></dt>
<dt><span class="section"><a href="sf_gamma/gamma_ratios.html">Ratios of Gamma Functions</a></span></dt>
<dt><span class="section"><a href="sf_gamma/igamma.html">Incomplete Gamma Functions</a></span></dt>
<dt><span class="section"><a href="sf_gamma/igamma_inv.html">Incomplete Gamma Function
diff --git a/libs/math/doc/html/math_toolkit/sf_gamma/digamma.html b/libs/math/doc/html/math_toolkit/sf_gamma/digamma.html
index 58fe9c37f..cf915ee8b 100644
--- a/libs/math/doc/html/math_toolkit/sf_gamma/digamma.html
+++ b/libs/math/doc/html/math_toolkit/sf_gamma/digamma.html
@@ -3,11 +3,11 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Digamma</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_gamma.html" title="Gamma Functions">
<link rel="prev" href="lgamma.html" title="Log Gamma">
-<link rel="next" href="gamma_ratios.html" title="Ratios of Gamma Functions">
+<link rel="next" href="trigamma.html" title="Trigamma">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
@@ -20,7 +20,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="lgamma.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="gamma_ratios.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+<a accesskey="p" href="lgamma.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="trigamma.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
@@ -51,10 +51,10 @@
defined as the logarithmic derivative of the gamma function:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/digamma1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/digamma1.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/digamma.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/digamma.svg" align="middle"></span>
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
@@ -63,11 +63,6 @@
documentation for more details</a>.
</p>
<p>
- There is no fully generic version of this function: all the implementations
- are tuned to specific accuracy levels, the most precise of which delivers
- 34-digits of precision.
- </p>
-<p>
The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
type calculation rules</em></span></a>: the result is of type <code class="computeroutput"><span class="keyword">double</span></code> when T is an integer type, and type
T otherwise.
@@ -308,7 +303,7 @@
For arguments &gt; BIG the asymptotic expansion:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/digamma2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/digamma2.svg"></span>
</p>
<p>
can be used. However, this expansion is divergent after a few terms: exactly
@@ -320,6 +315,17 @@
small number of terms and evaluated as a polynomial in <code class="computeroutput"><span class="number">1</span><span class="special">/(</span><span class="identifier">x</span><span class="special">*</span><span class="identifier">x</span><span class="special">)</span></code>.
</p>
<p>
+ The arbitrary precision version of this function uses recurrence relations
+ until x &gt; BIG, and then evaluation via the asymptotic expansion above.
+ As special cases integer and half integer arguments are handled via:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/digamma4.svg"></span>
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/digamma5.svg"></span>
+ </p>
+<p>
The rational approximation <a class="link" href="../sf_implementation.html#math_toolkit.sf_implementation.rational_approximations_used">devised
by JM</a> in the range [1,2] is derived as follows.
</p>
@@ -329,7 +335,7 @@
the form used is:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/digamma3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/digamma3.svg"></span>
</p>
<p>
Where P(x) and Q(x) are the polynomials from the rational form of the Lanczos
@@ -379,7 +385,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="lgamma.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="gamma_ratios.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+<a accesskey="p" href="lgamma.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="trigamma.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>
diff --git a/libs/math/doc/html/math_toolkit/sf_gamma/gamma_derivatives.html b/libs/math/doc/html/math_toolkit/sf_gamma/gamma_derivatives.html
index 8b1b5f36f..d24f43447 100644
--- a/libs/math/doc/html/math_toolkit/sf_gamma/gamma_derivatives.html
+++ b/libs/math/doc/html/math_toolkit/sf_gamma/gamma_derivatives.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Derivative of the Incomplete Gamma Function</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_gamma.html" title="Gamma Functions">
<link rel="prev" href="igamma_inv.html" title="Incomplete Gamma Function Inverses">
<link rel="next" href="../factorials.html" title="Factorials and Binomial Coefficients">
@@ -53,7 +53,7 @@
gamma function.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/derivative1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/derivative1.svg"></span>
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
diff --git a/libs/math/doc/html/math_toolkit/sf_gamma/gamma_ratios.html b/libs/math/doc/html/math_toolkit/sf_gamma/gamma_ratios.html
index b2a44d905..2bb703977 100644
--- a/libs/math/doc/html/math_toolkit/sf_gamma/gamma_ratios.html
+++ b/libs/math/doc/html/math_toolkit/sf_gamma/gamma_ratios.html
@@ -3,10 +3,10 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Ratios of Gamma Functions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_gamma.html" title="Gamma Functions">
-<link rel="prev" href="digamma.html" title="Digamma">
+<link rel="prev" href="polygamma.html" title="Polygamma">
<link rel="next" href="igamma.html" title="Incomplete Gamma Functions">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@@ -20,7 +20,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="digamma.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="igamma.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+<a accesskey="p" href="polygamma.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="igamma.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
@@ -58,7 +58,7 @@
Returns the ratio of gamma functions:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/gamma_ratio0.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/gamma_ratio0.svg"></span>
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
@@ -80,7 +80,7 @@
Returns the ratio of gamma functions:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/gamma_ratio1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/gamma_ratio1.svg"></span>
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
@@ -100,7 +100,7 @@
otherwise the result type is simple T1.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/tgamma_delta_ratio.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/tgamma_delta_ratio.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.sf_gamma.gamma_ratios.h1"></a>
@@ -349,7 +349,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="digamma.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="igamma.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+<a accesskey="p" href="polygamma.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="igamma.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>
diff --git a/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html b/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html
index 095c79798..c7118eaf0 100644
--- a/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html
+++ b/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Incomplete Gamma Functions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_gamma.html" title="Gamma Functions">
<link rel="prev" href="gamma_ratios.html" title="Ratios of Gamma Functions">
<link rel="next" href="igamma_inv.html" title="Incomplete Gamma Function Inverses">
@@ -97,13 +97,13 @@
Returns the normalised lower incomplete gamma function of a and z:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/igamma4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/igamma4.svg"></span>
</p>
<p>
This function changes rapidly from 0 to 1 around the point z == a:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/gamma_p.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/gamma_p.svg" align="middle"></span>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_q</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">);</span>
@@ -115,13 +115,13 @@
Returns the normalised upper incomplete gamma function of a and z:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/igamma3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/igamma3.svg"></span>
</p>
<p>
This function changes rapidly from 1 to 0 around the point z == a:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/gamma_q.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/gamma_q.svg" align="middle"></span>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma_lower</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">);</span>
@@ -134,7 +134,7 @@
z:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/igamma2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/igamma2.svg"></span>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">);</span>
@@ -147,7 +147,7 @@
z:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/igamma1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/igamma1.svg"></span>
</p>
<h5>
<a name="math_toolkit.sf_gamma.igamma.h2"></a>
@@ -842,19 +842,19 @@
via:
</p>
<p>
- 1) <span class="inlinemediaobject"><img src="../../../equations/igamma5.png"></span>
+ 1) <span class="inlinemediaobject"><img src="../../../equations/igamma5.svg"></span>
</p>
<p>
- 2) <span class="inlinemediaobject"><img src="../../../equations/igamma6.png"></span>
+ 2) <span class="inlinemediaobject"><img src="../../../equations/igamma6.svg"></span>
</p>
<p>
- 3) <span class="inlinemediaobject"><img src="../../../equations/igamma7.png"></span>
+ 3) <span class="inlinemediaobject"><img src="../../../equations/igamma7.svg"></span>
</p>
<p>
The lower incomplete gamma is computed from its series representation:
</p>
<p>
- 4) <span class="inlinemediaobject"><img src="../../../equations/igamma8.png"></span>
+ 4) <span class="inlinemediaobject"><img src="../../../equations/igamma8.svg"></span>
</p>
<p>
Or by subtraction of the upper integral from either &#915;(a) or 1 when <span class="emphasis"><em>x
@@ -864,7 +864,7 @@
The upper integral is computed from Legendre's continued fraction representation:
</p>
<p>
- 5) <span class="inlinemediaobject"><img src="../../../equations/igamma9.png"></span>
+ 5) <span class="inlinemediaobject"><img src="../../../equations/igamma9.svg"></span>
</p>
<p>
When <span class="emphasis"><em>(x &gt; 1.1)</em></span> or by subtraction of the lower integral
@@ -876,14 +876,14 @@
area. However there is another series representation for the lower integral:
</p>
<p>
- 6) <span class="inlinemediaobject"><img src="../../../equations/igamma10.png"></span>
+ 6) <span class="inlinemediaobject"><img src="../../../equations/igamma10.svg"></span>
</p>
<p>
That lends itself to calculation of the upper integral via rearrangement
to:
</p>
<p>
- 7) <span class="inlinemediaobject"><img src="../../../equations/igamma11.png"></span>
+ 7) <span class="inlinemediaobject"><img src="../../../equations/igamma11.svg"></span>
</p>
<p>
Refer to the documentation for <a class="link" href="../powers/powm1.html" title="powm1">powm1</a>
@@ -911,14 +911,14 @@
30</em></span> then the following finite sum is used:
</p>
<p>
- 9) <span class="inlinemediaobject"><img src="../../../equations/igamma1f.png"></span>
+ 9) <span class="inlinemediaobject"><img src="../../../equations/igamma1f.svg"></span>
</p>
<p>
While for half integers in the range <span class="emphasis"><em>0.5 &lt;= a &lt; 30</em></span>
then the following finite sum is used:
</p>
<p>
- 10) <span class="inlinemediaobject"><img src="../../../equations/igamma2f.png"></span>
+ 10) <span class="inlinemediaobject"><img src="../../../equations/igamma2f.svg"></span>
</p>
<p>
These are both more stable and more efficient than the continued fraction
@@ -930,16 +930,16 @@
In this area an expansion due to Temme is used:
</p>
<p>
- 11) <span class="inlinemediaobject"><img src="../../../equations/igamma16.png"></span>
+ 11) <span class="inlinemediaobject"><img src="../../../equations/igamma16.svg"></span>
</p>
<p>
- 12) <span class="inlinemediaobject"><img src="../../../equations/igamma17.png"></span>
+ 12) <span class="inlinemediaobject"><img src="../../../equations/igamma17.svg"></span>
</p>
<p>
- 13) <span class="inlinemediaobject"><img src="../../../equations/igamma18.png"></span>
+ 13) <span class="inlinemediaobject"><img src="../../../equations/igamma18.svg"></span>
</p>
<p>
- 14) <span class="inlinemediaobject"><img src="../../../equations/igamma19.png"></span>
+ 14) <span class="inlinemediaobject"><img src="../../../equations/igamma19.svg"></span>
</p>
<p>
The double sum is truncated to a fixed number of terms - to give a specific
@@ -974,7 +974,7 @@
approximation</a> gives the greatest accuracy:
</p>
<p>
- 15) <span class="inlinemediaobject"><img src="../../../equations/igamma12.png"></span>
+ 15) <span class="inlinemediaobject"><img src="../../../equations/igamma12.svg"></span>
</p>
<p>
In the event that this causes underflow/overflow then the exponent can be
@@ -988,7 +988,7 @@
can be avoided by using:
</p>
<p>
- 16) <span class="inlinemediaobject"><img src="../../../equations/igamma13.png"></span>
+ 16) <span class="inlinemediaobject"><img src="../../../equations/igamma13.svg"></span>
</p>
<p>
when <span class="emphasis"><em>a-x</em></span> is small and a and x are large. There is still
diff --git a/libs/math/doc/html/math_toolkit/sf_gamma/igamma_inv.html b/libs/math/doc/html/math_toolkit/sf_gamma/igamma_inv.html
index c315b98f2..6d9fa71bc 100644
--- a/libs/math/doc/html/math_toolkit/sf_gamma/igamma_inv.html
+++ b/libs/math/doc/html/math_toolkit/sf_gamma/igamma_inv.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Incomplete Gamma Function Inverses</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_gamma.html" title="Gamma Functions">
<link rel="prev" href="igamma.html" title="Incomplete Gamma Functions">
<link rel="next" href="gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">
diff --git a/libs/math/doc/html/math_toolkit/sf_gamma/lgamma.html b/libs/math/doc/html/math_toolkit/sf_gamma/lgamma.html
index a8df176c2..5be633960 100644
--- a/libs/math/doc/html/math_toolkit/sf_gamma/lgamma.html
+++ b/libs/math/doc/html/math_toolkit/sf_gamma/lgamma.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Log Gamma</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_gamma.html" title="Gamma Functions">
<link rel="prev" href="tgamma.html" title="Gamma">
<link rel="next" href="digamma.html" title="Digamma">
@@ -57,7 +57,7 @@
is defined by:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/lgamm1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/lgamm1.svg"></span>
</p>
<p>
The second form of the function takes a pointer to an integer, which if non-null
@@ -70,7 +70,7 @@
documentation for more details</a>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/lgamma.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/lgamma.svg" align="middle"></span>
</p>
<p>
There are effectively two versions of this function internally: a fully generic
@@ -359,7 +359,7 @@
for large arguments:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/gamma6.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/gamma6.svg"></span>
</p>
<p>
For small arguments, the logarithm of tgamma is used.
@@ -369,7 +369,7 @@
formula is used:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/lgamm3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/lgamm3.svg"></span>
</p>
<p>
For types of known precision, the <a class="link" href="../lanczos.html" title="The Lanczos Approximation">Lanczos
@@ -378,7 +378,7 @@
<a class="link" href="../lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a> is:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/lgamm4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/lgamm4.svg"></span>
</p>
<p>
Where L<sub>e,g</sub> &#160; is the Lanczos sum, scaled by e<sup>g</sup>.
@@ -447,7 +447,7 @@
-&gt; 1</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/lgamm5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/lgamm5.svg"></span>
</p>
<p>
The C<sub>k</sub> &#160; terms in the above are the same as in the <a class="link" href="../lanczos.html" title="The Lanczos Approximation">Lanczos
@@ -457,7 +457,7 @@
A similar rearrangement can be performed at <span class="emphasis"><em>z = 2</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/lgamm6.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/lgamm6.svg"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/sf_gamma/polygamma.html b/libs/math/doc/html/math_toolkit/sf_gamma/polygamma.html
new file mode 100644
index 000000000..de3526403
--- /dev/null
+++ b/libs/math/doc/html/math_toolkit/sf_gamma/polygamma.html
@@ -0,0 +1,285 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Polygamma</title>
+<link rel="stylesheet" href="../../math.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="../sf_gamma.html" title="Gamma Functions">
+<link rel="prev" href="trigamma.html" title="Trigamma">
+<link rel="next" href="gamma_ratios.html" title="Ratios of Gamma Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center"><a href="../../../../../../index.html">Home</a></td>
+<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
+<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
+<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
+<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="trigamma.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="gamma_ratios.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.sf_gamma.polygamma"></a><a class="link" href="polygamma.html" title="Polygamma">Polygamma</a>
+</h3></div></div></div>
+<h5>
+<a name="math_toolkit.sf_gamma.polygamma.h0"></a>
+ <span class="phrase"><a name="math_toolkit.sf_gamma.polygamma.synopsis"></a></span><a class="link" href="polygamma.html#math_toolkit.sf_gamma.polygamma.synopsis">Synopsis</a>
+ </h5>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">polygamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">polygamma</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">polygamma</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces</span>
+</pre>
+<h5>
+<a name="math_toolkit.sf_gamma.polygamma.h1"></a>
+ <span class="phrase"><a name="math_toolkit.sf_gamma.polygamma.description"></a></span><a class="link" href="polygamma.html#math_toolkit.sf_gamma.polygamma.description">Description</a>
+ </h5>
+<p>
+ Returns the polygamma function of <span class="emphasis"><em>x</em></span>. Polygamma is defined
+ as the n'th derivative of the digamma function:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/polygamma1.svg"></span>
+ </p>
+<p>
+ The following graphs illustrate the behaviour of the function for odd and
+ even order:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../graphs/polygamma2.svg" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/polygamma3.svg" align="middle"></span>
+ </p>
+<p>
+ The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
+ be used to control the behaviour of the function: how it handles errors,
+ what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">policy
+ documentation for more details</a>.
+ </p>
+<p>
+ The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+ type calculation rules</em></span></a>: the result is of type <code class="computeroutput"><span class="keyword">double</span></code> when T is an integer type, and type
+ T otherwise.
+ </p>
+<h5>
+<a name="math_toolkit.sf_gamma.polygamma.h2"></a>
+ <span class="phrase"><a name="math_toolkit.sf_gamma.polygamma.accuracy"></a></span><a class="link" href="polygamma.html#math_toolkit.sf_gamma.polygamma.accuracy">Accuracy</a>
+ </h5>
+<p>
+ The following table shows the peak errors (in units of epsilon) found on
+ various platforms with various floating point types. Unless otherwise specified
+ any floating point type that is narrower than the one shown will have <a class="link" href="../relative_error.html#math_toolkit.relative_error.zero_error">effectively zero error</a>.
+ </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+ <p>
+ Significand Size
+ </p>
+ </th>
+<th>
+ <p>
+ Platform and Compiler
+ </p>
+ </th>
+<th>
+ <p>
+ Small-medium positive arguments
+ </p>
+ </th>
+<th>
+ <p>
+ Small-medium negative x
+ </p>
+ </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+ <p>
+ 53
+ </p>
+ </td>
+<td>
+ <p>
+ Win32 Visual C++ 12
+ </p>
+ </td>
+<td>
+ <p>
+ Peak=5.0 Mean=1
+ </p>
+ </td>
+<td>
+ <p>
+ Peak=1200 Mean=65
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ 64
+ </p>
+ </td>
+<td>
+ <p>
+ Win64 Mingw GCC
+ </p>
+ </td>
+<td>
+ <p>
+ Peak=16 Mean=3
+ </p>
+ </td>
+<td>
+ <p>
+ Peak=33 Mean=3
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ 113
+ </p>
+ </td>
+<td>
+ <p>
+ Win64 Mingw GCC __float128
+ </p>
+ </td>
+<td>
+ <p>
+ Peak=6.5 Mean=1
+ </p>
+ </td>
+<td>
+ <p>
+ Peak=30 Mean=4
+ </p>
+ </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+ As shown above, error rates are generally very acceptable for moderately
+ sized arguments. Error rates should stay low for exact inputs, however, please
+ note that the function becomes exceptionally sensitive to small changes in
+ input for large n and negative x, indeed for cases where <span class="emphasis"><em>n!</em></span>
+ would overflow, the function changes directly from -&#8734; to +&#8734; somewhere between
+ each negative integer - <span class="emphasis"><em>these cases are not handled correctly</em></span>.
+ </p>
+<p>
+ <span class="bold"><strong>For these reasons results should be treated with extreme
+ caution when <span class="emphasis"><em>n</em></span> is large and x negative</strong></span>.
+ </p>
+<h5>
+<a name="math_toolkit.sf_gamma.polygamma.h3"></a>
+ <span class="phrase"><a name="math_toolkit.sf_gamma.polygamma.testing"></a></span><a class="link" href="polygamma.html#math_toolkit.sf_gamma.polygamma.testing">Testing</a>
+ </h5>
+<p>
+ Testing is against Mathematica generated spot values to 35 digit precision.
+ </p>
+<h5>
+<a name="math_toolkit.sf_gamma.polygamma.h4"></a>
+ <span class="phrase"><a name="math_toolkit.sf_gamma.polygamma.implementation"></a></span><a class="link" href="polygamma.html#math_toolkit.sf_gamma.polygamma.implementation">Implementation</a>
+ </h5>
+<p>
+ For x &lt; 0 the following reflection formula is used:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/polygamma2.svg"></span>
+ </p>
+<p>
+ The n'th derivative of <span class="emphasis"><em>cot(x)</em></span> is tabulated for small
+ <span class="emphasis"><em>n</em></span>, and for larger n has the general form:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/polygamma3.svg"></span>
+ </p>
+<p>
+ The coefficients of the cosine terms can be calculated iteratively starting
+ from <span class="emphasis"><em>C<sub>1,0</sub> = -1</em></span> and then using
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/polygamma7.svg"></span>
+ </p>
+<p>
+ to generate coefficients for n+1.
+ </p>
+<p>
+ Note that every other coefficient is zero, and therefore what we have are
+ even or odd polynomials depending on whether n is even or odd.
+ </p>
+<p>
+ Once x is positive then we have two methods available to us, for small x
+ we use the series expansion:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/polygamma4.svg"></span>
+ </p>
+<p>
+ Note that the evaluation of zeta functions at integer values is essentially
+ a table lookup as <a class="link" href="../zetas/zeta.html" title="Riemann Zeta Function">zeta</a> is
+ optimized for those cases.
+ </p>
+<p>
+ For large x we use the asymptotic expansion:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/polygamma5.svg"></span>
+ </p>
+<p>
+ For x in-between the two extremes we use the relation:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/polygamma6.svg"></span>
+ </p>
+<p>
+ to make x large enough for the asymptotic expansion to be used.
+ </p>
+<p>
+ There are also two special cases:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/polygamma8.svg"></span>
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/polygamma9.svg"></span>
+ </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
+ Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
+ Holin, Bruno Lalande, John Maddock, Johan R&#229;de, Gautam Sewani, Benjamin Sobotta,
+ Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+ </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="trigamma.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="gamma_ratios.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>
diff --git a/libs/math/doc/html/math_toolkit/sf_gamma/tgamma.html b/libs/math/doc/html/math_toolkit/sf_gamma/tgamma.html
index 937d4e55b..5f2e09031 100644
--- a/libs/math/doc/html/math_toolkit/sf_gamma/tgamma.html
+++ b/libs/math/doc/html/math_toolkit/sf_gamma/tgamma.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Gamma</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_gamma.html" title="Gamma Functions">
<link rel="prev" href="../sf_gamma.html" title="Gamma Functions">
<link rel="next" href="lgamma.html" title="Log Gamma">
@@ -62,10 +62,10 @@
Returns the "true gamma" (hence name tgamma) of value z:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/gamm1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/gamm1.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/tgamma.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/tgamma.svg" align="middle"></span>
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
@@ -393,7 +393,7 @@
function is implemented Sterling's approximation for lgamma for large z:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/gamma6.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/gamma6.svg"></span>
</p>
<p>
Following exponentiation, downward recursion is then used for small values
@@ -409,19 +409,19 @@
&gt; 1 via:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/gamm3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/gamm3.svg"></span>
</p>
<p>
For very small z, this helps to preserve the identity:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/gamm4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/gamm4.svg"></span>
</p>
<p>
For z &lt; -20 the reflection formula:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/gamm5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/gamm5.svg"></span>
</p>
<p>
is used. Particular care has to be taken to evaluate the <code class="literal">z * sin(&#960; &#160; *
diff --git a/libs/math/doc/html/math_toolkit/sf_gamma/trigamma.html b/libs/math/doc/html/math_toolkit/sf_gamma/trigamma.html
new file mode 100644
index 000000000..b7d758b85
--- /dev/null
+++ b/libs/math/doc/html/math_toolkit/sf_gamma/trigamma.html
@@ -0,0 +1,217 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Trigamma</title>
+<link rel="stylesheet" href="../../math.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="../sf_gamma.html" title="Gamma Functions">
+<link rel="prev" href="digamma.html" title="Digamma">
+<link rel="next" href="polygamma.html" title="Polygamma">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center"><a href="../../../../../../index.html">Home</a></td>
+<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
+<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
+<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
+<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="digamma.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="polygamma.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.sf_gamma.trigamma"></a><a class="link" href="trigamma.html" title="Trigamma">Trigamma</a>
+</h3></div></div></div>
+<h5>
+<a name="math_toolkit.sf_gamma.trigamma.h0"></a>
+ <span class="phrase"><a name="math_toolkit.sf_gamma.trigamma.synopsis"></a></span><a class="link" href="trigamma.html#math_toolkit.sf_gamma.trigamma.synopsis">Synopsis</a>
+ </h5>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">trigamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">trigamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">trigamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces</span>
+</pre>
+<h5>
+<a name="math_toolkit.sf_gamma.trigamma.h1"></a>
+ <span class="phrase"><a name="math_toolkit.sf_gamma.trigamma.description"></a></span><a class="link" href="trigamma.html#math_toolkit.sf_gamma.trigamma.description">Description</a>
+ </h5>
+<p>
+ Returns the trigamma function of <span class="emphasis"><em>x</em></span>. Trigamma is defined
+ as the derivative of the digamma function:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/trigamma1.svg"></span>
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../graphs/trigamma.svg" align="middle"></span>
+ </p>
+<p>
+ The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
+ be used to control the behaviour of the function: how it handles errors,
+ what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">policy
+ documentation for more details</a>.
+ </p>
+<p>
+ The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+ type calculation rules</em></span></a>: the result is of type <code class="computeroutput"><span class="keyword">double</span></code> when T is an integer type, and type
+ T otherwise.
+ </p>
+<h5>
+<a name="math_toolkit.sf_gamma.trigamma.h2"></a>
+ <span class="phrase"><a name="math_toolkit.sf_gamma.trigamma.accuracy"></a></span><a class="link" href="trigamma.html#math_toolkit.sf_gamma.trigamma.accuracy">Accuracy</a>
+ </h5>
+<p>
+ The following table shows the peak errors (in units of epsilon) found on
+ various platforms with various floating point types. Unless otherwise specified
+ any floating point type that is narrower than the one shown will have <a class="link" href="../relative_error.html#math_toolkit.relative_error.zero_error">effectively zero error</a>.
+ </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+ <p>
+ Significand Size
+ </p>
+ </th>
+<th>
+ <p>
+ Platform and Compiler
+ </p>
+ </th>
+<th>
+ <p>
+ Random Values
+ </p>
+ </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+ <p>
+ 53
+ </p>
+ </td>
+<td>
+ <p>
+ Win32 Visual C++ 12
+ </p>
+ </td>
+<td>
+ <p>
+ Peak=1.0 Mean=0.4
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ 64
+ </p>
+ </td>
+<td>
+ <p>
+ Win64 Mingw GCC
+ </p>
+ </td>
+<td>
+ <p>
+ Peak=1.4 Mean=0.4
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ 113
+ </p>
+ </td>
+<td>
+ <p>
+ Win64 Mingw GCC __float128
+ </p>
+ </td>
+<td>
+ <p>
+ Peak=1.0 Mean=0.5
+ </p>
+ </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+ As shown above, error rates are generally very low for built in types. For
+ multiprecision types, error rates are typically in the order of a few epsilon.
+ </p>
+<h5>
+<a name="math_toolkit.sf_gamma.trigamma.h3"></a>
+ <span class="phrase"><a name="math_toolkit.sf_gamma.trigamma.testing"></a></span><a class="link" href="trigamma.html#math_toolkit.sf_gamma.trigamma.testing">Testing</a>
+ </h5>
+<p>
+ Testing is against Mathematica generated spot values to 35 digit precision.
+ </p>
+<h5>
+<a name="math_toolkit.sf_gamma.trigamma.h4"></a>
+ <span class="phrase"><a name="math_toolkit.sf_gamma.trigamma.implementation"></a></span><a class="link" href="trigamma.html#math_toolkit.sf_gamma.trigamma.implementation">Implementation</a>
+ </h5>
+<p>
+ The arbitrary precision version of this function simply calls <a class="link" href="polygamma.html" title="Polygamma">polygamma</a>.
+ </p>
+<p>
+ For built in fixed precision types, negative arguments are first made positive
+ via:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/trigamma2.svg"></span>
+ </p>
+<p>
+ Then arguments in the range [0, 1) are shifted to &gt;= 1 via:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/trigamma3.svg"></span>
+ </p>
+<p>
+ Then evaluation is via one of a number of rational approximations, for small
+ x these are of the form:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/trigamma4.svg"></span>
+ </p>
+<p>
+ and for large x of the form:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/trigamma5.svg"></span>
+ </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
+ Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
+ Holin, Bruno Lalande, John Maddock, Johan R&#229;de, Gautam Sewani, Benjamin Sobotta,
+ Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+ </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="digamma.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="polygamma.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>
diff --git a/libs/math/doc/html/math_toolkit/sf_implementation.html b/libs/math/doc/html/math_toolkit/sf_implementation.html
index 5a9bd254a..e769c8419 100644
--- a/libs/math/doc/html/math_toolkit/sf_implementation.html
+++ b/libs/math/doc/html/math_toolkit/sf_implementation.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Additional Implementation Notes</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../backgrounders.html" title="Chapter&#160;16.&#160;Backgrounders">
<link rel="prev" href="../backgrounders.html" title="Chapter&#160;16.&#160;Backgrounders">
<link rel="next" href="special_tut.html" title="Tutorial: How to Write a New Special Function">
@@ -710,7 +710,20 @@
/cygdrive/c/progra~1/Inkscape/inkscape -d 120 -e $(cygpath -a -w $(basename $file .svg).png) $(cygpath -a -w $file);
done</pre>
<p>
- Currently Inkscape seems to generate the better looking png's.
+ Using BASH
+ </p>
+<pre class="programlisting"># Convert single SVG to PNG file.
+# /c/progra~1/Inkscape/inkscape -d 120 -e a.png a.svg
+</pre>
+<p>
+ or to convert All files in folder SVG to PNG.
+ </p>
+<pre class="programlisting">for file in *.svg; do
+/c/progra~1/Inkscape/inkscape -d 120 -e $(basename $file .svg).png $file
+done
+</pre>
+<p>
+ Currently Inkscape seems to generate the better looking PNGs.
</p>
<p>
The PDF is generated into \pdf\math.pdf using a command from a shell or command
diff --git a/libs/math/doc/html/math_toolkit/sf_poly.html b/libs/math/doc/html/math_toolkit/sf_poly.html
index 14b261e40..9d7a302cb 100644
--- a/libs/math/doc/html/math_toolkit/sf_poly.html
+++ b/libs/math/doc/html/math_toolkit/sf_poly.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Polynomials</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
<link rel="prev" href="sf_erf/error_inv.html" title="Error Function Inverses">
<link rel="next" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.sf_poly"></a><a class="link" href="sf_poly.html" title="Polynomials">Polynomials</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="sf_poly/legendre.html">Legendre (and Associated)
Polynomials</a></span></dt>
<dt><span class="section"><a href="sf_poly/laguerre.html">Laguerre (and Associated)
diff --git a/libs/math/doc/html/math_toolkit/sf_poly/hermite.html b/libs/math/doc/html/math_toolkit/sf_poly/hermite.html
index 140db0932..24ed0fe44 100644
--- a/libs/math/doc/html/math_toolkit/sf_poly/hermite.html
+++ b/libs/math/doc/html/math_toolkit/sf_poly/hermite.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Hermite Polynomials</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_poly.html" title="Polynomials">
<link rel="prev" href="laguerre.html" title="Laguerre (and Associated) Polynomials">
<link rel="next" href="sph_harm.html" title="Spherical Harmonics">
@@ -66,7 +66,7 @@
at point <span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/hermite_0.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/hermite_0.svg"></span>
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
@@ -78,7 +78,7 @@
The following graph illustrates the behaviour of the first few Hermite Polynomials:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/hermite.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/hermite.svg" align="middle"></span>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hermite_next</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">Hn</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">Hnm1</span><span class="special">);</span>
@@ -89,7 +89,7 @@
same <span class="emphasis"><em>x</em></span>, and for rising <span class="emphasis"><em>n</em></span>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/hermite_1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/hermite_1.svg"></span>
</p>
<p>
For example we could produce a vector of the first 10 polynomial values using:
diff --git a/libs/math/doc/html/math_toolkit/sf_poly/laguerre.html b/libs/math/doc/html/math_toolkit/sf_poly/laguerre.html
index ae91c8b7c..4e683e3e5 100644
--- a/libs/math/doc/html/math_toolkit/sf_poly/laguerre.html
+++ b/libs/math/doc/html/math_toolkit/sf_poly/laguerre.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Laguerre (and Associated) Polynomials</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_poly.html" title="Polynomials">
<link rel="prev" href="legendre.html" title="Legendre (and Associated) Polynomials">
<link rel="next" href="hermite.html" title="Hermite Polynomials">
@@ -83,13 +83,13 @@
at point <span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/laguerre_0.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/laguerre_0.svg"></span>
</p>
<p>
The following graph illustrates the behaviour of the first few Laguerre Polynomials:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/laguerre.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/laguerre.svg" align="middle"></span>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
@@ -102,7 +102,7 @@
and order <span class="emphasis"><em>m</em></span> at point <span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/laguerre_1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/laguerre_1.svg"></span>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">laguerre_next</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">Ln</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">Lnm1</span><span class="special">);</span>
@@ -113,7 +113,7 @@
same <span class="emphasis"><em>x</em></span>, and for rising <span class="emphasis"><em>n</em></span>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/laguerre_2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/laguerre_2.svg"></span>
</p>
<p>
For example we could produce a vector of the first 10 polynomial values using:
@@ -157,7 +157,7 @@
at the same <span class="emphasis"><em>x</em></span>, and for rising degree <span class="emphasis"><em>n</em></span>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/laguerre_3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/laguerre_3.svg"></span>
</p>
<p>
For example we could produce a vector of the first 10 polynomial values using:
diff --git a/libs/math/doc/html/math_toolkit/sf_poly/legendre.html b/libs/math/doc/html/math_toolkit/sf_poly/legendre.html
index 6750f978a..458fc02b9 100644
--- a/libs/math/doc/html/math_toolkit/sf_poly/legendre.html
+++ b/libs/math/doc/html/math_toolkit/sf_poly/legendre.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Legendre (and Associated) Polynomials</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_poly.html" title="Polynomials">
<link rel="prev" href="../sf_poly.html" title="Polynomials">
<link rel="next" href="laguerre.html" title="Laguerre (and Associated) Polynomials">
@@ -88,7 +88,7 @@
Returns the Legendre Polynomial of the first kind:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/legendre_0.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/legendre_0.svg"></span>
</p>
<p>
Requires -1 &lt;= x &lt;= 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
@@ -103,7 +103,7 @@
The following graph illustrates the behaviour of the first few Legendre Polynomials:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/legendre_p.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/legendre_p.svg" align="middle"></span>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
@@ -115,7 +115,7 @@
Returns the associated Legendre polynomial of the first kind:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/legendre_1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/legendre_1.svg"></span>
</p>
<p>
Requires -1 &lt;= x &lt;= 1, otherwise returns the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>.
@@ -125,7 +125,7 @@
handled via the identity relations:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/legendre_3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/legendre_3.svg"></span>
</p>
<div class="caution"><table border="0" summary="Caution">
<tr>
@@ -171,7 +171,7 @@
to the Legendre differential equation, for example:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/legendre_2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/legendre_2.svg"></span>
</p>
<p>
Requires -1 &lt;= x &lt;= 1, otherwise <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
@@ -182,7 +182,7 @@
kind:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/legendre_q.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/legendre_q.svg" align="middle"></span>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_next</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">Pl</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">Plm1</span><span class="special">);</span>
@@ -195,7 +195,7 @@
second kinds.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/legendre_4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/legendre_4.svg"></span>
</p>
<p>
For example we could produce a vector of the first 10 polynomial values using:
@@ -243,7 +243,7 @@
at the same <span class="emphasis"><em>x</em></span>, and for rising <span class="emphasis"><em>l</em></span>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/legendre_5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/legendre_5.svg"></span>
</p>
<p>
For example we could produce a vector of the first m+10 polynomial values
diff --git a/libs/math/doc/html/math_toolkit/sf_poly/sph_harm.html b/libs/math/doc/html/math_toolkit/sf_poly/sph_harm.html
index c975b8749..45ec13c49 100644
--- a/libs/math/doc/html/math_toolkit/sf_poly/sph_harm.html
+++ b/libs/math/doc/html/math_toolkit/sf_poly/sph_harm.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Spherical Harmonics</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sf_poly.html" title="Polynomials">
<link rel="prev" href="hermite.html" title="Hermite Polynomials">
<link rel="next" href="../bessel.html" title="Bessel Functions">
@@ -78,7 +78,7 @@
Returns the value of the Spherical Harmonic Y<sub>n</sub><sup>m</sup>(theta, phi):
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/spherical_0.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/spherical_0.svg"></span>
</p>
<p>
The spherical harmonics Y<sub>n</sub><sup>m</sup>(theta, phi) are the angular portion of the solution
@@ -130,7 +130,7 @@
Returns the real part of Y<sub>n</sub><sup>m</sup>(theta, phi):
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/spherical_1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/spherical_1.svg"></span>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">spherical_harmonic_i</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
@@ -142,7 +142,7 @@
Returns the imaginary part of Y<sub>n</sub><sup>m</sup>(theta, phi):
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/spherical_2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/spherical_2.svg"></span>
</p>
<h5>
<a name="math_toolkit.sf_poly.sph_harm.h2"></a>
diff --git a/libs/math/doc/html/math_toolkit/sign_functions.html b/libs/math/doc/html/math_toolkit/sign_functions.html
index d8788676d..df3577942 100644
--- a/libs/math/doc/html/math_toolkit/sign_functions.html
+++ b/libs/math/doc/html/math_toolkit/sign_functions.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Sign Manipulation Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../utils.html" title="Chapter&#160;2.&#160;Floating Point Utilities">
<link rel="prev" href="fpclass.html" title="Floating-Point Classification: Infinities and NaNs">
<link rel="next" href="fp_facets.html" title="Facets for Floating-Point Infinities and NaNs">
diff --git a/libs/math/doc/html/math_toolkit/sinc.html b/libs/math/doc/html/math_toolkit/sinc.html
index 7e48446c9..0b95a5e4f 100644
--- a/libs/math/doc/html/math_toolkit/sinc.html
+++ b/libs/math/doc/html/math_toolkit/sinc.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Sinus Cardinal and Hyperbolic Sinus Cardinal Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
<link rel="prev" href="powers/ct_pow.html" title="Compile Time Power of a Runtime Base">
<link rel="next" href="sinc/sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">
@@ -27,7 +27,7 @@
<a name="math_toolkit.sinc"></a><a class="link" href="sinc.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions">Sinus Cardinal and Hyperbolic Sinus
Cardinal Functions</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="sinc/sinc_overview.html">Sinus Cardinal and Hyperbolic
Sinus Cardinal Functions Overview</a></span></dt>
<dt><span class="section"><a href="sinc/sinc_pi.html">sinc_pi</a></span></dt>
diff --git a/libs/math/doc/html/math_toolkit/sinc/sinc_overview.html b/libs/math/doc/html/math_toolkit/sinc/sinc_overview.html
index 1b8649aea..f07c80e5a 100644
--- a/libs/math/doc/html/math_toolkit/sinc/sinc_overview.html
+++ b/libs/math/doc/html/math_toolkit/sinc/sinc_overview.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sinc.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions">
<link rel="prev" href="../sinc.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions">
<link rel="next" href="sinc_pi.html" title="sinc_pi">
@@ -33,7 +33,7 @@
&gt; 0</code>) is defined by
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb20.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb20.svg"></span>
</p>
<p>
it sees heavy use in signal processing tasks.
@@ -44,7 +44,7 @@
indices <code class="literal">a &gt; 0</code>) is defined by
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb22.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb22.svg"></span>
</p>
<p>
These two families of functions are composed of entire functions.
diff --git a/libs/math/doc/html/math_toolkit/sinc/sinc_pi.html b/libs/math/doc/html/math_toolkit/sinc/sinc_pi.html
index 60e74d263..5116691e0 100644
--- a/libs/math/doc/html/math_toolkit/sinc/sinc_pi.html
+++ b/libs/math/doc/html/math_toolkit/sinc/sinc_pi.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>sinc_pi</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sinc.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions">
<link rel="prev" href="sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">
<link rel="next" href="sinhc_pi.html" title="sinhc_pi">
@@ -51,7 +51,7 @@
series are used at the origin to ensure accuracy.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/sinc_pi.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/sinc_pi.svg" align="middle"></span>
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
diff --git a/libs/math/doc/html/math_toolkit/sinc/sinhc_pi.html b/libs/math/doc/html/math_toolkit/sinc/sinhc_pi.html
index 461568b31..d67562001 100644
--- a/libs/math/doc/html/math_toolkit/sinc/sinhc_pi.html
+++ b/libs/math/doc/html/math_toolkit/sinc/sinhc_pi.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>sinhc_pi</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../sinc.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions">
<link rel="prev" href="sinc_pi.html" title="sinc_pi">
<link rel="next" href="../inv_hyper.html" title="Inverse Hyperbolic Functions">
@@ -61,7 +61,7 @@
documentation for more details</a>.
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/sinhc_pi.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/sinhc_pi.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
diff --git a/libs/math/doc/html/math_toolkit/spec.html b/libs/math/doc/html/math_toolkit/spec.html
index 2d387d99d..a1421a114 100644
--- a/libs/math/doc/html/math_toolkit/spec.html
+++ b/libs/math/doc/html/math_toolkit/spec.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Quaternion Specializations</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="quat.html" title="Template Class quaternion">
<link rel="next" href="mem_typedef.html" title="Quaternion Member Typedefs">
diff --git a/libs/math/doc/html/math_toolkit/special_tut.html b/libs/math/doc/html/math_toolkit/special_tut.html
index c70783748..4e141c3bc 100644
--- a/libs/math/doc/html/math_toolkit/special_tut.html
+++ b/libs/math/doc/html/math_toolkit/special_tut.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Tutorial: How to Write a New Special Function</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../backgrounders.html" title="Chapter&#160;16.&#160;Backgrounders">
<link rel="prev" href="sf_implementation.html" title="Additional Implementation Notes">
<link rel="next" href="special_tut/special_tut_impl.html" title="Implementation">
@@ -27,7 +27,7 @@
<a name="math_toolkit.special_tut"></a><a class="link" href="special_tut.html" title="Tutorial: How to Write a New Special Function">Tutorial: How to Write a New
Special Function</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="special_tut/special_tut_impl.html">Implementation</a></span></dt>
<dt><span class="section"><a href="special_tut/special_tut_test.html">Testing</a></span></dt>
</dl></div>
diff --git a/libs/math/doc/html/math_toolkit/special_tut/special_tut_impl.html b/libs/math/doc/html/math_toolkit/special_tut/special_tut_impl.html
index cf25ccd61..6a2b41312 100644
--- a/libs/math/doc/html/math_toolkit/special_tut/special_tut_impl.html
+++ b/libs/math/doc/html/math_toolkit/special_tut/special_tut_impl.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Implementation</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special_tut.html" title="Tutorial: How to Write a New Special Function">
<link rel="prev" href="../special_tut.html" title="Tutorial: How to Write a New Special Function">
<link rel="next" href="special_tut_test.html" title="Testing">
diff --git a/libs/math/doc/html/math_toolkit/special_tut/special_tut_test.html b/libs/math/doc/html/math_toolkit/special_tut/special_tut_test.html
index 9298c6fb6..ccbb81194 100644
--- a/libs/math/doc/html/math_toolkit/special_tut/special_tut_test.html
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<link rel="prev" href="../dist.html" title="Chapter&#160;5.&#160;Statistical Distributions and Functions">
<link rel="next" href="stat_tut/overview.html" title="Overview of Distributions">
@@ -26,7 +26,7 @@
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</h2></div></div></div>
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+<div class="toc"><dl>
<dt><span class="section"><a href="stat_tut/overview.html">Overview of Distributions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="stat_tut/overview/headers.html">Headers and
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/dist_params.html b/libs/math/doc/html/math_toolkit/stat_tut/dist_params.html
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--- a/libs/math/doc/html/math_toolkit/stat_tut/dist_params.html
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Discrete Probability Distributions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
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-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
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<link rel="up" href="../stat_tut.html" title="Statistical Distributions Tutorial">
<link rel="prev" href="variates.html" title="Random Variates and Distribution Parameters">
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diff --git a/libs/math/doc/html/math_toolkit/stat_tut/overview.html b/libs/math/doc/html/math_toolkit/stat_tut/overview.html
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<link rel="up" href="../stat_tut.html" title="Statistical Distributions Tutorial">
<link rel="prev" href="../stat_tut.html" title="Statistical Distributions Tutorial">
<link rel="next" href="overview/headers.html" title="Headers and Namespaces">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h3 class="title">
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</h3></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="overview/headers.html">Headers and
Namespaces</a></span></dt>
<dt><span class="section"><a href="overview/objects.html">Distributions
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/overview/complements.html b/libs/math/doc/html/math_toolkit/stat_tut/overview/complements.html
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--- a/libs/math/doc/html/math_toolkit/stat_tut/overview/complements.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Complements are supported too - and when to use them</title>
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-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Overview of Distributions">
<link rel="prev" href="generic.html" title="Generic operations common to all distributions are non-member functions">
<link rel="next" href="parameters.html" title="Parameters can be calculated">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/overview/generic.html b/libs/math/doc/html/math_toolkit/stat_tut/overview/generic.html
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--- a/libs/math/doc/html/math_toolkit/stat_tut/overview/generic.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Generic operations common to all distributions are non-member functions</title>
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-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
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+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Overview of Distributions">
<link rel="prev" href="objects.html" title="Distributions are Objects">
<link rel="next" href="complements.html" title="Complements are supported too - and when to use them">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/overview/headers.html b/libs/math/doc/html/math_toolkit/stat_tut/overview/headers.html
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--- a/libs/math/doc/html/math_toolkit/stat_tut/overview/headers.html
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Headers and Namespaces</title>
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-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
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+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Overview of Distributions">
<link rel="prev" href="../overview.html" title="Overview of Distributions">
<link rel="next" href="objects.html" title="Distributions are Objects">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/overview/objects.html b/libs/math/doc/html/math_toolkit/stat_tut/overview/objects.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Distributions are Objects</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Overview of Distributions">
<link rel="prev" href="headers.html" title="Headers and Namespaces">
<link rel="next" href="generic.html" title="Generic operations common to all distributions are non-member functions">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/overview/parameters.html b/libs/math/doc/html/math_toolkit/stat_tut/overview/parameters.html
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--- a/libs/math/doc/html/math_toolkit/stat_tut/overview/parameters.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/overview/parameters.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Parameters can be calculated</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Overview of Distributions">
<link rel="prev" href="complements.html" title="Complements are supported too - and when to use them">
<link rel="next" href="summary.html" title="Summary">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/overview/summary.html b/libs/math/doc/html/math_toolkit/stat_tut/overview/summary.html
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--- a/libs/math/doc/html/math_toolkit/stat_tut/overview/summary.html
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Summary</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Overview of Distributions">
<link rel="prev" href="parameters.html" title="Parameters can be calculated">
<link rel="next" href="../weg.html" title="Worked Examples">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/variates.html b/libs/math/doc/html/math_toolkit/stat_tut/variates.html
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Random Variates and Distribution Parameters</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
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+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../stat_tut.html" title="Statistical Distributions Tutorial">
<link rel="prev" href="weg/c_sharp.html" title="Using the Distributions from Within C#">
<link rel="next" href="dist_params.html" title="Discrete Probability Distributions">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Worked Examples</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
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+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../stat_tut.html" title="Statistical Distributions Tutorial">
<link rel="prev" href="overview/summary.html" title="Summary">
<link rel="next" href="weg/dist_construct_eg.html" title="Distribution Construction Examples">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.stat_tut.weg"></a><a class="link" href="weg.html" title="Worked Examples">Worked Examples</a>
</h3></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="weg/dist_construct_eg.html">Distribution
Construction Examples</a></span></dt>
<dt><span class="section"><a href="weg/st_eg.html">Student's t Distribution
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Binomial Distribution Examples</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../weg.html" title="Worked Examples">
<link rel="prev" href="f_eg.html" title="F Distribution Examples">
<link rel="next" href="binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">
@@ -27,7 +27,7 @@
<a name="math_toolkit.stat_tut.weg.binom_eg"></a><a class="link" href="binom_eg.html" title="Binomial Distribution Examples">Binomial Distribution
Examples</a>
</h4></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="binom_eg/binomial_coinflip_example.html">Binomial
Coin-Flipping Example</a></span></dt>
<dt><span class="section"><a href="binom_eg/binomial_quiz_example.html">Binomial
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_conf.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_conf.html
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--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_conf.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
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+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../binom_eg.html" title="Binomial Distribution Examples">
<link rel="prev" href="binomial_quiz_example.html" title="Binomial Quiz Example">
<link rel="next" href="binom_size_eg.html" title="Estimating Sample Sizes for a Binomial Distribution.">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Estimating Sample Sizes for a Binomial Distribution.</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
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+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../binom_eg.html" title="Binomial Distribution Examples">
<link rel="prev" href="binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">
<link rel="next" href="../geometric_eg.html" title="Geometric Distribution Examples">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Binomial Coin-Flipping Example</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../binom_eg.html" title="Binomial Distribution Examples">
<link rel="prev" href="../binom_eg.html" title="Binomial Distribution Examples">
<link rel="next" href="binomial_quiz_example.html" title="Binomial Quiz Example">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Binomial Quiz Example</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../binom_eg.html" title="Binomial Distribution Examples">
<link rel="prev" href="binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">
<link rel="next" href="binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/c_sharp.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/c_sharp.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Using the Distributions from Within C#</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
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+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../weg.html" title="Worked Examples">
<link rel="prev" href="nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">
<link rel="next" href="../variates.html" title="Random Variates and Distribution Parameters">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg.html
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@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chi Squared Distribution Examples</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
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-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
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+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../weg.html" title="Worked Examples">
<link rel="prev" href="st_eg/paired_st.html" title="Comparing two paired samples with the Student's t distribution">
<link rel="next" href="cs_eg/chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">
@@ -27,7 +27,7 @@
<a name="math_toolkit.stat_tut.weg.cs_eg"></a><a class="link" href="cs_eg.html" title="Chi Squared Distribution Examples">Chi Squared Distribution
Examples</a>
</h4></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="cs_eg/chi_sq_intervals.html">Confidence
Intervals on the Standard Deviation</a></span></dt>
<dt><span class="section"><a href="cs_eg/chi_sq_test.html">Chi-Square
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html
index 933230470..fa60188a8 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Confidence Intervals on the Standard Deviation</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../cs_eg.html" title="Chi Squared Distribution Examples">
<link rel="prev" href="../cs_eg.html" title="Chi Squared Distribution Examples">
<link rel="next" href="chi_sq_test.html" title="Chi-Square Test for the Standard Deviation">
@@ -73,10 +73,10 @@
by:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../../equations/chi_squ_tut1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../../equations/chi_squ_tut1.svg"></span>
</p>
<p>
- Where <span class="inlinemediaobject"><img src="../../../../../equations/chi_squ_tut2.png"></span> is the upper critical value, and <span class="inlinemediaobject"><img src="../../../../../equations/chi_squ_tut3.png"></span> is
+ Where <span class="inlinemediaobject"><img src="../../../../../equations/chi_squ_tut2.svg"></span> is the upper critical value, and <span class="inlinemediaobject"><img src="../../../../../equations/chi_squ_tut3.svg"></span> is
the lower critical value of the Chi Squared distribution.
</p>
<p>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html
index f66ddd7f4..978ebca24 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../cs_eg.html" title="Chi Squared Distribution Examples">
<link rel="prev" href="chi_sq_test.html" title="Chi-Square Test for the Standard Deviation">
<link rel="next" href="../f_eg.html" title="F Distribution Examples">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html
index 44ef240d9..678cbb63d 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chi-Square Test for the Standard Deviation</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../cs_eg.html" title="Chi Squared Distribution Examples">
<link rel="prev" href="chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">
<link rel="next" href="chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/dist_construct_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/dist_construct_eg.html
index 9673089ee..c17dd22ce 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/dist_construct_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/dist_construct_eg.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Distribution Construction Examples</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../weg.html" title="Worked Examples">
<link rel="prev" href="../weg.html" title="Worked Examples">
<link rel="next" href="st_eg.html" title="Student's t Distribution Examples">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/error_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/error_eg.html
index c82e5a893..0f811c1a4 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/error_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/error_eg.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Error Handling Example</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../weg.html" title="Worked Examples">
<link rel="prev" href="nccs_eg/nccs_power_eg.html" title="Tables of the power function of the chi2 test.">
<link rel="next" href="find_eg.html" title="Find Location and Scale Examples">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/f_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/f_eg.html
index ca944ea20..5d2cdcbbb 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/f_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/f_eg.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>F Distribution Examples</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../weg.html" title="Worked Examples">
<link rel="prev" href="cs_eg/chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">
<link rel="next" href="binom_eg.html" title="Binomial Distribution Examples">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg.html
index 66fa78eb6..137b2bb90 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Find Location and Scale Examples</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../weg.html" title="Worked Examples">
<link rel="prev" href="error_eg.html" title="Error Handling Example">
<link rel="next" href="find_eg/find_location_eg.html" title="Find Location (Mean) Example">
@@ -27,7 +27,7 @@
<a name="math_toolkit.stat_tut.weg.find_eg"></a><a class="link" href="find_eg.html" title="Find Location and Scale Examples">Find Location and
Scale Examples</a>
</h4></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="find_eg/find_location_eg.html">Find
Location (Mean) Example</a></span></dt>
<dt><span class="section"><a href="find_eg/find_scale_eg.html">Find
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_location_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_location_eg.html
index 661eb9e8e..7dc08eacc 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_location_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_location_eg.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Find Location (Mean) Example</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../find_eg.html" title="Find Location and Scale Examples">
<link rel="prev" href="../find_eg.html" title="Find Location and Scale Examples">
<link rel="next" href="find_scale_eg.html" title="Find Scale (Standard Deviation) Example">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html
index a95b892c0..39e476fcf 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Find mean and standard deviation example</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../find_eg.html" title="Find Location and Scale Examples">
<link rel="prev" href="find_scale_eg.html" title="Find Scale (Standard Deviation) Example">
<link rel="next" href="../nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html
index 547dc2bb1..fc4051275 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Find Scale (Standard Deviation) Example</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../find_eg.html" title="Find Location and Scale Examples">
<link rel="prev" href="find_location_eg.html" title="Find Location (Mean) Example">
<link rel="next" href="find_mean_and_sd_eg.html" title="Find mean and standard deviation example">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/geometric_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/geometric_eg.html
index 2588abd4b..90cfe0e41 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/geometric_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/geometric_eg.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Geometric Distribution Examples</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../weg.html" title="Worked Examples">
<link rel="prev" href="binom_eg/binom_size_eg.html" title="Estimating Sample Sizes for a Binomial Distribution.">
<link rel="next" href="neg_binom_eg.html" title="Negative Binomial Distribution Examples">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/inverse_chi_squared_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/inverse_chi_squared_eg.html
index a13c8920e..ab7b0462d 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/inverse_chi_squared_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/inverse_chi_squared_eg.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Inverse Chi-Squared Distribution Bayes Example</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../weg.html" title="Worked Examples">
<link rel="prev" href="normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">
<link rel="next" href="nccs_eg.html" title="Non Central Chi Squared Example">
@@ -257,7 +257,7 @@
a distribution clearly shifted to greater values (see figure).
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/prior_posterior_plot.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../../graphs/prior_posterior_plot.svg" align="middle"></span>
</p>
<pre class="programlisting"><span class="identifier">inverse_chi_squared</span> <span class="identifier">posterior</span><span class="special">(</span><span class="identifier">posteriorDF</span><span class="special">,</span> <span class="identifier">posteriorScale</span><span class="special">);</span>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/nag_library.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/nag_library.html
index ac37b44fc..404926ae8 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/nag_library.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/nag_library.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Comparison with C, R, FORTRAN-style Free Functions</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../weg.html" title="Worked Examples">
<link rel="prev" href="find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">
<link rel="next" href="c_sharp.html" title="Using the Distributions from Within C#">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/nccs_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/nccs_eg.html
index 1c40e23e1..da12e4524 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/nccs_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/nccs_eg.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Non Central Chi Squared Example</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../weg.html" title="Worked Examples">
<link rel="prev" href="inverse_chi_squared_eg.html" title="Inverse Chi-Squared Distribution Bayes Example">
<link rel="next" href="nccs_eg/nccs_power_eg.html" title="Tables of the power function of the chi2 test.">
@@ -27,7 +27,7 @@
<a name="math_toolkit.stat_tut.weg.nccs_eg"></a><a class="link" href="nccs_eg.html" title="Non Central Chi Squared Example">Non Central Chi
Squared Example</a>
</h4></div></div></div>
-<div class="toc"><dl class="toc"><dt><span class="section"><a href="nccs_eg/nccs_power_eg.html">Tables
+<div class="toc"><dl><dt><span class="section"><a href="nccs_eg/nccs_power_eg.html">Tables
of the power function of the chi<sup>2</sup> test.</a></span></dt></dl></div>
<p>
(See also the reference documentation for the <a class="link" href="../../dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/nccs_eg/nccs_power_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/nccs_eg/nccs_power_eg.html
index 2b07d004f..3c079e283 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/nccs_eg/nccs_power_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/nccs_eg/nccs_power_eg.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Tables of the power function of the chi2 test.</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../nccs_eg.html" title="Non Central Chi Squared Example">
<link rel="prev" href="../nccs_eg.html" title="Non Central Chi Squared Example">
<link rel="next" href="../error_eg.html" title="Error Handling Example">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg.html
index b3be77970..6c82250e5 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Negative Binomial Distribution Examples</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../weg.html" title="Worked Examples">
<link rel="prev" href="geometric_eg.html" title="Geometric Distribution Examples">
<link rel="next" href="neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">
@@ -27,7 +27,7 @@
<a name="math_toolkit.stat_tut.weg.neg_binom_eg"></a><a class="link" href="neg_binom_eg.html" title="Negative Binomial Distribution Examples">Negative Binomial
Distribution Examples</a>
</h4></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="neg_binom_eg/neg_binom_conf.html">Calculating
Confidence Limits on the Frequency of Occurrence for the Negative Binomial
Distribution</a></span></dt>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_conf.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_conf.html
index 494b3b508..0082c1578 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_conf.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_conf.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../neg_binom_eg.html" title="Negative Binomial Distribution Examples">
<link rel="prev" href="../neg_binom_eg.html" title="Negative Binomial Distribution Examples">
<link rel="next" href="neg_binom_size_eg.html" title="Estimating Sample Sizes for the Negative Binomial.">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html
index 123a82228..b7221e9d1 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Estimating Sample Sizes for the Negative Binomial.</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../neg_binom_eg.html" title="Negative Binomial Distribution Examples">
<link rel="prev" href="neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">
<link rel="next" href="negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html
index b32d69004..9e898d993 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Negative Binomial Sales Quota Example.</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../neg_binom_eg.html" title="Negative Binomial Distribution Examples">
<link rel="prev" href="neg_binom_size_eg.html" title="Estimating Sample Sizes for the Negative Binomial.">
<link rel="next" href="negative_binomial_example2.html" title="Negative Binomial Table Printing Example.">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html
index 1549ca375..929eaa002 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Negative Binomial Table Printing Example.</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../neg_binom_eg.html" title="Negative Binomial Distribution Examples">
<link rel="prev" href="negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">
<link rel="next" href="../normal_example.html" title="Normal Distribution Examples">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/normal_example.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/normal_example.html
index 167f7b626..e58818544 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/normal_example.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/normal_example.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Normal Distribution Examples</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../weg.html" title="Worked Examples">
<link rel="prev" href="neg_binom_eg/negative_binomial_example2.html" title="Negative Binomial Table Printing Example.">
<link rel="next" href="normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">
@@ -27,7 +27,7 @@
<a name="math_toolkit.stat_tut.weg.normal_example"></a><a class="link" href="normal_example.html" title="Normal Distribution Examples">Normal Distribution
Examples</a>
</h4></div></div></div>
-<div class="toc"><dl class="toc"><dt><span class="section"><a href="normal_example/normal_misc.html">Some
+<div class="toc"><dl><dt><span class="section"><a href="normal_example/normal_misc.html">Some
Miscellaneous Examples of the Normal (Gaussian) Distribution</a></span></dt></dl></div>
<p>
(See also the reference documentation for the <a class="link" href="../../dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/normal_example/normal_misc.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/normal_example/normal_misc.html
index df87bf1ef..3a311eda6 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/normal_example/normal_misc.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/normal_example/normal_misc.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Some Miscellaneous Examples of the Normal (Gaussian) Distribution</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../normal_example.html" title="Normal Distribution Examples">
<link rel="prev" href="../normal_example.html" title="Normal Distribution Examples">
<link rel="next" href="../inverse_chi_squared_eg.html" title="Inverse Chi-Squared Distribution Bayes Example">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg.html
index 16a8c2cc8..94fc7dc9b 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Student's t Distribution Examples</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../weg.html" title="Worked Examples">
<link rel="prev" href="dist_construct_eg.html" title="Distribution Construction Examples">
<link rel="next" href="st_eg/tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">
@@ -27,7 +27,7 @@
<a name="math_toolkit.stat_tut.weg.st_eg"></a><a class="link" href="st_eg.html" title="Student's t Distribution Examples">Student's t Distribution
Examples</a>
</h4></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="st_eg/tut_mean_intervals.html">Calculating
confidence intervals on the mean with the Students-t distribution</a></span></dt>
<dt><span class="section"><a href="st_eg/tut_mean_test.html">Testing
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/paired_st.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/paired_st.html
index 5e3041392..8c2d35d6c 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/paired_st.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/paired_st.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Comparing two paired samples with the Student's t distribution</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../st_eg.html" title="Student's t Distribution Examples">
<link rel="prev" href="two_sample_students_t.html" title="Comparing the means of two samples with the Students-t test">
<link rel="next" href="../cs_eg.html" title="Chi Squared Distribution Examples">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_intervals.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_intervals.html
index 0334212bc..fc9afbd49 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_intervals.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_intervals.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Calculating confidence intervals on the mean with the Students-t distribution</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../st_eg.html" title="Student's t Distribution Examples">
<link rel="prev" href="../st_eg.html" title="Student's t Distribution Examples">
<link rel="next" href="tut_mean_test.html" title='Testing a sample mean for difference from a "true" mean'>
@@ -40,7 +40,7 @@
The formula for the interval can be expressed as:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../../equations/dist_tutorial4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../../equations/dist_tutorial4.svg"></span>
</p>
<p>
Where, <span class="emphasis"><em>Y<sub>s</sub></em></span> is the sample mean, <span class="emphasis"><em>s</em></span>
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_size.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_size.html
index ae9f7af70..d8ed35276 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_size.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_size.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../st_eg.html" title="Student's t Distribution Examples">
<link rel="prev" href="tut_mean_test.html" title='Testing a sample mean for difference from a "true" mean'>
<link rel="next" href="two_sample_students_t.html" title="Comparing the means of two samples with the Students-t test">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_test.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_test.html
index 9506245aa..4735d0cf7 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_test.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_test.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Testing a sample mean for difference from a "true" mean</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../st_eg.html" title="Student's t Distribution Examples">
<link rel="prev" href="tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">
<link rel="next" href="tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">
diff --git a/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/two_sample_students_t.html b/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/two_sample_students_t.html
index 1dea9896c..5d7144903 100644
--- a/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/two_sample_students_t.html
+++ b/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/two_sample_students_t.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Comparing the means of two samples with the Students-t test</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../st_eg.html" title="Student's t Distribution Examples">
<link rel="prev" href="tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">
<link rel="next" href="paired_st.html" title="Comparing two paired samples with the Student's t distribution">
@@ -76,7 +76,7 @@
variances the needed formulae are:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../../equations/dist_tutorial1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../../equations/dist_tutorial1.svg"></span>
</p>
<p>
where Sp is the "pooled" standard deviation of the two samples,
@@ -261,14 +261,14 @@
are not equal. In this case the formula for the t-statistic becomes:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../../equations/dist_tutorial2.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../../equations/dist_tutorial2.svg"></span>
</p>
<p>
And for the combined degrees of freedom we use the <a href="http://en.wikipedia.org/wiki/Welch-Satterthwaite_equation" target="_top">Welch-Satterthwaite</a>
approximation:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../../../equations/dist_tutorial3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../../../equations/dist_tutorial3.svg"></span>
</p>
<p>
Note that this is one of the rare situations where the degrees-of-freedom
diff --git a/libs/math/doc/html/math_toolkit/synopsis.html b/libs/math/doc/html/math_toolkit/synopsis.html
index 67a9f44e9..4b82ba3fa 100644
--- a/libs/math/doc/html/math_toolkit/synopsis.html
+++ b/libs/math/doc/html/math_toolkit/synopsis.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Synopsis</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../gcd_lcm.html" title="Chapter&#160;11.&#160;Integer Utilities (Greatest Common Divisor and Least Common Multiple)">
<link rel="prev" href="introduction.html" title="Introduction">
<link rel="next" href="gcd_function_object.html" title="GCD Function Object">
diff --git a/libs/math/doc/html/math_toolkit/threads.html b/libs/math/doc/html/math_toolkit/threads.html
index c8b02baf7..448146d5b 100644
--- a/libs/math/doc/html/math_toolkit/threads.html
+++ b/libs/math/doc/html/math_toolkit/threads.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Thread Safety</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="intro_pol_overview.html" title="Policies">
<link rel="next" href="perf_over1.html" title="Performance">
diff --git a/libs/math/doc/html/math_toolkit/tr1_ref.html b/libs/math/doc/html/math_toolkit/tr1_ref.html
index 0e9a19542..b68f824af 100644
--- a/libs/math/doc/html/math_toolkit/tr1_ref.html
+++ b/libs/math/doc/html/math_toolkit/tr1_ref.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>TR1 C Functions Quick Reference</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../extern_c.html" title='Chapter&#160;7.&#160;TR1 and C99 external "C" Functions'>
<link rel="prev" href="c99.html" title="C99 C Functions">
<link rel="next" href="../inverse_complex.html" title="Chapter&#160;8.&#160;Complex Number Functions">
@@ -174,7 +174,7 @@
The assoc_laguerre functions return:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/laguerre_1.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/laguerre_1.svg"></span>
</p>
<p>
See also <a class="link" href="sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">laguerre</a> for
@@ -189,7 +189,7 @@
The assoc_legendre functions return:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/legendre_1b.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/legendre_1b.svg"></span>
</p>
<p>
See also <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a> for
@@ -204,7 +204,7 @@
Returns the beta function of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/beta1.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/beta1.svg"></span>
</p>
<p>
See also <a class="link" href="sf_beta/beta_function.html" title="Beta">beta</a> for
@@ -219,7 +219,7 @@
Returns the complete elliptic integral of the first kind of <span class="emphasis"><em>k</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/ellint6.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/ellint6.svg"></span>
</p>
<p>
See also <a class="link" href="ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">ellint_1</a> for the
@@ -234,7 +234,7 @@
Returns the complete elliptic integral of the second kind of <span class="emphasis"><em>k</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/ellint7.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/ellint7.svg"></span>
</p>
<p>
See also <a class="link" href="ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">ellint_2</a> for the
@@ -250,7 +250,7 @@
and <span class="emphasis"><em>nu</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/ellint8.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/ellint8.svg"></span>
</p>
<p>
See also <a class="link" href="ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">ellint_3</a> for the
@@ -266,7 +266,7 @@
and <span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/mbessel2.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/mbessel2.svg"></span>
</p>
<p>
See also <a class="link" href="bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_i</a> for
@@ -282,7 +282,7 @@
<span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/bessel2.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/bessel2.svg"></span>
</p>
<p>
See also <a class="link" href="bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>
@@ -298,7 +298,7 @@
and <span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/mbessel3.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/mbessel3.svg"></span>
</p>
<p>
See also <a class="link" href="bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_k</a> for
@@ -315,7 +315,7 @@
and <span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/bessel3.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/bessel3.svg"></span>
</p>
<p>
See also <a class="link" href="bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>
@@ -331,7 +331,7 @@
and <span class="emphasis"><em>phi</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/ellint2.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/ellint2.svg"></span>
</p>
<p>
See also <a class="link" href="ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">ellint_1</a> for the
@@ -347,7 +347,7 @@
and <span class="emphasis"><em>phi</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/ellint3.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/ellint3.svg"></span>
</p>
<p>
See also <a class="link" href="ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">ellint_2</a> for the
@@ -363,7 +363,7 @@
<span class="emphasis"><em>nu</em></span> and <span class="emphasis"><em>phi</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/ellint4.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/ellint4.svg"></span>
</p>
<p>
See also <a class="link" href="ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">ellint_3</a> for the
@@ -378,7 +378,7 @@
Returns the exponential integral Ei of <span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/expint_i_1.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/expint_i_1.svg"></span>
</p>
<p>
See also <a class="link" href="expint/expint_i.html" title="Exponential Integral Ei">expint</a> for the
@@ -393,7 +393,7 @@
Returns the n'th Hermite polynomial of <span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/hermite_0.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/hermite_0.svg"></span>
</p>
<p>
See also <a class="link" href="sf_poly/hermite.html" title="Hermite Polynomials">hermite</a> for the
@@ -408,7 +408,7 @@
Returns the n'th Laguerre polynomial of <span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/laguerre_0.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/laguerre_0.svg"></span>
</p>
<p>
See also <a class="link" href="sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">laguerre</a> for
@@ -423,7 +423,7 @@
Returns the l'th Legendre polynomial of <span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/legendre_0.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/legendre_0.svg"></span>
</p>
<p>
See also <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a> for
@@ -438,7 +438,7 @@
Returns the Riemann Zeta function of <span class="emphasis"><em>x</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/zeta1.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/zeta1.svg"></span>
</p>
<p>
See also <a class="link" href="zetas/zeta.html" title="Riemann Zeta Function">zeta</a> for the full template
@@ -454,7 +454,7 @@
j<sub>n</sub>(x):
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/sbessel2.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/sbessel2.svg"></span>
</p>
<p>
See also <a class="link" href="bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sph_bessel</a> for
@@ -470,7 +470,7 @@
<span class="emphasis"><em>m</em></span> and <span class="emphasis"><em>theta</em></span>:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/spherical_3.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/spherical_3.svg"></span>
</p>
<p>
See also <a class="link" href="sf_poly/sph_harm.html" title="Spherical Harmonics">spherical_harmonic</a>
@@ -486,7 +486,7 @@
Returns the spherical Neumann function of <span class="emphasis"><em>x</em></span> y<sub>n</sub>(x):
</p>
<p>
- <span class="inlinemediaobject"><img src="../../equations/sbessel2.png"></span>
+ <span class="inlinemediaobject"><img src="../../equations/sbessel2.svg"></span>
</p>
<p>
See also <a class="link" href="bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sph_bessel</a> for
diff --git a/libs/math/doc/html/math_toolkit/trans.html b/libs/math/doc/html/math_toolkit/trans.html
index e4377281f..79651e7b3 100644
--- a/libs/math/doc/html/math_toolkit/trans.html
+++ b/libs/math/doc/html/math_toolkit/trans.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Quaternion Transcendentals</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="create.html" title="Quaternion Creation Functions">
<link rel="next" href="quat_tests.html" title="Test Program">
diff --git a/libs/math/doc/html/math_toolkit/tuning.html b/libs/math/doc/html/math_toolkit/tuning.html
index e0bb558de..5e6773349 100644
--- a/libs/math/doc/html/math_toolkit/tuning.html
+++ b/libs/math/doc/html/math_toolkit/tuning.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Performance Tuning Macros</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../perf.html" title="Chapter&#160;15.&#160;Performance">
<link rel="prev" href="comp_compilers.html" title="Comparing Compilers">
<link rel="next" href="comparisons.html" title="Comparisons to Other Open Source Libraries">
diff --git a/libs/math/doc/html/math_toolkit/tutorial.html b/libs/math/doc/html/math_toolkit/tutorial.html
index 0cf3d7295..0b704f36b 100644
--- a/libs/math/doc/html/math_toolkit/tutorial.html
+++ b/libs/math/doc/html/math_toolkit/tutorial.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Tutorial</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../constants.html" title="Chapter&#160;4.&#160;Mathematical Constants">
<link rel="prev" href="constants_intro.html" title="Introduction">
<link rel="next" href="tutorial/non_templ.html" title="Use in non-template code">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.tutorial"></a><a class="link" href="tutorial.html" title="Tutorial">Tutorial</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc">
+<div class="toc"><dl>
<dt><span class="section"><a href="tutorial/non_templ.html">Use in non-template
code</a></span></dt>
<dt><span class="section"><a href="tutorial/templ.html">Use in template code</a></span></dt>
diff --git a/libs/math/doc/html/math_toolkit/tutorial/non_templ.html b/libs/math/doc/html/math_toolkit/tutorial/non_templ.html
index f524f63cd..9de44c412 100644
--- a/libs/math/doc/html/math_toolkit/tutorial/non_templ.html
+++ b/libs/math/doc/html/math_toolkit/tutorial/non_templ.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Use in non-template code</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../tutorial.html" title="Tutorial">
<link rel="prev" href="../tutorial.html" title="Tutorial">
<link rel="next" href="templ.html" title="Use in template code">
diff --git a/libs/math/doc/html/math_toolkit/tutorial/templ.html b/libs/math/doc/html/math_toolkit/tutorial/templ.html
index 781eb7c1c..4e9b628bf 100644
--- a/libs/math/doc/html/math_toolkit/tutorial/templ.html
+++ b/libs/math/doc/html/math_toolkit/tutorial/templ.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Use in template code</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../tutorial.html" title="Tutorial">
<link rel="prev" href="non_templ.html" title="Use in non-template code">
<link rel="next" href="user_def.html" title="Use With User-Defined Types">
diff --git a/libs/math/doc/html/math_toolkit/tutorial/user_def.html b/libs/math/doc/html/math_toolkit/tutorial/user_def.html
index 0cf7b1f91..0d22e5603 100644
--- a/libs/math/doc/html/math_toolkit/tutorial/user_def.html
+++ b/libs/math/doc/html/math_toolkit/tutorial/user_def.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Use With User-Defined Types</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../tutorial.html" title="Tutorial">
<link rel="prev" href="templ.html" title="Use in template code">
<link rel="next" href="../constants.html" title="The Mathematical Constants">
diff --git a/libs/math/doc/html/math_toolkit/value_op.html b/libs/math/doc/html/math_toolkit/value_op.html
index 8cd69c86a..dfc860dea 100644
--- a/libs/math/doc/html/math_toolkit/value_op.html
+++ b/libs/math/doc/html/math_toolkit/value_op.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Quaternion Value Operations</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../quaternions.html" title="Chapter&#160;9.&#160;Quaternions">
<link rel="prev" href="quat_non_mem.html" title="Quaternion Non-Member Operators">
<link rel="next" href="create.html" title="Quaternion Creation Functions">
diff --git a/libs/math/doc/html/math_toolkit/zetas.html b/libs/math/doc/html/math_toolkit/zetas.html
index c724535ad..9024ff7f6 100644
--- a/libs/math/doc/html/math_toolkit/zetas.html
+++ b/libs/math/doc/html/math_toolkit/zetas.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Zeta Functions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">
<link rel="prev" href="jacobi/jacobi_sn.html" title="Jacobi Elliptic Function sn">
<link rel="next" href="zetas/zeta.html" title="Riemann Zeta Function">
@@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.zetas"></a><a class="link" href="zetas.html" title="Zeta Functions">Zeta Functions</a>
</h2></div></div></div>
-<div class="toc"><dl class="toc"><dt><span class="section"><a href="zetas/zeta.html">Riemann Zeta Function</a></span></dt></dl></div>
+<div class="toc"><dl><dt><span class="section"><a href="zetas/zeta.html">Riemann Zeta Function</a></span></dt></dl></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
diff --git a/libs/math/doc/html/math_toolkit/zetas/zeta.html b/libs/math/doc/html/math_toolkit/zetas/zeta.html
index 7f3919801..e7bfb1024 100644
--- a/libs/math/doc/html/math_toolkit/zetas/zeta.html
+++ b/libs/math/doc/html/math_toolkit/zetas/zeta.html
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Riemann Zeta Function</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0">
<link rel="up" href="../zetas.html" title="Zeta Functions">
<link rel="prev" href="../zetas.html" title="Zeta Functions">
<link rel="next" href="../expint.html" title="Exponential Integrals">
@@ -67,13 +67,13 @@
function</a> of z:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/zeta1.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/zeta1.svg"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/zeta1.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/zeta1.svg" align="middle"></span>
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../graphs/zeta2.png" align="middle"></span>
+ <span class="inlinemediaobject"><img src="../../../graphs/zeta2.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.zetas.zeta.h2"></a>
@@ -248,13 +248,13 @@
make their arguments positive:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/zeta3.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/zeta3.svg"></span>
</p>
<p>
The generic versions of these functions are implemented using the series:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/zeta6.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/zeta6.svg"></span>
</p>
<p>
When the significand (mantissa) size is recognised (currently for 53, 64
@@ -266,7 +266,7 @@
For 0 &lt; z &lt; 1 the approximating form is:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/zeta4.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/zeta4.svg"></span>
</p>
<p>
For a rational approximation R(1-z) and a constant C.
@@ -275,7 +275,7 @@
For 1 &lt; z &lt; 4 the approximating form is:
</p>
<p>
- <span class="inlinemediaobject"><img src="../../../equations/zeta5.png"></span>
+ <span class="inlinemediaobject"><img src="../../../equations/zeta5.svg"></span>
</p>
<p>
For a rational approximation R(n-z) and a constant C and integer n.
@@ -292,6 +292,23 @@
of: &#949;/R(0). This saves us quite a few digits when dealing with large z, especially
when &#949; is small.
</p>
+<p>
+ Finally, there are some special cases for integer arguments, there are closed
+ forms for negative or even integers:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/zeta7.svg"></span>
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/zeta8.svg"></span>
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/zeta9.svg"></span>
+ </p>
+<p>
+ and for positive odd integers we simply cache pre-computed values as these
+ are of great benefit to some infinite series calculations.
+ </p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
diff --git a/libs/math/doc/html/octonions.html b/libs/math/doc/html/octonions.html
index 5bfff4c03..5afefe7d2 100644
--- a/libs/math/doc/html/octonions.html
+++ b/libs/math/doc/html/octonions.html
@@ -3,9 +3,9 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;10.&#160;Octonions</title>
<link rel="stylesheet" href="math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.1.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.2.0">
<link rel="prev" href="math_toolkit/quat_todo.html" title="To Do">
<link rel="next" href="math_toolkit/oct_overview.html" title="Overview">
</head>
@@ -27,7 +27,7 @@
<a name="octonions"></a>Chapter&#160;10.&#160;Octonions</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
-<dl class="toc">
+<dl>
<dt><span class="section"><a href="math_toolkit/oct_overview.html">Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_header.html">Header File</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_synopsis.html">Synopsis</a></span></dt>
diff --git a/libs/math/doc/html/overview.html b/libs/math/doc/html/overview.html
index 616de46f6..817f3d573 100644
--- a/libs/math/doc/html/overview.html
+++ b/libs/math/doc/html/overview.html
@@ -3,10 +3,10 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;1.&#160;Overview</title>
<link rel="stylesheet" href="math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.1.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.1.0">
-<link rel="prev" href="index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.2.0">
+<link rel="prev" href="index.html" title="Math Toolkit 2.2.0">
<link rel="next" href="math_toolkit/main_intro.html" title="About the Math Toolkit">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@@ -27,7 +27,7 @@
<a name="overview"></a>Chapter&#160;1.&#160;Overview</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
-<dl class="toc">
+<dl>
<dt><span class="section"><a href="math_toolkit/main_intro.html">About the Math Toolkit</a></span></dt>
<dt><span class="section"><a href="math_toolkit/navigation.html">Navigation</a></span></dt>
<dt><span class="section"><a href="math_toolkit/conventions.html">Document Conventions</a></span></dt>
diff --git a/libs/math/doc/html/perf.html b/libs/math/doc/html/perf.html
index 44ccb788f..847604704 100644
--- a/libs/math/doc/html/perf.html
+++ b/libs/math/doc/html/perf.html
@@ -3,9 +3,9 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;15.&#160;Performance</title>
<link rel="stylesheet" href="math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.1.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.2.0">
<link rel="prev" href="math_toolkit/pol_ref/pol_ref_ref.html" title="Policy Class Reference">
<link rel="next" href="math_toolkit/perf_over2.html" title="Performance Overview">
</head>
@@ -27,7 +27,7 @@
<a name="perf"></a>Chapter&#160;15.&#160;Performance</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
-<dl class="toc">
+<dl>
<dt><span class="section"><a href="math_toolkit/perf_over2.html">Performance Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/interp.html">Interpreting these Results</a></span></dt>
<dt><span class="section"><a href="math_toolkit/getting_best.html">Getting the Best Performance
diff --git a/libs/math/doc/html/policy.html b/libs/math/doc/html/policy.html
index 53a73bf10..b0f77f736 100644
--- a/libs/math/doc/html/policy.html
+++ b/libs/math/doc/html/policy.html
@@ -3,9 +3,9 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc</title>
<link rel="stylesheet" href="math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.1.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.2.0">
<link rel="prev" href="math_toolkit/archetypes.html" title="Conceptual Archetypes for Reals and Distributions">
<link rel="next" href="math_toolkit/pol_overview.html" title="Policy Overview">
</head>
@@ -27,7 +27,7 @@
<a name="policy"></a>Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
-<dl class="toc">
+<dl>
<dt><span class="section"><a href="math_toolkit/pol_overview.html">Policy Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial.html">Policy Tutorial</a></span></dt>
<dd><dl>
diff --git a/libs/math/doc/html/quaternions.html b/libs/math/doc/html/quaternions.html
index cdfdf68c1..8064a73b0 100644
--- a/libs/math/doc/html/quaternions.html
+++ b/libs/math/doc/html/quaternions.html
@@ -3,9 +3,9 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;9.&#160;Quaternions</title>
<link rel="stylesheet" href="math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.1.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.2.0">
<link rel="prev" href="math_toolkit/complex_history.html" title="History">
<link rel="next" href="math_toolkit/quat_overview.html" title="Overview">
</head>
@@ -27,7 +27,7 @@
<a name="quaternions"></a>Chapter&#160;9.&#160;Quaternions</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
-<dl class="toc">
+<dl>
<dt><span class="section"><a href="math_toolkit/quat_overview.html">Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_header.html">Header File</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_synopsis.html">Synopsis</a></span></dt>
diff --git a/libs/math/doc/html/special.html b/libs/math/doc/html/special.html
index baf8670d2..79d9381d6 100644
--- a/libs/math/doc/html/special.html
+++ b/libs/math/doc/html/special.html
@@ -3,9 +3,9 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;6.&#160;Special Functions</title>
<link rel="stylesheet" href="math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.1.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.2.0">
<link rel="prev" href="math_toolkit/future.html" title="Extras/Future Directions">
<link rel="next" href="math_toolkit/number_series.html" title="Number Series">
</head>
@@ -27,7 +27,7 @@
<a name="special"></a>Chapter&#160;6.&#160;Special Functions</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
-<dl class="toc">
+<dl>
<dt><span class="section"><a href="math_toolkit/number_series.html">Number Series</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/number_series/bernoulli_numbers.html">Bernoulli
@@ -40,6 +40,8 @@
<dt><span class="section"><a href="math_toolkit/sf_gamma/tgamma.html">Gamma</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/lgamma.html">Log Gamma</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/digamma.html">Digamma</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/sf_gamma/trigamma.html">Trigamma</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/sf_gamma/polygamma.html">Polygamma</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/gamma_ratios.html">Ratios of Gamma Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/igamma.html">Incomplete Gamma Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/igamma_inv.html">Incomplete Gamma Function
@@ -117,6 +119,10 @@
Second Kind - Legendre Form</a></span></dt>
<dt><span class="section"><a href="math_toolkit/ellint/ellint_3.html">Elliptic Integrals of the
Third Kind - Legendre Form</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/ellint/ellint_d.html">Elliptic Integral D - Legendre
+ Form</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/ellint/jacobi_zeta.html">Jacobi Zeta Function</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/ellint/heuman_lambda.html">Heuman Lambda Function</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/jacobi.html">Jacobi Elliptic Functions</a></span></dt>
<dd><dl>
diff --git a/libs/math/doc/html/status.html b/libs/math/doc/html/status.html
index 5ec841e7b..ad786691d 100644
--- a/libs/math/doc/html/status.html
+++ b/libs/math/doc/html/status.html
@@ -3,9 +3,9 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;17.&#160;Library Status</title>
<link rel="stylesheet" href="math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.1.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.2.0">
<link rel="prev" href="math_toolkit/refs.html" title="References">
<link rel="next" href="math_toolkit/history2.html" title="History and What's New">
</head>
@@ -27,7 +27,7 @@
<a name="status"></a>Chapter&#160;17.&#160;Library Status</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
-<dl class="toc">
+<dl>
<dt><span class="section"><a href="math_toolkit/history2.html">History and What's New</a></span></dt>
<dt><span class="section"><a href="math_toolkit/issues.html">Known Issues, and TODO List</a></span></dt>
<dt><span class="section"><a href="math_toolkit/credits.html">Credits and Acknowledgements</a></span></dt>
diff --git a/libs/math/doc/html/toolkit.html b/libs/math/doc/html/toolkit.html
index c0ec6ad66..3006effe5 100644
--- a/libs/math/doc/html/toolkit.html
+++ b/libs/math/doc/html/toolkit.html
@@ -3,9 +3,9 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;12.&#160;Internals (Series, Rationals and Continued Fractions, Root Finding, Function Minimization, Testing and Development Tools)</title>
<link rel="stylesheet" href="math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.1.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.2.0">
<link rel="prev" href="math_toolkit/gcd_credits.html" title="Credits">
<link rel="next" href="math_toolkit/internals_overview.html" title="Overview">
</head>
@@ -28,7 +28,7 @@
Minimization, Testing and Development Tools)</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
-<dl class="toc">
+<dl>
<dt><span class="section"><a href="math_toolkit/internals_overview.html">Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals1.html">Utilities &amp; internals</a></span></dt>
<dd><dl>
diff --git a/libs/math/doc/html/using_udt.html b/libs/math/doc/html/using_udt.html
index 496158cf4..8dc2c6d22 100644
--- a/libs/math/doc/html/using_udt.html
+++ b/libs/math/doc/html/using_udt.html
@@ -3,9 +3,9 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;13.&#160;Use with User-Defined Floating-Point Types - Boost.Multiprecision and others</title>
<link rel="stylesheet" href="math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.1.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.2.0">
<link rel="prev" href="math_toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">
<link rel="next" href="math_toolkit/high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">
</head>
@@ -28,7 +28,7 @@
others</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
-<dl class="toc">
+<dl>
<dt><span class="section"><a href="math_toolkit/high_precision.html">Using Boost.Math with High-Precision
Floating-Point Libraries</a></span></dt>
<dd><dl>
diff --git a/libs/math/doc/html/utils.html b/libs/math/doc/html/utils.html
index d29b8d59c..af8055021 100644
--- a/libs/math/doc/html/utils.html
+++ b/libs/math/doc/html/utils.html
@@ -3,9 +3,9 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;2.&#160;Floating Point Utilities</title>
<link rel="stylesheet" href="math.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
-<link rel="home" href="index.html" title="Math Toolkit 2.1.0">
-<link rel="up" href="index.html" title="Math Toolkit 2.1.0">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="index.html" title="Math Toolkit 2.2.0">
+<link rel="up" href="index.html" title="Math Toolkit 2.2.0">
<link rel="prev" href="math_toolkit/contact.html" title="Contact Info and Support">
<link rel="next" href="math_toolkit/rounding.html" title="Rounding Truncation and Integer Conversion">
</head>
@@ -27,7 +27,7 @@
<a name="utils"></a>Chapter&#160;2.&#160;Floating Point Utilities</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
-<dl class="toc">
+<dl>
<dt><span class="section"><a href="math_toolkit/rounding.html">Rounding Truncation and Integer
Conversion</a></span></dt>
<dd><dl>
diff --git a/libs/math/doc/math.qbk b/libs/math/doc/math.qbk
index 58fc7604b..d01244880 100644
--- a/libs/math/doc/math.qbk
+++ b/libs/math/doc/math.qbk
@@ -9,7 +9,7 @@
]
[authors [Agrawal, Nikhar], [Bikineev, Anton], [Bristow, Paul A.], [Holin, Hubert], [Guazzone, Marco], [Kormanyos, Christopher], [Lalande, Bruno], [Maddock, John], [Råde, Johan], [Sobotta, Benjamin], [Sewani, Gautam], [van den Berg, Thijs], [Walker, Daryle], [Zhang, Xiaogang]]
[/last-revision $Date$]
- [version 2.1.0]
+ [version 2.2.0]
]
[template mathpart[id title]
@@ -21,7 +21,7 @@
[template equation[name] '''<inlinemediaobject>
<imageobject role="html">
-<imagedata fileref="../equations/'''[name]'''.png"></imagedata>
+<imagedata fileref="../equations/'''[name]'''.svg"></imagedata>
</imageobject>
<imageobject role="print">
<imagedata fileref="../equations/'''[name]'''.svg"></imagedata>
@@ -30,7 +30,7 @@
[template graph[name] '''<inlinemediaobject>
<imageobject role="html">
-<imagedata align="center" fileref="../graphs/'''[name]'''.png"></imagedata>
+<imagedata align="center" fileref="../graphs/'''[name]'''.svg"></imagedata>
</imageobject>
<imageobject role="print">
<imagedata align="center" fileref="../graphs/'''[name]'''.svg"></imagedata>
@@ -99,6 +99,8 @@ and use the function's name as the link text.]
[/gammas]
[def __lgamma [link math_toolkit.sf_gamma.lgamma lgamma]]
[def __digamma [link math_toolkit.sf_gamma.digamma digamma]]
+[def __trigamma [link math_toolkit.sf_gamma.trigamma trigamma]]
+[def __polygamma [link math_toolkit.sf_gamma.polygamma polygamma]]
[def __tgamma_ratio [link math_toolkit.sf_gamma.gamma_ratios tgamma_ratio]]
[def __tgamma_delta_ratio [link math_toolkit.sf_gamma.gamma_ratios tgamma_delta_ratio]]
[def __tgamma [link math_toolkit.sf_gamma.tgamma tgamma]]
@@ -148,6 +150,9 @@ and use the function's name as the link text.]
[def __ellint_1 [link math_toolkit.ellint.ellint_1 ellint_1]]
[def __ellint_2 [link math_toolkit.ellint.ellint_2 ellint_2]]
[def __ellint_3 [link math_toolkit.ellint.ellint_3 ellint_3]]
+[def __ellint_d [link math_toolkit.ellint.ellint_d ellint_d]]
+[def __jacobi_zeta [link math_toolkit.ellint.jacobi_zeta jacobi_zeta]]
+[def __heuman_lambda [link math_toolkit.ellint.heuman_lambda heuman_lambda]]
[/ Bernoulli functions and numbers]
[def __bernoulli_numbers [link math_toolkit.number_series.bernoulli_numbers Bernoulli numbers]]
@@ -237,6 +242,9 @@ and use the function's name as the link text.]
[/polynomials]
[def __laguerre [link math_toolkit.sf_poly.laguerre laguerre]]
[def __legendre [link math_toolkit.sf_poly.legendre legendre_p]]
+[def __legendre_p [link math_toolkit.sf_poly.legendre legendre_p]]
+[def __legendre_q [link math_toolkit.sf_poly.legendre legendre_q]]
+[def __legendre_next [link math_toolkit.sf_poly.legendre legendre_next]]
[def __hermite [link math_toolkit.sf_poly.hermite hermite]]
[/Misc]
@@ -268,8 +276,8 @@ and use the function's name as the link text.]
[def __support [link math_toolkit.dist_ref.nmp.support support]]
[def __algorithms [link math_toolkit.dist_ref.dist_algorithms algorithms]]
-
[/ distribution def names end in distrib to avoid clashes]
+[def __arcsine_distrib [link math_toolkit.dist_ref.dists.arcsine_dist Arcsine Distribution]]
[def __beta_distrib [link math_toolkit.dist_ref.dists.beta_dist Beta Distribution]]
[def __binomial_distrib [link math_toolkit.dist_ref.dists.binomial_dist Binomial Distribution]]
[def __cauchy_distrib [link math_toolkit.dist_ref.dists.cauchy_dist Cauchy Distribution]]
@@ -353,6 +361,7 @@ and use the function's name as the link text.]
[def __e_float [@http://calgo.acm.org/910.zip e_float (TOMS Algorithm 910)]]
[def __Abramowitz_Stegun M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, NBS (1964)]
[def _DMLF [@http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions]]
+[def __epsilon [@http://en.wikipedia.org/wiki/Machine_epsilon machine epsilon]]
[/ Some composite templates]
[template super[x]'''<superscript>'''[x]'''</superscript>''']
@@ -464,6 +473,8 @@ and as a CD ISBN 0-9504833-2-X 978-0-9504833-2-0, Classification 519.2-dc22.
[include sf/tgamma.qbk]
[include sf/lgamma.qbk]
[include sf/digamma.qbk]
+[include sf/trigamma.qbk]
+[include sf/polygamma.qbk]
[include sf/gamma_ratios.qbk]
[include sf/igamma.qbk]
[include sf/igamma_inv.qbk]
diff --git a/libs/math/doc/overview/credits.qbk b/libs/math/doc/overview/credits.qbk
index 3b713509b..f816a8229 100644
--- a/libs/math/doc/overview/credits.qbk
+++ b/libs/math/doc/overview/credits.qbk
@@ -103,6 +103,11 @@ no longer restricted to built-in floating-point types like double.
Christopher Kormanyos wrote some examples for using __multiprecision,
and added methods for finding zeros of Bessel Functions.
+Marco Guazzone provided the hyper-geometric distribution.
+
+Rocco Romeo has found numerous small bugs and generally stress tested the
+special functions code to near destruction!
+
[endsect] [/section:credits Credits and Acknowledgements]
[/
diff --git a/libs/math/doc/overview/issues.qbk b/libs/math/doc/overview/issues.qbk
index 0205b3e36..1f7641c1d 100644
--- a/libs/math/doc/overview/issues.qbk
+++ b/libs/math/doc/overview/issues.qbk
@@ -49,12 +49,6 @@ basic arithmetic operations. Maybe this is telling us something, or maybe not
[h4 Elliptic Integrals]
-* Carlson's algorithms are essentially unchanged from Xiaogang Zhang's
-Google Summer of Code student project, and are based on Carlson's
-original papers. However, Carlson has revised his algorithms since then
-(refer to the references in the elliptic integral docs for a list), to
-improve performance and accuracy, we may be able to take advantage
-of these improvements too (Low Priority).
* [para Carlson's algorithms (mainly R[sub J]) are somewhat prone to
internal overflow/underflow when the arguments are very large or small.
The homogeneity relations:]
@@ -63,23 +57,11 @@ The homogeneity relations:]
[para R[sub J](ka, kb, kc, kr) = k[super -3/2] R[sub J](a, b, c, r)]
[para could be used to sidestep trouble here: provided the problem domains
can be accurately identified. (Medium Priority).]
-* Carlson's R[sub C] can be reduced to elementary funtions (asin and log),
-would it be more efficient evaluated this way, rather than by Carlson's
-algorithms? (Low Priority).
-* Should we add an implementation of Carlson's R[sub G]? It's not
-required for the Legendre form integrals, but some people may find it
-useful (Low Priority).
-* There are a several other integrals: D([phi], k), Z([beta], k),
-[Lambda][sub 0]([beta], k) and Bulirsch's ['el] functions that could
+* There are a several other integrals: Bulirsch's ['el] functions that could
be implemented using Carlson's integrals (Low Priority).
* The integrals K(k) and E(k) could be implemented using rational
approximations (both for efficiency and accuracy),
assuming we can find them. (Medium Priority).
-* There is a sub-domain of __ellint_3 that is unimplemented (see the docs
-for details), currently
-it's not clear how to solve this issue, or if it's ever likely
-to be an real problem in practice - especially as most other implementations
-don't support this domain either (Medium Priority).
[h4 Owen's T Function]
@@ -101,6 +83,8 @@ as a better approximation for very large degrees of freedom?
[h4 Feature Requests]
+We have a request for the Lambert W function, see [@https://svn.boost.org/trac/boost/ticket/11027 #11027].
+
The following table lists distributions that are found in other packages
but which are not yet present here, the more frequently the distribution
is found, the higher the priority for implementing it:
diff --git a/libs/math/doc/overview/roadmap.qbk b/libs/math/doc/overview/roadmap.qbk
index 4c9879ed3..be11c53e3 100644
--- a/libs/math/doc/overview/roadmap.qbk
+++ b/libs/math/doc/overview/roadmap.qbk
@@ -6,6 +6,21 @@ Currently open bug reports can be viewed
All bug reports including closed ones can be viewed
[@https://svn.boost.org/trac/boost/query?status=assigned&status=closed&status=new&status=reopened&component=math&col=id&col=summary&col=status&col=type&col=milestone&col=component&order=priority here].
+[h4 Math-2.2.0 (boost-1.58.0)]
+
+* Added two new special functions - __trigamma and __polygamma.
+* Fixed namespace scope constants so they are constexpr on conforming compilers, see https://svn.boost.org/trac/boost/ticket/10901.
+* Fixed various cases of spurious under/overflow in the incomplete beta and gamma functions, plus the elliptic integrals,
+with thanks to Rocco Romeo.
+* Fix 3-arg __legendre_p and __legendre_q functions to not call the policy based overload if the final argument
+is not actually a policy.
+* Cleaned up some dead code in the incomplete beta function, see [@https://svn.boost.org/trac/boost/ticket/10985 #10985].
+* Fixed extreme-value pdf for large valued inputs, see [@https://svn.boost.org/trac/boost/ticket/10938 #10938].
+* Large update to the Elliptic integral code to use Carlson's latest algorithms - these should be more stable, more accurate
+and slightly faster than before. Also added support for Carlson's RG integral.
+* Added __ellint_d, __jacobi_zeta and __heuman_lambda elliptic integrals.
+* Switched documentation to use SVG rather than PNG graphs and equations - browsers seem to have finally caught up!
+
[h4 Math-2.1.0 (boost-1.57.0)]
* Added __hyperexponential_distrib.
diff --git a/libs/math/doc/sf/bernoulli_numbers.qbk b/libs/math/doc/sf/bernoulli_numbers.qbk
new file mode 100644
index 000000000..d97cad6e2
--- /dev/null
+++ b/libs/math/doc/sf/bernoulli_numbers.qbk
@@ -0,0 +1,223 @@
+[section:bernoulli_numbers Bernoulli Numbers]
+
+[@https://en.wikipedia.org/wiki/Bernoulli_number Bernoulli numbers]
+are a sequence of rational numbers useful for the Taylor series expansion,
+Euler-Maclaurin formula, and the Riemann zeta function.
+
+Bernoulli numbers are used in evaluation of some Boost.Math functions,
+including the __tgamma, __lgamma and polygamma functions.
+
+[h4 Single Bernoulli number]
+
+[h4 Synopsis]
+
+``
+#include <boost/math/special_functions/bernoulli.hpp>
+``
+
+ namespace boost { namespace math {
+
+ template <class T>
+ T bernoulli_b2n(const int n); // Single Bernoulli number (default policy).
+
+ template <class T, class Policy>
+ T bernoulli_b2n(const int n, const Policy &pol); // User policy for errors etc.
+
+ }} // namespaces
+
+[h4 Description]
+
+Both return the (2 * n)[super th] Bernoulli number B[sub 2n].
+
+Note that since all odd numbered Bernoulli numbers are zero (apart from B[sub 1] which is [plusminus][frac12])
+the interface will only return the even numbered Bernoulli numbers.
+
+This function uses fast table lookup for low-indexed Bernoulli numbers, while larger values are calculated
+as needed and then cached. The caching mechanism requires a certain amount of thread safety code, so
+`unchecked_bernoulli_b2n` may provide a better interface for performance critical code.
+
+The final __Policy argument is optional and can be used to control the behaviour of the function:
+how it handles errors, what level of precision to use, etc.
+
+Refer to __policy_section for more details.
+
+[h4 Examples]
+
+[import ../../example/bernoulli_example.cpp]
+[bernoulli_example_1]
+
+[bernoulli_output_1]
+
+[h4 Single (unchecked) Bernoulli number]
+
+[h4 Synopsis]
+``
+#include <boost/math/special_functions/bernoulli.hpp>
+
+``
+
+ template <>
+ struct max_bernoulli_b2n<T>;
+
+ template<class T>
+ inline T unchecked_bernoulli_b2n(unsigned n);
+
+`unchecked_bernoulli_b2n` provides access to Bernoulli numbers [*without any checks for overflow or invalid parameters].
+It is implemented as a direct (and very fast) table lookup, and while not recommended for general use it can be useful
+inside inner loops where the ultimate performance is required, and error checking is moved outside the loop.
+
+The largest value you can pass to `unchecked_bernoulli_b2n<>` is `max_bernoulli_b2n<>::value`: passing values greater than
+that will result in a buffer overrun error, so it's clearly important to place the error handling in your own code
+when using this direct interface.
+
+The value of `boost::math::max_bernoulli_b2n<T>::value` varies by the type T, for types `float`/`double`/`long double`
+it's the largest value which doesn't overflow the target type: for example, `boost::math::max_bernoulli_b2n<double>::value` is 129.
+However, for multiprecision types, it's the largest value for which the result can be represented as the ratio of two 64-bit
+integers, for example `boost::math::max_bernoulli_b2n<boost::multiprecision::cpp_dec_float_50>::value` is just 17. Of course
+larger indexes can be passed to `bernoulli_b2n<T>(n)`, but then you lose fast table lookup (i.e. values may need to be calculated).
+
+[bernoulli_example_4]
+[bernoulli_output_4]
+
+[h4 Multiple Bernoulli Numbers]
+
+[h4 Synopsis]
+
+``
+#include <boost/math/special_functions/bernoulli.hpp>
+``
+
+ namespace boost { namespace math {
+
+ // Multiple Bernoulli numbers (default policy).
+ template <class T, class OutputIterator>
+ OutputIterator bernoulli_b2n(
+ int start_index,
+ unsigned number_of_bernoullis_b2n,
+ OutputIterator out_it);
+
+ // Multiple Bernoulli numbers (user policy).
+ template <class T, class OutputIterator, class Policy>
+ OutputIterator bernoulli_b2n(
+ int start_index,
+ unsigned number_of_bernoullis_b2n,
+ OutputIterator out_it,
+ const Policy& pol);
+ }} // namespaces
+
+[h4 Description]
+
+Two versions of the Bernoulli number function are provided to compute multiple Bernoulli numbers
+with one call (one with default policy and the other allowing a user-defined policy).
+
+These return a series of Bernoulli numbers:
+
+[:B[sub 2*start_index],B[sub 2*(start_index+1)],...,B[sub 2*(start_index+number_of_bernoullis_b2n-1)]]
+
+[h4 Examples]
+[bernoulli_example_2]
+[bernoulli_output_2]
+[bernoulli_example_3]
+[bernoulli_output_3]
+
+The source of this example is at [@../../example/bernoulli_example.cpp bernoulli_example.cpp]
+
+[h4 Accuracy]
+
+All the functions usually return values within one ULP (unit in the last place) for the floating-point type.
+
+[h4 Implementation]
+
+The implementation details are in [@../../include/boost/math/special_functions/detail/bernoulli_details.hpp bernoulli_details.hpp]
+and [@../../include/boost/math/special_functions/detail/unchecked_bernoulli.hpp unchecked_bernoulli.hpp].
+
+For `i <= max_bernoulli_index<T>::value` this is implemented by simple table lookup from a statically initialized table;
+for larger values of `i`, this is implemented by the Tangent Numbers algorithm as described in the paper:
+Fast Computation of Bernoulli, Tangent and Secant Numbers, Richard P. Brent and David Harvey,
+[@http://arxiv.org/pdf/1108.0286v3.pdf] (2011).
+
+[@http://mathworld.wolfram.com/TangentNumber.html Tangent (or Zag) numbers]
+(an even alternating permutation number) are defined
+and their generating function is also given therein.
+
+The relation of Tangent numbers with Bernoulli numbers ['B[sub i]]
+is given by Brent and Harvey's equation 14:
+
+__spaces[equation tangent_numbers]
+
+Their relation with Bernoulli numbers ['B[sub i]] are defined by
+
+if i > 0 and i is even then
+__spaces[equation bernoulli_numbers] [br]
+elseif i == 0 then ['B[sub i]] = 1 [br]
+elseif i == 1 then ['B[sub i]] = -1/2 [br]
+elseif i < 0 or i is odd then ['B[sub i]] = 0
+
+Note that computed values are stored in a fixed-size table, access is thread safe via atomic operations (i.e. lock
+free programming), this imparts a much lower overhead on access to cached values than might otherwise be expected -
+typically for multiprecision types the cost of thread synchronisation is negligible, while for built in types
+this code is not normally executed anyway. For very large arguments which cannot be reasonably computed or
+stored in our cache, an asymptotic expansion [@http://www.luschny.de/math/primes/bernincl.html due to Luschny] is used:
+
+[equation bernoulli_numbers2]
+
+[endsect] [/section:bernoulli_numbers Bernoulli Numbers]
+
+
+[section:tangent_numbers Tangent Numbers]
+
+[@http://en.wikipedia.org/wiki/Tangent_numbers Tangent numbers],
+also called a zag function. See also
+[@http://mathworld.wolfram.com/TangentNumber.html Tangent number].
+
+From the number, An, of alternating permutations of the set {1, ..., n},
+the numbers A2n+1 with odd indices are called tangent numbers or zag numbers.
+The first few values are 1, 2, 16, 272, 7936, 353792, 22368256, 1903757312 ...
+(sequence [@http://oeis.org/A000182 A000182 in OEIS]).
+They are called tangent numbers because they appear as
+numerators in the Maclaurin series of tan x.
+
+Tangent numbers are used in the computation of Bernoulli numbers,
+but are also made available here.
+
+[h4 Synopsis]
+``
+#include <boost/math/special_functions/detail/bernoulli.hpp>
+``
+
+ template <class T>
+ T tangent_t2n(const int i); // Single tangent number (default policy).
+
+ template <class T, class Policy>
+ T tangent_t2n(const int i, const Policy &pol); // Single tangent number (user policy).
+
+ // Multiple tangent numbers (default policy).
+ template <class T, class OutputIterator>
+ OutputIterator tangent_t2n(const int start_index,
+ const unsigned number_of_tangent_t2n,
+ OutputIterator out_it);
+
+ // Multiple tangent numbers (user policy).
+ template <class T, class OutputIterator, class Policy>
+ OutputIterator tangent_t2n(const int start_index,
+ const unsigned number_of_tangent_t2n,
+ OutputIterator out_it,
+ const Policy& pol);
+
+[h4 Examples]
+
+[tangent_example_1]
+
+The output is:
+[tangent_output_1]
+
+The source of this example is at [../../example/bernoulli_example.cpp bernoulli_example.cpp]
+
+[endsect] [/section:tangent_numbers Tangent Numbers]
+
+[/
+ Copyright 2013, 2014 Nikhar Agrawal, Christopher Kormanyos, John Maddock, Paul A. Bristow.
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt).
+]
diff --git a/libs/math/doc/sf/digamma.qbk b/libs/math/doc/sf/digamma.qbk
index cf3b9c232..d62466ac3 100644
--- a/libs/math/doc/sf/digamma.qbk
+++ b/libs/math/doc/sf/digamma.qbk
@@ -27,10 +27,6 @@ derivative of the gamma function:
[optional_policy]
-There is no fully generic version of this function: all the implementations
-are tuned to specific accuracy levels, the most precise of which delivers
-34-digits of precision.
-
The return type of this function is computed using the __arg_pomotion_rules:
the result is of type `double` when T is an integer type, and type T otherwise.
@@ -97,6 +93,14 @@ Choosing BIG=10 for up to 80-bit reals, and BIG=20 for 128-bit reals allows
the series to truncated after a suitably small number of terms and evaluated
as a polynomial in `1/(x*x)`.
+The arbitrary precision version of this function uses recurrence relations until
+x > BIG, and then evaluation via the asymptotic expansion above. As special cases
+integer and half integer arguments are handled via:
+
+[equation digamma4]
+
+[equation digamma5]
+
The rational approximation [jm_rationals] in the range [1,2] is derived as follows.
First a high precision approximation to digamma was constructed using a 60-term
diff --git a/libs/math/doc/sf/ellint_carlson.qbk b/libs/math/doc/sf/ellint_carlson.qbk
index 512c4d416..b6f2aa42f 100644
--- a/libs/math/doc/sf/ellint_carlson.qbk
+++ b/libs/math/doc/sf/ellint_carlson.qbk
@@ -69,6 +69,21 @@ LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
}} // namespaces
+``
+ #include <boost/math/special_functions/ellint_rg.hpp>
+``
+
+ namespace boost { namespace math {
+
+ template <class T1, class T2, class T3>
+ ``__sf_result`` ellint_rg(T1 x, T2 y, T3 z)
+
+ template <class T1, class T2, class T3, class ``__Policy``>
+ ``__sf_result`` ellint_rg(T1 x, T2 y, T3 z, const ``__Policy``&)
+
+ }} // namespaces
+
+
[heading Description]
@@ -154,6 +169,20 @@ using the relation:
[equation ellint18]
+ template <class T1, class T2, class T3>
+ ``__sf_result`` ellint_rg(T1 x, T2 y, T3 z)
+
+ template <class T1, class T2, class T3, class ``__Policy``>
+ ``__sf_result`` ellint_rg(T1 x, T2 y, T3 z, const ``__Policy``&)
+
+Returns Carlson's elliptic integral R[sub G]:
+
+[equation ellint27]
+
+Requires that x and y are non-negative, otherwise returns the result of __domain_error.
+
+[optional_policy]
+
[heading Testing]
There are two sets of tests.
@@ -199,7 +228,7 @@ closer and closer. When they are nearly equal, the special case equation
is used. More specifically, ['[R F]] is evaluated from a Taylor series
expansion to the fifth order. The calculations of the other three integrals
-are analogous.
+are analogous, except for R[sub C] which can be computed from elementary functions.
For ['p < 0] in ['R[sub J](x, y, z, p)] and ['y < 0] in ['R[sub C](x, y)],
the integrals are singular and their
diff --git a/libs/math/doc/sf/ellint_introduction.qbk b/libs/math/doc/sf/ellint_introduction.qbk
index 12a375a5f..80c11f659 100644
--- a/libs/math/doc/sf/ellint_introduction.qbk
+++ b/libs/math/doc/sf/ellint_introduction.qbk
@@ -103,6 +103,14 @@ Complete Elliptic Integral of the Third Kind (Legendre form)
[equation ellint8]
+Legendre also defined a forth integral D([phi],k) which is a combination of the other three:
+
+[equation ellint_d]
+
+Like the other Legendre integrals this comes in both complete and incomplete forms.
+
+[h4 Carlson Elliptic Integrals]
+
Carlson [[link ellint_ref_carlson77 Carlson77]] [[link ellint_ref_carlson78 Carlson78]] gives an alternative definition of
elliptic integral's canonical forms:
@@ -137,6 +145,9 @@ where ['x] is nonnegative and ['y] is nonzero.
['R[sub D](x, y, z) = R[sub J](x, y, z, z)]]
+Carlson's Symmetric Integral
+
+[equation ellint27]
[h4 Duplication Theorem]
@@ -155,6 +166,20 @@ In particular,
[equation ellint15]
+[h4 Miscellaneous Elliptic Integrals]
+
+There are two functions related to the elliptic integrals which otherwise
+defy categorisation, these are the Jacobi Zeta function:
+
+[equation jacobi_zeta]
+
+and the Heuman Lambda function:
+
+[equation heuman_lambda]
+
+Both of these functions are easily implemented in terms of Carlson's integrals, and are
+provided in this library as __jacobi_zeta and __heuman_lambda.
+
[h4 Numerical Algorithms]
The conventional methods for computing elliptic integrals are Gauss
diff --git a/libs/math/doc/sf/ellint_legendre.qbk b/libs/math/doc/sf/ellint_legendre.qbk
index 0808058df..a366db948 100644
--- a/libs/math/doc/sf/ellint_legendre.qbk
+++ b/libs/math/doc/sf/ellint_legendre.qbk
@@ -337,3 +337,228 @@ and
[equation ellint26]
[endsect]
+
+[section:ellint_d Elliptic Integral D - Legendre Form]
+
+[heading Synopsis]
+
+``
+ #include <boost/math/special_functions/ellint_d.hpp>
+``
+
+ namespace boost { namespace math {
+
+ template <class T1, class T2>
+ ``__sf_result`` ellint_d(T1 k, T2 phi);
+
+ template <class T1, class T2, class ``__Policy``>
+ ``__sf_result`` ellint_d(T1 k, T2 phi, const ``__Policy``&);
+
+ template <class T1>
+ ``__sf_result`` ellint_d(T1 k);
+
+ template <class T1, class ``__Policy``>
+ ``__sf_result`` ellint_d(T1 k, const ``__Policy``&);
+
+ }} // namespaces
+
+[heading Description]
+
+These two functions evaluate the incomplete elliptic integral
+['D([phi], k)] and its complete counterpart ['D(k) = D([pi]/2, k)].
+
+The return type of these functions is computed using the __arg_pomotion_rules
+when the arguments are of different types: when they are the same type then the result
+is the same type as the arguments.
+
+ template <class T1, class T2>
+ ``__sf_result`` ellint_d(T1 k, T2 phi);
+
+ template <class T1, class T2, class ``__Policy``>
+ ``__sf_result`` ellint_3(T1 k, T2 phi, const ``__Policy``&);
+
+Returns the incomplete elliptic integral:
+
+[equation ellint_d]
+
+Requires ['-1 <= k <= 1], otherwise
+returns the result of __domain_error (outside this range the result
+would be complex).
+
+[optional_policy]
+
+ template <class T1>
+ ``__sf_result`` ellint_d(T1 k);
+
+ template <class T1, class ``__Policy``>
+ ``__sf_result`` ellint_d(T1 k, const ``__Policy``&);
+
+Returns the complete elliptic integral ['D(k) = D([pi]/2, k)]
+
+Requires ['-1 <= k <= 1] otherwise returns the
+result of __domain_error (outside this range the result would be complex).
+
+[optional_policy]
+
+[heading Accuracy]
+
+These functions are trivially computed in terms of other elliptic integrals
+and generally have very low error rates (a few epsilon) unless parameter [phi]
+is very large, in which case the usual trigonometric function argument-reduction issues apply.
+
+[heading Testing]
+
+The tests use a mixture of spot test values calculated using
+values calculated at wolframalpha.com, and random test data generated using
+MPFR at 1000-bit precision and a deliberately naive implementation in terms of
+the Legendre integrals.
+
+[heading Implementation]
+
+The implementation for D([phi], k) first performs argument reduction using the relations:
+
+['D(-[phi], k) = -D([phi], k)]
+
+and
+
+['D(n[pi]+[phi], k) = 2nD(k) + D([phi], k)]
+
+to move [phi][space] to the range \[0, [pi]\/2\].
+
+The functions are then implemented in terms of Carlson's integral R[sub D]
+using the relation:
+
+[equation ellint_d]
+
+[endsect]
+
+[section:jacobi_zeta Jacobi Zeta Function]
+
+[heading Synopsis]
+
+``
+ #include <boost/math/special_functions/jacobi_zeta.hpp>
+``
+
+ namespace boost { namespace math {
+
+ template <class T1, class T2>
+ ``__sf_result`` jacobi_zeta(T1 k, T2 phi);
+
+ template <class T1, class T2, class ``__Policy``>
+ ``__sf_result`` jacobi_zeta(T1 k, T2 phi, const ``__Policy``&);
+
+ }} // namespaces
+
+[heading Description]
+
+This function evaluates the Jacobi Zeta Function ['Z([phi], k)]
+
+[equation jacobi_zeta]
+
+The return type of this function is computed using the __arg_pomotion_rules
+when the arguments are of different types: when they are the same type then the result
+is the same type as the arguments.
+
+Requires ['-1 <= k <= 1], otherwise
+returns the result of __domain_error (outside this range the result
+would be complex).
+
+[optional_policy]
+
+Note that there is no complete analogue of this function (where [phi] = [pi] / 2)
+as this takes the value 0 for all ['k].
+
+[heading Accuracy]
+
+These functions are trivially computed in terms of other elliptic integrals
+and generally have very low error rates (a few epsilon) unless parameter [phi]
+is very large, in which case the usual trigonometric function argument-reduction issues apply.
+
+[heading Testing]
+
+The tests use a mixture of spot test values calculated using
+values calculated at wolframalpha.com, and random test data generated using
+MPFR at 1000-bit precision and a deliberately naive implementation in terms of
+the Legendre integrals.
+
+[heading Implementation]
+
+The implementation for Z([phi], k) first makes the argument [phi] positive using:
+
+['Z(-[phi], k) = -Z([phi], k)]
+
+The function is then implemented in terms of Carlson's integral R[sub J]
+using the relation:
+
+[equation jacobi_zeta]
+
+There is one special case where the above relation fails: when ['k = 1], in that case
+the function simplifies to
+
+['Z([phi], 1) = sign(cos([phi])) sin([phi])]
+
+[endsect]
+
+[section:heuman_lambda Heuman Lambda Function]
+
+[heading Synopsis]
+
+``
+ #include <boost/math/special_functions/heuman_lambda.hpp>
+``
+
+ namespace boost { namespace math {
+
+ template <class T1, class T2>
+ ``__sf_result`` heuman_lambda(T1 k, T2 phi);
+
+ template <class T1, class T2, class ``__Policy``>
+ ``__sf_result`` heuman_lambda(T1 k, T2 phi, const ``__Policy``&);
+
+ }} // namespaces
+
+[heading Description]
+
+This function evaluates the Heuman Lambda Function ['[Lambda][sub 0]([phi], k)]
+
+[equation heuman_lambda]
+
+The return type of this function is computed using the __arg_pomotion_rules
+when the arguments are of different types: when they are the same type then the result
+is the same type as the arguments.
+
+Requires ['-1 <= k <= 1], otherwise
+returns the result of __domain_error (outside this range the result
+would be complex).
+
+[optional_policy]
+
+Note that there is no complete analogue of this function (where [phi] = [pi] / 2)
+as this takes the value 1 for all ['k].
+
+[heading Accuracy]
+
+These functions are trivially computed in terms of other elliptic integrals
+and generally have very low error rates (a few epsilon) unless parameter [phi]
+is very large, in which case the usual trigonometric function argument-reduction issues apply.
+
+[heading Testing]
+
+The tests use a mixture of spot test values calculated using
+values calculated at wolframalpha.com, and random test data generated using
+MPFR at 1000-bit precision and a deliberately naive implementation in terms of
+the Legendre integrals.
+
+[heading Implementation]
+
+The function is then implemented in terms of Carlson's integrals R[sub J] and R[sub F]
+using the relation:
+
+[equation heuman_lambda]
+
+This relation fails for ['|[phi]| >= [pi]/2] in which case the definition in terms of the
+Jacobi Zeta is used.
+
+[endsect]
+
diff --git a/libs/math/doc/sf/number_series.qbk b/libs/math/doc/sf/number_series.qbk
index 1e1019247..631cc294d 100644
--- a/libs/math/doc/sf/number_series.qbk
+++ b/libs/math/doc/sf/number_series.qbk
@@ -65,7 +65,7 @@ Refer to __policy_section for more details.
inline T unchecked_bernoulli_b2n(unsigned n);
`unchecked_bernoulli_b2n` provides access to Bernoulli numbers [*without any checks for overflow or invalid parameters].
-It is implemented as a direct (and very fast) table lookup, and while not recomended for general use it can be useful
+It is implemented as a direct (and very fast) table lookup, and while not recommended for general use it can be useful
inside inner loops where the ultimate performance is required, and error checking is moved outside the loop.
The largest value you can pass to `unchecked_bernoulli_b2n<>` is `max_bernoulli_b2n<>::value`: passing values greater than
@@ -76,7 +76,7 @@ The value of `boost::math::max_bernoulli_b2n<T>::value` varies by the type T, fo
it's the largest value which doesn't overflow the target type: for example, `boost::math::max_bernoulli_b2n<double>::value` is 129.
However, for multiprecision types, it's the largest value for which the result can be represented as the ratio of two 64-bit
integers, for example `boost::math::max_bernoulli_b2n<boost::multiprecision::cpp_dec_float_50>::value` is just 17. Of course
-larger indexes can be passed to `bernoulli_b2n<T>(n)`, but then then you loose fast table lookup (i.e. values may need to be calculated).
+larger indexes can be passed to `bernoulli_b2n<T>(n)`, but then you lose fast table lookup (i.e. values may need to be calculated).
[bernoulli_example_4]
[bernoulli_output_4]
@@ -156,8 +156,8 @@ elseif i == 1 then ['B[sub i]] = -1/2 [br]
elseif i < 0 or i is odd then ['B[sub i]] = 0
Note that computed values are stored in a fixed-size table, access is thread safe via atomic operations (i.e. lock
-free programming), this imparts a much lower overhead on access to cached values than might overwise be expected -
-typically for multiprecision types the cost of thread synchronisation is negligable, while for built in types
+free programming), this imparts a much lower overhead on access to cached values than might otherwise be expected -
+typically for multiprecision types the cost of thread synchronisation is negligible, while for built in types
this code is not normally executed anyway. For very large arguments which cannot be reasonably computed or
stored in our cache, an asymptotic expansion [@http://www.luschny.de/math/primes/bernincl.html due to Luschny] is used:
diff --git a/libs/math/doc/sf/polygamma.qbk b/libs/math/doc/sf/polygamma.qbk
new file mode 100644
index 000000000..19ff6a712
--- /dev/null
+++ b/libs/math/doc/sf/polygamma.qbk
@@ -0,0 +1,115 @@
+[section:polygamma Polygamma]
+
+[h4 Synopsis]
+
+``
+#include <boost/math/special_functions/polygamma.hpp>
+``
+
+ namespace boost{ namespace math{
+
+ template <class T>
+ ``__sf_result`` polygamma(int n, T z);
+
+ template <class T, class ``__Policy``>
+ ``__sf_result`` polygamma(int n, T z, const ``__Policy``&);
+
+ }} // namespaces
+
+[h4 Description]
+
+Returns the polygamma function of /x/. Polygamma is defined as the n'th
+derivative of the digamma function:
+
+[equation polygamma1]
+
+The following graphs illustrate the behaviour of the function for odd and even order:
+
+[graph polygamma2]
+[graph polygamma3]
+
+[optional_policy]
+
+The return type of this function is computed using the __arg_pomotion_rules:
+the result is of type `double` when T is an integer type, and type T otherwise.
+
+[h4 Accuracy]
+
+The following table shows the peak errors (in units of epsilon)
+found on various platforms with various floating point types.
+Unless otherwise specified any floating point type that is narrower
+than the one shown will have __zero_error.
+
+[table
+[[Significand Size] [Platform and Compiler] [Small-medium positive arguments] [Small-medium negative x] ]
+[[53] [Win32 Visual C++ 12] [Peak=5.0 Mean=1] [Peak=1200 Mean=65]]
+[[64] [Win64 Mingw GCC] [Peak=16 Mean=3] [Peak=33 Mean=3] ]
+[[113] [Win64 Mingw GCC __float128] [Peak=6.5 Mean=1][Peak=30 Mean=4] ]
+]
+
+As shown above, error rates are generally very acceptable for moderately sized
+arguments. Error rates should stay low for exact inputs, however, please note that the
+function becomes exceptionally sensitive to small changes in input for large n and negative x,
+indeed for cases where ['n!] would overflow, the function changes directly from -[infin] to
++[infin] somewhere between each negative integer - ['these cases are not handled correctly].
+
+[*For these reasons results should be treated with extreme caution when /n/ is large and x negative].
+
+[h4 Testing]
+
+Testing is against Mathematica generated spot values to 35 digit precision.
+
+[h4 Implementation]
+
+For x < 0 the following reflection formula is used:
+
+[equation polygamma2]
+
+The n'th derivative of ['cot(x)] is tabulated for small /n/, and for larger n
+has the general form:
+
+[equation polygamma3]
+
+The coefficients of the cosine terms can be calculated iteratively starting
+from ['C[sub 1,0] = -1] and then using
+
+[equation polygamma7]
+
+to generate coefficients for n+1.
+
+Note that every other coefficient is zero, and therefore what we have are
+even or odd polynomials depending on whether n is even or odd.
+
+Once x is positive then we have two methods available to us, for small x
+we use the series expansion:
+
+[equation polygamma4]
+
+Note that the evaluation of zeta functions at integer values is essentially a table lookup
+as __zeta is optimized for those cases.
+
+For large x we use the asymptotic expansion:
+
+[equation polygamma5]
+
+For x in-between the two extremes we use the relation:
+
+[equation polygamma6]
+
+to make x large enough for the asymptotic expansion to be used.
+
+There are also two special cases:
+
+[equation polygamma8]
+
+[equation polygamma9]
+
+[endsect][/section:polygamma The Polygamma Function]
+
+[/
+ Copyright 2014 John Maddock and Paul A. Bristow.
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt).
+]
+
diff --git a/libs/math/doc/sf/trigamma.qbk b/libs/math/doc/sf/trigamma.qbk
new file mode 100644
index 000000000..827c8fb52
--- /dev/null
+++ b/libs/math/doc/sf/trigamma.qbk
@@ -0,0 +1,84 @@
+[section:trigamma Trigamma]
+
+[h4 Synopsis]
+
+``
+#include <boost/math/special_functions/trigamma.hpp>
+``
+
+ namespace boost{ namespace math{
+
+ template <class T>
+ ``__sf_result`` trigamma(T z);
+
+ template <class T, class ``__Policy``>
+ ``__sf_result`` trigamma(T z, const ``__Policy``&);
+
+ }} // namespaces
+
+[h4 Description]
+
+Returns the trigamma function of /x/. Trigamma is defined as the
+derivative of the digamma function:
+
+[equation trigamma1]
+
+[graph trigamma]
+
+[optional_policy]
+
+The return type of this function is computed using the __arg_pomotion_rules:
+the result is of type `double` when T is an integer type, and type T otherwise.
+
+[h4 Accuracy]
+
+The following table shows the peak errors (in units of epsilon)
+found on various platforms with various floating point types.
+Unless otherwise specified any floating point type that is narrower
+than the one shown will have __zero_error.
+
+[table
+[[Significand Size] [Platform and Compiler] [Random Values] ]
+[[53] [Win32 Visual C++ 12] [Peak=1.0 Mean=0.4] ]
+[[64] [Win64 Mingw GCC] [Peak=1.4 Mean=0.4] ]
+[[113] [Win64 Mingw GCC __float128] [Peak=1.0 Mean=0.5] ]
+]
+
+As shown above, error rates are generally very low for built in types.
+For multiprecision types, error rates are typically in the order of a
+few epsilon.
+
+[h4 Testing]
+
+Testing is against Mathematica generated spot values to 35 digit precision.
+
+[h4 Implementation]
+
+The arbitrary precision version of this function simply calls __polygamma.
+
+For built in fixed precision types, negative arguments are first made positive via:
+
+[equation trigamma2]
+
+Then arguments in the range \[0, 1) are shifted to >= 1 via:
+
+[equation trigamma3]
+
+Then evaluation is via one of a number of rational approximations, for small x these are
+of the form:
+
+[equation trigamma4]
+
+and for large x of the form:
+
+[equation trigamma5]
+
+[endsect][/section:digamma The Trigamma Function]
+
+[/
+ Copyright 2014 John Maddock and Paul A. Bristow.
+ Distributed under the Boost Software License, Version 1.0.
+ (See accompanying file LICENSE_1_0.txt or copy at
+ http://www.boost.org/LICENSE_1_0.txt).
+]
+
diff --git a/libs/math/doc/sf/zeta.qbk b/libs/math/doc/sf/zeta.qbk
index 08186c6a4..b8520685c 100644
--- a/libs/math/doc/sf/zeta.qbk
+++ b/libs/math/doc/sf/zeta.qbk
@@ -112,6 +112,18 @@ required for R(z-n) is not full machine precision, but an absolute error
of: [epsilon]/R(0). This saves us quite a few digits when dealing with large
z, especially when [epsilon] is small.
+Finally, there are some special cases for integer arguments, there are
+closed forms for negative or even integers:
+
+[equation zeta7]
+
+[equation zeta8]
+
+[equation zeta9]
+
+and for positive odd integers we simply cache pre-computed values as these are of great
+benefit to some infinite series calculations.
+
[endsect]
[/ :error_function The Error Functions]