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| author | Lorry Tar Creator <lorry-tar-importer@baserock.org> | 2015-04-08 03:09:47 +0000 |
|---|---|---|
| committer | <> | 2015-05-05 14:37:32 +0000 |
| commit | f2541bb90af059680aa7036f315f052175999355 (patch) | |
| tree | a5b214744b256f07e1dc2bd7273035a7808c659f /libs/math/doc/html | |
| parent | ed232fdd34968697a68783b3195b1da4226915b5 (diff) | |
| download | boost-tarball-master.tar.gz | |
Imported from /home/lorry/working-area/delta_boost-tarball/boost_1_58_0.tar.bz2.HEADboost_1_58_0master
Diffstat (limited to 'libs/math/doc/html')
378 files changed, 3336 insertions, 1451 deletions
diff --git a/libs/math/doc/html/backgrounders.html b/libs/math/doc/html/backgrounders.html index 0e382e4c5..15177772c 100644 --- a/libs/math/doc/html/backgrounders.html +++ b/libs/math/doc/html/backgrounders.html @@ -3,9 +3,9 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Chapter 16. Backgrounders</title> <link rel="stylesheet" href="math.css" type="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/perf_test_app.html" title="The Performance Test Application"> <link rel="next" href="math_toolkit/sf_implementation.html" title="Additional Implementation Notes"> </head> @@ -27,7 +27,7 @@ <a name="backgrounders"></a>Chapter 16. Backgrounders</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/sf_implementation.html">Additional Implementation Notes</a></span></dt> <dt><span class="section"><a href="math_toolkit/special_tut.html">Tutorial: How to Write a New diff --git a/libs/math/doc/html/constants.html b/libs/math/doc/html/constants.html index ed325b398..f30ed5252 100644 --- a/libs/math/doc/html/constants.html +++ b/libs/math/doc/html/constants.html @@ -3,9 +3,9 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Chapter 4. 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"> -<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/float128/typeinfo.html" title="typeinfo"> <link rel="next" href="math_toolkit/constants_intro.html" title="Introduction"> </head> @@ -27,7 +27,7 @@ <a name="constants"></a>Chapter 4. Mathematical Constants</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/constants_intro.html">Introduction</a></span></dt> <dt><span class="section"><a href="math_toolkit/tutorial.html">Tutorial</a></span></dt> <dd><dl> diff --git a/libs/math/doc/html/cstdfloat.html b/libs/math/doc/html/cstdfloat.html index 4130a79c9..9d0dde2a5 100644 --- a/libs/math/doc/html/cstdfloat.html +++ b/libs/math/doc/html/cstdfloat.html @@ -3,9 +3,9 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Chapter 3. Specified-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"> -<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/next_float/float_advance.html" title="Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance"> <link rel="next" href="math_toolkit/overview.html" title="Overview"> </head> @@ -27,7 +27,7 @@ <a name="cstdfloat"></a>Chapter 3. Specified-width floating-point typedefs</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/overview.html">Overview</a></span></dt> <dt><span class="section"><a href="math_toolkit/rationale.html">Rationale</a></span></dt> <dt><span class="section"><a href="math_toolkit/exact_typdefs.html">Exact-Width Floating-Point diff --git a/libs/math/doc/html/dist.html b/libs/math/doc/html/dist.html index 954ff7403..4c12500c8 100644 --- a/libs/math/doc/html/dist.html +++ b/libs/math/doc/html/dist.html @@ -3,9 +3,9 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Chapter 5. Statistical Distributions and 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/constants_faq.html" title="FAQs"> <link rel="next" href="math_toolkit/stat_tut.html" title="Statistical Distributions Tutorial"> </head> @@ -27,7 +27,7 @@ <a name="dist"></a>Chapter 5. Statistical Distributions and 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/stat_tut.html">Statistical Distributions Tutorial</a></span></dt> <dd><dl> <dt><span class="section"><a href="math_toolkit/stat_tut/overview.html">Overview of Distributions</a></span></dt> @@ -138,6 +138,7 @@ <dt><span class="section"><a href="math_toolkit/dist_ref/nmp.html">Non-Member Properties</a></span></dt> <dt><span class="section"><a href="math_toolkit/dist_ref/dists.html">Distributions</a></span></dt> <dd><dl> +<dt><span class="section"><a href="math_toolkit/dist_ref/dists/arcine_dist.html">Arcsine Distribution</a></span></dt> <dt><span class="section"><a href="math_toolkit/dist_ref/dists/bernoulli_dist.html">Bernoulli Distribution</a></span></dt> <dt><span class="section"><a href="math_toolkit/dist_ref/dists/beta_dist.html">Beta Distribution</a></span></dt> diff --git a/libs/math/doc/html/extern_c.html b/libs/math/doc/html/extern_c.html index fd35bb2ae..e3230ceff 100644 --- a/libs/math/doc/html/extern_c.html +++ b/libs/math/doc/html/extern_c.html @@ -3,9 +3,9 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Chapter 7. TR1 and C99 external "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"> -<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/owens_t.html" title="Owen's T function"> <link rel="next" href="math_toolkit/main_tr1.html" title="C99 and TR1 C Functions Overview"> </head> @@ -27,7 +27,7 @@ <a name="extern_c"></a>Chapter 7. TR1 and C99 external "C" 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/main_tr1.html">C99 and TR1 C Functions Overview</a></span></dt> <dt><span class="section"><a href="math_toolkit/c99.html">C99 C Functions</a></span></dt> <dt><span class="section"><a href="math_toolkit/tr1_ref.html">TR1 C Functions Quick Reference</a></span></dt> diff --git a/libs/math/doc/html/gcd_lcm.html b/libs/math/doc/html/gcd_lcm.html index 1c67f06b7..769147099 100644 --- a/libs/math/doc/html/gcd_lcm.html +++ b/libs/math/doc/html/gcd_lcm.html @@ -3,9 +3,9 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Chapter 11. Integer Utilities (Greatest Common Divisor and Least Common Multiple)</title> <link rel="stylesheet" href="math.css" type="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/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 11. 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 index 42ed0f6be..47b83b6f3 100644 --- a/libs/math/doc/html/index.html +++ b/libs/math/doc/html/index.html @@ -1,10 +1,10 @@ <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 1. 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 +++ b/libs/math/doc/html/indexes.html @@ -3,9 +3,9 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Chapter 18. 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 18. 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 index 66a6067a9..babed9a5f 100644 --- a/libs/math/doc/html/indexes/s01.html +++ b/libs/math/doc/html/indexes/s01.html @@ -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 18. Indexes"> <link rel="prev" href="../indexes.html" title="Chapter 18. 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> @@ -648,6 +649,7 @@ <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> @@ -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 @@ <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> @@ -1112,6 +1122,10 @@ <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</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> @@ -1352,6 +1366,10 @@ <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_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> @@ -2360,6 +2380,7 @@ <li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions"><span class="index-entry-level-1">Ratios of Gamma Functions</span></a></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><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 index a4b032dac..803d75df7 100644 --- a/libs/math/doc/html/indexes/s02.html +++ b/libs/math/doc/html/indexes/s02.html @@ -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 18. 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 index ef3f5ee86..1275ef703 100644 --- a/libs/math/doc/html/indexes/s03.html +++ b/libs/math/doc/html/indexes/s03.html @@ -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 18. 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 18. 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 18. 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 --- a/libs/math/doc/html/inverse_complex.html +++ b/libs/math/doc/html/inverse_complex.html @@ -3,9 +3,9 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Chapter 8. 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 8. 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 --- a/libs/math/doc/html/math_toolkit/acknowledgement.html +++ 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 9. 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 10. 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 +++ b/libs/math/doc/html/math_toolkit/acos.html @@ -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 8. 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 index a6b47b149..ec591e6de 100644 --- a/libs/math/doc/html/math_toolkit/acosh.html +++ b/libs/math/doc/html/math_toolkit/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="../inverse_complex.html" title="Chapter 8. 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 --- a/libs/math/doc/html/math_toolkit/airy.html +++ b/libs/math/doc/html/math_toolkit/airy.html @@ -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 6. 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"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<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="../airy.html" title="Airy Functions"> <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 index fcfb35106..1255acf7f 100644 --- a/libs/math/doc/html/math_toolkit/airy/aip.html +++ 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"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<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 14. 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 index a71aafb1f..095216f3e 100644 --- a/libs/math/doc/html/math_toolkit/airy/bi.html +++ b/libs/math/doc/html/math_toolkit/airy/bi.html @@ -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"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<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="ai.html" title="Airy Ai Function"> <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> + <span class="inlinemediaobject"><img src="../../../equations/airy.svg"></span> </p> <p> The final <a class="link" href="../../policy.html" title="Chapter 14. 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> + <span class="inlinemediaobject"><img src="../../../graphs/airy_bi.svg" align="middle"></span> </p> <h5> <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> - <span class="inlinemediaobject"><img src="../../../equations/airy_bi.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/airy_bi.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/bip.html b/libs/math/doc/html/math_toolkit/airy/bip.html index 4a5b4ebd7..8355fd9b0 100644 --- a/libs/math/doc/html/math_toolkit/airy/bip.html +++ b/libs/math/doc/html/math_toolkit/airy/bip.html @@ -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"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<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="aip.html" title="Airy Ai' Function"> <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 14. 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> </p> <h5> <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> <p> - <span class="inlinemediaobject"><img src="../../../equations/airy_bip.png"></span> + <span class="inlinemediaobject"><img src="../../../equations/airy_bip.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/archetypes.html b/libs/math/doc/html/math_toolkit/archetypes.html index b1ddeeadc..81f3c00e5 100644 --- a/libs/math/doc/html/math_toolkit/archetypes.html +++ b/libs/math/doc/html/math_toolkit/archetypes.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Conceptual Archetypes for Reals and 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="../using_udt.html" title="Chapter 13. Use with User-Defined Floating-Point Types - Boost.Multiprecision and others"> <link rel="prev" href="dist_concept.html" title="Conceptual Requirements for Distribution Types"> <link rel="next" href="../policy.html" title="Chapter 14. 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 8. 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 8. 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 8. 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 8. 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 6. 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 -∞   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 > 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   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>   and Y<sub>v</sub>   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>μ</sub>, J<sub>μ+1</sub>, Y<sub>μ</sub>, Y<sub>μ+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>ν</sub> and Y<sub>μ</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>   and h<sub>k</sub>   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 ν   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>   and Y<sub>n</sub>   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>   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>   and K<sub>1</sub>   which are calculated using rational the approximations @@ -377,17 +377,17 @@ I<sub>v</sub>x   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 ν   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 μ   = ν - floor(ν + 1/2), then μ   is the fractional part of ν   such that |μ| <= 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>   and h<sub>k</sub>   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>   function is cyclic like J<sub>v</sub>   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>   is also cyclic for large x, but tends to -∞   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 < 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 1. 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 7. 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 15. 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 15. 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 11. Integer Utilities (Greatest Common Divisor and Least Common Multiple)"> <link rel="prev" href="run_time.html" title="Run-time GCD & LCM Determination"> <link rel="next" href="gcd_header.html" title="Header <boost/math/common_factor.hpp>"> 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 1. 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 8. Complex Number Functions"> <link rel="prev" href="atanh.html" title="atanh"> <link rel="next" href="../quaternions.html" title="Chapter 9. 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 8. Complex Number Functions"> <link rel="prev" href="../inverse_complex.html" title="Chapter 8. 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 13. 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 1. 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 4. 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 4. Mathematical Constants"> <link rel="prev" href="new_const.html" title="Defining New Constants"> <link rel="next" href="../dist.html" title="Chapter 5. 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 4. Mathematical Constants"> <link rel="prev" href="../constants.html" title="Chapter 4. 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 1. Overview"> <link rel="prev" href="main_faq.html" title="Frequently Asked Questions FAQ"> <link rel="next" href="../utils.html" title="Chapter 2. 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 1. 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 9. 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 17. Library Status"> <link rel="prev" href="issues.html" title="Known Issues, and TODO List"> <link rel="next" href="../indexes.html" title="Chapter 18. 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 11. Integer Utilities (Greatest Common Divisor and Least Common Multiple)"> <link rel="prev" href="gcd_header.html" title="Header <boost/math/common_factor.hpp>"> <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 1. 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 13. 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 index 614ca8414..33fbe27a6 100644 --- 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 5. 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 index 5fa251e87..16d39506b 100644 --- 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 index 1cf1a59f1..d309622be 100644 --- 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> @@ -20,13 +20,14 @@ </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> <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 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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> +<div class="section"> +<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"><</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">></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"><</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 14. 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<></a> <span class="special">></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"><</span><span class="keyword">double</span><span class="special">></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"><</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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></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 <= x <= 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> +     f(x; x_min, x_max) = 1 /(π⋅√((x - x_min)⋅(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> +     F(x) = 2⋅arcsin(√((x-x_min)/(x_max - x))) / π + </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 < 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"><></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"><</span><span class="keyword">double</span><span class="special">></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"><></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> +   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"><<</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"><<</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> = ½ 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 ¼, 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"><<</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"><<</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"><<</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"><<</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"><<</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"><<</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"><<</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"><<</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"><<</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"><<</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"><<</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"><<</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 α = 1/2 and β = 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>   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 ∈ [a, b], default x ∈ [0, 1] + </p> + </td> +</tr> +<tr> +<td> + <p> + pdf + </p> + </td> +<td> + <p> + f(x; a, b) = 1/(π⋅√(x - a)⋅(b - x)) + </p> + </td> +</tr> +<tr> +<td> + <p> + cdf + </p> + </td> +<td> + <p> + F(x) = 2/π⋅sin<sup>-1</sup>(√(x - a) / (b - a) ) + </p> + </td> +</tr> +<tr> +<td> + <p> + cdf of complement + </p> + </td> +<td> + <p> + 2/(π⋅cos<sup>-1</sup>(√(x - a) / (b - a))) + </p> + </td> +</tr> +<tr> +<td> + <p> + quantile + </p> + </td> +<td> + <p> + -a⋅sin<sup>2</sup>(½π⋅p) + a + b⋅sin<sup>2</sup>(½π⋅p) + </p> + </td> +</tr> +<tr> +<td> + <p> + quantile from the complement + </p> + </td> +<td> + <p> + -a⋅cos<sup>2</sup>(½π⋅p) + a + b⋅cos<sup>2</sup>(½π⋅q) + </p> + </td> +</tr> +<tr> +<td> + <p> + mean + </p> + </td> +<td> + <p> + ½(a+b) + </p> + </td> +</tr> +<tr> +<td> + <p> + median + </p> + </td> +<td> + <p> + ½(a+b) + </p> + </td> +</tr> +<tr> +<td> + <p> + mode + </p> + </td> +<td> + <p> + x ∈ [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">-></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 © 2006-2010, 2012-2014 Nikhar Agrawal, + Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert + Holin, Bruno Lalande, John Maddock, Johan Råde, 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 α = β = 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>   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 μ<sub>i</sub>   and variances σ<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 ν: </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 α  = k and β  = 1 / θ, 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>λ=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"><</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">></span> <span class="identifier">hyperexponential_distribution</span><span class="special">(</span><span class="identifier">RateIterT</span> <span class="keyword">const</span><span class="special">&</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 >= 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 > 104729, the user should expect to loose around + in this area where N > 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 ν and ξ: </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 μ and λ: </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 (μ and λ) 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;λ/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 λ: </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 = λ/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 @@ μ<sub>i</sub> and variances σ<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 λ 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 λ: </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 λ'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 λ: </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 ν and δ: </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 Φ(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 μ  and standard deviation σ  it has the PDF: </p> <p> -   <span class="inlinemediaobject"><img src="../../../../equations/normal_ref1.png"></span> +   <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> -   <span class="inlinemediaobject"><img src="../../../../equations/normal_cdf.png"></span> +   <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 @@ β: </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 α: </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 λ. @@ -73,7 +73,7 @@ The following graph illustrates how the PDF varies with the parameter λ: </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 σ: </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> -     <span class="inlinemediaobject"><img src="../../../../equations/normal01_pdf.png"></span> +     <span class="inlinemediaobject"><img src="../../../../equations/normal01_pdf.svg"></span> </p> <p> and the cumulative distribution function </p> <p> -     <span class="inlinemediaobject"><img src="../../../../equations/normal01_cdf.png"></span> +     <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> -     <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_pdf0.png"></span> +     <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> -     <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_pdf.png"></span> +     <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> -     <span class="inlinemediaobject"><img src="../../../../equations/skew_normal_cdf.png"></span> +     <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>Φ(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 δ is related to the shape α by δ = α / (1 + α²), 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>Φ(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>μ</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 ν: </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 @@ α: </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 β: </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 6. 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(π/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 <= k <= 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 <= k <= 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(π/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 <= k <= 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 <= k <= 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, π/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 @@ φ, 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 <= k <= 1</em></span> and <span class="emphasis"><em>n < 1/sin<sup>2</sup>(φ)</em></span>, @@ -101,7 +101,7 @@ Returns the complete elliptic integral of the first kind <span class="emphasis"><em>Π(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 <= k <= 1</em></span> and <span class="emphasis"><em>n < 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 < 0 the relations (A&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>Π(n, φ+mπ, k) = Π(n, φ, k) + 2mΠ(n, k) ; n <= 1</em></span> </p> <p> - <span class="emphasis"><em>Π(n, φ+mπ, k) = Π(n, φ, k) ; n > 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>Π(n, φ+mπ, k) = Π(n, φ, k) ; n > 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 φ   to the range [0, π/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"><</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">></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"><</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> +<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"><</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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&)</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"><</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> <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 > 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"><</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> +<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"><</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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&)</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 14. 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 14. 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 < 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"><</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">></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"><</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> +<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"><</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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">></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"><</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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</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(φ, + k)</em></span> and its complete counterpart <span class="emphasis"><em>D(k) = D(π/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"><</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> +<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"><</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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</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 <= k <= 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 14. 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 14. Policies: Controlling Precision, Error Handling etc">policy + documentation for more details</a>. + </p> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">></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"><</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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span> +</pre> +<p> + Returns the complete elliptic integral <span class="emphasis"><em>D(k) = D(π/2, k)</em></span> + </p> +<p> + Requires <span class="emphasis"><em>-1 <= k <= 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 14. 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 14. 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 + φ +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(φ, k) first performs argument reduction using the + relations: + </p> +<p> + <span class="emphasis"><em>D(-φ, k) = -D(φ, k)</em></span> + </p> +<p> + and + </p> +<p> + <span class="emphasis"><em>D(nπ+φ, k) = 2nD(k) + D(φ, k)</em></span> + </p> +<p> + to move φ   to the range [0, π/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 © 2006-2010, 2012-2014 Nikhar Agrawal, + Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert + Holin, Bruno Lalande, John Maddock, Johan Råde, 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(φ,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"><</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">></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"><</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> +<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"><</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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</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>Λ<sub>0</sub>(φ, 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 <= k <= 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 14. 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 14. 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 φ = π / 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 + φ +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>|φ| >= π/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 © 2006-2010, 2012-2014 Nikhar Agrawal, + Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert + Holin, Bruno Lalande, John Maddock, Johan Råde, 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"> +</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_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"><</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">></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"><</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> +<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"><</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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</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(φ, 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 <= k <= 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 14. 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 14. 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 φ = π / 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 + φ +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(φ, k) first makes the argument φ positive using: + </p> +<p> + <span class="emphasis"><em>Z(-φ, k) = -Z(φ, 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(φ, 1) = sign(cos(φ)) sin(φ)</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 © 2006-2010, 2012-2014 Nikhar Agrawal, + Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert + Holin, Bruno Lalande, John Maddock, Johan Råde, 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 1. 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 3. 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 3. 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 9. 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 6. 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 > 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 < z < 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">></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"> <link rel="up" href="../special.html" title="Chapter 6. Special Functions"> <link rel="prev" href="sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function"> <link rel="next" href="factorials/sf_factorial.html" title="Factorial"> @@ -26,7 +26,7 @@ <div class="titlepage"><div><div><h2 class="title" style="clear: both"> <a name="math_toolkit.factorials"></a><a class="link" href="factorials.html" title="Factorials and Binomial Coefficients">Factorials and Binomial Coefficients</a> </h2></div></div></div> -<div class="toc"><dl class="toc"> +<div class="toc"><dl> <dt><span class="section"><a href="factorials/sf_factorial.html">Factorial</a></span></dt> <dt><span class="section"><a href="factorials/sf_double_factorial.html">Double Factorial</a></span></dt> <dt><span class="section"><a href="factorials/sf_rising_factorial.html">Rising Factorial</a></span></dt> diff --git a/libs/math/doc/html/math_toolkit/factorials/sf_binomial.html b/libs/math/doc/html/math_toolkit/factorials/sf_binomial.html index 85a613c0c..3afdb8f74 100644 --- a/libs/math/doc/html/math_toolkit/factorials/sf_binomial.html +++ b/libs/math/doc/html/math_toolkit/factorials/sf_binomial.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>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"> <link rel="up" href="../factorials.html" title="Factorials and Binomial Coefficients"> <link rel="prev" href="sf_falling_factorial.html" title="Falling Factorial"> <link rel="next" href="../sf_beta.html" title="Beta Functions"> diff --git a/libs/math/doc/html/math_toolkit/factorials/sf_double_factorial.html b/libs/math/doc/html/math_toolkit/factorials/sf_double_factorial.html index 7b774d14e..e01a820b5 100644 --- a/libs/math/doc/html/math_toolkit/factorials/sf_double_factorial.html +++ b/libs/math/doc/html/math_toolkit/factorials/sf_double_factorial.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Double Factorial</title> <link rel="stylesheet" href="../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0"> <link rel="up" href="../factorials.html" title="Factorials and Binomial Coefficients"> <link rel="prev" href="sf_factorial.html" title="Factorial"> <link rel="next" href="sf_rising_factorial.html" title="Rising Factorial"> diff --git a/libs/math/doc/html/math_toolkit/factorials/sf_factorial.html b/libs/math/doc/html/math_toolkit/factorials/sf_factorial.html index edbd8ae51..9ea157409 100644 --- a/libs/math/doc/html/math_toolkit/factorials/sf_factorial.html +++ b/libs/math/doc/html/math_toolkit/factorials/sf_factorial.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Factorial</title> <link rel="stylesheet" href="../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0"> <link rel="up" href="../factorials.html" title="Factorials and Binomial Coefficients"> <link rel="prev" href="../factorials.html" title="Factorials and Binomial Coefficients"> <link rel="next" href="sf_double_factorial.html" title="Double Factorial"> 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 index 0efb6ba22..e522f0972 100644 --- a/libs/math/doc/html/math_toolkit/factorials/sf_falling_factorial.html +++ b/libs/math/doc/html/math_toolkit/factorials/sf_falling_factorial.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Falling Factorial</title> <link rel="stylesheet" href="../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0"> <link rel="up" href="../factorials.html" title="Factorials and Binomial Coefficients"> <link rel="prev" href="sf_rising_factorial.html" title="Rising Factorial"> <link rel="next" href="sf_binomial.html" title="Binomial Coefficients"> diff --git a/libs/math/doc/html/math_toolkit/factorials/sf_rising_factorial.html b/libs/math/doc/html/math_toolkit/factorials/sf_rising_factorial.html index 0537d7e77..f92147bf6 100644 --- a/libs/math/doc/html/math_toolkit/factorials/sf_rising_factorial.html +++ b/libs/math/doc/html/math_toolkit/factorials/sf_rising_factorial.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Rising Factorial</title> <link rel="stylesheet" href="../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0"> <link rel="up" href="../factorials.html" title="Factorials and Binomial Coefficients"> <link rel="prev" href="sf_double_factorial.html" title="Double Factorial"> <link rel="next" href="sf_falling_factorial.html" title="Falling Factorial"> diff --git a/libs/math/doc/html/math_toolkit/fastest_typdefs.html b/libs/math/doc/html/math_toolkit/fastest_typdefs.html index 1085d591f..2308dbc0b 100644 --- a/libs/math/doc/html/math_toolkit/fastest_typdefs.html +++ b/libs/math/doc/html/math_toolkit/fastest_typdefs.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Fastest 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 3. Specified-width floating-point typedefs"> <link rel="prev" href="minimum_typdefs.html" title="Minimum-width floating-point typedefs"> <link rel="next" href="greatest_typdefs.html" title="Greatest-width floating-point typedef"> diff --git a/libs/math/doc/html/math_toolkit/float128.html b/libs/math/doc/html/math_toolkit/float128.html index 414cfa0bd..96865120a 100644 --- a/libs/math/doc/html/math_toolkit/float128.html +++ b/libs/math/doc/html/math_toolkit/float128.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Implementation of Float128 type</title> <link rel="stylesheet" href="../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../index.html" title="Math Toolkit 2.1.0"> +<meta name="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 3. Specified-width floating-point typedefs"> <link rel="prev" href="examples.html" title="Examples"> <link rel="next" href="float128/overloading_template_functions_w.html" title="Overloading template functions with float128_t"> @@ -26,7 +26,7 @@ <div class="titlepage"><div><div><h2 class="title" style="clear: both"> <a name="math_toolkit.float128"></a><a class="link" href="float128.html" title="Implementation of Float128 type">Implementation of Float128 type</a> </h2></div></div></div> -<div class="toc"><dl class="toc"> +<div class="toc"><dl> <dt><span class="section"><a href="float128/overloading_template_functions_w.html">Overloading template functions with float128_t</a></span></dt> <dt><span class="section"><a href="float128/exp_function.html">Exponential function</a></span></dt> diff --git a/libs/math/doc/html/math_toolkit/float128/exp_function.html b/libs/math/doc/html/math_toolkit/float128/exp_function.html index 1e65bcb09..03949347a 100644 --- a/libs/math/doc/html/math_toolkit/float128/exp_function.html +++ b/libs/math/doc/html/math_toolkit/float128/exp_function.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Exponential 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="../float128.html" title="Implementation of Float128 type"> <link rel="prev" href="overloading_template_functions_w.html" title="Overloading template functions with float128_t"> <link rel="next" href="typeinfo.html" title="typeinfo"> diff --git a/libs/math/doc/html/math_toolkit/float128/overloading_template_functions_w.html b/libs/math/doc/html/math_toolkit/float128/overloading_template_functions_w.html index 99c91d321..82b5a2732 100644 --- a/libs/math/doc/html/math_toolkit/float128/overloading_template_functions_w.html +++ b/libs/math/doc/html/math_toolkit/float128/overloading_template_functions_w.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Overloading template functions with float128_t</title> <link rel="stylesheet" href="../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0"> <link rel="up" href="../float128.html" title="Implementation of Float128 type"> <link rel="prev" href="../float128.html" title="Implementation of Float128 type"> <link rel="next" href="exp_function.html" title="Exponential function"> diff --git a/libs/math/doc/html/math_toolkit/float128/typeinfo.html b/libs/math/doc/html/math_toolkit/float128/typeinfo.html index c2207d33d..c306289d2 100644 --- a/libs/math/doc/html/math_toolkit/float128/typeinfo.html +++ b/libs/math/doc/html/math_toolkit/float128/typeinfo.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>typeinfo</title> <link rel="stylesheet" href="../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0"> <link rel="up" href="../float128.html" title="Implementation of Float128 type"> <link rel="prev" href="exp_function.html" title="Exponential function"> <link rel="next" href="../../constants.html" title="Chapter 4. Mathematical Constants"> diff --git a/libs/math/doc/html/math_toolkit/fp_facets.html b/libs/math/doc/html/math_toolkit/fp_facets.html index 7f11fc246..e7a79e2ba 100644 --- a/libs/math/doc/html/math_toolkit/fp_facets.html +++ b/libs/math/doc/html/math_toolkit/fp_facets.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Facets for Floating-Point Infinities and NaNs</title> <link rel="stylesheet" href="../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../index.html" title="Math Toolkit 2.1.0"> +<meta name="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 2. Floating Point Utilities"> <link rel="prev" href="sign_functions.html" title="Sign Manipulation Functions"> <link rel="next" href="fp_facets/facets_intro.html" title="Introduction"> @@ -27,7 +27,7 @@ <a name="math_toolkit.fp_facets"></a><a class="link" href="fp_facets.html" title="Facets for Floating-Point Infinities and NaNs">Facets for Floating-Point Infinities and NaNs</a> </h2></div></div></div> -<div class="toc"><dl class="toc"> +<div class="toc"><dl> <dt><span class="section"><a href="fp_facets/facets_intro.html">Introduction</a></span></dt> <dt><span class="section"><a href="fp_facets/reference.html">Reference</a></span></dt> <dt><span class="section"><a href="fp_facets/examples.html">Examples</a></span></dt> diff --git a/libs/math/doc/html/math_toolkit/fp_facets/examples.html b/libs/math/doc/html/math_toolkit/fp_facets/examples.html index e99ac994d..b4de3fbf6 100644 --- a/libs/math/doc/html/math_toolkit/fp_facets/examples.html +++ b/libs/math/doc/html/math_toolkit/fp_facets/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="../fp_facets.html" title="Facets for Floating-Point Infinities and NaNs"> <link rel="prev" href="reference.html" title="Reference"> <link rel="next" href="portability.html" title="Portability"> diff --git a/libs/math/doc/html/math_toolkit/fp_facets/facets_intro.html b/libs/math/doc/html/math_toolkit/fp_facets/facets_intro.html index d29eaf0f7..7289b1293 100644 --- a/libs/math/doc/html/math_toolkit/fp_facets/facets_intro.html +++ b/libs/math/doc/html/math_toolkit/fp_facets/facets_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="../fp_facets.html" title="Facets for Floating-Point Infinities and NaNs"> <link rel="prev" href="../fp_facets.html" title="Facets for Floating-Point Infinities and NaNs"> <link rel="next" href="reference.html" title="Reference"> diff --git a/libs/math/doc/html/math_toolkit/fp_facets/portability.html b/libs/math/doc/html/math_toolkit/fp_facets/portability.html index ebcc2eeca..7db5f9e43 100644 --- a/libs/math/doc/html/math_toolkit/fp_facets/portability.html +++ b/libs/math/doc/html/math_toolkit/fp_facets/portability.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Portability</title> <link rel="stylesheet" href="../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<link rel="home" href="../../index.html" title="Math Toolkit 2.2.0"> <link rel="up" href="../fp_facets.html" title="Facets for Floating-Point Infinities and NaNs"> <link rel="prev" href="examples.html" title="Examples"> <link rel="next" href="rationale.html" title="Design Rationale"> diff --git a/libs/math/doc/html/math_toolkit/fp_facets/rationale.html b/libs/math/doc/html/math_toolkit/fp_facets/rationale.html index c66cc6a25..d7af2853a 100644 --- a/libs/math/doc/html/math_toolkit/fp_facets/rationale.html +++ b/libs/math/doc/html/math_toolkit/fp_facets/rationale.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Design 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="../fp_facets.html" title="Facets for Floating-Point Infinities and NaNs"> <link rel="prev" href="portability.html" title="Portability"> <link rel="next" href="../next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values"> diff --git a/libs/math/doc/html/math_toolkit/fp_facets/reference.html b/libs/math/doc/html/math_toolkit/fp_facets/reference.html index 5e91b4ae8..31c2ff524 100644 --- a/libs/math/doc/html/math_toolkit/fp_facets/reference.html +++ b/libs/math/doc/html/math_toolkit/fp_facets/reference.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>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="../fp_facets.html" title="Facets for Floating-Point Infinities and NaNs"> <link rel="prev" href="facets_intro.html" title="Introduction"> <link rel="next" href="examples.html" title="Examples"> diff --git a/libs/math/doc/html/math_toolkit/fpclass.html b/libs/math/doc/html/math_toolkit/fpclass.html index 9183a9bd0..5e37af979 100644 --- a/libs/math/doc/html/math_toolkit/fpclass.html +++ b/libs/math/doc/html/math_toolkit/fpclass.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Floating-Point Classification: Infinities and NaNs</title> <link rel="stylesheet" href="../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../index.html" title="Math Toolkit 2.1.0"> +<meta name="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 2. Floating Point Utilities"> <link rel="prev" href="rounding/modf.html" title="Integer and Fractional Part Splitting (modf)"> <link rel="next" href="sign_functions.html" title="Sign Manipulation Functions"> diff --git a/libs/math/doc/html/math_toolkit/future.html b/libs/math/doc/html/math_toolkit/future.html index f1d830053..032491ce0 100644 --- a/libs/math/doc/html/math_toolkit/future.html +++ b/libs/math/doc/html/math_toolkit/future.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Extras/Future Directions</title> <link rel="stylesheet" href="../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../index.html" title="Math Toolkit 2.1.0"> +<meta name="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 5. Statistical Distributions and Functions"> <link rel="prev" href="dist_ref/dist_algorithms.html" title="Distribution Algorithms"> <link rel="next" href="../special.html" title="Chapter 6. Special Functions"> diff --git a/libs/math/doc/html/math_toolkit/gcd_credits.html b/libs/math/doc/html/math_toolkit/gcd_credits.html index f9c62b0fc..b8284e5a4 100644 --- a/libs/math/doc/html/math_toolkit/gcd_credits.html +++ b/libs/math/doc/html/math_toolkit/gcd_credits.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Credits</title> <link rel="stylesheet" href="../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../index.html" title="Math Toolkit 2.1.0"> +<meta name="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 11. Integer Utilities (Greatest Common Divisor and Least Common Multiple)"> <link rel="prev" href="gcd_history.html" title="History"> <link rel="next" href="../toolkit.html" title="Chapter 12. Internals (Series, Rationals and Continued Fractions, Root Finding, Function Minimization, Testing and Development Tools)"> diff --git a/libs/math/doc/html/math_toolkit/gcd_function_object.html b/libs/math/doc/html/math_toolkit/gcd_function_object.html index adc1eb42a..a8c769c32 100644 --- a/libs/math/doc/html/math_toolkit/gcd_function_object.html +++ b/libs/math/doc/html/math_toolkit/gcd_function_object.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>GCD 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 11. 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 <boost/math/common_factor.hpp></title> <link rel="stylesheet" href="../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../index.html" title="Math Toolkit 2.1.0"> +<meta name="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 11. 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 11. 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 15. 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 3. 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 6. 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 13. Use with User-Defined Floating-Point Types - Boost.Multiprecision and others"> <link rel="prev" href="../using_udt.html" title="Chapter 13. 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 1. 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 1. 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 17. Library Status"> <link rel="prev" href="../status.html" title="Chapter 17. 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 (Boost-1.56.0)</a> </h5> @@ -110,7 +154,7 @@ </li> </ul></div> <h5> -<a name="math_toolkit.history2.h2"></a> +<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 & 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 12. 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 & internals">Utilities & 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 & 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 & 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 & 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 & 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 & 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 & 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 & internals"> <link rel="prev" href="roots.html" title="Root Finding With Derivatives: Newton-Raphson, Halley & 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 & internals"> <link rel="prev" href="../internals1.html" title="Utilities & 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 & 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 12. 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 13. 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 12. Internals (Series, Rationals and Continued Fractions, Root Finding, Function Minimization, Testing and Development Tools)"> <link rel="prev" href="../toolkit.html" title="Chapter 12. Internals (Series, Rationals and Continued Fractions, Root Finding, Function Minimization, Testing and Development Tools)"> <link rel="next" href="internals1.html" title="Utilities & 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 15. 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 1. 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 11. Integer Utilities (Greatest Common Divisor and Least Common Multiple)"> <link rel="prev" href="../gcd_lcm.html" title="Chapter 11. 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 6. 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 14. 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 > x > ε 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<T>::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<T>::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<T>::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+ε[</code>) as <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb17.png"></span>. + and can be computed (for <code class="literal">[-1;-1+ε[</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 17. 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(φ, k), Z(β, k), Λ<sub>0</sub>(β, 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 6. 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 φ 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 > 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> < ε</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 16. 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 > 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 11. 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 & 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 3. 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 1. 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 1. Overview"> <link rel="prev" href="../overview.html" title="Chapter 1. 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 7. TR1 and C99 external "C" Functions'> <link rel="prev" href="../extern_c.html" title='Chapter 7. 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 9. 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 3. 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 1. 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 1. 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 4. 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 2. 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 3. 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 6. Special Functions"> <link rel="prev" href="../special.html" title="Chapter 6. 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"><</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">>::</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"><</span><span class="identifier">T</span><span class="special">>(</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> -    <span class="inlinemediaobject"><img src="../../../equations/tangent_numbers.png"></span> +    <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 > 0 and i is even then    <span class="inlinemediaobject"><img src="../../../equations/bernoulli_numbers.png"></span> <br> elseif + if i > 0 and i is even then    <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 < 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 10. 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 10. 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 10. 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 10. 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 10. 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"> -<link rel="home" href="../index.html" title="Math Toolkit 2.1.0"> +<meta name="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 10. Octonions"> <link rel="prev" href="../octonions.html" title="Chapter 10. Octonions"> <link rel="next" href="oct_header.html" title="Header File"> diff --git a/libs/math/doc/html/math_toolkit/oct_specialization.html b/libs/math/doc/html/math_toolkit/oct_specialization.html index 18f32a2c4..9a4f94e89 100644 --- a/libs/math/doc/html/math_toolkit/oct_specialization.html +++ b/libs/math/doc/html/math_toolkit/oct_specialization.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Octonion 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="../octonions.html" title="Chapter 10. Octonions"> <link rel="prev" href="octonion.html" title="Template Class octonion"> <link rel="next" href="oct_typedefs.html" title="Octonion Member Typedefs"> diff --git a/libs/math/doc/html/math_toolkit/oct_synopsis.html b/libs/math/doc/html/math_toolkit/oct_synopsis.html index e8906b62f..2eac74af7 100644 --- a/libs/math/doc/html/math_toolkit/oct_synopsis.html +++ b/libs/math/doc/html/math_toolkit/oct_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="../octonions.html" title="Chapter 10. Octonions"> <link rel="prev" href="oct_header.html" title="Header File"> <link rel="next" href="octonion.html" title="Template Class octonion"> diff --git a/libs/math/doc/html/math_toolkit/oct_tests.html b/libs/math/doc/html/math_toolkit/oct_tests.html index c34bf9ad7..16eb8982f 100644 --- a/libs/math/doc/html/math_toolkit/oct_tests.html +++ b/libs/math/doc/html/math_toolkit/oct_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="../octonions.html" title="Chapter 10. Octonions"> <link rel="prev" href="oct_trans.html" title="Octonions Transcendentals"> <link rel="next" href="acknowledgements.html" title="Acknowledgements"> diff --git a/libs/math/doc/html/math_toolkit/oct_todo.html b/libs/math/doc/html/math_toolkit/oct_todo.html index a7876a53f..72ce113de 100644 --- a/libs/math/doc/html/math_toolkit/oct_todo.html +++ b/libs/math/doc/html/math_toolkit/oct_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="../octonions.html" title="Chapter 10. Octonions"> <link rel="prev" href="oct_history.html" title="History"> <link rel="next" href="../gcd_lcm.html" title="Chapter 11. Integer Utilities (Greatest Common Divisor and Least Common Multiple)"> diff --git a/libs/math/doc/html/math_toolkit/oct_trans.html b/libs/math/doc/html/math_toolkit/oct_trans.html index cbb4d60d7..76b6041fc 100644 --- a/libs/math/doc/html/math_toolkit/oct_trans.html +++ b/libs/math/doc/html/math_toolkit/oct_trans.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Octonions 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="../octonions.html" title="Chapter 10. Octonions"> <link rel="prev" href="oct_create.html" title="Octonion Creation Functions"> <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 index 6560fd89a..b0f127b2e 100644 --- a/libs/math/doc/html/math_toolkit/oct_typedefs.html +++ b/libs/math/doc/html/math_toolkit/oct_typedefs.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Octonion 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="../octonions.html" title="Chapter 10. 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 index 77a23bf1b..925d8b49c 100644 --- a/libs/math/doc/html/math_toolkit/oct_value_ops.html +++ b/libs/math/doc/html/math_toolkit/oct_value_ops.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Octonion 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="../octonions.html" title="Chapter 10. Octonions"> <link rel="prev" href="oct_non_mem.html" title="Octonion Non-Member Operators"> <link rel="next" href="oct_create.html" title="Octonion Creation Functions"> diff --git a/libs/math/doc/html/math_toolkit/octonion.html b/libs/math/doc/html/math_toolkit/octonion.html index 3bbc5d799..acff39c03 100644 --- a/libs/math/doc/html/math_toolkit/octonion.html +++ b/libs/math/doc/html/math_toolkit/octonion.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Template Class octonion</title> <link rel="stylesheet" href="../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../index.html" title="Math Toolkit 2.1.0"> +<meta name="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 10. Octonions"> <link rel="prev" href="oct_synopsis.html" title="Synopsis"> <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 index 96a867f1d..6ecfc559a 100644 --- a/libs/math/doc/html/math_toolkit/overview.html +++ b/libs/math/doc/html/math_toolkit/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="../cstdfloat.html" title="Chapter 3. Specified-width floating-point typedefs"> <link rel="prev" href="../cstdfloat.html" title="Chapter 3. 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 index 7106aa730..c584f51fa 100644 --- a/libs/math/doc/html/math_toolkit/overview_tr1.html +++ b/libs/math/doc/html/math_toolkit/overview_tr1.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>C99 and C++ TR1 C-style 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="../overview.html" title="Chapter 1. Overview"> <link rel="prev" href="history1.html" title="History and What's New"> <link rel="next" href="main_faq.html" title="Frequently Asked Questions FAQ"> diff --git a/libs/math/doc/html/math_toolkit/owens_t.html b/libs/math/doc/html/math_toolkit/owens_t.html index 640c190ad..518968185 100644 --- a/libs/math/doc/html/math_toolkit/owens_t.html +++ b/libs/math/doc/html/math_toolkit/owens_t.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Owen's T 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="../special.html" title="Chapter 6. Special Functions"> <link rel="prev" href="inv_hyper/atanh.html" title="atanh"> <link rel="next" href="../extern_c.html" title='Chapter 7. TR1 and C99 external "C" Functions'> @@ -57,7 +57,7 @@ for more details</a>. </p> <p> -     <span class="inlinemediaobject"><img src="../../equations/owens_t.png"></span> +     <span class="inlinemediaobject"><img src="../../equations/owens_t.svg"></span> </p> <p> <span class="inlinemediaobject"><img src="../../graphs/plot_owens_t.png"></span> @@ -77,7 +77,7 @@ That is the area shaded in the figure below (Owens 1956). </p> <p> - <span class="inlinemediaobject"><img src="../../graphs/owens_integration_area.png" align="middle"></span> + <span class="inlinemediaobject"><img src="../../graphs/owens_integration_area.svg" align="middle"></span> </p> <p> and is also illustrated by a 3D plot. diff --git a/libs/math/doc/html/math_toolkit/perf_over1.html b/libs/math/doc/html/math_toolkit/perf_over1.html index ba72a0d04..8c5e7d8a2 100644 --- a/libs/math/doc/html/math_toolkit/perf_over1.html +++ b/libs/math/doc/html/math_toolkit/perf_over1.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>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"> +<meta name="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 1. Overview"> <link rel="prev" href="threads.html" title="Thread Safety"> <link rel="next" href="building.html" title="If and How to Build a Boost.Math Library, and its Examples and Tests"> diff --git a/libs/math/doc/html/math_toolkit/perf_over2.html b/libs/math/doc/html/math_toolkit/perf_over2.html index f3490c2b5..47166bc0d 100644 --- a/libs/math/doc/html/math_toolkit/perf_over2.html +++ b/libs/math/doc/html/math_toolkit/perf_over2.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Performance 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="../perf.html" title="Chapter 15. Performance"> <link rel="prev" href="../perf.html" title="Chapter 15. Performance"> <link rel="next" href="interp.html" title="Interpreting these Results"> diff --git a/libs/math/doc/html/math_toolkit/perf_test_app.html b/libs/math/doc/html/math_toolkit/perf_test_app.html index d78c57a48..838eee0c6 100644 --- a/libs/math/doc/html/math_toolkit/perf_test_app.html +++ b/libs/math/doc/html/math_toolkit/perf_test_app.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>The Performance Test Application</title> <link rel="stylesheet" href="../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../index.html" title="Math Toolkit 2.1.0"> +<meta name="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 15. Performance"> <link rel="prev" href="comparisons.html" title="Comparisons to Other Open Source Libraries"> <link rel="next" href="../backgrounders.html" title="Chapter 16. Backgrounders"> diff --git a/libs/math/doc/html/math_toolkit/pol_overview.html b/libs/math/doc/html/math_toolkit/pol_overview.html index 7d6d92879..8a316129a 100644 --- a/libs/math/doc/html/math_toolkit/pol_overview.html +++ b/libs/math/doc/html/math_toolkit/pol_overview.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Policy 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="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc"> <link rel="prev" href="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc"> <link rel="next" href="pol_tutorial.html" title="Policy Tutorial"> diff --git a/libs/math/doc/html/math_toolkit/pol_ref.html b/libs/math/doc/html/math_toolkit/pol_ref.html index 8bbe12243..72effc07e 100644 --- a/libs/math/doc/html/math_toolkit/pol_ref.html +++ b/libs/math/doc/html/math_toolkit/pol_ref.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Policy 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="../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc"> <link rel="prev" href="pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions"> <link rel="next" href="pol_ref/error_handling_policies.html" title="Error Handling Policies"> @@ -26,7 +26,7 @@ <div class="titlepage"><div><div><h2 class="title" style="clear: both"> <a name="math_toolkit.pol_ref"></a><a class="link" href="pol_ref.html" title="Policy Reference">Policy Reference</a> </h2></div></div></div> -<div class="toc"><dl class="toc"> +<div class="toc"><dl> <dt><span class="section"><a href="pol_ref/error_handling_policies.html">Error Handling Policies</a></span></dt> <dt><span class="section"><a href="pol_ref/internal_promotion.html">Internal Floating-point diff --git a/libs/math/doc/html/math_toolkit/pol_ref/assert_undefined.html b/libs/math/doc/html/math_toolkit/pol_ref/assert_undefined.html index 47fc34083..d64605816 100644 --- a/libs/math/doc/html/math_toolkit/pol_ref/assert_undefined.html +++ b/libs/math/doc/html/math_toolkit/pol_ref/assert_undefined.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Mathematically Undefined Function 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="internal_promotion.html" title="Internal Floating-point Promotion Policies"> <link rel="next" href="discrete_quant_ref.html" title="Discrete Quantile Policies"> diff --git a/libs/math/doc/html/math_toolkit/pol_ref/discrete_quant_ref.html b/libs/math/doc/html/math_toolkit/pol_ref/discrete_quant_ref.html index 7d88652aa..e46d3820f 100644 --- a/libs/math/doc/html/math_toolkit/pol_ref/discrete_quant_ref.html +++ b/libs/math/doc/html/math_toolkit/pol_ref/discrete_quant_ref.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Discrete Quantile 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="assert_undefined.html" title="Mathematically Undefined Function Policies"> <link rel="next" href="precision_pol.html" title="Precision Policies"> diff --git a/libs/math/doc/html/math_toolkit/pol_ref/error_handling_policies.html b/libs/math/doc/html/math_toolkit/pol_ref/error_handling_policies.html index 900e7ea02..3ef507220 100644 --- a/libs/math/doc/html/math_toolkit/pol_ref/error_handling_policies.html +++ b/libs/math/doc/html/math_toolkit/pol_ref/error_handling_policies.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Error Handling 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="../pol_ref.html" title="Policy Reference"> <link rel="next" href="internal_promotion.html" title="Internal Floating-point Promotion Policies"> diff --git a/libs/math/doc/html/math_toolkit/pol_ref/internal_promotion.html b/libs/math/doc/html/math_toolkit/pol_ref/internal_promotion.html index 5d3a3dbdc..5b3f2df01 100644 --- a/libs/math/doc/html/math_toolkit/pol_ref/internal_promotion.html +++ b/libs/math/doc/html/math_toolkit/pol_ref/internal_promotion.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Internal Floating-point Promotion 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="error_handling_policies.html" title="Error Handling Policies"> <link rel="next" href="assert_undefined.html" title="Mathematically Undefined Function Policies"> diff --git a/libs/math/doc/html/math_toolkit/pol_ref/iteration_pol.html b/libs/math/doc/html/math_toolkit/pol_ref/iteration_pol.html index 5a8cf8d4e..0386512f0 100644 --- a/libs/math/doc/html/math_toolkit/pol_ref/iteration_pol.html +++ 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 15. 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 14. 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 6. 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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</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 9. 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 9. 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 9. 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 9. 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 9. 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 9. Quaternions"> <link rel="prev" href="../quaternions.html" title="Chapter 9. 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 9. 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 9. 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 9. Quaternions"> <link rel="prev" href="quat_history.html" title="History"> <link rel="next" href="../octonions.html" title="Chapter 10. 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 3. 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 11. 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 16. Backgrounders"> <link rel="prev" href="remez.html" title="The Remez Method"> <link rel="next" href="../status.html" title="Chapter 17. 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 16. 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 16. 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 1. 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 2. Floating Point Utilities"> <link rel="prev" href="../utils.html" title="Chapter 2. 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 & 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 11. 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 6. 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 14. 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"><</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> <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"><</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> <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"><</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> <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 << 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">></span> @@ -394,7 +394,7 @@ (<code class="literal">q<sup>1/p</sup> < 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 < a and x < 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 6. 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"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></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"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></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 6. 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 14. 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 > 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 > 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 14. 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 14. 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 14. 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"><</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> <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"><</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> <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"><</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> <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 Γ(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 > 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 <= a < 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>   is the Lanczos sum, scaled by e<sup>g</sup>. @@ -447,7 +447,7 @@ -> 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>   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"><</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">></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"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></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"><</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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</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 14. 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 14. 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 -∞ to +∞ 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 < 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 © 2006-2010, 2012-2014 Nikhar Agrawal, + Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert + Holin, Bruno Lalande, John Maddock, Johan Råde, 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 14. 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 @@ > 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 < -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(π   * 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"><</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">></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"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></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"><</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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></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 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</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 14. 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 14. 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 >= 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 © 2006-2010, 2012-2014 Nikhar Agrawal, + Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert + Holin, Bruno Lalande, John Maddock, Johan Råde, 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 16. Backgrounders"> <link rel="prev" href="../backgrounders.html" title="Chapter 16. 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 6. 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 14. 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"><</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> <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"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></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"><</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> <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 <= x <= 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"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></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 <= x <= 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 <= x <= 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"><</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> <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"><</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> <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 2. 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 6. 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 @@ > 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 > 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 14. 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 9. 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 16. 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 +++ b/libs/math/doc/html/math_toolkit/special_tut/special_tut_test.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>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="../special_tut.html" title="Tutorial: How to Write a New Special Function"> <link rel="prev" href="special_tut_impl.html" title="Implementation"> <link rel="next" href="../relative_error.html" title="Relative Error"> diff --git a/libs/math/doc/html/math_toolkit/stat_tut.html b/libs/math/doc/html/math_toolkit/stat_tut.html index 41c66bae1..6d17be639 100644 --- a/libs/math/doc/html/math_toolkit/stat_tut.html +++ b/libs/math/doc/html/math_toolkit/stat_tut.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Statistical Distributions 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="../dist.html" title="Chapter 5. Statistical Distributions and Functions"> <link rel="prev" href="../dist.html" title="Chapter 5. Statistical Distributions and Functions"> <link rel="next" href="stat_tut/overview.html" title="Overview of Distributions"> @@ -26,7 +26,7 @@ <div class="titlepage"><div><div><h2 class="title" style="clear: both"> <a name="math_toolkit.stat_tut"></a><a class="link" href="stat_tut.html" title="Statistical Distributions Tutorial">Statistical Distributions Tutorial</a> </h2></div></div></div> -<div class="toc"><dl class="toc"> +<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 index c9690c827..bee6f0b0d 100644 --- a/libs/math/doc/html/math_toolkit/stat_tut/dist_params.html +++ b/libs/math/doc/html/math_toolkit/stat_tut/dist_params.html @@ -3,8 +3,8 @@ <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"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../index.html" title="Math Toolkit 2.1.0"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<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="variates.html" title="Random Variates and Distribution Parameters"> <link rel="next" href="../dist_ref.html" title="Statistical Distributions Reference"> diff --git a/libs/math/doc/html/math_toolkit/stat_tut/overview.html b/libs/math/doc/html/math_toolkit/stat_tut/overview.html index 79b8f0b2f..ff5e477d9 100644 --- a/libs/math/doc/html/math_toolkit/stat_tut/overview.html +++ b/libs/math/doc/html/math_toolkit/stat_tut/overview.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Overview of 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="../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"> <a name="math_toolkit.stat_tut.overview"></a><a class="link" href="overview.html" title="Overview of Distributions">Overview of Distributions</a> </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 index a36b04642..c1f0e6842 100644 --- a/libs/math/doc/html/math_toolkit/stat_tut/overview/complements.html +++ b/libs/math/doc/html/math_toolkit/stat_tut/overview/complements.html @@ -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> <link rel="stylesheet" href="../../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0"> +<meta name="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 index 857a1643f..764083333 100644 --- a/libs/math/doc/html/math_toolkit/stat_tut/overview/generic.html +++ b/libs/math/doc/html/math_toolkit/stat_tut/overview/generic.html @@ -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> <link rel="stylesheet" href="../../../math.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0"> +<meta name="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="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 index 5e6fc156e..9e848c688 100644 --- a/libs/math/doc/html/math_toolkit/stat_tut/overview/headers.html +++ b/libs/math/doc/html/math_toolkit/stat_tut/overview/headers.html @@ -3,8 +3,8 @@ <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Headers and 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="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 index da38569d7..82ded5562 100644 --- a/libs/math/doc/html/math_toolkit/stat_tut/overview/objects.html +++ b/libs/math/doc/html/math_toolkit/stat_tut/overview/objects.html @@ -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 index 261a6b622..aba38cef3 100644 --- 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 index db8618f39..58d403a05 100644 --- a/libs/math/doc/html/math_toolkit/stat_tut/overview/summary.html +++ b/libs/math/doc/html/math_toolkit/stat_tut/overview/summary.html @@ -3,8 +3,8 @@ <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 index 6881d0d3e..c92a6dd33 100644 --- a/libs/math/doc/html/math_toolkit/stat_tut/variates.html +++ b/libs/math/doc/html/math_toolkit/stat_tut/variates.html @@ -3,8 +3,8 @@ <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"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<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 index 44e349d9f..a8e2ba635 100644 --- a/libs/math/doc/html/math_toolkit/stat_tut/weg.html +++ b/libs/math/doc/html/math_toolkit/stat_tut/weg.html @@ -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"> +<meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> +<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 index d37299a9a..e974d921b 100644 --- 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 @@ -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 index 624ffa123..51cbd961d 100644 --- 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 @@ -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"> -<link rel="home" href="../../../../index.html" title="Math Toolkit 2.1.0"> +<meta name="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_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 index 7023bafdc..21ebf6def 100644 --- 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 @@ -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"> +<meta name="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_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 index d938e07be..f22e275d5 100644 --- 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 @@ -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 index 2f792e3e0..136dbad55 100644 --- 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 @@ -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 index 2bb852a9d..2762b4991 100644 --- 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 @@ -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"> +<meta name="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="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 index 6f4853fae..6daab806b 100644 --- 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 @@ -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"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<link rel="home" href="../../../index.html" title="Math Toolkit 2.1.0"> +<meta name="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="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 11. 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 1. 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 7. 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 8. 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 9. 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 15. 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 4. 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 9. 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 6. 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 < z < 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 < z < 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: ε/R(0). This saves us quite a few digits when dealing with large z, especially when ε 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 10. 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 10. 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 1. 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 1. 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 15. 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 15. 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 14. 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 14. 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 9. 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 9. 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 6. 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 6. 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 17. 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 17. 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 12. 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 & 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 13. 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 2. 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 2. 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> |