diff options
Diffstat (limited to 'libs/math/doc/graphs')
-rw-r--r-- | libs/math/doc/graphs/arcsine01_cdf.png | bin | 0 -> 45312 bytes | |||
-rw-r--r-- | libs/math/doc/graphs/arcsine01_cdf.svg | 70 | ||||
-rw-r--r-- | libs/math/doc/graphs/arcsine01_pdf.png | bin | 0 -> 40844 bytes | |||
-rw-r--r-- | libs/math/doc/graphs/arcsine01_pdf.svg | 66 | ||||
-rw-r--r-- | libs/math/doc/graphs/arcsine_cdf.png | bin | 0 -> 71714 bytes | |||
-rw-r--r-- | libs/math/doc/graphs/arcsine_cdf.svg | 77 | ||||
-rw-r--r-- | libs/math/doc/graphs/arcsine_pdf.png | bin | 0 -> 63439 bytes | |||
-rw-r--r-- | libs/math/doc/graphs/arcsine_pdf.svg | 73 | ||||
-rw-r--r-- | libs/math/doc/graphs/dist_graphs.cpp | 45 | ||||
-rwxr-xr-x | libs/math/doc/graphs/generate.sh | 6 | ||||
-rw-r--r-- | libs/math/doc/graphs/polygamma2.png | bin | 0 -> 28765 bytes | |||
-rw-r--r-- | libs/math/doc/graphs/polygamma2.svg | 70 | ||||
-rw-r--r-- | libs/math/doc/graphs/polygamma3.png | bin | 0 -> 32173 bytes | |||
-rw-r--r-- | libs/math/doc/graphs/polygamma3.svg | 67 | ||||
-rw-r--r-- | libs/math/doc/graphs/sf_graphs.cpp | 94 | ||||
-rw-r--r-- | libs/math/doc/graphs/trigamma.png | bin | 0 -> 30578 bytes | |||
-rw-r--r-- | libs/math/doc/graphs/trigamma.svg | 70 |
17 files changed, 591 insertions, 47 deletions
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x="375" y="40" text-anchor="middle" font-size="20" font-family="Lucida Sans Unicode">Arcsine Distribution PDF</text></g> +<g id="plotXValues"></g> +<g id="plotYValues"></g> +</svg> diff --git a/libs/math/doc/graphs/dist_graphs.cpp b/libs/math/doc/graphs/dist_graphs.cpp index 07f2f7316..515d392ef 100644 --- a/libs/math/doc/graphs/dist_graphs.cpp +++ b/libs/math/doc/graphs/dist_graphs.cpp @@ -79,33 +79,34 @@ public: void add(const Dist& d, const std::string& name) { - // - // Add to our list for later: - // + // Add name of distribution to our list for later: m_distributions.push_back(std::make_pair(name, d)); // - // Get the extent: - // + // Get the extent of the distribution from the support: double a, b; std::tr1::tie(a, b) = support(d); // - // PDF maximimum is at the mode: - // + // PDF maximimum is at the mode (probably): double mod; try { mod = mode(d); } catch(const std::domain_error& ) - { + { // but if not use the lower limit of support. mod = a; } if((mod <= a) && !is_discrete_distribution<Dist>::value) - { - if((a != 0) && (fabs(a) > 1e-2)) - mod = a * (1 + 1e-2); + { // Continuous distribution at or below lower limit of support. + double margin = 1e-2; // Margin of 1% (say) to get lowest off the 'end stop'. + if((a != 0) && (fabs(a) > margin)) + { + mod = a * (1 + ((a > 0) ? margin : -margin)); + } else - mod = 1e-2; + { // Case of mod near zero? + mod = margin; + } } double peek_y = pdf(d, mod); double min_y = peek_y / 20; @@ -266,6 +267,7 @@ public: .line_color(colors[color_index]) .line_width(1.) .shape(none); + //.bezier_on(true) // Bezier can't cope with badly behaved like uniform & triangular. ++color_index; color_index = color_index % (sizeof(colors)/sizeof(colors[0])); @@ -322,6 +324,9 @@ private: int main() { + try + { + distribution_plotter<boost::math::gamma_distribution<> > gamma_plotter; gamma_plotter.add(boost::math::gamma_distribution<>(0.75), "shape = 0.75"); @@ -653,6 +658,16 @@ int main() hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(450, 50, 500), "N=500, r=50, n=450"); hypergeometric_plotter2.plot("Hypergeometric Distribution PDF", "hypergeometric_pdf_2.svg"); + } + catch (std::exception ex) + { + std::cout << ex.what() << std::endl; + } + + + + /* these graphs for hyperexponential distribution not used. + distribution_plotter<boost::math::hyperexponential_distribution<> > hyperexponential_plotter; { @@ -695,11 +710,13 @@ int main() hyperexponential_plotter3.add(boost::math::hyperexponential_distribution<>(probs1,rates1), "α=(1.0), λ=(2.0)"); const double probs2[] = {0.5,0.5}; const double rates2[] = {0.3,1.5}; - hyperexponential_plotter3.add(boost::math::hyperexponential_distribution<>(probs2_1,rates2_1), "α=(0.5,0.5), λ=(0.3,1.5)"); + hyperexponential_plotter3.add(boost::math::hyperexponential_distribution<>(probs2,rates2), "α=(0.5,0.5), λ=(0.3,1.5)"); const double probs3[] = {1.0/3.0,1.0/3.0,1.0/3.0}; const double rates3[] = {0.2,1.5,3.0}; - hyperexponential_plotter3.add(boost::math::hyperexponential_distribution<>(probs2_2,rates2_2), "α=(1.0/3.0,1.0/3.0,1.0/3.0), λ=(0.2,1.5,3.0)"); + hyperexponential_plotter3.add(boost::math::hyperexponential_distribution<>(probs2,rates2), "α=(1.0/3.0,1.0/3.0,1.0/3.0), λ=(0.2,1.5,3.0)"); } hyperexponential_plotter3.plot("Hyperexponential Distribution PDF (Different Number of Phases, Same Mean)", "hyperexponential_pdf_samemean.svg"); + */ + } // int main() diff --git a/libs/math/doc/graphs/generate.sh b/libs/math/doc/graphs/generate.sh index bff99777e..d9659141f 100755 --- a/libs/math/doc/graphs/generate.sh +++ b/libs/math/doc/graphs/generate.sh @@ -8,15 +8,15 @@ # Paths to tools come first, change these to match your system: # math2svg='m:\download\open\SVGMath-0.3.1\math2svg.py' -python=/cygdrive/c/Python26/python.exe -inkscape=/cygdrive/c/progra~1/Inkscape/inkscape +python='/cygdrive/c/program files/Python27/python.exe' +inkscape='/cygdrive/c/Program Files (x86)/Inkscape/inkscape.exe' 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-220,10 +220,10 @@ double find_end_point(F f, double x0, double target, bool rising, double x_off = { boost::math::tools::eps_tolerance<double> tol(50); boost::uintmax_t max_iter = 1000; - return boost::math::tools::bracket_and_solve_root( + return x_off + boost::math::tools::bracket_and_solve_root( location_finder<F>(f, target, x_off), x0, - double(1.5), + 1.5, rising, tol, max_iter).first; @@ -248,10 +248,11 @@ int main() double (*f2i)(int, double); double (*f3)(double, double, double); double (*f4)(double, double, double, double); + double max_val; f = boost::math::zeta; - plot.add(f, 1 + find_end_point(f, 0.1, 40.0, false, 1.0), 10, ""); - plot.add(f, -20, 1 + find_end_point(f, -0.1, -40.0, false, 1.0), ""); + plot.add(f, find_end_point(f, 0.1, 40.0, false, 1.0), 10, ""); + plot.add(f, -20, find_end_point(f, -0.1, -40.0, false, 1.0), ""); plot.plot("Zeta Function Over [-20,10]", "zeta1.svg", "z", "zeta(z)"); plot.clear(); @@ -259,34 +260,34 @@ int main() plot.plot("Zeta Function Over [-14,0]", "zeta2.svg", "z", "zeta(z)"); f = boost::math::tgamma; - double max_val = f(6); + max_val = f(6); plot.clear(); plot.add(f, find_end_point(f, 0.1, max_val, false), 6, ""); - plot.add(f, -1 + find_end_point(f, 0.1, -max_val, true, -1), find_end_point(f, -0.1, -max_val, false), ""); - plot.add(f, -2 + find_end_point(f, 0.1, max_val, false, -2), -1 + find_end_point(f, -0.1, max_val, true, -1), ""); - plot.add(f, -3 + find_end_point(f, 0.1, -max_val, true, -3), -2 + find_end_point(f, -0.1, -max_val, false, -2), ""); - plot.add(f, -4 + find_end_point(f, 0.1, max_val, false, -4), -3 + find_end_point(f, -0.1, max_val, true, -3), ""); + plot.add(f, find_end_point(f, 0.1, -max_val, true, -1), find_end_point(f, -0.1, -max_val, false), ""); + plot.add(f, find_end_point(f, 0.1, max_val, false, -2), find_end_point(f, -0.1, max_val, true, -1), ""); + plot.add(f, find_end_point(f, 0.1, -max_val, true, -3), find_end_point(f, -0.1, -max_val, false, -2), ""); + plot.add(f, find_end_point(f, 0.1, max_val, false, -4), find_end_point(f, -0.1, max_val, true, -3), ""); plot.plot("tgamma", "tgamma.svg", "z", "tgamma(z)"); f = boost::math::lgamma; max_val = f(10); plot.clear(); plot.add(f, find_end_point(f, 0.1, max_val, false), 10, ""); - plot.add(f, -1 + find_end_point(f, 0.1, max_val, false, -1), find_end_point(f, -0.1, max_val, true), ""); - plot.add(f, -2 + find_end_point(f, 0.1, max_val, false, -2), -1 + find_end_point(f, -0.1, max_val, true, -1), ""); - plot.add(f, -3 + find_end_point(f, 0.1, max_val, false, -3), -2 + find_end_point(f, -0.1, max_val, true, -2), ""); - plot.add(f, -4 + find_end_point(f, 0.1, max_val, false, -4), -3 + find_end_point(f, -0.1, max_val, true, -3), ""); - plot.add(f, -5 + find_end_point(f, 0.1, max_val, false, -5), -4 + find_end_point(f, -0.1, max_val, true, -4), ""); + plot.add(f, find_end_point(f, 0.1, max_val, false, -1), find_end_point(f, -0.1, max_val, true), ""); + plot.add(f, find_end_point(f, 0.1, max_val, false, -2), find_end_point(f, -0.1, max_val, true, -1), ""); + plot.add(f, find_end_point(f, 0.1, max_val, false, -3), find_end_point(f, -0.1, max_val, true, -2), ""); + plot.add(f, find_end_point(f, 0.1, max_val, false, -4), find_end_point(f, -0.1, max_val, true, -3), ""); + plot.add(f, find_end_point(f, 0.1, max_val, false, -5), find_end_point(f, -0.1, max_val, true, -4), ""); plot.plot("lgamma", "lgamma.svg", "z", "lgamma(z)"); f = boost::math::digamma; max_val = 10; plot.clear(); plot.add(f, find_end_point(f, 0.1, -max_val, true), 10, ""); - plot.add(f, -1 + find_end_point(f, 0.1, -max_val, true, -1), find_end_point(f, -0.1, max_val, true), ""); - plot.add(f, -2 + find_end_point(f, 0.1, -max_val, true, -2), -1 + find_end_point(f, -0.1, max_val, true, -1), ""); - plot.add(f, -3 + find_end_point(f, 0.1, -max_val, true, -3), -2 + find_end_point(f, -0.1, max_val, true, -2), ""); - plot.add(f, -4 + find_end_point(f, 0.1, -max_val, true, -4), -3 + find_end_point(f, -0.1, max_val, true, -3), ""); + plot.add(f, find_end_point(f, 0.1, -max_val, true, -1), find_end_point(f, -0.1, max_val, true), ""); + plot.add(f, find_end_point(f, 0.1, -max_val, true, -2), find_end_point(f, -0.1, max_val, true, -1), ""); + plot.add(f, find_end_point(f, 0.1, -max_val, true, -3), find_end_point(f, -0.1, max_val, true, -2), ""); + plot.add(f, find_end_point(f, 0.1, -max_val, true, -4), find_end_point(f, -0.1, max_val, true, -3), ""); plot.plot("digamma", "digamma.svg", "z", "digamma(z)"); f = boost::math::erf; @@ -300,16 +301,16 @@ int main() f = boost::math::erf_inv; plot.clear(); - plot.add(f, -1 + find_end_point(f, 0.1, -3, true, -1), 1 + find_end_point(f, -0.1, 3, true, 1), ""); + plot.add(f, find_end_point(f, 0.1, -3, true, -1), find_end_point(f, -0.1, 3, true, 1), ""); plot.plot("erf_inv", "erf_inv.svg", "z", "erf_inv(z)"); f = boost::math::erfc_inv; plot.clear(); - plot.add(f, find_end_point(f, 0.1, 3, false), 2 + find_end_point(f, -0.1, -3, false, 2), ""); + plot.add(f, find_end_point(f, 0.1, 3, false), find_end_point(f, -0.1, -3, false, 2), ""); plot.plot("erfc_inv", "erfc_inv.svg", "z", "erfc_inv(z)"); f = boost::math::log1p; plot.clear(); - plot.add(f, -1 + find_end_point(f, 0.1, -10, true, -1), 10, ""); + plot.add(f, find_end_point(f, 0.1, -10, true, -1), 10, ""); plot.plot("log1p", "log1p.svg", "z", "log1p(z)"); f = boost::math::expm1; @@ -324,7 +325,7 @@ int main() f = sqrt1pm1; plot.clear(); - plot.add(f, -1 + find_end_point(f, 0.1, -10, true, -1), 5, ""); + plot.add(f, find_end_point(f, 0.1, -10, true, -1), 5, ""); plot.plot("sqrt1pm1", "sqrt1pm1.svg", "z", "sqrt1pm1(z)"); f2 = boost::math::powm1; @@ -359,7 +360,7 @@ int main() f = boost::math::atanh; plot.clear(); - plot.add(f, -1 + find_end_point(f, 0.1, -5, true, -1), 1 + find_end_point(f, -0.1, 5, true, 1), ""); + plot.add(f, find_end_point(f, 0.1, -5, true, -1), find_end_point(f, -0.1, 5, true, 1), ""); plot.plot("atanh", "atanh.svg", "z", "atanh(z)"); f2 = boost::math::tgamma_delta_ratio; @@ -450,15 +451,15 @@ int main() "n = 2"); plot.add(boost::bind(f2u, 3, _1), find_end_point(boost::bind(f2u, 3, _1), -2, 20, false), - 8 + find_end_point(boost::bind(f2u, 3, _1), 1, 20, false, 8), + find_end_point(boost::bind(f2u, 3, _1), 1, 20, false, 8), "n = 3"); plot.add(boost::bind(f2u, 4, _1), find_end_point(boost::bind(f2u, 4, _1), -2, 20, false), - 8 + find_end_point(boost::bind(f2u, 4, _1), 1, 20, true, 8), + find_end_point(boost::bind(f2u, 4, _1), 1, 20, true, 8), "n = 4"); plot.add(boost::bind(f2u, 5, _1), find_end_point(boost::bind(f2u, 5, _1), -2, 20, false), - 8 + find_end_point(boost::bind(f2u, 5, _1), 1, 20, true, 8), + find_end_point(boost::bind(f2u, 5, _1), 1, 20, true, 8), "n = 5"); plot.plot("Laguerre Polynomials", "laguerre.svg", "x", "laguerre(n, x)"); @@ -555,17 +556,17 @@ int main() plot.add(boost::bind(f3, _1, 0.25, boost::math::constants::pi<double>() / 2), find_end_point( boost::bind(f3, _1, 0.25, boost::math::constants::pi<double>() / 2), - 0.5, 4, false, -1) - 1, + 0.5, 4, false, -1), find_end_point( boost::bind(f3, _1, 0.25, boost::math::constants::pi<double>() / 2), - -0.5, 4, true, 1) + 1, "n=0.25 φ=π/2"); + -0.5, 4, true, 1), "n=0.25 φ=π/2"); plot.add(boost::bind(f3, _1, 0.75, boost::math::constants::pi<double>() / 2), find_end_point( boost::bind(f3, _1, 0.75, boost::math::constants::pi<double>() / 2), - 0.5, 4, false, -1) - 1, + 0.5, 4, false, -1), find_end_point( boost::bind(f3, _1, 0.75, boost::math::constants::pi<double>() / 2), - -0.5, 4, true, 1) + 1, "n=0.75 φ=π/2"); + -0.5, 4, true, 1), "n=0.75 φ=π/2"); plot.plot("Elliptic Of the Third Kind", "ellint_3.svg", "k", "ellint_3(k, n, phi)"); f2 = boost::math::jacobi_sn; @@ -696,6 +697,39 @@ int main() plot.add(f, -20, 3, ""); plot.plot("Bi'", "airy_bip.svg", "z", "airy_bi_prime(z)"); + f = boost::math::trigamma; + max_val = 30; + plot.clear(); + plot.add(f, find_end_point(f, 0.1, max_val, false), 5, ""); + plot.add(f, find_end_point(f, 0.1, max_val, false, -1), find_end_point(f, -0.1, max_val, true), ""); + plot.add(f, find_end_point(f, 0.1, max_val, false, -2), find_end_point(f, -0.1, max_val, true, -1), ""); + plot.add(f, find_end_point(f, 0.1, max_val, false, -3), find_end_point(f, -0.1, max_val, true, -2), ""); + plot.add(f, find_end_point(f, 0.1, max_val, false, -4), find_end_point(f, -0.1, max_val, true, -3), ""); + plot.add(f, find_end_point(f, 0.1, max_val, false, -5), find_end_point(f, -0.1, max_val, true, -4), ""); + plot.plot("Trigamma", "trigamma.svg", "x", "trigamma(x)"); + + f2i = boost::math::polygamma; + max_val = -50; + plot.clear(); + plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true), 5, ""); + plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -1), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true), ""); + plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -2), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true, -1), ""); + plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -3), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true, -2), ""); + plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -4), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true, -3), ""); + plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -5), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true, -4), ""); + plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -6), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true, -5), ""); + plot.plot("Polygamma", "polygamma2.svg", "x", "polygamma(2, x)"); + + max_val = 800; + plot.clear(); + plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false), 5, ""); + plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -1), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true), ""); + plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -2), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true, -1), ""); + plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -3), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true, -2), ""); + plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -4), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true, -3), ""); + plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -5), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true, -4), ""); + plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -6), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true, -5), ""); + plot.plot("Polygamma", "polygamma3.svg", "x", 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