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Diffstat (limited to 'ml/dlib/dlib/test/numerical_integration.cpp')
| -rw-r--r-- | ml/dlib/dlib/test/numerical_integration.cpp | 228 |
1 files changed, 228 insertions, 0 deletions
diff --git a/ml/dlib/dlib/test/numerical_integration.cpp b/ml/dlib/dlib/test/numerical_integration.cpp new file mode 100644 index 000000000..d0e247623 --- /dev/null +++ b/ml/dlib/dlib/test/numerical_integration.cpp @@ -0,0 +1,228 @@ +// Copyright (C) 2013 Steve Taylor (steve98654@gmail.com) +// License: Boost Software License See LICENSE.txt for the full license. + +// This function test battery is given in: +// +// Test functions taken from Pedro Gonnet's dissertation at ETH: +// Adaptive Quadrature Re-Revisited +// http://e-collection.library.ethz.ch/eserv/eth:65/eth-65-02.pdf + +#include <math.h> +#include <dlib/matrix.h> +#include <dlib/numeric_constants.h> +#include <dlib/numerical_integration.h> +#include "tester.h" + +namespace +{ + using namespace test; + using namespace dlib; + using namespace std; + + logger dlog("test.numerical_integration"); + + class numerical_integration_tester : public tester + { + public: + numerical_integration_tester ( + ) : + tester ("test_numerical_integration", + "Runs tests on the numerical integration function.", + 0 + ) + {} + + void perform_test() + { + + dlog <<dlib::LINFO << "Testing integrate_function_adapt_simpson"; + + matrix<double,23,1> m; + double tol = 1e-10; + double eps = 1e-8; + + m(0) = integrate_function_adapt_simp(&gg1, 0.0, 1.0, tol); + m(1) = integrate_function_adapt_simp(&gg2, 0.0, 1.0, tol); + m(2) = integrate_function_adapt_simp(&gg3, 0.0, 1.0, tol); + m(3) = integrate_function_adapt_simp(&gg4, 0.0, 1.0, tol); + m(4) = integrate_function_adapt_simp(&gg5, -1.0, 1.0, tol); + m(5) = integrate_function_adapt_simp(&gg6, 0.0, 1.0, tol); + m(6) = integrate_function_adapt_simp(&gg7, 0.0, 1.0, tol); + m(7) = integrate_function_adapt_simp(&gg8, 0.0, 1.0, tol); + m(8) = integrate_function_adapt_simp(&gg9, 0.0, 1.0, tol); + m(9) = integrate_function_adapt_simp(&gg10, 0.0, 1.0, tol); + m(10) = integrate_function_adapt_simp(&gg11, 0.0, 1.0, tol); + m(11) = integrate_function_adapt_simp(&gg12, 1e-6, 1.0, tol); + m(12) = integrate_function_adapt_simp(&gg13, 0.0, 10.0, tol); + m(13) = integrate_function_adapt_simp(&gg14, 0.0, 10.0, tol); + m(14) = integrate_function_adapt_simp(&gg15, 0.0, 10.0, tol); + m(15) = integrate_function_adapt_simp(&gg16, 0.01, 1.0, tol); + m(16) = integrate_function_adapt_simp(&gg17, 0.0, pi, tol); + m(17) = integrate_function_adapt_simp(&gg18, 0.0, 1.0, tol); + m(18) = integrate_function_adapt_simp(&gg19, -1.0, 1.0, tol); + m(19) = integrate_function_adapt_simp(&gg20, 0.0, 1.0, tol); + m(20) = integrate_function_adapt_simp(&gg21, 0.0, 1.0, tol); + m(21) = integrate_function_adapt_simp(&gg22, 0.0, 5.0, tol); + + // Here we compare the approximated integrals against + // highly accurate approximations generated either from + // the exact integral values or Mathematica's NIntegrate + // function using a working precision of 20. + + DLIB_TEST(abs(m(0) - 1.7182818284590452354) < 1e-11); + DLIB_TEST(abs(m(1) - 0.7000000000000000000) < eps); + DLIB_TEST(abs(m(2) - 0.6666666666666666667) < eps); + DLIB_TEST(abs(m(3) - 0.2397141133444008336) < eps); + DLIB_TEST(abs(m(4) - 1.5822329637296729331) < 1e-11); + DLIB_TEST(abs(m(5) - 0.4000000000000000000) < eps); + DLIB_TEST(abs(m(6) - 2.0000000000000000000) < 1e-4); + DLIB_TEST(abs(m(7) - 0.8669729873399110375) < eps); + DLIB_TEST(abs(m(8) - 1.1547005383792515290) < eps); + DLIB_TEST(abs(m(9) - 0.6931471805599453094) < eps); + DLIB_TEST(abs(m(10) - 0.3798854930417224753) < eps); + DLIB_TEST(abs(m(11) - 0.7775036341124982763) < eps); + DLIB_TEST(abs(m(12) - 0.5000000000000000000) < eps); + DLIB_TEST(abs(m(13) - 1.0000000000000000000) < eps); + DLIB_TEST(abs(m(14) - 0.4993633810764567446) < eps); + DLIB_TEST(abs(m(15) - 0.1121393035410217 ) < eps); + DLIB_TEST(abs(m(16) - 0.2910187828600526985) < eps); + DLIB_TEST(abs(m(17) + 0.4342944819032518276) < 1e-5); + DLIB_TEST(abs(m(18) - 1.56439644406905 ) < eps); + DLIB_TEST(abs(m(19) - 0.1634949430186372261) < eps); + DLIB_TEST(abs(m(20) - 0.0134924856494677726) < eps); + } + + static double gg1(double x) + { + return pow(e,x); + } + + static double gg2(double x) + { + if(x > 0.3) + { + return 1.0; + } + else + { + return 0; + } + } + + static double gg3(double x) + { + return pow(x,0.5); + } + + static double gg4(double x) + { + return 23.0/25.0*cosh(x)-cos(x); + } + + static double gg5(double x) + { + return 1/(pow(x,4) + pow(x,2) + 0.9); + } + + static double gg6(double x) + { + return pow(x,1.5); + } + + static double gg7(double x) + { + return pow(x,-0.5); + } + + static double gg8(double x) + { + return 1/(1 + pow(x,4)); + } + + static double gg9(double x) + { + return 2/(2 + sin(10*pi*x)); + } + + static double gg10(double x) + { + return 1/(1+x); + } + + static double gg11(double x) + { + return 1.0/(1 + pow(e,x)); + } + + static double gg12(double x) + { + return x/(pow(e,x)-1.0); + } + + static double gg13(double x) + { + return sqrt(50.0)*pow(e,-50.0*pi*x*x); + } + + static double gg14(double x) + { + return 25.0*pow(e,-25.0*x); + } + + static double gg15(double x) + { + return 50.0/(pi*(2500.0*x*x+1)); + } + + static double gg16(double x) + { + return 50.0*pow((sin(50.0*pi*x)/(50.0*pi*x)),2); + } + + static double gg17(double x) + { + return cos(cos(x)+3*sin(x)+2*cos(2*x)+3*cos(3*x)); + } + + static double gg18(double x) + { + return log10(x); + } + + static double gg19(double x) + { + return 1/(1.005+x*x); + } + + static double gg20(double x) + { + return 1/cosh(20.0*(x-1.0/5.0)) + 1/cosh(400.0*(x-2.0/5.0)) + + 1/cosh(8000.0*(x-3.0/5.0)); + } + + static double gg21(double x) + { + return 1.0/(1.0+(230.0*x-30.0)*(230.0*x-30.0)); + } + + static double gg22(double x) + { + if(x < 1) + { + return (x + 1.0); + } + else if(x >= 1 && x <= 3) + { + return (3.0 - x); + } + else + { + return 2.0; + } + } + + }; + + numerical_integration_tester a; +} + |