diff options
Diffstat (limited to 'unsupported/test/special_functions.cpp')
| -rw-r--r-- | unsupported/test/special_functions.cpp | 234 |
1 files changed, 193 insertions, 41 deletions
diff --git a/unsupported/test/special_functions.cpp b/unsupported/test/special_functions.cpp index 057fb3e92..589bb76e1 100644 --- a/unsupported/test/special_functions.cpp +++ b/unsupported/test/special_functions.cpp @@ -7,9 +7,21 @@ // Public License v. 2.0. If a copy of the MPL was not distributed // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. +#include <limits.h> #include "main.h" #include "../Eigen/SpecialFunctions" +// Hack to allow "implicit" conversions from double to Scalar via comma-initialization. +template<typename Derived> +Eigen::CommaInitializer<Derived> operator<<(Eigen::DenseBase<Derived>& dense, double v) { + return (dense << static_cast<typename Derived::Scalar>(v)); +} + +template<typename XprType> +Eigen::CommaInitializer<XprType>& operator,(Eigen::CommaInitializer<XprType>& ci, double v) { + return (ci, static_cast<typename XprType::Scalar>(v)); +} + template<typename X, typename Y> void verify_component_wise(const X& x, const Y& y) { @@ -64,8 +76,8 @@ template<typename ArrayType> void array_special_functions() // igamma(a, x) = gamma(a, x) / Gamma(a) // where Gamma and gamma are considered the standard unnormalized // upper and lower incomplete gamma functions, respectively. - ArrayType a = m1.abs() + 2; - ArrayType x = m2.abs() + 2; + ArrayType a = m1.abs() + Scalar(2); + ArrayType x = m2.abs() + Scalar(2); ArrayType zero = ArrayType::Zero(rows, cols); ArrayType one = ArrayType::Constant(rows, cols, Scalar(1.0)); ArrayType a_m1 = a - one; @@ -74,6 +86,7 @@ template<typename ArrayType> void array_special_functions() ArrayType gamma_a_x = Eigen::igamma(a, x) * a.lgamma().exp(); ArrayType gamma_a_m1_x = Eigen::igamma(a_m1, x) * a_m1.lgamma().exp(); + // Gamma(a, 0) == Gamma(a) VERIFY_IS_APPROX(Eigen::igammac(a, zero), one); @@ -81,10 +94,23 @@ template<typename ArrayType> void array_special_functions() VERIFY_IS_APPROX(Gamma_a_x + gamma_a_x, a.lgamma().exp()); // Gamma(a, x) == (a - 1) * Gamma(a-1, x) + x^(a-1) * exp(-x) - VERIFY_IS_APPROX(Gamma_a_x, (a - 1) * Gamma_a_m1_x + x.pow(a-1) * (-x).exp()); + VERIFY_IS_APPROX(Gamma_a_x, (a - Scalar(1)) * Gamma_a_m1_x + x.pow(a-Scalar(1)) * (-x).exp()); // gamma(a, x) == (a - 1) * gamma(a-1, x) - x^(a-1) * exp(-x) - VERIFY_IS_APPROX(gamma_a_x, (a - 1) * gamma_a_m1_x - x.pow(a-1) * (-x).exp()); + VERIFY_IS_APPROX(gamma_a_x, (a - Scalar(1)) * gamma_a_m1_x - x.pow(a-Scalar(1)) * (-x).exp()); + } + { + // Verify for large a and x that values are between 0 and 1. + ArrayType m1 = ArrayType::Random(rows,cols); + ArrayType m2 = ArrayType::Random(rows,cols); + int max_exponent = std::numeric_limits<Scalar>::max_exponent10; + ArrayType a = m1.abs() * Scalar(pow(10., max_exponent - 1)); + ArrayType x = m2.abs() * Scalar(pow(10., max_exponent - 1)); + for (int i = 0; i < a.size(); ++i) { + Scalar igam = numext::igamma(a(i), x(i)); + VERIFY(0 <= igam); + VERIFY(igam <= 1); + } } { @@ -93,27 +119,37 @@ template<typename ArrayType> void array_special_functions() Scalar x_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)}; // location i*6+j corresponds to a_s[i], x_s[j]. - Scalar igamma_s[][6] = {{0.0, nan, nan, nan, nan, nan}, - {0.0, 0.6321205588285578, 0.7768698398515702, - 0.9816843611112658, 9.999500016666262e-05, 1.0}, - {0.0, 0.4275932955291202, 0.608374823728911, - 0.9539882943107686, 7.522076445089201e-07, 1.0}, - {0.0, 0.01898815687615381, 0.06564245437845008, - 0.5665298796332909, 4.166333347221828e-18, 1.0}, - {0.0, 0.9999780593618628, 0.9999899967080838, - 0.9999996219837988, 0.9991370418689945, 1.0}, - {0.0, 0.0, 0.0, 0.0, 0.0, 0.5042041932513908}}; - Scalar igammac_s[][6] = {{nan, nan, nan, nan, nan, nan}, - {1.0, 0.36787944117144233, 0.22313016014842982, - 0.018315638888734182, 0.9999000049998333, 0.0}, - {1.0, 0.5724067044708798, 0.3916251762710878, - 0.04601170568923136, 0.9999992477923555, 0.0}, - {1.0, 0.9810118431238462, 0.9343575456215499, - 0.4334701203667089, 1.0, 0.0}, - {1.0, 2.1940638138146658e-05, 1.0003291916285e-05, - 3.7801620118431334e-07, 0.0008629581310054535, - 0.0}, - {1.0, 1.0, 1.0, 1.0, 1.0, 0.49579580674813944}}; + Scalar igamma_s[][6] = { + {Scalar(0.0), nan, nan, nan, nan, nan}, + {Scalar(0.0), Scalar(0.6321205588285578), Scalar(0.7768698398515702), + Scalar(0.9816843611112658), Scalar(9.999500016666262e-05), + Scalar(1.0)}, + {Scalar(0.0), Scalar(0.4275932955291202), Scalar(0.608374823728911), + Scalar(0.9539882943107686), Scalar(7.522076445089201e-07), + Scalar(1.0)}, + {Scalar(0.0), Scalar(0.01898815687615381), + Scalar(0.06564245437845008), Scalar(0.5665298796332909), + Scalar(4.166333347221828e-18), Scalar(1.0)}, + {Scalar(0.0), Scalar(0.9999780593618628), Scalar(0.9999899967080838), + Scalar(0.9999996219837988), Scalar(0.9991370418689945), Scalar(1.0)}, + {Scalar(0.0), Scalar(0.0), Scalar(0.0), Scalar(0.0), Scalar(0.0), + Scalar(0.5042041932513908)}}; + Scalar igammac_s[][6] = { + {nan, nan, nan, nan, nan, nan}, + {Scalar(1.0), Scalar(0.36787944117144233), + Scalar(0.22313016014842982), Scalar(0.018315638888734182), + Scalar(0.9999000049998333), Scalar(0.0)}, + {Scalar(1.0), Scalar(0.5724067044708798), Scalar(0.3916251762710878), + Scalar(0.04601170568923136), Scalar(0.9999992477923555), + Scalar(0.0)}, + {Scalar(1.0), Scalar(0.9810118431238462), Scalar(0.9343575456215499), + Scalar(0.4334701203667089), Scalar(1.0), Scalar(0.0)}, + {Scalar(1.0), Scalar(2.1940638138146658e-05), + Scalar(1.0003291916285e-05), Scalar(3.7801620118431334e-07), + Scalar(0.0008629581310054535), Scalar(0.0)}, + {Scalar(1.0), Scalar(1.0), Scalar(1.0), Scalar(1.0), Scalar(1.0), + Scalar(0.49579580674813944)}}; + for (int i = 0; i < 6; ++i) { for (int j = 0; j < 6; ++j) { if ((std::isnan)(igamma_s[i][j])) { @@ -133,12 +169,32 @@ template<typename ArrayType> void array_special_functions() } #endif // EIGEN_HAS_C99_MATH + // Check the ndtri function against scipy.special.ndtri + { + ArrayType x(7), res(7), ref(7); + x << 0.5, 0.2, 0.8, 0.9, 0.1, 0.99, 0.01; + ref << 0., -0.8416212335729142, 0.8416212335729142, 1.2815515655446004, -1.2815515655446004, 2.3263478740408408, -2.3263478740408408; + CALL_SUBTEST( verify_component_wise(ref, ref); ); + CALL_SUBTEST( res = x.ndtri(); verify_component_wise(res, ref); ); + CALL_SUBTEST( res = ndtri(x); verify_component_wise(res, ref); ); + + // ndtri(normal_cdf(x)) ~= x + CALL_SUBTEST( + ArrayType m1 = ArrayType::Random(32); + using std::sqrt; + + ArrayType cdf_val = (m1 / Scalar(sqrt(2.))).erf(); + cdf_val = (cdf_val + Scalar(1)) / Scalar(2); + verify_component_wise(cdf_val.ndtri(), m1);); + + } + // Check the zeta function against scipy.special.zeta { - ArrayType x(7), q(7), res(7), ref(7); - x << 1.5, 4, 10.5, 10000.5, 3, 1, 0.9; - q << 2, 1.5, 3, 1.0001, -2.5, 1.2345, 1.2345; - ref << 1.61237534869, 0.234848505667, 1.03086757337e-5, 0.367879440865, 0.054102025820864097, plusinf, nan; + ArrayType x(10), q(10), res(10), ref(10); + x << 1.5, 4, 10.5, 10000.5, 3, 1, 0.9, 2, 3, 4; + q << 2, 1.5, 3, 1.0001, -2.5, 1.2345, 1.2345, -1, -2, -3; + ref << 1.61237534869, 0.234848505667, 1.03086757337e-5, 0.367879440865, 0.054102025820864097, plusinf, nan, plusinf, nan, plusinf; CALL_SUBTEST( verify_component_wise(ref, ref); ); CALL_SUBTEST( res = x.zeta(q); verify_component_wise(res, ref); ); CALL_SUBTEST( res = zeta(x,q); verify_component_wise(res, ref); ); @@ -146,22 +202,21 @@ template<typename ArrayType> void array_special_functions() // digamma { - ArrayType x(7), res(7), ref(7); - x << 1, 1.5, 4, -10.5, 10000.5, 0, -1; - ref << -0.5772156649015329, 0.03648997397857645, 1.2561176684318, 2.398239129535781, 9.210340372392849, plusinf, plusinf; + ArrayType x(9), res(9), ref(9); + x << 1, 1.5, 4, -10.5, 10000.5, 0, -1, -2, -3; + ref << -0.5772156649015329, 0.03648997397857645, 1.2561176684318, 2.398239129535781, 9.210340372392849, nan, nan, nan, nan; CALL_SUBTEST( verify_component_wise(ref, ref); ); CALL_SUBTEST( res = x.digamma(); verify_component_wise(res, ref); ); CALL_SUBTEST( res = digamma(x); verify_component_wise(res, ref); ); } - #if EIGEN_HAS_C99_MATH { - ArrayType n(11), x(11), res(11), ref(11); - n << 1, 1, 1, 1.5, 17, 31, 28, 8, 42, 147, 170; - x << 2, 3, 25.5, 1.5, 4.7, 11.8, 17.7, 30.2, 15.8, 54.1, 64; - ref << 0.644934066848, 0.394934066848, 0.0399946696496, nan, 293.334565435, 0.445487887616, -2.47810300902e-07, -8.29668781082e-09, -0.434562276666, 0.567742190178, -0.0108615497927; + ArrayType n(16), x(16), res(16), ref(16); + n << 1, 1, 1, 1.5, 17, 31, 28, 8, 42, 147, 170, -1, 0, 1, 2, 3; + x << 2, 3, 25.5, 1.5, 4.7, 11.8, 17.7, 30.2, 15.8, 54.1, 64, -1, -2, -3, -4, -5; + ref << 0.644934066848, 0.394934066848, 0.0399946696496, nan, 293.334565435, 0.445487887616, -2.47810300902e-07, -8.29668781082e-09, -0.434562276666, 0.567742190178, -0.0108615497927, nan, nan, plusinf, nan, plusinf; CALL_SUBTEST( verify_component_wise(ref, ref); ); if(sizeof(RealScalar)>=8) { // double @@ -288,8 +343,8 @@ template<typename ArrayType> void array_special_functions() ArrayType m3 = ArrayType::Random(32); ArrayType one = ArrayType::Constant(32, Scalar(1.0)); const Scalar eps = std::numeric_limits<Scalar>::epsilon(); - ArrayType a = (m1 * 4.0).exp(); - ArrayType b = (m2 * 4.0).exp(); + ArrayType a = (m1 * Scalar(4)).exp(); + ArrayType b = (m2 * Scalar(4)).exp(); ArrayType x = m3.abs(); // betainc(a, 1, x) == x**a @@ -335,11 +390,108 @@ template<typename ArrayType> void array_special_functions() ArrayType test = betainc(a, b + one, x) + eps; verify_component_wise(test, expected);); } -#endif +#endif // EIGEN_HAS_C99_MATH + + /* Code to generate the data for the following two test cases. + N = 5 + np.random.seed(3) + + a = np.logspace(-2, 3, 6) + a = np.ravel(np.tile(np.reshape(a, [-1, 1]), [1, N])) + x = np.random.gamma(a, 1.0) + x = np.maximum(x, np.finfo(np.float32).tiny) + + def igamma(a, x): + return mpmath.gammainc(a, 0, x, regularized=True) + + def igamma_der_a(a, x): + res = mpmath.diff(lambda a_prime: igamma(a_prime, x), a) + return np.float64(res) + + def gamma_sample_der_alpha(a, x): + igamma_x = igamma(a, x) + def igammainv_of_igamma(a_prime): + return mpmath.findroot(lambda x_prime: igamma(a_prime, x_prime) - + igamma_x, x, solver='newton') + return np.float64(mpmath.diff(igammainv_of_igamma, a)) + + v_igamma_der_a = np.vectorize(igamma_der_a)(a, x) + v_gamma_sample_der_alpha = np.vectorize(gamma_sample_der_alpha)(a, x) + */ + +#if EIGEN_HAS_C99_MATH + // Test igamma_der_a + { + ArrayType a(30); + ArrayType x(30); + ArrayType res(30); + ArrayType v(30); + + a << 0.01, 0.01, 0.01, 0.01, 0.01, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0, 1.0, 1.0, + 1.0, 1.0, 10.0, 10.0, 10.0, 10.0, 10.0, 100.0, 100.0, 100.0, 100.0, + 100.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0; + + x << 1.25668890405e-26, 1.17549435082e-38, 1.20938905072e-05, + 1.17549435082e-38, 1.17549435082e-38, 5.66572070696e-16, + 0.0132865061065, 0.0200034203853, 6.29263709118e-17, 1.37160367764e-06, + 0.333412038288, 1.18135687766, 0.580629033777, 0.170631439426, + 0.786686768458, 7.63873279537, 13.1944344379, 11.896042354, + 10.5830172417, 10.5020942233, 92.8918587747, 95.003720371, + 86.3715926467, 96.0330217672, 82.6389930677, 968.702906754, + 969.463546828, 1001.79726022, 955.047416547, 1044.27458568; + + v << -32.7256441441, -36.4394150514, -9.66467612263, -36.4394150514, + -36.4394150514, -1.0891900302, -2.66351229645, -2.48666868596, + -0.929700494428, -3.56327722764, -0.455320135314, -0.391437214323, + -0.491352055991, -0.350454834292, -0.471773162921, -0.104084440522, + -0.0723646747909, -0.0992828975532, -0.121638215446, -0.122619605294, + -0.0317670267286, -0.0359974812869, -0.0154359225363, -0.0375775365921, + -0.00794899153653, -0.00777303219211, -0.00796085782042, + -0.0125850719397, -0.00455500206958, -0.00476436993148; + + CALL_SUBTEST(res = igamma_der_a(a, x); verify_component_wise(res, v);); + } + + // Test gamma_sample_der_alpha + { + ArrayType alpha(30); + ArrayType sample(30); + ArrayType res(30); + ArrayType v(30); + + alpha << 0.01, 0.01, 0.01, 0.01, 0.01, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0, 1.0, + 1.0, 1.0, 1.0, 10.0, 10.0, 10.0, 10.0, 10.0, 100.0, 100.0, 100.0, 100.0, + 100.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0; + + sample << 1.25668890405e-26, 1.17549435082e-38, 1.20938905072e-05, + 1.17549435082e-38, 1.17549435082e-38, 5.66572070696e-16, + 0.0132865061065, 0.0200034203853, 6.29263709118e-17, 1.37160367764e-06, + 0.333412038288, 1.18135687766, 0.580629033777, 0.170631439426, + 0.786686768458, 7.63873279537, 13.1944344379, 11.896042354, + 10.5830172417, 10.5020942233, 92.8918587747, 95.003720371, + 86.3715926467, 96.0330217672, 82.6389930677, 968.702906754, + 969.463546828, 1001.79726022, 955.047416547, 1044.27458568; + + v << 7.42424742367e-23, 1.02004297287e-34, 0.0130155240738, + 1.02004297287e-34, 1.02004297287e-34, 1.96505168277e-13, 0.525575786243, + 0.713903991771, 2.32077561808e-14, 0.000179348049886, 0.635500453302, + 1.27561284917, 0.878125852156, 0.41565819538, 1.03606488534, + 0.885964824887, 1.16424049334, 1.10764479598, 1.04590810812, + 1.04193666963, 0.965193152414, 0.976217589464, 0.93008035061, + 0.98153216096, 0.909196397698, 0.98434963993, 0.984738050206, + 1.00106492525, 0.97734200649, 1.02198794179; + + CALL_SUBTEST(res = gamma_sample_der_alpha(alpha, sample); + verify_component_wise(res, v);); + } +#endif // EIGEN_HAS_C99_MATH } -void test_special_functions() +EIGEN_DECLARE_TEST(special_functions) { CALL_SUBTEST_1(array_special_functions<ArrayXf>()); CALL_SUBTEST_2(array_special_functions<ArrayXd>()); + // TODO(cantonios): half/bfloat16 don't have enough precision to reproduce results above. + // CALL_SUBTEST_3(array_special_functions<ArrayX<Eigen::half>>()); + // CALL_SUBTEST_4(array_special_functions<ArrayX<Eigen::bfloat16>>()); } |