| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. |
| // |
| // Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr> |
| // |
| // This Source Code Form is subject to the terms of the Mozilla |
| // 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) { |
| for (Index i = 0; i < x.size(); ++i) { |
| if ((numext::isfinite)(y(i))) |
| VERIFY_IS_APPROX(x(i), y(i)); |
| else if ((numext::isnan)(y(i))) |
| VERIFY((numext::isnan)(x(i))); |
| else |
| VERIFY_IS_EQUAL(x(i), y(i)); |
| } |
| } |
| |
| template <typename ArrayType> |
| void array_special_functions() { |
| using std::abs; |
| using std::sqrt; |
| typedef typename ArrayType::Scalar Scalar; |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| |
| Scalar plusinf = std::numeric_limits<Scalar>::infinity(); |
| Scalar nan = std::numeric_limits<Scalar>::quiet_NaN(); |
| |
| Index rows = internal::random<Index>(1, 30); |
| Index cols = 1; |
| |
| // API |
| { |
| ArrayType m1 = ArrayType::Random(rows, cols); |
| #if EIGEN_HAS_C99_MATH |
| VERIFY_IS_APPROX(m1.lgamma(), lgamma(m1)); |
| VERIFY_IS_APPROX(m1.digamma(), digamma(m1)); |
| VERIFY_IS_APPROX(m1.erf(), erf(m1)); |
| VERIFY_IS_APPROX(m1.erfc(), erfc(m1)); |
| #endif // EIGEN_HAS_C99_MATH |
| } |
| |
| #if EIGEN_HAS_C99_MATH |
| // check special functions (comparing against numpy implementation) |
| if (!NumTraits<Scalar>::IsComplex) { |
| { |
| ArrayType m1 = ArrayType::Random(rows, cols); |
| ArrayType m2 = ArrayType::Random(rows, cols); |
| |
| // Test various propreties of igamma & igammac. These are normalized |
| // gamma integrals where |
| // igammac(a, x) = Gamma(a, x) / Gamma(a) |
| // 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() + 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; |
| ArrayType Gamma_a_x = Eigen::igammac(a, x) * a.lgamma().exp(); |
| ArrayType Gamma_a_m1_x = Eigen::igammac(a_m1, x) * a_m1.lgamma().exp(); |
| 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); |
| |
| // Gamma(a, x) + gamma(a, x) == Gamma(a) |
| 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 - 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 - 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); |
| } |
| } |
| |
| { |
| // Check exact values of igamma and igammac against a third party calculation. |
| Scalar a_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)}; |
| 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] = { |
| {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])) { |
| VERIFY((std::isnan)(numext::igamma(a_s[i], x_s[j]))); |
| } else { |
| VERIFY_IS_APPROX(numext::igamma(a_s[i], x_s[j]), igamma_s[i][j]); |
| } |
| |
| if ((std::isnan)(igammac_s[i][j])) { |
| VERIFY((std::isnan)(numext::igammac(a_s[i], x_s[j]))); |
| } else { |
| VERIFY_IS_APPROX(numext::igammac(a_s[i], x_s[j]), igammac_s[i][j]); |
| } |
| } |
| } |
| } |
| } |
| #endif // EIGEN_HAS_C99_MATH |
| |
| // Check the ndtri function against scipy.special.ndtri |
| { |
| ArrayType x(11), res(11), ref(11); |
| x << 0.5, 0.2, 0.8, 0.9, 0.1, 0.99, 0.01, 0, 1, -0.01, 1.01; |
| ref << 0., -0.8416212335729142, 0.8416212335729142, 1.2815515655446004, -1.2815515655446004, 2.3263478740408408, |
| -2.3263478740408408, -plusinf, plusinf, nan, nan; |
| 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(11), q(11), res(11), ref(11); |
| x << 1.5, 4, 10.5, 10000.5, 3, 1, 0.9, 2, 3, 4, 2000; |
| q << 2, 1.5, 3, 1.0001, -2.5, 1.2345, 1.2345, -1, -2, -3, 2000; |
| ref << 1.61237534869, 0.234848505667, 1.03086757337e-5, 0.367879440865, 0.054102025820864097, plusinf, nan, plusinf, |
| nan, plusinf, 0; |
| 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);); |
| } |
| |
| // digamma |
| { |
| 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(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 |
| // Reason for commented line: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232 |
| // CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res, ref); ); |
| CALL_SUBTEST(res = polygamma(n, x); verify_component_wise(res, ref);); |
| } else { |
| // CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res.head(8), ref.head(8)); ); |
| CALL_SUBTEST(res = polygamma(n, x); verify_component_wise(res.head(8), ref.head(8));); |
| } |
| } |
| #endif |
| |
| #if EIGEN_HAS_C99_MATH |
| { |
| // Inputs and ground truth generated with scipy via: |
| // a = np.logspace(-3, 3, 5) - 1e-3 |
| // b = np.logspace(-3, 3, 5) - 1e-3 |
| // x = np.linspace(-0.1, 1.1, 5) |
| // (full_a, full_b, full_x) = np.vectorize(lambda a, b, x: (a, b, x))(*np.ix_(a, b, x)) |
| // full_a = full_a.flatten().tolist() # same for full_b, full_x |
| // v = scipy.special.betainc(full_a, full_b, full_x).flatten().tolist() |
| // |
| // Note in Eigen, we call betainc with arguments in the order (x, a, b). |
| ArrayType a(125); |
| ArrayType b(125); |
| ArrayType x(125); |
| ArrayType v(125); |
| ArrayType res(125); |
| |
| a << 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, |
| 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, |
| 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, |
| 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, |
| 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, |
| 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, |
| 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, |
| 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 31.62177660168379, |
| 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, |
| 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, |
| 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, |
| 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, |
| 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999, 999.999, |
| 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, |
| 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999; |
| |
| b << 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, |
| 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379, 31.62177660168379, |
| 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, |
| 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999, |
| 0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, |
| 31.62177660168379, 999.999, 999.999, 999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, |
| 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, |
| 0.999, 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999, |
| 999.999, 999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379, |
| 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, |
| 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999, 999.999, |
| 999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379, |
| 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, |
| 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999, 999.999, |
| 999.999, 999.999, 999.999; |
| |
| x << -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, |
| 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, |
| 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, |
| 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, |
| 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, |
| -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1; |
| |
| v << nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, |
| nan, nan, nan, nan, nan, nan, nan, nan, nan, 0.47972119876364683, 0.5, 0.5202788012363533, nan, nan, |
| 0.9518683957740043, 0.9789663010413743, 0.9931729188073435, nan, nan, 0.999995949033062, 0.9999999999993698, |
| 0.9999999999999999, nan, nan, 0.9999999999999999, 0.9999999999999999, 0.9999999999999999, nan, nan, nan, nan, |
| nan, nan, nan, 0.006827081192655869, 0.0210336989586256, 0.04813160422599567, nan, nan, 0.20014344256217678, |
| 0.5000000000000001, 0.7998565574378232, nan, nan, 0.9991401428435834, 0.999999999698403, 0.9999999999999999, |
| nan, nan, 0.9999999999999999, 0.9999999999999999, 0.9999999999999999, nan, nan, nan, nan, nan, nan, nan, |
| 1.0646600232370887e-25, 6.301722877826246e-13, 4.050966937974938e-06, nan, nan, 7.864342668429763e-23, |
| 3.015969667594166e-10, 0.0008598571564165444, nan, nan, 6.031987710123844e-08, 0.5000000000000007, |
| 0.9999999396801229, nan, nan, 0.9999999999999999, 0.9999999999999999, 0.9999999999999999, nan, nan, nan, nan, |
| nan, nan, nan, 0.0, 7.029920380986636e-306, 2.2450728208591345e-101, nan, nan, 0.0, 9.275871147869727e-302, |
| 1.2232913026152827e-97, nan, nan, 0.0, 3.0891393081932924e-252, 2.9303043666183996e-60, nan, nan, |
| 2.248913486879199e-196, 0.5000000000004947, 0.9999999999999999, nan; |
| |
| CALL_SUBTEST(res = betainc(a, b, x); verify_component_wise(res, v);); |
| } |
| |
| // Test various properties of betainc |
| { |
| ArrayType m1 = ArrayType::Random(32); |
| ArrayType m2 = ArrayType::Random(32); |
| ArrayType m3 = ArrayType::Random(32); |
| ArrayType one = ArrayType::Constant(32, Scalar(1.0)); |
| const Scalar eps = std::numeric_limits<Scalar>::epsilon(); |
| ArrayType a = (m1 * Scalar(4)).exp(); |
| ArrayType b = (m2 * Scalar(4)).exp(); |
| ArrayType x = m3.abs(); |
| |
| // betainc(a, 1, x) == x**a |
| CALL_SUBTEST(ArrayType test = betainc(a, one, x); ArrayType expected = x.pow(a); |
| verify_component_wise(test, expected);); |
| |
| // betainc(1, b, x) == 1 - (1 - x)**b |
| CALL_SUBTEST(ArrayType test = betainc(one, b, x); ArrayType expected = one - (one - x).pow(b); |
| verify_component_wise(test, expected);); |
| |
| // betainc(a, b, x) == 1 - betainc(b, a, 1-x) |
| CALL_SUBTEST(ArrayType test = betainc(a, b, x) + betainc(b, a, one - x); ArrayType expected = one; |
| verify_component_wise(test, expected);); |
| |
| // betainc(a+1, b, x) = betainc(a, b, x) - x**a * (1 - x)**b / (a * beta(a, b)) |
| CALL_SUBTEST( |
| ArrayType num = x.pow(a) * (one - x).pow(b); |
| ArrayType denom = a * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp(); |
| // Add eps to rhs and lhs so that component-wise test doesn't result in |
| // nans when both outputs are zeros. |
| ArrayType expected = betainc(a, b, x) - num / denom + eps; |
| ArrayType test = betainc(a + one, b, x) + eps; if (sizeof(Scalar) >= 8) { // double |
| verify_component_wise(test, expected); |
| } else { |
| // Reason for limited test: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232 |
| verify_component_wise(test.head(8), expected.head(8)); |
| }); |
| |
| // betainc(a, b+1, x) = betainc(a, b, x) + x**a * (1 - x)**b / (b * beta(a, b)) |
| CALL_SUBTEST( |
| // Add eps to rhs and lhs so that component-wise test doesn't result in |
| // nans when both outputs are zeros. |
| ArrayType num = x.pow(a) * (one - x).pow(b); |
| ArrayType denom = b * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp(); |
| ArrayType expected = betainc(a, b, x) + num / denom + eps; ArrayType test = betainc(a, b + one, x) + eps; |
| verify_component_wise(test, expected);); |
| } |
| #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 |
| } |
| |
| 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>>()); |
| } |
