498 lines
22 KiB
C++
498 lines
22 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include <limits.h>
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#include "main.h"
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#include "../Eigen/SpecialFunctions"
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// Hack to allow "implicit" conversions from double to Scalar via comma-initialization.
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template<typename Derived>
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Eigen::CommaInitializer<Derived> operator<<(Eigen::DenseBase<Derived>& dense, double v) {
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return (dense << static_cast<typename Derived::Scalar>(v));
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}
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template<typename XprType>
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Eigen::CommaInitializer<XprType>& operator,(Eigen::CommaInitializer<XprType>& ci, double v) {
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return (ci, static_cast<typename XprType::Scalar>(v));
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}
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template<typename X, typename Y>
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void verify_component_wise(const X& x, const Y& y)
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{
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for(Index i=0; i<x.size(); ++i)
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{
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if((numext::isfinite)(y(i)))
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VERIFY_IS_APPROX( x(i), y(i) );
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else if((numext::isnan)(y(i)))
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VERIFY((numext::isnan)(x(i)));
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else
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VERIFY_IS_EQUAL( x(i), y(i) );
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}
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}
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template<typename ArrayType> void array_special_functions()
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{
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using std::abs;
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using std::sqrt;
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typedef typename ArrayType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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Scalar plusinf = std::numeric_limits<Scalar>::infinity();
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Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
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Index rows = internal::random<Index>(1,30);
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Index cols = 1;
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// API
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{
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ArrayType m1 = ArrayType::Random(rows,cols);
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#if EIGEN_HAS_C99_MATH
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VERIFY_IS_APPROX(m1.lgamma(), lgamma(m1));
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VERIFY_IS_APPROX(m1.digamma(), digamma(m1));
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VERIFY_IS_APPROX(m1.erf(), erf(m1));
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VERIFY_IS_APPROX(m1.erfc(), erfc(m1));
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#endif // EIGEN_HAS_C99_MATH
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}
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#if EIGEN_HAS_C99_MATH
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// check special functions (comparing against numpy implementation)
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if (!NumTraits<Scalar>::IsComplex)
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{
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{
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ArrayType m1 = ArrayType::Random(rows,cols);
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ArrayType m2 = ArrayType::Random(rows,cols);
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// Test various propreties of igamma & igammac. These are normalized
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// gamma integrals where
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// igammac(a, x) = Gamma(a, x) / Gamma(a)
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// igamma(a, x) = gamma(a, x) / Gamma(a)
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// where Gamma and gamma are considered the standard unnormalized
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// upper and lower incomplete gamma functions, respectively.
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ArrayType a = m1.abs() + Scalar(2);
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ArrayType x = m2.abs() + Scalar(2);
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ArrayType zero = ArrayType::Zero(rows, cols);
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ArrayType one = ArrayType::Constant(rows, cols, Scalar(1.0));
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ArrayType a_m1 = a - one;
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ArrayType Gamma_a_x = Eigen::igammac(a, x) * a.lgamma().exp();
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ArrayType Gamma_a_m1_x = Eigen::igammac(a_m1, x) * a_m1.lgamma().exp();
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ArrayType gamma_a_x = Eigen::igamma(a, x) * a.lgamma().exp();
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ArrayType gamma_a_m1_x = Eigen::igamma(a_m1, x) * a_m1.lgamma().exp();
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// Gamma(a, 0) == Gamma(a)
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VERIFY_IS_APPROX(Eigen::igammac(a, zero), one);
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// Gamma(a, x) + gamma(a, x) == Gamma(a)
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VERIFY_IS_APPROX(Gamma_a_x + gamma_a_x, a.lgamma().exp());
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// Gamma(a, x) == (a - 1) * Gamma(a-1, x) + x^(a-1) * exp(-x)
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VERIFY_IS_APPROX(Gamma_a_x, (a - Scalar(1)) * Gamma_a_m1_x + x.pow(a-Scalar(1)) * (-x).exp());
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// gamma(a, x) == (a - 1) * gamma(a-1, x) - x^(a-1) * exp(-x)
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VERIFY_IS_APPROX(gamma_a_x, (a - Scalar(1)) * gamma_a_m1_x - x.pow(a-Scalar(1)) * (-x).exp());
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}
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{
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// Verify for large a and x that values are between 0 and 1.
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ArrayType m1 = ArrayType::Random(rows,cols);
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ArrayType m2 = ArrayType::Random(rows,cols);
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int max_exponent = std::numeric_limits<Scalar>::max_exponent10;
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ArrayType a = m1.abs() * Scalar(pow(10., max_exponent - 1));
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ArrayType x = m2.abs() * Scalar(pow(10., max_exponent - 1));
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for (int i = 0; i < a.size(); ++i) {
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Scalar igam = numext::igamma(a(i), x(i));
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VERIFY(0 <= igam);
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VERIFY(igam <= 1);
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}
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}
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{
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// Check exact values of igamma and igammac against a third party calculation.
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Scalar a_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};
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Scalar x_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};
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// location i*6+j corresponds to a_s[i], x_s[j].
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Scalar igamma_s[][6] = {
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{Scalar(0.0), nan, nan, nan, nan, nan},
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{Scalar(0.0), Scalar(0.6321205588285578), Scalar(0.7768698398515702),
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Scalar(0.9816843611112658), Scalar(9.999500016666262e-05),
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Scalar(1.0)},
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{Scalar(0.0), Scalar(0.4275932955291202), Scalar(0.608374823728911),
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Scalar(0.9539882943107686), Scalar(7.522076445089201e-07),
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Scalar(1.0)},
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{Scalar(0.0), Scalar(0.01898815687615381),
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Scalar(0.06564245437845008), Scalar(0.5665298796332909),
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Scalar(4.166333347221828e-18), Scalar(1.0)},
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{Scalar(0.0), Scalar(0.9999780593618628), Scalar(0.9999899967080838),
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Scalar(0.9999996219837988), Scalar(0.9991370418689945), Scalar(1.0)},
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{Scalar(0.0), Scalar(0.0), Scalar(0.0), Scalar(0.0), Scalar(0.0),
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Scalar(0.5042041932513908)}};
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Scalar igammac_s[][6] = {
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{nan, nan, nan, nan, nan, nan},
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{Scalar(1.0), Scalar(0.36787944117144233),
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Scalar(0.22313016014842982), Scalar(0.018315638888734182),
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Scalar(0.9999000049998333), Scalar(0.0)},
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{Scalar(1.0), Scalar(0.5724067044708798), Scalar(0.3916251762710878),
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Scalar(0.04601170568923136), Scalar(0.9999992477923555),
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Scalar(0.0)},
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{Scalar(1.0), Scalar(0.9810118431238462), Scalar(0.9343575456215499),
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Scalar(0.4334701203667089), Scalar(1.0), Scalar(0.0)},
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{Scalar(1.0), Scalar(2.1940638138146658e-05),
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Scalar(1.0003291916285e-05), Scalar(3.7801620118431334e-07),
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Scalar(0.0008629581310054535), Scalar(0.0)},
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{Scalar(1.0), Scalar(1.0), Scalar(1.0), Scalar(1.0), Scalar(1.0),
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Scalar(0.49579580674813944)}};
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for (int i = 0; i < 6; ++i) {
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for (int j = 0; j < 6; ++j) {
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if ((std::isnan)(igamma_s[i][j])) {
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VERIFY((std::isnan)(numext::igamma(a_s[i], x_s[j])));
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} else {
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VERIFY_IS_APPROX(numext::igamma(a_s[i], x_s[j]), igamma_s[i][j]);
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}
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if ((std::isnan)(igammac_s[i][j])) {
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VERIFY((std::isnan)(numext::igammac(a_s[i], x_s[j])));
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} else {
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VERIFY_IS_APPROX(numext::igammac(a_s[i], x_s[j]), igammac_s[i][j]);
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}
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}
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}
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}
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}
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#endif // EIGEN_HAS_C99_MATH
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// Check the ndtri function against scipy.special.ndtri
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{
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ArrayType x(7), res(7), ref(7);
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x << 0.5, 0.2, 0.8, 0.9, 0.1, 0.99, 0.01;
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ref << 0., -0.8416212335729142, 0.8416212335729142, 1.2815515655446004, -1.2815515655446004, 2.3263478740408408, -2.3263478740408408;
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CALL_SUBTEST( verify_component_wise(ref, ref); );
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CALL_SUBTEST( res = x.ndtri(); verify_component_wise(res, ref); );
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CALL_SUBTEST( res = ndtri(x); verify_component_wise(res, ref); );
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// ndtri(normal_cdf(x)) ~= x
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CALL_SUBTEST(
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ArrayType m1 = ArrayType::Random(32);
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using std::sqrt;
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ArrayType cdf_val = (m1 / Scalar(sqrt(2.))).erf();
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cdf_val = (cdf_val + Scalar(1)) / Scalar(2);
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verify_component_wise(cdf_val.ndtri(), m1););
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}
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// Check the zeta function against scipy.special.zeta
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{
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ArrayType x(10), q(10), res(10), ref(10);
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x << 1.5, 4, 10.5, 10000.5, 3, 1, 0.9, 2, 3, 4;
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q << 2, 1.5, 3, 1.0001, -2.5, 1.2345, 1.2345, -1, -2, -3;
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ref << 1.61237534869, 0.234848505667, 1.03086757337e-5, 0.367879440865, 0.054102025820864097, plusinf, nan, plusinf, nan, plusinf;
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CALL_SUBTEST( verify_component_wise(ref, ref); );
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CALL_SUBTEST( res = x.zeta(q); verify_component_wise(res, ref); );
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CALL_SUBTEST( res = zeta(x,q); verify_component_wise(res, ref); );
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}
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// digamma
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{
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ArrayType x(9), res(9), ref(9);
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x << 1, 1.5, 4, -10.5, 10000.5, 0, -1, -2, -3;
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ref << -0.5772156649015329, 0.03648997397857645, 1.2561176684318, 2.398239129535781, 9.210340372392849, nan, nan, nan, nan;
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CALL_SUBTEST( verify_component_wise(ref, ref); );
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CALL_SUBTEST( res = x.digamma(); verify_component_wise(res, ref); );
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CALL_SUBTEST( res = digamma(x); verify_component_wise(res, ref); );
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}
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#if EIGEN_HAS_C99_MATH
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{
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ArrayType n(16), x(16), res(16), ref(16);
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n << 1, 1, 1, 1.5, 17, 31, 28, 8, 42, 147, 170, -1, 0, 1, 2, 3;
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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;
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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;
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CALL_SUBTEST( verify_component_wise(ref, ref); );
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if(sizeof(RealScalar)>=8) { // double
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// Reason for commented line: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232
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// CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res, ref); );
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CALL_SUBTEST( res = polygamma(n,x); verify_component_wise(res, ref); );
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}
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else {
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// CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res.head(8), ref.head(8)); );
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CALL_SUBTEST( res = polygamma(n,x); verify_component_wise(res.head(8), ref.head(8)); );
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}
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}
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#endif
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#if EIGEN_HAS_C99_MATH
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{
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// Inputs and ground truth generated with scipy via:
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// a = np.logspace(-3, 3, 5) - 1e-3
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// b = np.logspace(-3, 3, 5) - 1e-3
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// x = np.linspace(-0.1, 1.1, 5)
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// (full_a, full_b, full_x) = np.vectorize(lambda a, b, x: (a, b, x))(*np.ix_(a, b, x))
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// full_a = full_a.flatten().tolist() # same for full_b, full_x
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// v = scipy.special.betainc(full_a, full_b, full_x).flatten().tolist()
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//
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// Note in Eigen, we call betainc with arguments in the order (x, a, b).
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ArrayType a(125);
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ArrayType b(125);
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ArrayType x(125);
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ArrayType v(125);
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ArrayType res(125);
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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,
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0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
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0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
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0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
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0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
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0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
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0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
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0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
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0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
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0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
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0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
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0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
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0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
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31.62177660168379, 31.62177660168379, 31.62177660168379,
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31.62177660168379, 31.62177660168379, 31.62177660168379,
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31.62177660168379, 31.62177660168379, 31.62177660168379,
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31.62177660168379, 31.62177660168379, 31.62177660168379,
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31.62177660168379, 31.62177660168379, 31.62177660168379,
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31.62177660168379, 31.62177660168379, 31.62177660168379,
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31.62177660168379, 31.62177660168379, 31.62177660168379,
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31.62177660168379, 31.62177660168379, 31.62177660168379,
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31.62177660168379, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
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999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
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999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
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999.999, 999.999, 999.999;
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b << 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379,
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0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999,
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0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379,
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31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999,
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999.999, 999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0,
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0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
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0.03062277660168379, 0.03062277660168379, 0.999, 0.999, 0.999, 0.999,
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0.999, 31.62177660168379, 31.62177660168379, 31.62177660168379,
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31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
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999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
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0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
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0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,
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31.62177660168379, 31.62177660168379, 31.62177660168379,
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31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
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999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
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0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
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0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,
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31.62177660168379, 31.62177660168379, 31.62177660168379,
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31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
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999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
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0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
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0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,
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31.62177660168379, 31.62177660168379, 31.62177660168379,
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31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
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999.999, 999.999;
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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,
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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,
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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,
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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,
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-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,
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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,
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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,
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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,
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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>>());
|
|
}
|