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In addition to igamma(a, x), this code implements: * igamma_der_a(a, x) = d igamma(a, x) / da -- derivative of igamma with respect to the parameter * gamma_sample_der_alpha(alpha, sample) -- reparameterization derivative of a Gamma(alpha, 1) random variable sample with respect to the alpha parameter The derivatives are computed by forward mode differentiation of the igamma(a, x) code. Although gamma_sample_der_alpha can be implemented via igamma_der_a, a separate function is more accurate and efficient due to analytical cancellation of some terms. All three functions are implemented by a method parameterized with "mode" that always computes the derivatives, but does not return them unless required by the mode. The compiler is expected to (and, based on benchmarks, does) skip the unnecessary computations depending on the mode.
64 lines
3.0 KiB
C++
64 lines
3.0 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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// 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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#ifndef EIGEN_SPECIALFUNCTIONS_HALF_H
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#define EIGEN_SPECIALFUNCTIONS_HALF_H
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namespace Eigen {
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namespace numext {
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#if EIGEN_HAS_C99_MATH
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template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half lgamma(const Eigen::half& a) {
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return Eigen::half(Eigen::numext::lgamma(static_cast<float>(a)));
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}
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template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half digamma(const Eigen::half& a) {
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return Eigen::half(Eigen::numext::digamma(static_cast<float>(a)));
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}
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template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half zeta(const Eigen::half& x, const Eigen::half& q) {
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return Eigen::half(Eigen::numext::zeta(static_cast<float>(x), static_cast<float>(q)));
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}
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template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half polygamma(const Eigen::half& n, const Eigen::half& x) {
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return Eigen::half(Eigen::numext::polygamma(static_cast<float>(n), static_cast<float>(x)));
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}
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template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half erf(const Eigen::half& a) {
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return Eigen::half(Eigen::numext::erf(static_cast<float>(a)));
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}
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template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half erfc(const Eigen::half& a) {
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return Eigen::half(Eigen::numext::erfc(static_cast<float>(a)));
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}
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template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igamma(const Eigen::half& a, const Eigen::half& x) {
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return Eigen::half(Eigen::numext::igamma(static_cast<float>(a), static_cast<float>(x)));
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}
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template <>
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igamma_der_a(const Eigen::half& a, const Eigen::half& x) {
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return Eigen::half(Eigen::numext::igamma_der_a(static_cast<float>(a), static_cast<float>(x)));
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}
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template <>
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half gamma_sample_der_alpha(const Eigen::half& alpha, const Eigen::half& sample) {
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return Eigen::half(Eigen::numext::gamma_sample_der_alpha(static_cast<float>(alpha), static_cast<float>(sample)));
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}
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template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igammac(const Eigen::half& a, const Eigen::half& x) {
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return Eigen::half(Eigen::numext::igammac(static_cast<float>(a), static_cast<float>(x)));
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}
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template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half betainc(const Eigen::half& a, const Eigen::half& b, const Eigen::half& x) {
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return Eigen::half(Eigen::numext::betainc(static_cast<float>(a), static_cast<float>(b), static_cast<float>(x)));
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}
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template <>
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half i0e(const Eigen::half& x) {
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return Eigen::half(Eigen::numext::i0e(static_cast<float>(x)));
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}
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template <>
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half i1e(const Eigen::half& x) {
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return Eigen::half(Eigen::numext::i1e(static_cast<float>(x)));
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}
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#endif
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} // end namespace numext
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} // end namespace Eigen
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#endif // EIGEN_SPECIALFUNCTIONS_HALF_H
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