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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.
86 lines
3.9 KiB
C++
86 lines
3.9 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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#ifndef EIGEN_SPECIALFUNCTIONS_PACKETMATH_H
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#define EIGEN_SPECIALFUNCTIONS_PACKETMATH_H
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namespace Eigen {
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namespace internal {
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/** \internal \returns the ln(|gamma(\a a)|) (coeff-wise) */
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template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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Packet plgamma(const Packet& a) { using numext::lgamma; return lgamma(a); }
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/** \internal \returns the derivative of lgamma, psi(\a a) (coeff-wise) */
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template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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Packet pdigamma(const Packet& a) { using numext::digamma; return digamma(a); }
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/** \internal \returns the zeta function of two arguments (coeff-wise) */
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template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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Packet pzeta(const Packet& x, const Packet& q) { using numext::zeta; return zeta(x, q); }
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/** \internal \returns the polygamma function (coeff-wise) */
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template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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Packet ppolygamma(const Packet& n, const Packet& x) { using numext::polygamma; return polygamma(n, x); }
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/** \internal \returns the erf(\a a) (coeff-wise) */
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template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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Packet perf(const Packet& a) { using numext::erf; return erf(a); }
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/** \internal \returns the erfc(\a a) (coeff-wise) */
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template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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Packet perfc(const Packet& a) { using numext::erfc; return erfc(a); }
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/** \internal \returns the incomplete gamma function igamma(\a a, \a x) */
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template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
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Packet pigamma(const Packet& a, const Packet& x) { using numext::igamma; return igamma(a, x); }
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/** \internal \returns the derivative of the incomplete gamma function
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* igamma_der_a(\a a, \a x) */
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template <typename Packet>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pigamma_der_a(const Packet& a, const Packet& x) {
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using numext::igamma_der_a; return igamma_der_a(a, x);
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}
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/** \internal \returns compute the derivative of the sample
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* of Gamma(alpha, 1) random variable with respect to the parameter a
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* gamma_sample_der_alpha(\a alpha, \a sample) */
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template <typename Packet>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pgamma_sample_der_alpha(const Packet& alpha, const Packet& sample) {
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using numext::gamma_sample_der_alpha; return gamma_sample_der_alpha(alpha, sample);
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}
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/** \internal \returns the complementary incomplete gamma function igammac(\a a, \a x) */
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template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
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Packet pigammac(const Packet& a, const Packet& x) { using numext::igammac; return igammac(a, x); }
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/** \internal \returns the complementary incomplete gamma function betainc(\a a, \a b, \a x) */
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template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
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Packet pbetainc(const Packet& a, const Packet& b,const Packet& x) { using numext::betainc; return betainc(a, b, x); }
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/** \internal \returns the exponentially scaled modified Bessel function of
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* order zero i0e(\a a) (coeff-wise) */
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template <typename Packet>
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EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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Packet pi0e(const Packet& x) { using numext::i0e; return i0e(x); }
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/** \internal \returns the exponentially scaled modified Bessel function of
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* order one i1e(\a a) (coeff-wise) */
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template <typename Packet>
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EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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Packet pi1e(const Packet& x) { using numext::i1e; return i1e(x); }
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} // end namespace internal
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} // end namespace Eigen
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#endif // EIGEN_SPECIALFUNCTIONS_PACKETMATH_H
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