unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsArrayAPI.h

// 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/.

#ifndef EIGEN_SPECIALFUNCTIONS_ARRAYAPI_H
#define EIGEN_SPECIALFUNCTIONS_ARRAYAPI_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

/** \cpp11 \returns an expression of the coefficient-wise igamma(\a a, \a x) to the given arrays.
 *
 * This function computes the coefficient-wise incomplete gamma function.
 *
 * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
 * or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar
 * type T to be supported.
 *
 * \sa Eigen::igammac(), Eigen::lgamma()
 */
template <typename Derived, typename ExponentDerived>
EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>,
                                               const Derived, const ExponentDerived>
igamma(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x) {
  return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived,
                              const ExponentDerived>(a.derived(), x.derived());
}

/** \cpp11 \returns an expression of the coefficient-wise igamma_der_a(\a a, \a x) to the given arrays.
 *
 * This function computes the coefficient-wise derivative of the incomplete
 * gamma function with respect to the parameter a.
 *
 * \note This function supports only float and double scalar types in c++11
 * mode. To support other scalar types,
 * or float/double in non c++11 mode, the user has to provide implementations
 * of igamma_der_a(T,T) for any scalar
 * type T to be supported.
 *
 * \sa Eigen::igamma(), Eigen::lgamma()
 */
template <typename Derived, typename ExponentDerived>
EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_der_a_op<typename Derived::Scalar>,
                                               const Derived, const ExponentDerived>
igamma_der_a(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x) {
  return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_der_a_op<typename Derived::Scalar>, const Derived,
                              const ExponentDerived>(a.derived(), x.derived());
}

/** \cpp11 \returns an expression of the coefficient-wise gamma_sample_der_alpha(\a alpha, \a sample) to the given
 * arrays.
 *
 * This function computes the coefficient-wise derivative of the sample
 * of a Gamma(alpha, 1) random variable with respect to the parameter alpha.
 *
 * \note This function supports only float and double scalar types in c++11
 * mode. To support other scalar types,
 * or float/double in non c++11 mode, the user has to provide implementations
 * of gamma_sample_der_alpha(T,T) for any scalar
 * type T to be supported.
 *
 * \sa Eigen::igamma(), Eigen::lgamma()
 */
template <typename AlphaDerived, typename SampleDerived>
EIGEN_STRONG_INLINE const
    Eigen::CwiseBinaryOp<Eigen::internal::scalar_gamma_sample_der_alpha_op<typename AlphaDerived::Scalar>,
                         const AlphaDerived, const SampleDerived>
    gamma_sample_der_alpha(const Eigen::ArrayBase<AlphaDerived>& alpha, const Eigen::ArrayBase<SampleDerived>& sample) {
  return Eigen::CwiseBinaryOp<Eigen::internal::scalar_gamma_sample_der_alpha_op<typename AlphaDerived::Scalar>,
                              const AlphaDerived, const SampleDerived>(alpha.derived(), sample.derived());
}

/** \cpp11 \returns an expression of the coefficient-wise igammac(\a a, \a x) to the given arrays.
 *
 * This function computes the coefficient-wise complementary incomplete gamma function.
 *
 * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
 * or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar
 * type T to be supported.
 *
 * \sa Eigen::igamma(), Eigen::lgamma()
 */
template <typename Derived, typename ExponentDerived>
EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>,
                                               const Derived, const ExponentDerived>
igammac(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x) {
  return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived,
                              const ExponentDerived>(a.derived(), x.derived());
}

/** \cpp11 \returns an expression of the coefficient-wise polygamma(\a n, \a x) to the given arrays.
 *
 * It returns the \a n -th derivative of the digamma(psi) evaluated at \c x.
 *
 * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
 * or float/double in non c++11 mode, the user has to provide implementations of polygamma(T,T) for any scalar
 * type T to be supported.
 *
 * \sa Eigen::digamma()
 */
// * \warning Be careful with the order of the parameters: x.polygamma(n) is equivalent to polygamma(n,x)
// * \sa ArrayBase::polygamma()
template <typename DerivedN, typename DerivedX>
EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>,
                                               const DerivedN, const DerivedX>
polygamma(const Eigen::ArrayBase<DerivedN>& n, const Eigen::ArrayBase<DerivedX>& x) {
  return Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>, const DerivedN,
                              const DerivedX>(n.derived(), x.derived());
}

/** \cpp11 \returns an expression of the coefficient-wise betainc(\a x, \a a, \a b) to the given arrays.
 *
 * This function computes the regularized incomplete beta function (integral).
 *
 * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
 * or float/double in non c++11 mode, the user has to provide implementations of betainc(T,T,T) for any scalar
 * type T to be supported.
 *
 * \sa Eigen::betainc(), Eigen::lgamma()
 */
template <typename ArgADerived, typename ArgBDerived, typename ArgXDerived>
EIGEN_STRONG_INLINE const Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>,
                                                const ArgADerived, const ArgBDerived, const ArgXDerived>
betainc(const Eigen::ArrayBase<ArgADerived>& a, const Eigen::ArrayBase<ArgBDerived>& b,
        const Eigen::ArrayBase<ArgXDerived>& x) {
  return Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>, const ArgADerived,
                               const ArgBDerived, const ArgXDerived>(a.derived(), b.derived(), x.derived());
}

/** \returns an expression of the coefficient-wise zeta(\a x, \a q) to the given arrays.
 *
 * It returns the Riemann zeta function of two arguments \a x and \a q:
 *
 * \param x is the exponent, it must be > 1
 * \param q is the shift, it must be > 0
 *
 * \note This function supports only float and double scalar types. To support other scalar types, the user has
 * to provide implementations of zeta(T,T) for any scalar type T to be supported.
 *
 * \sa ArrayBase::zeta()
 */
template <typename DerivedX, typename DerivedQ>
EIGEN_STRONG_INLINE const
    Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX, const DerivedQ>
    zeta(const Eigen::ArrayBase<DerivedX>& x, const Eigen::ArrayBase<DerivedQ>& q) {
  return Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX,
                              const DerivedQ>(x.derived(), q.derived());
}

}  // end namespace Eigen

#endif  // EIGEN_SPECIALFUNCTIONS_ARRAYAPI_H