mirror of
https://gitlab.com/libeigen/eigen.git
synced 2025-07-21 20:34:28 +08:00
325 lines
16 KiB
C++
325 lines
16 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
|
|
// for linear algebra.
|
|
//
|
|
// Copyright (C) 2010-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
|
|
// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
|
|
//
|
|
// 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_GLOBAL_FUNCTIONS_H
|
|
#define EIGEN_GLOBAL_FUNCTIONS_H
|
|
|
|
#ifdef EIGEN_PARSED_BY_DOXYGEN
|
|
|
|
#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \
|
|
/** \returns an expression of the coefficient-wise DOC_OP of \a x
|
|
|
|
DOC_DETAILS
|
|
|
|
\sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_##NAME">Math functions</a>, class CwiseUnaryOp
|
|
*/ \
|
|
template<typename Derived> \
|
|
inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
|
|
NAME(const Eigen::ArrayBase<Derived>& x);
|
|
|
|
#else
|
|
|
|
#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \
|
|
template<typename Derived> \
|
|
inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
|
|
(NAME)(const Eigen::ArrayBase<Derived>& x) { \
|
|
return Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived>(x.derived()); \
|
|
}
|
|
|
|
#endif // EIGEN_PARSED_BY_DOXYGEN
|
|
|
|
#define EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(NAME,FUNCTOR) \
|
|
\
|
|
template<typename Derived> \
|
|
struct NAME##_retval<ArrayBase<Derived> > \
|
|
{ \
|
|
typedef const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> type; \
|
|
}; \
|
|
template<typename Derived> \
|
|
struct NAME##_impl<ArrayBase<Derived> > \
|
|
{ \
|
|
static inline typename NAME##_retval<ArrayBase<Derived> >::type run(const Eigen::ArrayBase<Derived>& x) \
|
|
{ \
|
|
return typename NAME##_retval<ArrayBase<Derived> >::type(x.derived()); \
|
|
} \
|
|
};
|
|
|
|
namespace Eigen
|
|
{
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(real,scalar_real_op,real part,\sa ArrayBase::real)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(imag,scalar_imag_op,imaginary part,\sa ArrayBase::imag)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(conj,scalar_conjugate_op,complex conjugate,\sa ArrayBase::conjugate)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(inverse,scalar_inverse_op,inverse,\sa ArrayBase::inverse)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sin,scalar_sin_op,sine,\sa ArrayBase::sin)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cos,scalar_cos_op,cosine,\sa ArrayBase::cos)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tan,scalar_tan_op,tangent,\sa ArrayBase::tan)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(atan,scalar_atan_op,arc-tangent,\sa ArrayBase::atan)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asin,scalar_asin_op,arc-sine,\sa ArrayBase::asin)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acos,scalar_acos_op,arc-consine,\sa ArrayBase::acos)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sinh,scalar_sinh_op,hyperbolic sine,\sa ArrayBase::sinh)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cosh,scalar_cosh_op,hyperbolic cosine,\sa ArrayBase::cosh)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tanh,scalar_tanh_op,hyperbolic tangent,\sa ArrayBase::tanh)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(lgamma,scalar_lgamma_op,natural logarithm of the gamma function,\sa ArrayBase::lgamma)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(digamma,scalar_digamma_op,derivative of lgamma,\sa ArrayBase::digamma)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erf,scalar_erf_op,error function,\sa ArrayBase::erf)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erfc,scalar_erfc_op,complement error function,\sa ArrayBase::erfc)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp,scalar_exp_op,exponential,\sa ArrayBase::exp)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log,scalar_log_op,natural logarithm,\sa Eigen::log10 DOXCOMMA ArrayBase::log)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log1p,scalar_log1p_op,natural logarithm of 1 plus the value,\sa ArrayBase::log1p)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log10,scalar_log10_op,base 10 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs,scalar_abs_op,absolute value,\sa ArrayBase::abs DOXCOMMA MatrixBase::cwiseAbs)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs2,scalar_abs2_op,squared absolute value,\sa ArrayBase::abs2 DOXCOMMA MatrixBase::cwiseAbs2)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(arg,scalar_arg_op,complex argument,\sa ArrayBase::arg)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sqrt,scalar_sqrt_op,square root,\sa ArrayBase::sqrt DOXCOMMA MatrixBase::cwiseSqrt)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(square,scalar_square_op,square (power 2),\sa Eigen::abs2 DOXCOMMA Eigen::pow DOXCOMMA ArrayBase::square)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cube,scalar_cube_op,cube (power 3),\sa Eigen::pow DOXCOMMA ArrayBase::cube)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(round,scalar_round_op,nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(floor,scalar_floor_op,nearest integer not greater than the giben value,\sa Eigen::ceil DOXCOMMA ArrayBase::floor)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ceil,scalar_ceil_op,nearest integer not less than the giben value,\sa Eigen::floor DOXCOMMA ArrayBase::ceil)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isnan,scalar_isnan_op,not-a-number test,\sa Eigen::isinf DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isnan)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isinf,scalar_isinf_op,infinite value test,\sa Eigen::isnan DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isinf)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isfinite,scalar_isfinite_op,finite value test,\sa Eigen::isinf DOXCOMMA Eigen::isnan DOXCOMMA ArrayBase::isfinite)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sign,scalar_sign_op,sign (or 0),\sa ArrayBase::sign)
|
|
|
|
/** \returns an expression of the coefficient-wise power of \a x to the given constant \a exponent.
|
|
*
|
|
* \tparam ScalarExponent is the scalar type of \a exponent. It must be compatible with the scalar type of the given expression (\c Derived::Scalar).
|
|
*
|
|
* \sa ArrayBase::pow()
|
|
*
|
|
* \relates ArrayBase
|
|
*/
|
|
#ifdef EIGEN_PARSED_BY_DOXYGEN
|
|
template<typename Derived,typename ScalarExponent>
|
|
inline const CwiseBinaryOp<internal::scalar_pow_op<Derived::Scalar,ScalarExponent>,Derived,Constant<ScalarExponent> >
|
|
pow(const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent);
|
|
#else
|
|
template<typename Derived,typename ScalarExponent>
|
|
inline typename internal::enable_if< !(internal::is_same<typename Derived::Scalar,ScalarExponent>::value)
|
|
&& ScalarBinaryOpTraits<typename Derived::Scalar,ScalarExponent>::Defined,
|
|
const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,ScalarExponent,pow) >::type
|
|
pow(const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent) {
|
|
return x.derived().pow(exponent);
|
|
}
|
|
|
|
template<typename Derived>
|
|
inline const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,typename Derived::Scalar,pow)
|
|
pow(const Eigen::ArrayBase<Derived>& x, const typename Derived::Scalar& exponent) {
|
|
return x.derived().pow(exponent);
|
|
}
|
|
#endif
|
|
|
|
/** \returns an expression of the coefficient-wise power of \a x to the given array of \a exponents.
|
|
*
|
|
* This function computes the coefficient-wise power.
|
|
*
|
|
* Example: \include Cwise_array_power_array.cpp
|
|
* Output: \verbinclude Cwise_array_power_array.out
|
|
*
|
|
* \sa ArrayBase::pow()
|
|
*
|
|
* \relates ArrayBase
|
|
*/
|
|
template<typename Derived,typename ExponentDerived>
|
|
inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>
|
|
pow(const Eigen::ArrayBase<Derived>& x, const Eigen::ArrayBase<ExponentDerived>& exponents)
|
|
{
|
|
return Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>(
|
|
x.derived(),
|
|
exponents.derived()
|
|
);
|
|
}
|
|
|
|
/** \returns an expression of the coefficient-wise power of the scalar \a x to the given array of \a exponents.
|
|
*
|
|
* This function computes the coefficient-wise power between a scalar and an array of exponents.
|
|
*
|
|
* \tparam Scalar is the scalar type of \a x. It must be compatible with the scalar type of the given array expression (\c Derived::Scalar).
|
|
*
|
|
* Example: \include Cwise_scalar_power_array.cpp
|
|
* Output: \verbinclude Cwise_scalar_power_array.out
|
|
*
|
|
* \sa ArrayBase::pow()
|
|
*
|
|
* \relates ArrayBase
|
|
*/
|
|
#ifdef EIGEN_PARSED_BY_DOXYGEN
|
|
template<typename Scalar,typename Derived>
|
|
inline const CwiseBinaryOp<internal::scalar_pow_op<Scalar,Derived::Scalar>,Constant<Scalar>,Derived>
|
|
pow(const Scalar& x,const Eigen::ArrayBase<Derived>& x);
|
|
#else
|
|
template<typename Scalar, typename Derived>
|
|
inline typename internal::enable_if< !(internal::is_same<typename Derived::Scalar,Scalar>::value)
|
|
&& ScalarBinaryOpTraits<Scalar,typename Derived::Scalar>::Defined,
|
|
const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,pow) >::type
|
|
pow(const Scalar& x, const Eigen::ArrayBase<Derived>& exponents)
|
|
{
|
|
return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,pow)(
|
|
typename internal::plain_constant_type<Derived,Scalar>::type(exponents.rows(), exponents.cols(), x), exponents.derived() );
|
|
}
|
|
|
|
template<typename Derived>
|
|
inline const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename Derived::Scalar,Derived,pow)
|
|
pow(const typename Derived::Scalar& x, const Eigen::ArrayBase<Derived>& exponents)
|
|
{
|
|
return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename Derived::Scalar,Derived,pow)(
|
|
typename internal::plain_constant_type<Derived,typename Derived::Scalar>::type(exponents.rows(), exponents.cols(), x), exponents.derived() );
|
|
}
|
|
#endif
|
|
|
|
/**
|
|
* \brief Component-wise division of the scalar \a s by array elements of \a a.
|
|
*
|
|
* \tparam Scalar is the scalar type of \a x. It must be compatible with the scalar type of the given array expression (\c Derived::Scalar).
|
|
*
|
|
* \relates ArrayBase
|
|
**/
|
|
#ifdef EIGEN_PARSED_BY_DOXYGEN
|
|
template<typename Scalar,typename Derived>
|
|
inline const CwiseBinaryOp<internal::scalar_quotient_op<Scalar,Derived::Scalar>,Constant<Scalar>,Derived>
|
|
operator/(const Scalar& s,const Eigen::ArrayBase<Derived>& a);
|
|
#else
|
|
template<typename Scalar, typename Derived>
|
|
inline typename internal::enable_if< !(internal::is_same<typename Derived::Scalar,Scalar>::value)
|
|
&& ScalarBinaryOpTraits<Scalar,typename Derived::Scalar>::Defined,
|
|
const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,quotient) >::type
|
|
operator/(const Scalar& s, const Eigen::ArrayBase<Derived>& a)
|
|
{
|
|
return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,quotient)(
|
|
typename internal::plain_constant_type<Derived,Scalar>::type(a.rows(), a.cols(), s), a.derived() );
|
|
}
|
|
|
|
template<typename Derived>
|
|
inline const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename Derived::Scalar,Derived,quotient)
|
|
operator/(const typename Derived::Scalar& s, const Eigen::ArrayBase<Derived>& a)
|
|
{
|
|
return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename Derived::Scalar,Derived,quotient)(
|
|
typename internal::plain_constant_type<Derived,typename Derived::Scalar>::type(a.rows(), a.cols(), s), a.derived() );
|
|
}
|
|
#endif
|
|
|
|
/** \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>
|
|
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 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>
|
|
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>
|
|
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>
|
|
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 exposent, 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>
|
|
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()
|
|
);
|
|
}
|
|
|
|
namespace internal
|
|
{
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(real,scalar_real_op)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(imag,scalar_imag_op)
|
|
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(abs2,scalar_abs2_op)
|
|
}
|
|
}
|
|
|
|
// TODO: cleanly disable those functions that are not supported on Array (numext::real_ref, internal::random, internal::isApprox...)
|
|
|
|
#endif // EIGEN_GLOBAL_FUNCTIONS_H
|