/usr/include/xtensor/xmath.hpp is in xtensor-dev 0.10.11-1.
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1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 | /***************************************************************************
* Copyright (c) 2016, Johan Mabille, Sylvain Corlay and Wolf Vollprecht *
* *
* Distributed under the terms of the BSD 3-Clause License. *
* *
* The full license is in the file LICENSE, distributed with this software. *
****************************************************************************/
/**
* @brief standard mathematical functions for xexpressions
*/
#ifndef XMATH_HPP
#define XMATH_HPP
#include <cmath>
#include <complex>
#include <type_traits>
#include "xoperation.hpp"
#include "xreducer.hpp"
namespace xt
{
template <class T>
struct numeric_constants
{
static constexpr T PI = 3.141592653589793238463;
static constexpr T PI_2 = 1.57079632679489661923;
static constexpr T PI_4 = 0.785398163397448309616;
static constexpr T D_1_PI = 0.318309886183790671538;
static constexpr T D_2_PI = 0.636619772367581343076;
static constexpr T D_2_SQRTPI = 1.12837916709551257390;
static constexpr T SQRT2 = 1.41421356237309504880;
static constexpr T SQRT1_2 = 0.707106781186547524401;
static constexpr T E = 2.71828182845904523536;
static constexpr T LOG2E = 1.44269504088896340736;
static constexpr T LOG10E = 0.434294481903251827651;
static constexpr T LN2 = 0.693147180559945309417;
};
/***********
* Helpers *
***********/
namespace detail
{
template <class T>
struct bool_functor_return_type
{
using type = bool;
};
}
#define UNARY_MATH_FUNCTOR(NAME) \
template <class T> \
struct NAME##_fun \
{ \
using argument_type = T; \
using result_type = T; \
constexpr T operator()(const T& arg) const \
{ \
using std::NAME; \
return NAME(arg); \
} \
}
#define UNARY_MATH_FUNCTOR_COMPLEX_REDUCING(NAME) \
template <class T> \
struct NAME##_fun \
{ \
using argument_type = T; \
using result_type = complex_value_type_t<T>; \
constexpr result_type operator()(const T& arg) const \
{ \
using std::NAME; \
return NAME(arg); \
} \
}
#define BINARY_MATH_FUNCTOR(NAME) \
template <class T> \
struct NAME##_fun \
{ \
using first_argument_type = T; \
using second_argument_type = T; \
using result_type = T; \
constexpr T operator()(const T& arg1, const T& arg2) const \
{ \
using std::NAME; \
return NAME(arg1, arg2); \
} \
}
#define TERNARY_MATH_FUNCTOR(NAME) \
template <class T> \
struct NAME##_fun \
{ \
using first_argument_type = T; \
using second_argument_type = T; \
using third_argument_type = T; \
using result_type = T; \
constexpr T operator()(const T& arg1, const T& arg2, const T& arg3) const \
{ \
using std::NAME; \
return NAME(arg1, arg2, arg3); \
} \
}
#define UNARY_BOOL_FUNCTOR(NAME) \
template <class T> \
struct NAME##_fun \
{ \
using argument_type = T; \
using result_type = typename xt::detail::bool_functor_return_type<T>::type; \
constexpr result_type operator()(const T& arg) const \
{ \
using std::NAME; \
return NAME(arg); \
} \
}
namespace math
{
UNARY_MATH_FUNCTOR_COMPLEX_REDUCING(abs);
UNARY_MATH_FUNCTOR(fabs);
BINARY_MATH_FUNCTOR(fmod);
BINARY_MATH_FUNCTOR(remainder);
TERNARY_MATH_FUNCTOR(fma);
BINARY_MATH_FUNCTOR(fmax);
BINARY_MATH_FUNCTOR(fmin);
BINARY_MATH_FUNCTOR(fdim);
UNARY_MATH_FUNCTOR(exp);
UNARY_MATH_FUNCTOR(exp2);
UNARY_MATH_FUNCTOR(expm1);
UNARY_MATH_FUNCTOR(log);
UNARY_MATH_FUNCTOR(log10);
UNARY_MATH_FUNCTOR(log2);
UNARY_MATH_FUNCTOR(log1p);
BINARY_MATH_FUNCTOR(pow);
UNARY_MATH_FUNCTOR(sqrt);
UNARY_MATH_FUNCTOR(cbrt);
BINARY_MATH_FUNCTOR(hypot);
UNARY_MATH_FUNCTOR(sin);
UNARY_MATH_FUNCTOR(cos);
UNARY_MATH_FUNCTOR(tan);
UNARY_MATH_FUNCTOR(asin);
UNARY_MATH_FUNCTOR(acos);
UNARY_MATH_FUNCTOR(atan);
BINARY_MATH_FUNCTOR(atan2);
UNARY_MATH_FUNCTOR(sinh);
UNARY_MATH_FUNCTOR(cosh);
UNARY_MATH_FUNCTOR(tanh);
UNARY_MATH_FUNCTOR(asinh);
UNARY_MATH_FUNCTOR(acosh);
UNARY_MATH_FUNCTOR(atanh);
UNARY_MATH_FUNCTOR(erf);
UNARY_MATH_FUNCTOR(erfc);
UNARY_MATH_FUNCTOR(tgamma);
UNARY_MATH_FUNCTOR(lgamma);
UNARY_MATH_FUNCTOR(ceil);
UNARY_MATH_FUNCTOR(floor);
UNARY_MATH_FUNCTOR(trunc);
UNARY_MATH_FUNCTOR(round);
UNARY_MATH_FUNCTOR(nearbyint);
UNARY_MATH_FUNCTOR(rint);
UNARY_BOOL_FUNCTOR(isfinite);
UNARY_BOOL_FUNCTOR(isinf);
UNARY_BOOL_FUNCTOR(isnan);
}
#undef UNARY_BOOL_FUNCTOR
#undef TERNARY_MATH_FUNCTOR
#undef BINARY_MATH_FUNCTOR
#undef UNARY_MATH_FUNCTOR
#undef UNARY_MATH_FUNCTOR_COMPLEX_REDUCING
/*******************
* basic functions *
*******************/
/**
* @defgroup basic_functions Basic functions
*/
/**
* @ingroup basic_functions
* @brief Absolute value function.
*
* Returns an \ref xfunction for the element-wise absolute value
* of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto abs(E&& e) noexcept
-> detail::xfunction_type_t<math::abs_fun, E>
{
return detail::make_xfunction<math::abs_fun>(std::forward<E>(e));
}
/**
* @ingroup basic_functions
* @brief Absolute value function.
*
* Returns an \ref xfunction for the element-wise absolute value
* of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto fabs(E&& e) noexcept
-> detail::xfunction_type_t<math::fabs_fun, E>
{
return detail::make_xfunction<math::fabs_fun>(std::forward<E>(e));
}
/**
* @ingroup basic_functions
* @brief Remainder of the floating point division operation.
*
* Returns an \ref xfunction for the element-wise remainder of
* the floating point division operation <em>e1 / e2</em>.
* @param e1 an \ref xexpression or a scalar
* @param e2 an \ref xexpression or a scalar
* @return an \ref xfunction
* @note e1 and e2 can't be both scalars.
*/
template <class E1, class E2>
inline auto fmod(E1&& e1, E2&& e2) noexcept
-> detail::xfunction_type_t<math::fmod_fun, E1, E2>
{
return detail::make_xfunction<math::fmod_fun>(std::forward<E1>(e1), std::forward<E2>(e2));
}
/**
* @ingroup basic_functions
* @brief Signed remainder of the division operation.
*
* Returns an \ref xfunction for the element-wise signed remainder
* of the floating point division operation <em>e1 / e2</em>.
* @param e1 an \ref xexpression or a scalar
* @param e2 an \ref xexpression or a scalar
* @return an \ref xfunction
* @note e1 and e2 can't be both scalars.
*/
template <class E1, class E2>
inline auto remainder(E1&& e1, E2&& e2) noexcept
-> detail::xfunction_type_t<math::remainder_fun, E1, E2>
{
return detail::make_xfunction<math::remainder_fun>(std::forward<E1>(e1), std::forward<E2>(e2));
}
/**
* @ingroup basic_functions
* @brief Fused multiply-add operation.
*
* Returns an \ref xfunction for <em>e1 * e2 + e3</em> as if
* to infinite precision and rounded only once to fit the result type.
* @param e1 an \ref xfunction or a scalar
* @param e2 an \ref xfunction or a scalar
* @param e3 an \ref xfunction or a scalar
* @return an \ref xfunction
* @note e1, e2 and e3 can't be scalars every three.
*/
template <class E1, class E2, class E3>
inline auto fma(E1&& e1, E2&& e2, E3&& e3) noexcept
-> detail::xfunction_type_t<math::fma_fun, E1, E2, E3>
{
return detail::make_xfunction<math::fma_fun>(std::forward<E1>(e1), std::forward<E2>(e2), std::forward<E3>(e3));
}
/**
* @ingroup basic_functions
* @brief Maximum function.
*
* Returns an \ref xfunction for the element-wise maximum
* of \a e1 and \a e2.
* @param e1 an \ref xexpression or a scalar
* @param e2 an \ref xexpression or a scalar
* @return an \ref xfunction
* @note e1 and e2 can't be both scalars.
*/
template <class E1, class E2>
inline auto fmax(E1&& e1, E2&& e2) noexcept
-> detail::xfunction_type_t<math::fmax_fun, E1, E2>
{
return detail::make_xfunction<math::fmax_fun>(std::forward<E1>(e1), std::forward<E2>(e2));
}
/**
* @ingroup basic_functions
* @brief Minimum function.
*
* Returns an \ref xfunction for the element-wise minimum
* of \a e1 and \a e2.
* @param e1 an \ref xexpression or a scalar
* @param e2 an \ref xexpression or a scalar
* @return an \ref xfunction
* @note e1 and e2 can't be both scalars.
*/
template <class E1, class E2>
inline auto fmin(E1&& e1, E2&& e2) noexcept
-> detail::xfunction_type_t<math::fmin_fun, E1, E2>
{
return detail::make_xfunction<math::fmin_fun>(std::forward<E1>(e1), std::forward<E2>(e2));
}
/**
* @ingroup basic_functions
* @brief Positive difference function.
*
* Returns an \ref xfunction for the element-wise positive
* difference of \a e1 and \a e2.
* @param e1 an \ref xexpression or a scalar
* @param e2 an \ref xexpression or a scalar
* @return an \ref xfunction
* @note e1 and e2 can't be both scalars.
*/
template <class E1, class E2>
inline auto fdim(E1&& e1, E2&& e2) noexcept
-> detail::xfunction_type_t<math::fdim_fun, E1, E2>
{
return detail::make_xfunction<math::fdim_fun>(std::forward<E1>(e1), std::forward<E2>(e2));
}
namespace math
{
template <class T>
struct minimum
{
using result_type = T;
constexpr result_type operator()(const T& t1, const T& t2) const noexcept
{
return (t1 < t2) ? t1 : t2;
}
};
template <class T>
struct maximum
{
using result_type = T;
constexpr result_type operator()(const T& t1, const T& t2) const noexcept
{
return (t1 > t2) ? t1 : t2;
}
};
template <class T>
struct clamp_fun
{
using first_argument_type = T;
using second_argument_type = T;
using third_argument_type = T;
using result_type = T;
constexpr T operator()(const T& v, const T& lo, const T& hi) const
{
return v < lo ? lo : hi < v ? hi : v;
}
};
}
/**
* @ingroup basic_functions
* @brief Elementwise maximum
*
* Returns an \ref xfunction for the element-wise
* maximum between e1 and e2.
* @param e1 an \ref xexpression
* @param e2 an \ref xexpression
* @return an \ref xfunction
*/
template <class E1, class E2>
inline auto maximum(E1&& e1, E2&& e2) noexcept
-> detail::xfunction_type_t<math::maximum, E1, E2>
{
return detail::make_xfunction<math::maximum>(std::forward<E1>(e1), std::forward<E2>(e2));
}
/**
* @ingroup basic_functions
* @brief Elementwise minimum
*
* Returns an \ref xfunction for the element-wise
* minimum between e1 and e2.
* @param e1 an \ref xexpression
* @param e2 an \ref xexpression
* @return an \ref xfunction
*/
template <class E1, class E2>
inline auto minimum(E1&& e1, E2&& e2) noexcept
-> detail::xfunction_type_t<math::minimum, E1, E2>
{
return detail::make_xfunction<math::minimum>(std::forward<E1>(e1), std::forward<E2>(e2));
}
/**
* @ingroup basic_functions
* @brief Maximum element along given axis.
*
* Returns an \ref xreducer for the maximum of elements over given
* \em axes.
* @param e an \ref xexpression
* @param axes the axes along which the maximum is found (optional)
* @return an \ref xreducer
*/
template <class E, class X>
inline auto amax(E&& e, X&& axes) noexcept
{
using functor_type = math::maximum<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e), std::forward<X>(axes));
}
template <class E>
inline auto amax(E&& e) noexcept
{
using functor_type = math::maximum<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e));
}
#ifdef X_OLD_CLANG
template <class E, class I>
inline auto amax(E&& e, std::initializer_list<I> axes) noexcept
{
using functor_type = math::maximum<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e), axes);
}
#else
template <class E, class I, std::size_t N>
inline auto amax(E&& e, const I(&axes)[N]) noexcept
{
using functor_type = math::maximum<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e), axes);
}
#endif
/**
* @ingroup basic_functions
* @brief Minimum element along given axis.
*
* Returns an \ref xreducer for the minimum of elements over given
* \em axes.
* @param e an \ref xexpression
* @param axes the axes along which the minimum is found (optional)
* @return an \ref xreducer
*/
template <class E, class X>
inline auto amin(E&& e, X&& axes) noexcept
{
using functor_type = math::minimum<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e), std::forward<X>(axes));
}
template <class E>
inline auto amin(E&& e) noexcept
{
using functor_type = math::minimum<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e));
}
#ifdef X_OLD_CLANG
template <class E, class I>
inline auto amin(E&& e, std::initializer_list<I> axes) noexcept
{
using functor_type = math::minimum<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e), axes);
}
#else
template <class E, class I, std::size_t N>
inline auto amin(E&& e, const I(&axes)[N]) noexcept
{
using functor_type = math::minimum<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e), axes);
}
#endif
/**
* @ingroup basic_functions
* @brief Clip values between hi and lo
*
* Returns an \ref xfunction for the element-wise clipped
* values between lo and hi
* @param e1 an \ref xexpression or a scalar
* @param lo a scalar
* @param hi a scalar
*
* @return a \ref xfunction
*/
template <class E1, class E2, class E3>
inline auto clip(E1&& e1, E2&& lo, E3&& hi) noexcept
-> detail::xfunction_type_t<math::clamp_fun, E1, E2, E3>
{
return detail::make_xfunction<math::clamp_fun>(std::forward<E1>(e1), std::forward<E2>(lo), std::forward<E3>(hi));
}
namespace math
{
namespace detail
{
template <typename T>
constexpr std::enable_if_t<std::is_signed<T>::value, T>
sign_impl(T x)
{
return std::isnan(x) ? std::numeric_limits<T>::quiet_NaN() : x == 0 ? (T)copysign(T(0), x) : (T)copysign(T(1), x);
}
template <typename T>
inline std::enable_if_t<xt::detail::is_complex<T>::value, T>
sign_impl(T x)
{
typename T::value_type e = x.real() ? x.real() : x.imag();
return T(sign_impl(e), 0);
}
template <typename T>
constexpr std::enable_if_t<std::is_unsigned<T>::value, T>
sign_impl(T x)
{
return T(x > T(0));
}
}
template <class T>
struct sign_fun
{
using argument_type = T;
using result_type = T;
constexpr T operator()(const T& x) const
{
return detail::sign_impl(x);
}
};
}
/**
* @ingroup basic_functions
* @brief Returns an element-wise indication of the sign of a number
*
* If the number is positive, returns +1. If negative, -1. If the number
* is zero, returns 0.
*
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto sign(E&& e) noexcept
-> detail::xfunction_type_t<math::sign_fun, E>
{
return detail::make_xfunction<math::sign_fun>(std::forward<E>(e));
}
/*************************
* exponential functions *
*************************/
/**
* @defgroup exp_functions Exponential functions
*/
/**
* @ingroup exp_functions
* @brief Natural exponential function.
*
* Returns an \ref xfunction for the element-wise natural
* exponential of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto exp(E&& e) noexcept
-> detail::xfunction_type_t<math::exp_fun, E>
{
return detail::make_xfunction<math::exp_fun>(std::forward<E>(e));
}
/**
* @ingroup exp_functions
* @brief Base 2 exponential function.
*
* Returns an \ref xfunction for the element-wise base 2
* exponential of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto exp2(E&& e) noexcept
-> detail::xfunction_type_t<math::exp2_fun, E>
{
return detail::make_xfunction<math::exp2_fun>(std::forward<E>(e));
}
/**
* @ingroup exp_functions
* @brief Natural exponential minus one function.
*
* Returns an \ref xfunction for the element-wise natural
* exponential of \em e, minus 1.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto expm1(E&& e) noexcept
-> detail::xfunction_type_t<math::expm1_fun, E>
{
return detail::make_xfunction<math::expm1_fun>(std::forward<E>(e));
}
/**
* @ingroup exp_functions
* @brief Natural logarithm function.
*
* Returns an \ref xfunction for the element-wise natural
* logarithm of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto log(E&& e) noexcept
-> detail::xfunction_type_t<math::log_fun, E>
{
return detail::make_xfunction<math::log_fun>(std::forward<E>(e));
}
/**
* @ingroup exp_functions
* @brief Base 10 logarithm function.
*
* Returns an \ref xfunction for the element-wise base 10
* logarithm of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto log10(E&& e) noexcept
-> detail::xfunction_type_t<math::log10_fun, E>
{
return detail::make_xfunction<math::log10_fun>(std::forward<E>(e));
}
/**
* @ingroup exp_functions
* @brief Base 2 logarithm function.
*
* Returns an \ref xfunction for the element-wise base 2
* logarithm of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto log2(E&& e) noexcept
-> detail::xfunction_type_t<math::log2_fun, E>
{
return detail::make_xfunction<math::log2_fun>(std::forward<E>(e));
}
/**
* @ingroup exp_functions
* @brief Natural logarithm of one plus function.
*
* Returns an \ref xfunction for the element-wise natural
* logarithm of \em e, plus 1.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto log1p(E&& e) noexcept
-> detail::xfunction_type_t<math::log1p_fun, E>
{
return detail::make_xfunction<math::log1p_fun>(std::forward<E>(e));
}
/*******************
* power functions *
*******************/
/**
* @defgroup pow_functions Power functions
*/
/**
* @ingroup pow_functions
* @brief Power function.
*
* Returns an \ref xfunction for the element-wise value of
* of \em e1 raised to the power \em e2.
* @param e1 an \ref xexpression or a scalar
* @param e2 an \ref xexpression or a scalar
* @return an \ref xfunction
* @note e1 and e2 can't be both scalars.
*/
template <class E1, class E2>
inline auto pow(E1&& e1, E2&& e2) noexcept
-> detail::xfunction_type_t<math::pow_fun, E1, E2>
{
return detail::make_xfunction<math::pow_fun>(std::forward<E1>(e1), std::forward<E2>(e2));
}
/**
* @ingroup pow_functions
* @brief Square root function.
*
* Returns an \ref xfunction for the element-wise square
* root of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto sqrt(E&& e) noexcept
-> detail::xfunction_type_t<math::sqrt_fun, E>
{
return detail::make_xfunction<math::sqrt_fun>(std::forward<E>(e));
}
/**
* @ingroup pow_functions
* @brief Cubic root function.
*
* Returns an \ref xfunction for the element-wise cubic
* root of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto cbrt(E&& e) noexcept
-> detail::xfunction_type_t<math::cbrt_fun, E>
{
return detail::make_xfunction<math::cbrt_fun>(std::forward<E>(e));
}
/**
* @ingroup pow_functions
* @brief Hypotenuse function.
*
* Returns an \ref xfunction for the element-wise square
* root of the sum of the square of \em e1 and \em e2, avoiding
* overflow and underflow at intermediate stages of computation.
* @param e1 an \ref xexpression or a scalar
* @param e2 an \ref xexpression or a scalar
* @return an \ref xfunction
* @note e1 and e2 can't be both scalars.
*/
template <class E1, class E2>
inline auto hypot(E1&& e1, E2&& e2) noexcept
-> detail::xfunction_type_t<math::hypot_fun, E1, E2>
{
return detail::make_xfunction<math::hypot_fun>(std::forward<E1>(e1), std::forward<E2>(e2));
}
/***************************
* trigonometric functions *
***************************/
/**
* @defgroup trigo_functions Trigonometric function
*/
/**
* @ingroup trigo_functions
* @brief Sine function.
*
* Returns an \ref xfunction for the element-wise sine
* of \em e (measured in radians).
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto sin(E&& e) noexcept
-> detail::xfunction_type_t<math::sin_fun, E>
{
return detail::make_xfunction<math::sin_fun>(std::forward<E>(e));
}
/**
* @ingroup trigo_functions
* @brief Cosine function.
*
* Returns an \ref xfunction for the element-wise cosine
* of \em e (measured in radians).
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto cos(E&& e) noexcept
-> detail::xfunction_type_t<math::cos_fun, E>
{
return detail::make_xfunction<math::cos_fun>(std::forward<E>(e));
}
/**
* @ingroup trigo_functions
* @brief Tangent function.
*
* Returns an \ref xfunction for the element-wise tangent
* of \em e (measured in radians).
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto tan(E&& e) noexcept
-> detail::xfunction_type_t<math::tan_fun, E>
{
return detail::make_xfunction<math::tan_fun>(std::forward<E>(e));
}
/**
* @ingroup trigo_functions
* @brief Arcsine function.
*
* Returns an \ref xfunction for the element-wise arcsine
* of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto asin(E&& e) noexcept
-> detail::xfunction_type_t<math::asin_fun, E>
{
return detail::make_xfunction<math::asin_fun>(std::forward<E>(e));
}
/**
* @ingroup trigo_functions
* @brief Arccosine function.
*
* Returns an \ref xfunction for the element-wise arccosine
* of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto acos(E&& e) noexcept
-> detail::xfunction_type_t<math::acos_fun, E>
{
return detail::make_xfunction<math::acos_fun>(std::forward<E>(e));
}
/**
* @ingroup trigo_functions
* @brief Arctangent function.
*
* Returns an \ref xfunction for the element-wise arctangent
* of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto atan(E&& e) noexcept
-> detail::xfunction_type_t<math::atan_fun, E>
{
return detail::make_xfunction<math::atan_fun>(std::forward<E>(e));
}
/**
* @ingroup trigo_functions
* @brief Artangent function, using signs to determine quadrants.
*
* Returns an \ref xfunction for the element-wise arctangent
* of <em>e1 / e2</em>, using the signs of arguments to determine the
* correct quadrant.
* @param e1 an \ref xexpression or a scalar
* @param e2 an \ref xexpression or a scalar
* @return an \ref xfunction
* @note e1 and e2 can't be both scalars.
*/
template <class E1, class E2>
inline auto atan2(E1&& e1, E2&& e2) noexcept
-> detail::xfunction_type_t<math::atan2_fun, E1, E2>
{
return detail::make_xfunction<math::atan2_fun>(std::forward<E1>(e1), std::forward<E2>(e2));
}
/************************
* hyperbolic functions *
************************/
/**
* @defgroup hyper_functions Hyperbolic functions
*/
/**
* @ingroup hyper_functions
* @brief Hyperbolic sine function.
*
* Returns an \ref xfunction for the element-wise hyperbolic
* sine of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto sinh(E&& e) noexcept
-> detail::xfunction_type_t<math::sinh_fun, E>
{
return detail::make_xfunction<math::sinh_fun>(std::forward<E>(e));
}
/**
* @ingroup hyper_functions
* @brief Hyperbolic cosine function.
*
* Returns an \ref xfunction for the element-wise hyperbolic
* cosine of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto cosh(E&& e) noexcept
-> detail::xfunction_type_t<math::cosh_fun, E>
{
return detail::make_xfunction<math::cosh_fun>(std::forward<E>(e));
}
/**
* @ingroup hyper_functions
* @brief Hyperbolic tangent function.
*
* Returns an \ref xfunction for the element-wise hyperbolic
* tangent of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto tanh(E&& e) noexcept
-> detail::xfunction_type_t<math::tanh_fun, E>
{
return detail::make_xfunction<math::tanh_fun>(std::forward<E>(e));
}
/**
* @ingroup hyper_functions
* @brief Inverse hyperbolic sine function.
*
* Returns an \ref xfunction for the element-wise inverse hyperbolic
* sine of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto asinh(E&& e) noexcept
-> detail::xfunction_type_t<math::asinh_fun, E>
{
return detail::make_xfunction<math::asinh_fun>(std::forward<E>(e));
}
/**
* @ingroup hyper_functions
* @brief Inverse hyperbolic cosine function.
*
* Returns an \ref xfunction for the element-wise inverse hyperbolic
* cosine of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto acosh(E&& e) noexcept
-> detail::xfunction_type_t<math::acosh_fun, E>
{
return detail::make_xfunction<math::acosh_fun>(std::forward<E>(e));
}
/**
* @ingroup hyper_functions
* @brief Inverse hyperbolic tangent function.
*
* Returns an \ref xfunction for the element-wise inverse hyperbolic
* tangent of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto atanh(E&& e) noexcept
-> detail::xfunction_type_t<math::atanh_fun, E>
{
return detail::make_xfunction<math::atanh_fun>(std::forward<E>(e));
}
/*****************************
* error and gamma functions *
*****************************/
/**
* @defgroup err_functions Error and gamma functions
*/
/**
* @ingroup err_functions
* @brief Error function.
*
* Returns an \ref xfunction for the element-wise error function
* of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto erf(E&& e) noexcept
-> detail::xfunction_type_t<math::erf_fun, E>
{
return detail::make_xfunction<math::erf_fun>(std::forward<E>(e));
}
/**
* @ingroup err_functions
* @brief Complementary error function.
*
* Returns an \ref xfunction for the element-wise complementary
* error function of \em e, whithout loss of precision for large argument.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto erfc(E&& e) noexcept
-> detail::xfunction_type_t<math::erfc_fun, E>
{
return detail::make_xfunction<math::erfc_fun>(std::forward<E>(e));
}
/**
* @ingroup err_functions
* @brief Gamma function.
*
* Returns an \ref xfunction for the element-wise gamma function
* of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto tgamma(E&& e) noexcept
-> detail::xfunction_type_t<math::tgamma_fun, E>
{
return detail::make_xfunction<math::tgamma_fun>(std::forward<E>(e));
}
/**
* @ingroup err_functions
* @brief Natural logarithm of the gamma function.
*
* Returns an \ref xfunction for the element-wise logarithm of
* the asbolute value fo the gamma function of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto lgamma(E&& e) noexcept
-> detail::xfunction_type_t<math::lgamma_fun, E>
{
return detail::make_xfunction<math::lgamma_fun>(std::forward<E>(e));
}
/*********************************************
* nearest integer floating point operations *
*********************************************/
/**
* @defgroup nearint_functions Nearest integer floating point operations
*/
/**
* @ingroup nearint_functions
* @brief ceil function.
*
* Returns an \ref xfunction for the element-wise smallest integer value
* not less than \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto ceil(E&& e) noexcept
-> detail::xfunction_type_t<math::ceil_fun, E>
{
return detail::make_xfunction<math::ceil_fun>(std::forward<E>(e));
}
/**
* @ingroup nearint_functions
* @brief floor function.
*
* Returns an \ref xfunction for the element-wise smallest integer value
* not greater than \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto floor(E&& e) noexcept
-> detail::xfunction_type_t<math::floor_fun, E>
{
return detail::make_xfunction<math::floor_fun>(std::forward<E>(e));
}
/**
* @ingroup nearint_functions
* @brief trunc function.
*
* Returns an \ref xfunction for the element-wise nearest integer not greater
* in magnitude than \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto trunc(E&& e) noexcept
-> detail::xfunction_type_t<math::trunc_fun, E>
{
return detail::make_xfunction<math::trunc_fun>(std::forward<E>(e));
}
/**
* @ingroup nearint_functions
* @brief round function.
*
* Returns an \ref xfunction for the element-wise nearest integer value
* to \em e, rounding halfway cases away from zero, regardless of the
* current rounding mode.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto round(E&& e) noexcept
-> detail::xfunction_type_t<math::round_fun, E>
{
return detail::make_xfunction<math::round_fun>(std::forward<E>(e));
}
/**
* @ingroup nearint_functions
* @brief nearbyint function.
*
* Returns an \ref xfunction for the element-wise rounding of \em e to integer
* values in floating point format, using the current rounding mode. nearbyint
* never raises FE_INEXACT error.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto nearbyint(E&& e) noexcept
-> detail::xfunction_type_t<math::nearbyint_fun, E>
{
return detail::make_xfunction<math::nearbyint_fun>(std::forward<E>(e));
}
/**
* @ingroup nearint_functions
* @brief rint function.
*
* Returns an \ref xfunction for the element-wise rounding of \em e to integer
* values in floating point format, using the current rounding mode. Contrary
* to nearbyint, rint may raise FE_INEXACT error.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto rint(E&& e) noexcept
-> detail::xfunction_type_t<math::rint_fun, E>
{
return detail::make_xfunction<math::rint_fun>(std::forward<E>(e));
}
/****************************
* classification functions *
****************************/
/**
* @defgroup classif_functions Classification functions
*/
/**
* @ingroup classif_functions
* @brief finite value check
*
* Returns an \ref xfunction for the element-wise finite value check
* tangent of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto isfinite(E&& e) noexcept
-> detail::xfunction_type_t<math::isfinite_fun, E>
{
return detail::make_xfunction<math::isfinite_fun>(std::forward<E>(e));
}
/**
* @ingroup classif_functions
* @brief infinity check
*
* Returns an \ref xfunction for the element-wise infinity check
* tangent of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto isinf(E&& e) noexcept
-> detail::xfunction_type_t<math::isinf_fun, E>
{
return detail::make_xfunction<math::isinf_fun>(std::forward<E>(e));
}
/**
* @ingroup classif_functions
* @brief NaN check
*
* Returns an \ref xfunction for the element-wise NaN check
* tangent of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto isnan(E&& e) noexcept
-> detail::xfunction_type_t<math::isnan_fun, E>
{
return detail::make_xfunction<math::isnan_fun>(std::forward<E>(e));
}
namespace detail
{
template <class FUNCTOR, class T, std::size_t... Is>
inline auto get_functor(T&& args, std::index_sequence<Is...>)
{
return FUNCTOR(std::get<Is>(args)...);
}
template <template <class...> class F, class... A, class... E>
inline auto make_xfunction(std::tuple<A...>&& f_args, E&&... e) noexcept
{
using functor_type = F<common_value_type_t<std::decay_t<E>...>>;
using result_type = typename functor_type::result_type;
using type = xfunction<functor_type, result_type, const_xclosure_t<E>...>;
auto functor = get_functor<functor_type>(
std::forward<std::tuple<A...>>(f_args),
std::make_index_sequence<sizeof...(A)>{}
);
return type(std::move(functor), std::forward<E>(e)...);
}
template <class T>
struct isclose
{
using result_type = bool;
isclose(double rtol, double atol, bool equal_nan)
: m_rtol(rtol), m_atol(atol), m_equal_nan(equal_nan)
{
}
bool operator()(const T& a, const T& b) const
{
if (m_equal_nan && std::isnan(a) && std::isnan(b))
{
return true;
}
return std::abs(a - b) <= (m_atol + m_rtol * std::abs(b));
}
private:
double m_rtol;
double m_atol;
bool m_equal_nan;
};
}
/**
* @ingroup classif_functions
* @brief Element-wise closeness detection
*
* Returns an \ref xfunction that evaluates to
* true if the elements in ``e1`` and ``e2`` are close to each other
* according to parameters ``atol`` and ``rtol``.
* The equation is: ``std::abs(a - b) <= (m_atol + m_rtol * std::abs(b))``.
* @param e1 input array to compare
* @param e2 input array to compare
* @param rtol the relative tolerance parameter (default 1e-05)
* @param atol the absolute tolerance parameter (default 1e-08)
* @param equal_nan if true, isclose returns true if both elements of e1 and e2 are NaN
* @return an \ref xfunction
*/
template <class E1, class E2>
inline auto isclose(E1&& e1, E2&& e2, double rtol = 1e-05, double atol = 1e-08, bool equal_nan = false) noexcept
{
return detail::make_xfunction<detail::isclose>(std::make_tuple(rtol, atol, equal_nan),
std::forward<E1>(e1), std::forward<E2>(e2));
}
/**
* @ingroup classif_functions
* @brief Check if all elements in \em e1 are close to the
* corresponding elements in \em e2.
*
* Returns true if all elements in ``e1`` and ``e2`` are close to each other
* according to parameters ``atol`` and ``rtol``.
* @param e1 input array to compare
* @param e2 input arrays to compare
* @param rtol the relative tolerance parameter (default 1e-05)
* @param atol the absolute tolerance parameter (default 1e-08)
* @return a boolean
*/
template <class E1, class E2>
inline auto allclose(E1&& e1, E2&& e2, double rtol = 1e-05, double atol = 1e-08) noexcept
{
return xt::all(isclose(std::forward<E1>(e1), std::forward<E2>(e2), rtol, atol));
}
/**********************
* Reducing functions *
**********************/
/**
* @defgroup red_functions reducing functions
*/
/**
* @ingroup red_functions
* @brief Sum of elements over given axes.
*
* Returns an \ref xreducer for the sum of elements over given
* \em axes.
* @param e an \ref xexpression
* @param axes the axes along which the sum is performed (optional)
* @return an \ref xreducer
*/
template <class E, class X>
inline auto sum(E&& e, X&& axes) noexcept
{
using functor_type = std::plus<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e), std::forward<X>(axes));
}
template <class E>
inline auto sum(E&& e) noexcept
{
using functor_type = std::plus<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e));
}
#ifdef X_OLD_CLANG
template <class E, class I>
inline auto sum(E&& e, std::initializer_list<I> axes) noexcept
{
using functor_type = std::plus<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e), axes);
}
#else
template <class E, class I, std::size_t N>
inline auto sum(E&& e, const I (&axes)[N]) noexcept
{
using functor_type = std::plus<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e), axes);
}
#endif
/**
* @ingroup red_functions
* @brief Product of elements over given axes.
*
* Returns an \ref xreducer for the product of elements over given
* \em axes.
* @param e an \ref xexpression
* @param axes the axes along which the product is computed (optional)
* @return an \ref xreducer
*/
template <class E, class X>
inline auto prod(E&& e, X&& axes) noexcept
{
using functor_type = std::multiplies<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e), std::forward<X>(axes));
}
template <class E>
inline auto prod(E&& e) noexcept
{
using functor_type = std::multiplies<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e));
}
#ifdef X_OLD_CLANG
template <class E, class I>
inline auto prod(E&& e, std::initializer_list<I> axes) noexcept
{
using functor_type = std::multiplies<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e), axes);
}
#else
template <class E, class I, std::size_t N>
inline auto prod(E&& e, const I (&axes)[N]) noexcept
{
using functor_type = std::multiplies<typename std::decay_t<E>::value_type>;
return reduce(functor_type(), std::forward<E>(e), axes);
}
#endif
/**
* @ingroup red_functions
* @brief Mean of elements over given axes.
*
* Returns an \ref xreducer for the mean of elements over given
* \em axes.
* @param e an \ref xexpression
* @param axes the axes along which the mean is computed (optional)
* @return an \ref xexpression
*/
template <class E, class X>
inline auto mean(E&& e, X&& axes) noexcept
{
using value_type = typename std::decay_t<E>::value_type;
auto size = e.size();
auto s = sum(std::forward<E>(e), std::forward<X>(axes));
return std::move(s) / value_type(size / s.size());
}
template <class E>
inline auto mean(E&& e) noexcept
{
using value_type = typename std::decay_t<E>::value_type;
auto size = e.size();
return sum(std::forward<E>(e)) / value_type(size);
}
#ifdef X_OLD_CLANG
template <class E, class I>
inline auto mean(E&& e, std::initializer_list<I> axes) noexcept
{
using value_type = typename std::decay_t<E>::value_type;
auto size = e.size();
auto s = sum(std::forward<E>(e), axes);
return std::move(s) / value_type(size / s.size());
}
#else
template <class E, class I, std::size_t N>
inline auto mean(E&& e, const I (&axes)[N]) noexcept
{
using value_type = typename std::decay_t<E>::value_type;
auto size = e.size();
auto s = sum(std::forward<E>(e), axes);
return std::move(s) / value_type(size / s.size());
}
#endif
}
#endif
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