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pocketpy/3rd/numpy/include/xtensor/xmath.hpp
Anurag Bhat 86b4fc623c
Merge numpy to pocketpy (#303) 
* Merge numpy to pocketpy

* Add CI

* Fix CI
2024-09-02 16:22:41 +08:00

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/***************************************************************************
* Copyright (c) Johan Mabille, Sylvain Corlay and Wolf Vollprecht *
* Copyright (c) QuantStack *
* *
* 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 XTENSOR_MATH_HPP
#define XTENSOR_MATH_HPP
#include <algorithm>
#include <array>
#include <cmath>
#include <complex>
#include <type_traits>
#include <xtl/xcomplex.hpp>
#include <xtl/xsequence.hpp>
#include <xtl/xtype_traits.hpp>
#include "xaccumulator.hpp"
#include "xeval.hpp"
#include "xmanipulation.hpp"
#include "xoperation.hpp"
#include "xreducer.hpp"
#include "xslice.hpp"
#include "xstrided_view.hpp"
#include "xtensor_config.hpp"
namespace xt
{
template <class T = double>
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 *
***********/
#define XTENSOR_UNSIGNED_ABS_FUNC(T) \
constexpr inline T abs(const T& x) \
{ \
return x; \
}
#define XTENSOR_INT_SPECIALIZATION_IMPL(FUNC_NAME, RETURN_VAL, T) \
constexpr inline bool FUNC_NAME(const T& /*x*/) noexcept \
{ \
return RETURN_VAL; \
}
#define XTENSOR_INT_SPECIALIZATION(FUNC_NAME, RETURN_VAL) \
XTENSOR_INT_SPECIALIZATION_IMPL(FUNC_NAME, RETURN_VAL, char); \
XTENSOR_INT_SPECIALIZATION_IMPL(FUNC_NAME, RETURN_VAL, short); \
XTENSOR_INT_SPECIALIZATION_IMPL(FUNC_NAME, RETURN_VAL, int); \
XTENSOR_INT_SPECIALIZATION_IMPL(FUNC_NAME, RETURN_VAL, long); \
XTENSOR_INT_SPECIALIZATION_IMPL(FUNC_NAME, RETURN_VAL, long long); \
XTENSOR_INT_SPECIALIZATION_IMPL(FUNC_NAME, RETURN_VAL, unsigned char); \
XTENSOR_INT_SPECIALIZATION_IMPL(FUNC_NAME, RETURN_VAL, unsigned short); \
XTENSOR_INT_SPECIALIZATION_IMPL(FUNC_NAME, RETURN_VAL, unsigned int); \
XTENSOR_INT_SPECIALIZATION_IMPL(FUNC_NAME, RETURN_VAL, unsigned long); \
XTENSOR_INT_SPECIALIZATION_IMPL(FUNC_NAME, RETURN_VAL, unsigned long long);
#define XTENSOR_UNARY_MATH_FUNCTOR(NAME) \
struct NAME##_fun \
{ \
template <class T> \
constexpr auto operator()(const T& arg) const \
{ \
using math::NAME; \
return NAME(arg); \
} \
template <class B> \
constexpr auto simd_apply(const B& arg) const \
{ \
using math::NAME; \
return NAME(arg); \
} \
}
#define XTENSOR_UNARY_MATH_FUNCTOR_COMPLEX_REDUCING(NAME) \
struct NAME##_fun \
{ \
template <class T> \
constexpr auto operator()(const T& arg) const \
{ \
using math::NAME; \
return NAME(arg); \
} \
template <class B> \
constexpr auto simd_apply(const B& arg) const \
{ \
using math::NAME; \
return NAME(arg); \
} \
}
#define XTENSOR_BINARY_MATH_FUNCTOR(NAME) \
struct NAME##_fun \
{ \
template <class T1, class T2> \
constexpr auto operator()(const T1& arg1, const T2& arg2) const \
{ \
using math::NAME; \
return NAME(arg1, arg2); \
} \
template <class B> \
constexpr auto simd_apply(const B& arg1, const B& arg2) const \
{ \
using math::NAME; \
return NAME(arg1, arg2); \
} \
}
#define XTENSOR_TERNARY_MATH_FUNCTOR(NAME) \
struct NAME##_fun \
{ \
template <class T1, class T2, class T3> \
constexpr auto operator()(const T1& arg1, const T2& arg2, const T3& arg3) const \
{ \
using math::NAME; \
return NAME(arg1, arg2, arg3); \
} \
template <class B> \
auto simd_apply(const B& arg1, const B& arg2, const B& arg3) const \
{ \
using math::NAME; \
return NAME(arg1, arg2, arg3); \
} \
}
namespace math
{
using std::abs;
using std::fabs;
using std::acos;
using std::asin;
using std::atan;
using std::cos;
using std::sin;
using std::tan;
using std::acosh;
using std::asinh;
using std::atanh;
using std::cosh;
using std::sinh;
using std::tanh;
using std::cbrt;
using std::sqrt;
using std::exp;
using std::exp2;
using std::expm1;
using std::ilogb;
using std::log;
using std::log10;
using std::log1p;
using std::log2;
using std::logb;
using std::ceil;
using std::floor;
using std::llround;
using std::lround;
using std::nearbyint;
using std::remainder;
using std::rint;
using std::round;
using std::trunc;
using std::erf;
using std::erfc;
using std::lgamma;
using std::tgamma;
using std::arg;
using std::conj;
using std::imag;
using std::real;
using std::atan2;
// copysign is not in the std namespace for MSVC
#if !defined(_MSC_VER)
using std::copysign;
#endif
using std::fdim;
using std::fmax;
using std::fmin;
using std::fmod;
using std::hypot;
using std::pow;
using std::fma;
using std::fpclassify;
// Overload isinf, isnan and isfinite because glibc implementation
// might return int instead of bool and the SIMD detection requires
// bool return type.
template <class T>
inline std::enable_if_t<xtl::is_arithmetic<T>::value, bool> isinf(const T& t)
{
return bool(std::isinf(t));
}
template <class T>
inline std::enable_if_t<xtl::is_arithmetic<T>::value, bool> isnan(const T& t)
{
return bool(std::isnan(t));
}
template <class T>
inline std::enable_if_t<xtl::is_arithmetic<T>::value, bool> isfinite(const T& t)
{
return bool(std::isfinite(t));
}
// Overload isinf, isnan and isfinite for complex datatypes,
// following the Python specification:
template <class T>
inline bool isinf(const std::complex<T>& c)
{
return std::isinf(std::real(c)) || std::isinf(std::imag(c));
}
template <class T>
inline bool isnan(const std::complex<T>& c)
{
return std::isnan(std::real(c)) || std::isnan(std::imag(c));
}
template <class T>
inline bool isfinite(const std::complex<T>& c)
{
return !isinf(c) && !isnan(c);
}
// VS2015 STL defines isnan, isinf and isfinite as template
// functions, breaking ADL.
#if defined(_WIN32) && defined(XTENSOR_USE_XSIMD)
/*template <class T, class A>
inline xsimd::batch_bool<T, A> isinf(const xsimd::batch<T, A>& b)
{
return xsimd::isinf(b);
}
template <class T, class A>
inline xsimd::batch_bool<T, A> isnan(const xsimd::batch<T, A>& b)
{
return xsimd::isnan(b);
}
template <class T, class A>
inline xsimd::batch_bool<T, A> isfinite(const xsimd::batch<T, A>& b)
{
return xsimd::isfinite(b);
}*/
#endif
// The following specializations are needed to avoid 'ambiguous overload' errors,
// whereas 'unsigned char' and 'unsigned short' are automatically converted to 'int'.
// we're still adding those functions to silence warnings
XTENSOR_UNSIGNED_ABS_FUNC(unsigned char)
XTENSOR_UNSIGNED_ABS_FUNC(unsigned short)
XTENSOR_UNSIGNED_ABS_FUNC(unsigned int)
XTENSOR_UNSIGNED_ABS_FUNC(unsigned long)
XTENSOR_UNSIGNED_ABS_FUNC(unsigned long long)
#ifdef _WIN32
XTENSOR_INT_SPECIALIZATION(isinf, false);
XTENSOR_INT_SPECIALIZATION(isnan, false);
XTENSOR_INT_SPECIALIZATION(isfinite, true);
#endif
XTENSOR_UNARY_MATH_FUNCTOR_COMPLEX_REDUCING(abs);
XTENSOR_UNARY_MATH_FUNCTOR(fabs);
XTENSOR_BINARY_MATH_FUNCTOR(fmod);
XTENSOR_BINARY_MATH_FUNCTOR(remainder);
XTENSOR_TERNARY_MATH_FUNCTOR(fma);
XTENSOR_BINARY_MATH_FUNCTOR(fmax);
XTENSOR_BINARY_MATH_FUNCTOR(fmin);
XTENSOR_BINARY_MATH_FUNCTOR(fdim);
XTENSOR_UNARY_MATH_FUNCTOR(exp);
XTENSOR_UNARY_MATH_FUNCTOR(exp2);
XTENSOR_UNARY_MATH_FUNCTOR(expm1);
XTENSOR_UNARY_MATH_FUNCTOR(log);
XTENSOR_UNARY_MATH_FUNCTOR(log10);
XTENSOR_UNARY_MATH_FUNCTOR(log2);
XTENSOR_UNARY_MATH_FUNCTOR(log1p);
XTENSOR_BINARY_MATH_FUNCTOR(pow);
XTENSOR_UNARY_MATH_FUNCTOR(sqrt);
XTENSOR_UNARY_MATH_FUNCTOR(cbrt);
XTENSOR_BINARY_MATH_FUNCTOR(hypot);
XTENSOR_UNARY_MATH_FUNCTOR(sin);
XTENSOR_UNARY_MATH_FUNCTOR(cos);
XTENSOR_UNARY_MATH_FUNCTOR(tan);
XTENSOR_UNARY_MATH_FUNCTOR(asin);
XTENSOR_UNARY_MATH_FUNCTOR(acos);
XTENSOR_UNARY_MATH_FUNCTOR(atan);
XTENSOR_BINARY_MATH_FUNCTOR(atan2);
XTENSOR_UNARY_MATH_FUNCTOR(sinh);
XTENSOR_UNARY_MATH_FUNCTOR(cosh);
XTENSOR_UNARY_MATH_FUNCTOR(tanh);
XTENSOR_UNARY_MATH_FUNCTOR(asinh);
XTENSOR_UNARY_MATH_FUNCTOR(acosh);
XTENSOR_UNARY_MATH_FUNCTOR(atanh);
XTENSOR_UNARY_MATH_FUNCTOR(erf);
XTENSOR_UNARY_MATH_FUNCTOR(erfc);
XTENSOR_UNARY_MATH_FUNCTOR(tgamma);
XTENSOR_UNARY_MATH_FUNCTOR(lgamma);
XTENSOR_UNARY_MATH_FUNCTOR(ceil);
XTENSOR_UNARY_MATH_FUNCTOR(floor);
XTENSOR_UNARY_MATH_FUNCTOR(trunc);
XTENSOR_UNARY_MATH_FUNCTOR(round);
XTENSOR_UNARY_MATH_FUNCTOR(nearbyint);
XTENSOR_UNARY_MATH_FUNCTOR(rint);
XTENSOR_UNARY_MATH_FUNCTOR(isfinite);
XTENSOR_UNARY_MATH_FUNCTOR(isinf);
XTENSOR_UNARY_MATH_FUNCTOR(isnan);
}
#undef XTENSOR_UNARY_MATH_FUNCTOR
#undef XTENSOR_BINARY_MATH_FUNCTOR
#undef XTENSOR_TERNARY_MATH_FUNCTOR
#undef XTENSOR_UNARY_MATH_FUNCTOR_COMPLEX_REDUCING
#undef XTENSOR_UNSIGNED_ABS_FUNC
namespace detail
{
template <class R, class T>
std::enable_if_t<!has_iterator_interface<R>::value, R> fill_init(T init)
{
return R(init);
}
template <class R, class T>
std::enable_if_t<has_iterator_interface<R>::value, R> fill_init(T init)
{
R result;
std::fill(std::begin(result), std::end(result), init);
return result;
}
}
#define XTENSOR_REDUCER_FUNCTION(NAME, FUNCTOR, INIT_VALUE_TYPE, INIT) \
template < \
class T = void, \
class E, \
class X, \
class EVS = DEFAULT_STRATEGY_REDUCERS, \
XTL_REQUIRES(xtl::negation<is_reducer_options<X>>, xtl::negation<xtl::is_integral<std::decay_t<X>>>)> \
inline auto NAME(E&& e, X&& axes, EVS es = EVS()) \
{ \
using init_value_type = std::conditional_t<std::is_same<T, void>::value, INIT_VALUE_TYPE, T>; \
using functor_type = FUNCTOR; \
using init_value_fct = xt::const_value<init_value_type>; \
return xt::reduce( \
make_xreducer_functor(functor_type(), init_value_fct(detail::fill_init<init_value_type>(INIT))), \
std::forward<E>(e), \
std::forward<X>(axes), \
es \
); \
} \
\
template < \
class T = void, \
class E, \
class X, \
class EVS = DEFAULT_STRATEGY_REDUCERS, \
XTL_REQUIRES(xtl::negation<is_reducer_options<X>>, xtl::is_integral<std::decay_t<X>>)> \
inline auto NAME(E&& e, X axis, EVS es = EVS()) \
{ \
return NAME(std::forward<E>(e), {axis}, es); \
} \
\
template <class T = void, class E, class EVS = DEFAULT_STRATEGY_REDUCERS, XTL_REQUIRES(is_reducer_options<EVS>)> \
inline auto NAME(E&& e, EVS es = EVS()) \
{ \
using init_value_type = std::conditional_t<std::is_same<T, void>::value, INIT_VALUE_TYPE, T>; \
using functor_type = FUNCTOR; \
using init_value_fct = xt::const_value<init_value_type>; \
return xt::reduce( \
make_xreducer_functor(functor_type(), init_value_fct(detail::fill_init<init_value_type>(INIT))), \
std::forward<E>(e), \
es \
); \
} \
\
template <class T = void, class E, class I, std::size_t N, class EVS = DEFAULT_STRATEGY_REDUCERS> \
inline auto NAME(E&& e, const I(&axes)[N], EVS es = EVS()) \
{ \
using init_value_type = std::conditional_t<std::is_same<T, void>::value, INIT_VALUE_TYPE, T>; \
using functor_type = FUNCTOR; \
using init_value_fct = xt::const_value<init_value_type>; \
return xt::reduce( \
make_xreducer_functor(functor_type(), init_value_fct(detail::fill_init<init_value_type>(INIT))), \
std::forward<E>(e), \
axes, \
es \
); \
}
/*******************
* 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 = void>
struct minimum
{
template <class A1, class A2>
constexpr auto operator()(const A1& t1, const A2& t2) const noexcept
{
return xtl::select(t1 < t2, t1, t2);
}
template <class A1, class A2>
constexpr auto simd_apply(const A1& t1, const A2& t2) const noexcept
{
return xt_simd::select(t1 < t2, t1, t2);
}
};
template <class T = void>
struct maximum
{
template <class A1, class A2>
constexpr auto operator()(const A1& t1, const A2& t2) const noexcept
{
return xtl::select(t1 > t2, t1, t2);
}
template <class A1, class A2>
constexpr auto simd_apply(const A1& t1, const A2& t2) const noexcept
{
return xt_simd::select(t1 > t2, t1, t2);
}
};
struct clamp_fun
{
template <class A1, class A2, class A3>
constexpr auto operator()(const A1& v, const A2& lo, const A3& hi) const
{
return xtl::select(v < lo, lo, xtl::select(hi < v, hi, v));
}
template <class A1, class A2, class A3>
constexpr auto simd_apply(const A1& v, const A2& lo, const A3& hi) const
{
return xt_simd::select(v < lo, lo, xt_simd::select(hi < v, hi, v));
}
};
struct deg2rad
{
template <class A, std::enable_if_t<xtl::is_integral<A>::value, int> = 0>
constexpr double operator()(const A& a) const noexcept
{
return a * xt::numeric_constants<double>::PI / 180.0;
}
template <class A, std::enable_if_t<std::is_floating_point<A>::value, int> = 0>
constexpr auto operator()(const A& a) const noexcept
{
return a * xt::numeric_constants<A>::PI / A(180.0);
}
template <class A, std::enable_if_t<xtl::is_integral<A>::value, int> = 0>
constexpr double simd_apply(const A& a) const noexcept
{
return a * xt::numeric_constants<double>::PI / 180.0;
}
template <class A, std::enable_if_t<std::is_floating_point<A>::value, int> = 0>
constexpr auto simd_apply(const A& a) const noexcept
{
return a * xt::numeric_constants<A>::PI / A(180.0);
}
};
struct rad2deg
{
template <class A, std::enable_if_t<xtl::is_integral<A>::value, int> = 0>
constexpr double operator()(const A& a) const noexcept
{
return a * 180.0 / xt::numeric_constants<double>::PI;
}
template <class A, std::enable_if_t<std::is_floating_point<A>::value, int> = 0>
constexpr auto operator()(const A& a) const noexcept
{
return a * A(180.0) / xt::numeric_constants<A>::PI;
}
template <class A, std::enable_if_t<xtl::is_integral<A>::value, int> = 0>
constexpr double simd_apply(const A& a) const noexcept
{
return a * 180.0 / xt::numeric_constants<double>::PI;
}
template <class A, std::enable_if_t<std::is_floating_point<A>::value, int> = 0>
constexpr auto simd_apply(const A& a) const noexcept
{
return a * A(180.0) / xt::numeric_constants<A>::PI;
}
};
}
/**
* @ingroup basic_functions
* @brief Convert angles from degrees to radians.
*
* Returns an \ref xfunction for the element-wise corresponding
* angle in radians of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto deg2rad(E&& e) noexcept -> detail::xfunction_type_t<math::deg2rad, E>
{
return detail::make_xfunction<math::deg2rad>(std::forward<E>(e));
}
/**
* @ingroup basic_functions
* @brief Convert angles from degrees to radians.
*
* Returns an \ref xfunction for the element-wise corresponding
* angle in radians of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto radians(E&& e) noexcept -> detail::xfunction_type_t<math::deg2rad, E>
{
return detail::make_xfunction<math::deg2rad>(std::forward<E>(e));
}
/**
* @ingroup basic_functions
* @brief Convert angles from radians to degrees.
*
* Returns an \ref xfunction for the element-wise corresponding
* angle in degrees of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto rad2deg(E&& e) noexcept -> detail::xfunction_type_t<math::rad2deg, E>
{
return detail::make_xfunction<math::rad2deg>(std::forward<E>(e));
}
/**
* @ingroup basic_functions
* @brief Convert angles from radians to degrees.
*
* Returns an \ref xfunction for the element-wise corresponding
* angle in degrees of \em e.
* @param e an \ref xexpression
* @return an \ref xfunction
*/
template <class E>
inline auto degrees(E&& e) noexcept -> detail::xfunction_type_t<math::rad2deg, E>
{
return detail::make_xfunction<math::rad2deg>(std::forward<E>(e));
}
/**
* @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<void>, E1, E2>
{
return detail::make_xfunction<math::maximum<void>>(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<void>, E1, E2>
{
return detail::make_xfunction<math::minimum<void>>(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)
* @param es evaluation strategy of the reducer
* @return an \ref xreducer
*/
XTENSOR_REDUCER_FUNCTION(
amax,
math::maximum<void>,
typename std::decay_t<E>::value_type,
std::numeric_limits<xvalue_type_t<std::decay_t<E>>>::lowest()
)
/**
* @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)
* @param es evaluation strategy of the reducer
* @return an \ref xreducer
*/
XTENSOR_REDUCER_FUNCTION(
amin,
math::minimum<void>,
typename std::decay_t<E>::value_type,
std::numeric_limits<xvalue_type_t<std::decay_t<E>>>::max()
)
/**
* @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
{
template <class T>
struct sign_impl
{
template <class XT = T>
static constexpr std::enable_if_t<xtl::is_signed<XT>::value, T> run(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 <class XT = T>
static constexpr std::enable_if_t<xtl::is_complex<XT>::value, T> run(T x)
{
return T(
sign_impl<typename T::value_type>::run(
(x.real() != typename T::value_type(0)) ? x.real() : x.imag()
),
0
);
}
template <class XT = T>
static constexpr std::enable_if_t<std::is_unsigned<XT>::value, T> run(T x)
{
return T(x > T(0));
}
};
struct sign_fun
{
template <class T>
constexpr auto operator()(const T& x) const
{
return sign_impl<T>::run(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));
}
namespace detail
{
template <class F, class... T, typename = decltype(std::declval<F>()(std::declval<T>()...))>
std::true_type supports_test(const F&, const T&...);
std::false_type supports_test(...);
template <class... T>
struct supports;
template <class F, class... T>
struct supports<F(T...)> : decltype(supports_test(std::declval<F>(), std::declval<T>()...))
{
};
template <class F>
struct lambda_adapt
{
explicit lambda_adapt(F&& lmbd)
: m_lambda(std::move(lmbd))
{
}
template <class... T>
auto operator()(T... args) const
{
return m_lambda(args...);
}
template <class... T, XTL_REQUIRES(detail::supports<F(T...)>)>
auto simd_apply(T... args) const
{
return m_lambda(args...);
}
F m_lambda;
};
}
/**
* Create a xfunction from a lambda
*
* This function can be used to easily create performant xfunctions from lambdas:
*
* @code{cpp}
* template <class E1>
* inline auto square(E1&& e1) noexcept
* {
* auto fnct = [](auto x) -> decltype(x * x) {
* return x * x;
* };
* return make_lambda_xfunction(std::move(fnct), std::forward<E1>(e1));
* }
* @endcode
*
* Lambda function allow the reusal of a single arguments in multiple places (otherwise
* only correctly possible when using xshared_expressions). ``auto`` lambda functions are
* automatically vectorized with ``xsimd`` if possible (note that the trailing
* ``-> decltype(...)`` is mandatory for the feature detection to work).
*
* @param lambda the lambda to be vectorized
* @param args forwarded arguments
*
* @return lazy xfunction
*/
template <class F, class... E>
inline auto make_lambda_xfunction(F&& lambda, E&&... args)
{
using xfunction_type = typename detail::xfunction_type<detail::lambda_adapt<F>, E...>::type;
return xfunction_type(detail::lambda_adapt<F>(std::forward<F>(lambda)), std::forward<E>(args)...);
}
#define XTENSOR_GCC_VERSION (__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__)
// Workaround for MSVC 2015 & GCC 4.9
#if (defined(_MSC_VER) && _MSC_VER < 1910) || (defined(__GNUC__) && GCC_VERSION < 49999)
#define XTENSOR_DISABLE_LAMBDA_FCT
#endif
#ifdef XTENSOR_DISABLE_LAMBDA_FCT
struct square_fct
{
template <class T>
auto operator()(T x) const -> decltype(x * x)
{
return x * x;
}
};
struct cube_fct
{
template <class T>
auto operator()(T x) const -> decltype(x * x * x)
{
return x * x * x;
}
};
#endif
/**
* @ingroup pow_functions
* @brief Square power function, equivalent to e1 * e1.
*
* Returns an \ref xfunction for the element-wise value of
* of \em e1 * \em e1.
* @param e1 an \ref xexpression or a scalar
* @return an \ref xfunction
*/
template <class E1>
inline auto square(E1&& e1) noexcept
{
#ifdef XTENSOR_DISABLE_LAMBDA_FCT
return make_lambda_xfunction(square_fct{}, std::forward<E1>(e1));
#else
auto fnct = [](auto x) -> decltype(x * x)
{
return x * x;
};
return make_lambda_xfunction(std::move(fnct), std::forward<E1>(e1));
#endif
}
/**
* @ingroup pow_functions
* @brief Cube power function, equivalent to e1 * e1 * e1.
*
* Returns an \ref xfunction for the element-wise value of
* of \em e1 * \em e1.
* @param e1 an \ref xexpression or a scalar
* @return an \ref xfunction
*/
template <class E1>
inline auto cube(E1&& e1) noexcept
{
#ifdef XTENSOR_DISABLE_LAMBDA_FCT
return make_lambda_xfunction(cube_fct{}, std::forward<E1>(e1));
#else
auto fnct = [](auto x) -> decltype(x * x * x)
{
return x * x * x;
};
return make_lambda_xfunction(std::move(fnct), std::forward<E1>(e1));
#endif
}
#undef XTENSOR_GCC_VERSION
#undef XTENSOR_DISABLE_LAMBDA_FCT
namespace detail
{
// Thanks to Matt Pharr in http://pbrt.org/hair.pdf
template <std::size_t N>
struct pow_impl;
template <std::size_t N>
struct pow_impl
{
template <class T>
auto operator()(T v) const -> decltype(v * v)
{
T temp = pow_impl<N / 2>{}(v);
return temp * temp * pow_impl<N & 1>{}(v);
}
};
template <>
struct pow_impl<1>
{
template <class T>
auto operator()(T v) const -> T
{
return v;
}
};
template <>
struct pow_impl<0>
{
template <class T>
auto operator()(T /*v*/) const -> T
{
return T(1);
}
};
}
/**
* @ingroup pow_functions
* @brief Integer power function.
*
* Returns an \ref xfunction for the element-wise power of e1 to
* an integral constant.
*
* Instead of computing the power by using the (expensive) logarithm, this function
* computes the power in a number of straight-forward multiplication steps. This function
* is therefore much faster (even for high N) than the generic pow-function.
*
* For example, `e1^20` can be expressed as `(((e1^2)^2)^2)^2*(e1^2)^2`, which is just 5 multiplications.
*
* @param e an \ref xexpression
* @tparam N the exponent (has to be positive integer)
* @return an \ref xfunction
*/
template <std::size_t N, class E>
inline auto pow(E&& e) noexcept
{
static_assert(N > 0, "integer power cannot be negative");
return make_lambda_xfunction(detail::pow_impl<N>{}, std::forward<E>(e));
}
/**
* @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 <class F, class... A, class... E>
inline auto make_xfunction(std::tuple<A...>&& f_args, E&&... e) noexcept
{
using functor_type = F;
using expression_tag = xexpression_tag_t<E...>;
using type = select_xfunction_expression_t<expression_tag, functor_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)...);
}
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)
{
}
template <class A1, class A2>
bool operator()(const A1& a, const A2& b) const
{
using internal_type = xtl::promote_type_t<A1, A2, double>;
if (math::isnan(a) && math::isnan(b))
{
return m_equal_nan;
}
if (math::isinf(a) && math::isinf(b))
{
// check for both infinity signs equal
return a == b;
}
auto d = math::abs(internal_type(a) - internal_type(b));
return d <= m_atol
|| d <= m_rtol
* double((std::max)(math::abs(internal_type(a)), math::abs(internal_type(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)
* @param es evaluation strategy of the reducer
* @tparam T the value type used for internal computation. The default is
* `E::value_type`. `T` is also used for determining the value type
* of the result, which is the type of `T() + E::value_type()`.
* You can pass `big_promote_value_type_t<E>` to avoid overflow in computation.
* @return an \ref xreducer
*/
XTENSOR_REDUCER_FUNCTION(sum, detail::plus, typename std::decay_t<E>::value_type, 0)
/**
* @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)
* @param ddof delta degrees of freedom (optional).
* The divisor used in calculations is N - ddof, where N represents the number of
* elements. By default ddof is zero.
* @param es evaluation strategy of the reducer
* @tparam T the value type used for internal computation. The default is `E::value_type`.
* `T` is also used for determining the value type of the result, which is the type
* of `T() * E::value_type()`.
* You can pass `big_promote_value_type_t<E>` to avoid overflow in computation.
* @return an \ref xreducer
*/
XTENSOR_REDUCER_FUNCTION(prod, detail::multiplies, typename std::decay_t<E>::value_type, 1)
namespace detail
{
template <class T, class S, class ST>
inline auto mean_division(S&& s, ST e_size)
{
using value_type = typename std::conditional_t<std::is_same<T, void>::value, double, T>;
// Avoids floating point exception when s.size is 0
value_type div = s.size() != ST(0) ? static_cast<value_type>(e_size / s.size()) : value_type(0);
return std::move(s) / std::move(div);
}
template <
class T,
class E,
class X,
class D,
class EVS,
XTL_REQUIRES(xtl::negation<is_reducer_options<X>>, xtl::is_integral<D>)>
inline auto mean(E&& e, X&& axes, const D& ddof, EVS es)
{
// sum cannot always be a double. It could be a complex number which cannot operate on
// std::plus<double>.
using size_type = typename std::decay_t<E>::size_type;
const size_type size = e.size();
XTENSOR_ASSERT(static_cast<size_type>(ddof) <= size);
auto s = sum<T>(std::forward<E>(e), std::forward<X>(axes), es);
return mean_division<T>(std::move(s), size - static_cast<size_type>(ddof));
}
template <class T, class E, class I, std::size_t N, class D, class EVS>
inline auto mean(E&& e, const I (&axes)[N], const D& ddof, EVS es)
{
using size_type = typename std::decay_t<E>::size_type;
const size_type size = e.size();
XTENSOR_ASSERT(static_cast<size_type>(ddof) <= size);
auto s = sum<T>(std::forward<E>(e), axes, es);
return mean_division<T>(std::move(s), size - static_cast<size_type>(ddof));
}
template <class T, class E, class D, class EVS, XTL_REQUIRES(is_reducer_options<EVS>, xtl::is_integral<D>)>
inline auto mean_noaxis(E&& e, const D& ddof, EVS es)
{
using value_type = typename std::conditional_t<std::is_same<T, void>::value, double, T>;
using size_type = typename std::decay_t<E>::size_type;
const size_type size = e.size();
XTENSOR_ASSERT(static_cast<size_type>(ddof) <= size);
auto s = sum<T>(std::forward<E>(e), es);
return std::move(s) / static_cast<value_type>((size - static_cast<size_type>(ddof)));
}
}
/**
* @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)
* @param es the evaluation strategy (optional)
* @tparam T the value type used for internal computation. The default is
* `E::value_type`. `T` is also used for determining the value type
* of the result, which is the type of `T() + E::value_type()`.
* You can pass `big_promote_value_type_t<E>` to avoid overflow in computation.
* @return an \ref xexpression
*/
template <
class T = void,
class E,
class X,
class EVS = DEFAULT_STRATEGY_REDUCERS,
XTL_REQUIRES(xtl::negation<is_reducer_options<X>>)>
inline auto mean(E&& e, X&& axes, EVS es = EVS())
{
return detail::mean<T>(std::forward<E>(e), std::forward<X>(axes), 0u, es);
}
template <class T = void, class E, class EVS = DEFAULT_STRATEGY_REDUCERS, XTL_REQUIRES(is_reducer_options<EVS>)>
inline auto mean(E&& e, EVS es = EVS())
{
return detail::mean_noaxis<T>(std::forward<E>(e), 0u, es);
}
template <class T = void, class E, class I, std::size_t N, class EVS = DEFAULT_STRATEGY_REDUCERS>
inline auto mean(E&& e, const I (&axes)[N], EVS es = EVS())
{
return detail::mean<T>(std::forward<E>(e), axes, 0u, es);
}
/**
* @ingroup red_functions
* @brief Average of elements over given axes using weights.
*
* Returns an \ref xreducer for the mean of elements over given
* \em axes.
* @param e an \ref xexpression
* @param weights \ref xexpression containing weights associated with the values in \ref e
* @param axes the axes along which the mean is computed (optional)
* @tparam T the value type used for internal computation. The default is
* `E::value_type`. `T`is also used for determining the value type of the result,
* which is the type of `T() + E::value_type().
* You can pass `big_promote_value_type_t<E>` to avoid overflow in computation.
* @return an \ref xexpression
*
* @sa mean
*/
template <
class T = void,
class E,
class W,
class X,
class EVS = DEFAULT_STRATEGY_REDUCERS,
XTL_REQUIRES(is_reducer_options<EVS>, xtl::negation<xtl::is_integral<X>>)>
inline auto average(E&& e, W&& weights, X&& axes, EVS ev = EVS())
{
xindex_type_t<typename std::decay_t<E>::shape_type> broadcast_shape;
xt::resize_container(broadcast_shape, e.dimension());
auto ax = normalize_axis(e, axes);
if (weights.dimension() == 1)
{
if (weights.size() != e.shape()[ax[0]])
{
XTENSOR_THROW(std::runtime_error, "Weights need to have the same shape as expression at axes.");
}
std::fill(broadcast_shape.begin(), broadcast_shape.end(), std::size_t(1));
broadcast_shape[ax[0]] = weights.size();
}
else
{
if (!same_shape(e.shape(), weights.shape()))
{
XTENSOR_THROW(
std::runtime_error,
"Weights with dim > 1 need to have the same shape as expression."
);
}
std::copy(e.shape().begin(), e.shape().end(), broadcast_shape.begin());
}
constexpr layout_type L = default_assignable_layout(std::decay_t<W>::static_layout);
auto weights_view = reshape_view<L>(std::forward<W>(weights), std::move(broadcast_shape));
auto scl = sum<T>(weights_view, ax, xt::evaluation_strategy::immediate);
return sum<T>(std::forward<E>(e) * std::move(weights_view), std::move(ax), ev) / std::move(scl);
}
template <
class T = void,
class E,
class W,
class X,
class EVS = DEFAULT_STRATEGY_REDUCERS,
XTL_REQUIRES(is_reducer_options<EVS>, xtl::is_integral<X>)>
inline auto average(E&& e, W&& weights, X axis, EVS ev = EVS())
{
return average(std::forward<E>(e), std::forward<W>(weights), {axis}, std::forward<EVS>(ev));
}
template <class T = void, class E, class W, class X, std::size_t N, class EVS = DEFAULT_STRATEGY_REDUCERS>
inline auto average(E&& e, W&& weights, const X (&axes)[N], EVS ev = EVS())
{
// need to select the X&& overload and forward to different type
using ax_t = std::array<std::size_t, N>;
return average<T>(std::forward<E>(e), std::forward<W>(weights), xt::forward_normalize<ax_t>(e, axes), ev);
}
template <class T = void, class E, class W, class EVS = DEFAULT_STRATEGY_REDUCERS, XTL_REQUIRES(is_reducer_options<EVS>)>
inline auto average(E&& e, W&& weights, EVS ev = EVS())
{
if (weights.dimension() != e.dimension()
|| !std::equal(weights.shape().begin(), weights.shape().end(), e.shape().begin()))
{
XTENSOR_THROW(std::runtime_error, "Weights need to have the same shape as expression.");
}
auto div = sum<T>(weights, evaluation_strategy::immediate)();
auto s = sum<T>(std::forward<E>(e) * std::forward<W>(weights), ev) / std::move(div);
return s;
}
template <class T = void, class E, class EVS = DEFAULT_STRATEGY_REDUCERS, XTL_REQUIRES(is_reducer_options<EVS>)>
inline auto average(E&& e, EVS ev = EVS())
{
return mean<T>(e, ev);
}
namespace detail
{
template <typename E>
std::enable_if_t<std::is_lvalue_reference<E>::value, E> shared_forward(E e) noexcept
{
return e;
}
template <typename E>
std::enable_if_t<!std::is_lvalue_reference<E>::value, xshared_expression<E>> shared_forward(E e) noexcept
{
return make_xshared(std::move(e));
}
}
template <
class T = void,
class E,
class D,
class EVS = DEFAULT_STRATEGY_REDUCERS,
XTL_REQUIRES(is_reducer_options<EVS>, xtl::is_integral<D>)>
inline auto variance(E&& e, const D& ddof, EVS es = EVS())
{
auto cached_mean = mean<T>(e, es)();
return detail::mean_noaxis<T>(square(std::forward<E>(e) - std::move(cached_mean)), ddof, es);
}
template <class T = void, class E, class EVS = DEFAULT_STRATEGY_REDUCERS, XTL_REQUIRES(is_reducer_options<EVS>)>
inline auto variance(E&& e, EVS es = EVS())
{
return variance<T>(std::forward<E>(e), 0u, es);
}
template <class T = void, class E, class EVS = DEFAULT_STRATEGY_REDUCERS, XTL_REQUIRES(is_reducer_options<EVS>)>
inline auto stddev(E&& e, EVS es = EVS())
{
return sqrt(variance<T>(std::forward<E>(e), es));
}
/**
* @ingroup red_functions
* @brief Compute the variance along the specified axes
*
* Returns the variance of the array elements, a measure of the spread of a
* distribution. The variance is computed for the flattened array by default,
* otherwise over the specified axes.
*
* Note: this function is not yet specialized for complex numbers.
*
* @param e an \ref xexpression
* @param axes the axes along which the variance is computed (optional)
* @param ddof delta degrees of freedom (optional).
* The divisor used in calculations is N - ddof, where N represents the number of
* elements. By default ddof is zero.
* @param es evaluation strategy to use (lazy (default), or immediate)
* @tparam T the value type used for internal computation. The default is
* `E::value_type`. `T`is also used for determining the value type of the result,
* which is the type of `T() + E::value_type()`.
* You can pass `big_promote_value_type_t<E>` to avoid overflow in computation.
* @return an \ref xexpression
*
* @sa stddev, mean
*/
template <
class T = void,
class E,
class X,
class D,
class EVS = DEFAULT_STRATEGY_REDUCERS,
XTL_REQUIRES(xtl::negation<is_reducer_options<X>>, xtl::is_integral<D>)>
inline auto variance(E&& e, X&& axes, const D& ddof, EVS es = EVS())
{
decltype(auto) sc = detail::shared_forward<E>(e);
// note: forcing copy of first axes argument -- is there a better solution?
auto axes_copy = axes;
// always eval to prevent repeated evaluations in the next calls
auto inner_mean = eval(mean<T>(sc, std::move(axes_copy), evaluation_strategy::immediate));
// fake keep_dims = 1
// Since the inner_shape might have a reference semantic (e.g. xbuffer_adaptor in bindings)
// We need to map it to another type before modifying it.
// We pragmatically abuse `get_strides_t`
using tmp_shape_t = get_strides_t<typename std::decay_t<E>::shape_type>;
tmp_shape_t keep_dim_shape = xtl::forward_sequence<tmp_shape_t, decltype(e.shape())>(e.shape());
for (const auto& el : axes)
{
keep_dim_shape[el] = 1u;
}
auto mrv = reshape_view<XTENSOR_DEFAULT_LAYOUT>(std::move(inner_mean), std::move(keep_dim_shape));
return detail::mean<T>(square(sc - std::move(mrv)), std::forward<X>(axes), ddof, es);
}
template <
class T = void,
class E,
class X,
class EVS = DEFAULT_STRATEGY_REDUCERS,
XTL_REQUIRES(xtl::negation<is_reducer_options<X>>, xtl::negation<xtl::is_integral<std::decay_t<X>>>, is_reducer_options<EVS>)>
inline auto variance(E&& e, X&& axes, EVS es = EVS())
{
return variance<T>(std::forward<E>(e), std::forward<X>(axes), 0u, es);
}
/**
* @ingroup red_functions
* @brief Compute the standard deviation along the specified axis.
*
* Returns the standard deviation, a measure of the spread of a distribution,
* of the array elements. The standard deviation is computed for the flattened
* array by default, otherwise over the specified axis.
*
* Note: this function is not yet specialized for complex numbers.
*
* @param e an \ref xexpression
* @param axes the axes along which the standard deviation is computed (optional)
* @param es evaluation strategy to use (lazy (default), or immediate)
* @tparam T the value type used for internal computation. The default is
* `E::value_type`. `T`is also used for determining the value type of the result,
* which is the type of `T() + E::value_type()`.
* You can pass `big_promote_value_type_t<E>` to avoid overflow in computation.
* @return an \ref xexpression
*
* @sa variance, mean
*/
template <
class T = void,
class E,
class X,
class EVS = DEFAULT_STRATEGY_REDUCERS,
XTL_REQUIRES(xtl::negation<is_reducer_options<X>>)>
inline auto stddev(E&& e, X&& axes, EVS es = EVS())
{
return sqrt(variance<T>(std::forward<E>(e), std::forward<X>(axes), es));
}
template <class T = void, class E, class A, std::size_t N, class EVS = DEFAULT_STRATEGY_REDUCERS>
inline auto stddev(E&& e, const A (&axes)[N], EVS es = EVS())
{
return stddev<T>(
std::forward<E>(e),
xtl::forward_sequence<std::array<std::size_t, N>, decltype(axes)>(axes),
es
);
}
template <
class T = void,
class E,
class A,
std::size_t N,
class EVS = DEFAULT_STRATEGY_REDUCERS,
XTL_REQUIRES(is_reducer_options<EVS>)>
inline auto variance(E&& e, const A (&axes)[N], EVS es = EVS())
{
return variance<T>(
std::forward<E>(e),
xtl::forward_sequence<std::array<std::size_t, N>, decltype(axes)>(axes),
es
);
}
template <class T = void, class E, class A, std::size_t N, class D, class EVS = DEFAULT_STRATEGY_REDUCERS>
inline auto variance(E&& e, const A (&axes)[N], const D& ddof, EVS es = EVS())
{
return variance<T>(
std::forward<E>(e),
xtl::forward_sequence<std::array<std::size_t, N>, decltype(axes)>(axes),
ddof,
es
);
}
/**
* @ingroup red_functions
* @brief Minimum and maximum among the elements of an array or expression.
*
* Returns an \ref xreducer for the minimum and maximum of an expression's elements.
* @param e an \ref xexpression
* @param es evaluation strategy to use (lazy (default), or immediate)
* @return an \ref xexpression of type ``std::array<value_type, 2>``, whose first
* and second element represent the minimum and maximum respectively
*/
template <class E, class EVS = DEFAULT_STRATEGY_REDUCERS, XTL_REQUIRES(is_reducer_options<EVS>)>
inline auto minmax(E&& e, EVS es = EVS())
{
using std::max;
using std::min;
using value_type = typename std::decay_t<E>::value_type;
using result_type = std::array<value_type, 2>;
using init_value_fct = xt::const_value<result_type>;
auto reduce_func = [](auto r, const auto& v)
{
r[0] = (min) (r[0], v);
r[1] = (max) (r[1], v);
return r;
};
auto init_func = init_value_fct(
result_type{std::numeric_limits<value_type>::max(), std::numeric_limits<value_type>::lowest()}
);
auto merge_func = [](auto r, const auto& s)
{
r[0] = (min) (r[0], s[0]);
r[1] = (max) (r[1], s[1]);
return r;
};
return xt::reduce(
make_xreducer_functor(std::move(reduce_func), std::move(init_func), std::move(merge_func)),
std::forward<E>(e),
arange(e.dimension()),
es
);
}
/**
* @defgroup acc_functions accumulating functions
*/
/**
* @ingroup acc_functions
* @brief Cumulative sum.
*
* Returns the accumulated sum for the elements over given
* \em axis (or flattened).
* @param e an \ref xexpression
* @param axis the axes along which the cumulative sum is computed (optional)
* @tparam T the value type used for internal computation. The default is
* `E::value_type`. `T`is also used for determining the value type of the result,
* which is the type of `T() + E::value_type()`.
* You can pass `big_promote_value_type_t<E>` to avoid overflow in computation.
* @return an \ref xarray<T>
*/
template <class T = void, class E>
inline auto cumsum(E&& e, std::ptrdiff_t axis)
{
using init_value_type = std::conditional_t<std::is_same<T, void>::value, typename std::decay_t<E>::value_type, T>;
return accumulate(
make_xaccumulator_functor(detail::plus(), detail::accumulator_identity<init_value_type>()),
std::forward<E>(e),
axis
);
}
template <class T = void, class E>
inline auto cumsum(E&& e)
{
using init_value_type = std::conditional_t<std::is_same<T, void>::value, typename std::decay_t<E>::value_type, T>;
return accumulate(
make_xaccumulator_functor(detail::plus(), detail::accumulator_identity<init_value_type>()),
std::forward<E>(e)
);
}
/**
* @ingroup acc_functions
* @brief Cumulative product.
*
* Returns the accumulated product for the elements over given
* \em axis (or flattened).
* @param e an \ref xexpression
* @param axis the axes along which the cumulative product is computed (optional)
* @tparam T the value type used for internal computation. The default is
* `E::value_type`. `T`is also used for determining the value type of the result,
* which is the type of `T() * E::value_type()`.
* You can pass `big_promote_value_type_t<E>` to avoid overflow in computation.
* @return an \ref xarray<T>
*/
template <class T = void, class E>
inline auto cumprod(E&& e, std::ptrdiff_t axis)
{
using init_value_type = std::conditional_t<std::is_same<T, void>::value, typename std::decay_t<E>::value_type, T>;
return accumulate(
make_xaccumulator_functor(detail::multiplies(), detail::accumulator_identity<init_value_type>()),
std::forward<E>(e),
axis
);
}
template <class T = void, class E>
inline auto cumprod(E&& e)
{
using init_value_type = std::conditional_t<std::is_same<T, void>::value, typename std::decay_t<E>::value_type, T>;
return accumulate(
make_xaccumulator_functor(detail::multiplies(), detail::accumulator_identity<init_value_type>()),
std::forward<E>(e)
);
}
/*****************
* nan functions *
*****************/
namespace detail
{
struct nan_to_num_functor
{
template <class A>
inline auto operator()(const A& a) const
{
if (math::isnan(a))
{
return A(0);
}
if (math::isinf(a))
{
if (a < 0)
{
return std::numeric_limits<A>::lowest();
}
else
{
return (std::numeric_limits<A>::max)();
}
}
return a;
}
};
struct nan_min
{
template <class T, class U>
constexpr auto operator()(const T lhs, const U rhs) const
{
// Clunky expression for working with GCC 4.9
return math::isnan(lhs)
? rhs
: (math::isnan(rhs) ? lhs
: std::common_type_t<T, U>(
detail::make_xfunction<math::minimum<void>>(lhs, rhs)
));
}
};
struct nan_max
{
template <class T, class U>
constexpr auto operator()(const T lhs, const U rhs) const
{
// Clunky expression for working with GCC 4.9
return math::isnan(lhs)
? rhs
: (math::isnan(rhs) ? lhs
: std::common_type_t<T, U>(
detail::make_xfunction<math::maximum<void>>(lhs, rhs)
));
}
};
struct nan_plus
{
template <class T, class U>
constexpr auto operator()(const T lhs, const U rhs) const
{
return !math::isnan(rhs) ? lhs + rhs : lhs;
}
};
struct nan_multiplies
{
template <class T, class U>
constexpr auto operator()(const T lhs, const U rhs) const
{
return !math::isnan(rhs) ? lhs * rhs : lhs;
}
};
template <class T, int V>
struct nan_init
{
using value_type = T;
using result_type = T;
constexpr result_type operator()(const value_type lhs) const
{
return math::isnan(lhs) ? result_type(V) : lhs;
}
};
}
/**
* @defgroup nan_functions nan functions
*/
/**
* @ingroup nan_functions
* @brief Convert nan or +/- inf to numbers
*
* This functions converts NaN to 0, and +inf to the highest, -inf to the lowest
* floating point value of the same type.
*
* @param e input \ref xexpression
* @return an \ref xexpression
*/
template <class E>
inline auto nan_to_num(E&& e)
{
return detail::make_xfunction<detail::nan_to_num_functor>(std::forward<E>(e));
}
/**
* @ingroup nan_functions
* @brief Minimum element over given axes, ignoring NaNs.
*
* Returns an \ref xreducer for the minimum of elements over given
* @p axes, ignoring NaNs.
* @warning Casting the result to an integer type can cause undefined behavior.
* @param e an \ref xexpression
* @param axes the axes along which the minimum is found (optional)
* @param es evaluation strategy of the reducer (optional)
* @tparam T the result type. The default is `E::value_type`.
* @return an \ref xreducer
*/
XTENSOR_REDUCER_FUNCTION(nanmin, detail::nan_min, typename std::decay_t<E>::value_type, std::nan("0"))
/**
* @ingroup nan_functions
* @brief Maximum element along given axes, ignoring NaNs.
*
* Returns an \ref xreducer for the sum of elements over given
* @p axes, ignoring NaN.
* @warning Casting the result to an integer type can cause undefined behavior.
* @param e an \ref xexpression
* @param axes the axes along which the sum is performed (optional)
* @param es evaluation strategy of the reducer (optional)
* @tparam T the result type. The default is `E::value_type`.
* @return an \ref xreducer
*/
XTENSOR_REDUCER_FUNCTION(nanmax, detail::nan_max, typename std::decay_t<E>::value_type, std::nan("0"))
/**
* @ingroup nan_functions
* @brief Sum of elements over given axes, replacing NaN with 0.
*
* Returns an \ref xreducer for the sum of elements over given
* @p axes, ignoring NaN.
* @param e an \ref xexpression
* @param axes the axes along which the sum is performed (optional)
* @param es evaluation strategy of the reducer (optional)
* @tparam T the value type used for internal computation. The default is
* `E::value_type`. `T` is also used for determining the value type
* of the result, which is the type of `T() + E::value_type()`.
* You can pass `big_promote_value_type_t<E>` to avoid overflow in computation.
* @return an \ref xreducer
*/
XTENSOR_REDUCER_FUNCTION(nansum, detail::nan_plus, typename std::decay_t<E>::value_type, 0)
/**
* @ingroup nan_functions
* @brief Product of elements over given axes, replacing NaN with 1.
*
* Returns an \ref xreducer for the sum of elements over given
* @p axes, replacing nan with 1.
* @param e an \ref xexpression
* @param axes the axes along which the sum is performed (optional)
* @param es evaluation strategy of the reducer (optional)
* @tparam T the value type used for internal computation. The default is
* `E::value_type`. `T` is also used for determining the value type
* of the result, which is the type of `T() * E::value_type()`.
* You can pass `big_promote_value_type_t<E>` to avoid overflow in computation.
* @return an \ref xreducer
*/
XTENSOR_REDUCER_FUNCTION(nanprod, detail::nan_multiplies, typename std::decay_t<E>::value_type, 1)
#define COUNT_NON_ZEROS_CONTENT \
using value_type = typename std::decay_t<E>::value_type; \
using result_type = xt::detail::xreducer_size_type_t<value_type>; \
using init_value_fct = xt::const_value<result_type>; \
\
auto init_fct = init_value_fct(0); \
\
auto reduce_fct = [](const auto& lhs, const auto& rhs) \
{ \
using value_t = xt::detail::xreducer_temporary_type_t<std::decay_t<decltype(rhs)>>; \
using result_t = std::decay_t<decltype(lhs)>; \
\
return (rhs != value_t(0)) ? lhs + result_t(1) : lhs; \
}; \
auto merge_func = detail::plus();
template <class E, class EVS = DEFAULT_STRATEGY_REDUCERS, XTL_REQUIRES(is_reducer_options<EVS>)>
inline auto count_nonzero(E&& e, EVS es = EVS())
{
COUNT_NON_ZEROS_CONTENT;
return xt::reduce(
make_xreducer_functor(std::move(reduce_fct), std::move(init_fct), std::move(merge_func)),
std::forward<E>(e),
es
);
}
template <
class E,
class X,
class EVS = DEFAULT_STRATEGY_REDUCERS,
XTL_REQUIRES(xtl::negation<is_reducer_options<X>>, xtl::negation<xtl::is_integral<X>>)>
inline auto count_nonzero(E&& e, X&& axes, EVS es = EVS())
{
COUNT_NON_ZEROS_CONTENT;
return xt::reduce(
make_xreducer_functor(std::move(reduce_fct), std::move(init_fct), std::move(merge_func)),
std::forward<E>(e),
std::forward<X>(axes),
es
);
}
template <
class E,
class X,
class EVS = DEFAULT_STRATEGY_REDUCERS,
XTL_REQUIRES(xtl::negation<is_reducer_options<X>>, xtl::is_integral<X>)>
inline auto count_nonzero(E&& e, X axis, EVS es = EVS())
{
return count_nonzero(std::forward<E>(e), {axis}, es);
}
template <class E, class I, std::size_t N, class EVS = DEFAULT_STRATEGY_REDUCERS>
inline auto count_nonzero(E&& e, const I (&axes)[N], EVS es = EVS())
{
COUNT_NON_ZEROS_CONTENT;
return xt::reduce(
make_xreducer_functor(std::move(reduce_fct), std::move(init_fct), std::move(merge_func)),
std::forward<E>(e),
axes,
es
);
}
#undef COUNT_NON_ZEROS_CONTENT
template <class E, class EVS = DEFAULT_STRATEGY_REDUCERS, XTL_REQUIRES(is_reducer_options<EVS>)>
inline auto count_nonnan(E&& e, EVS es = EVS())
{
return xt::count_nonzero(!xt::isnan(std::forward<E>(e)), es);
}
template <
class E,
class X,
class EVS = DEFAULT_STRATEGY_REDUCERS,
XTL_REQUIRES(xtl::negation<is_reducer_options<X>>, xtl::negation<xtl::is_integral<X>>)>
inline auto count_nonnan(E&& e, X&& axes, EVS es = EVS())
{
return xt::count_nonzero(!xt::isnan(std::forward<E>(e)), std::forward<X>(axes), es);
}
template <
class E,
class X,
class EVS = DEFAULT_STRATEGY_REDUCERS,
XTL_REQUIRES(xtl::negation<is_reducer_options<X>>, xtl::is_integral<X>)>
inline auto count_nonnan(E&& e, X&& axes, EVS es = EVS())
{
return xt::count_nonzero(!xt::isnan(std::forward<E>(e)), {axes}, es);
}
template <class E, class I, std::size_t N, class EVS = DEFAULT_STRATEGY_REDUCERS>
inline auto count_nonnan(E&& e, const I (&axes)[N], EVS es = EVS())
{
return xt::count_nonzero(!xt::isnan(std::forward<E>(e)), axes, es);
}
/**
* @ingroup nan_functions
* @brief Cumulative sum, replacing nan with 0.
*
* Returns an xaccumulator for the sum of elements over given
* \em axis, replacing nan with 0.
* @param e an \ref xexpression
* @param axis the axis along which the elements are accumulated (optional)
* @tparam T the value type used for internal computation. The default is
* `E::value_type`. `T` is also used for determining the value type
* of the result, which is the type of `T() + E::value_type()`.
* You can pass `big_promote_value_type_t<E>` to avoid overflow in computation.
* @return an xaccumulator
*/
template <class T = void, class E>
inline auto nancumsum(E&& e, std::ptrdiff_t axis)
{
using init_value_type = std::conditional_t<std::is_same<T, void>::value, typename std::decay_t<E>::value_type, T>;
return accumulate(
make_xaccumulator_functor(detail::nan_plus(), detail::nan_init<init_value_type, 0>()),
std::forward<E>(e),
axis
);
}
template <class T = void, class E>
inline auto nancumsum(E&& e)
{
using init_value_type = std::conditional_t<std::is_same<T, void>::value, typename std::decay_t<E>::value_type, T>;
return accumulate(
make_xaccumulator_functor(detail::nan_plus(), detail::nan_init<init_value_type, 0>()),
std::forward<E>(e)
);
}
/**
* @ingroup nan_functions
* @brief Cumulative product, replacing nan with 1.
*
* Returns an xaccumulator for the product of elements over given
* \em axis, replacing nan with 1.
* @param e an \ref xexpression
* @param axis the axis along which the elements are accumulated (optional)
* @tparam T the value type used for internal computation. The default is
* `E::value_type`. `T` is also used for determining the value type
* of the result, which is the type of `T() * E::value_type()`.
* You can pass `big_promote_value_type_t<E>` to avoid overflow in computation.
* @return an xaccumulator
*/
template <class T = void, class E>
inline auto nancumprod(E&& e, std::ptrdiff_t axis)
{
using init_value_type = std::conditional_t<std::is_same<T, void>::value, typename std::decay_t<E>::value_type, T>;
return accumulate(
make_xaccumulator_functor(detail::nan_multiplies(), detail::nan_init<init_value_type, 1>()),
std::forward<E>(e),
axis
);
}
template <class T = void, class E>
inline auto nancumprod(E&& e)
{
using init_value_type = std::conditional_t<std::is_same<T, void>::value, typename std::decay_t<E>::value_type, T>;
return accumulate(
make_xaccumulator_functor(detail::nan_multiplies(), detail::nan_init<init_value_type, 1>()),
std::forward<E>(e)
);
}
namespace detail
{
template <class T>
struct diff_impl
{
template <class Arg>
inline void operator()(
Arg& ad,
const std::size_t& n,
xstrided_slice_vector& slice1,
xstrided_slice_vector& slice2,
std::size_t saxis
)
{
for (std::size_t i = 0; i < n; ++i)
{
slice2[saxis] = range(xnone(), ad.shape()[saxis] - 1);
ad = strided_view(ad, slice1) - strided_view(ad, slice2);
}
}
};
template <>
struct diff_impl<bool>
{
template <class Arg>
inline void operator()(
Arg& ad,
const std::size_t& n,
xstrided_slice_vector& slice1,
xstrided_slice_vector& slice2,
std::size_t saxis
)
{
for (std::size_t i = 0; i < n; ++i)
{
slice2[saxis] = range(xnone(), ad.shape()[saxis] - 1);
ad = not_equal(strided_view(ad, slice1), strided_view(ad, slice2));
}
}
};
}
/**
* @ingroup nan_functions
* @brief Mean of elements over given axes, excluding NaNs.
*
* Returns an \ref xreducer for the mean of elements over given
* \em axes, excluding NaNs.
* This is not the same as counting NaNs as zero, since excluding NaNs changes the number
* of elements considered in the statistic.
* @param e an \ref xexpression
* @param axes the axes along which the mean is computed (optional)
* @param es the evaluation strategy (optional)
* @tparam T the result type. The default is `E::value_type`.
* You can pass `big_promote_value_type_t<E>` to avoid overflow in computation.
* @return an \ref xexpression
*/
template <
class T = void,
class E,
class X,
class EVS = DEFAULT_STRATEGY_REDUCERS,
XTL_REQUIRES(xtl::negation<is_reducer_options<X>>)>
inline auto nanmean(E&& e, X&& axes, EVS es = EVS())
{
decltype(auto) sc = detail::shared_forward<E>(e);
// note: forcing copy of first axes argument -- is there a better solution?
auto axes_copy = axes;
using value_type = typename std::conditional_t<std::is_same<T, void>::value, double, T>;
using sum_type = typename std::conditional_t<
std::is_same<T, void>::value,
typename std::common_type_t<typename std::decay_t<E>::value_type, value_type>,
T>;
// sum cannot always be a double. It could be a complex number which cannot operate on
// std::plus<double>.
return nansum<sum_type>(sc, std::forward<X>(axes), es)
/ xt::cast<value_type>(count_nonnan(sc, std::move(axes_copy), es));
}
template <class T = void, class E, class EVS = DEFAULT_STRATEGY_REDUCERS, XTL_REQUIRES(is_reducer_options<EVS>)>
inline auto nanmean(E&& e, EVS es = EVS())
{
decltype(auto) sc = detail::shared_forward<E>(e);
using value_type = typename std::conditional_t<std::is_same<T, void>::value, double, T>;
using sum_type = typename std::conditional_t<
std::is_same<T, void>::value,
typename std::common_type_t<typename std::decay_t<E>::value_type, value_type>,
T>;
return nansum<sum_type>(sc, es) / xt::cast<value_type>(count_nonnan(sc, es));
}
template <class T = void, class E, class I, std::size_t N, class EVS = DEFAULT_STRATEGY_REDUCERS>
inline auto nanmean(E&& e, const I (&axes)[N], EVS es = EVS())
{
return nanmean<T>(
std::forward<E>(e),
xtl::forward_sequence<std::array<std::size_t, N>, decltype(axes)>(axes),
es
);
}
template <class T = void, class E, class EVS = DEFAULT_STRATEGY_REDUCERS, XTL_REQUIRES(is_reducer_options<EVS>)>
inline auto nanvar(E&& e, EVS es = EVS())
{
decltype(auto) sc = detail::shared_forward<E>(e);
return nanmean<T>(square(sc - nanmean<T>(sc)), es);
}
template <class T = void, class E, class EVS = DEFAULT_STRATEGY_REDUCERS, XTL_REQUIRES(is_reducer_options<EVS>)>
inline auto nanstd(E&& e, EVS es = EVS())
{
return sqrt(nanvar<T>(std::forward<E>(e), es));
}
/**
* @ingroup nan_functions
* @brief Compute the variance along the specified axes, excluding NaNs
*
* Returns the variance of the array elements, a measure of the spread of a
* distribution. The variance is computed for the flattened array by default,
* otherwise over the specified axes.
* Excluding NaNs changes the number of elements considered in the statistic.
*
* Note: this function is not yet specialized for complex numbers.
*
* @param e an \ref xexpression
* @param axes the axes along which the variance is computed (optional)
* @param es evaluation strategy to use (lazy (default), or immediate)
* @tparam T the result type. The default is `E::value_type`.
* You can pass `big_promote_value_type_t<E>` to avoid overflow in computation.
* @return an \ref xexpression
*
* @sa nanstd, nanmean
*/
template <
class T = void,
class E,
class X,
class EVS = DEFAULT_STRATEGY_REDUCERS,
XTL_REQUIRES(xtl::negation<is_reducer_options<X>>)>
inline auto nanvar(E&& e, X&& axes, EVS es = EVS())
{
decltype(auto) sc = detail::shared_forward<E>(e);
// note: forcing copy of first axes argument -- is there a better solution?
auto axes_copy = axes;
using result_type = typename std::conditional_t<std::is_same<T, void>::value, double, T>;
auto inner_mean = nanmean<result_type>(sc, std::move(axes_copy));
// fake keep_dims = 1
// Since the inner_shape might have a reference semantic (e.g. xbuffer_adaptor in bindings)
// We need to map it to another type before modifying it.
// We pragmatically abuse `get_strides_t`
using tmp_shape_t = get_strides_t<typename std::decay_t<E>::shape_type>;
tmp_shape_t keep_dim_shape = xtl::forward_sequence<tmp_shape_t, decltype(e.shape())>(e.shape());
for (const auto& el : axes)
{
keep_dim_shape[el] = 1;
}
auto mrv = reshape_view<XTENSOR_DEFAULT_LAYOUT>(std::move(inner_mean), std::move(keep_dim_shape));
return nanmean<result_type>(square(cast<result_type>(sc) - std::move(mrv)), std::forward<X>(axes), es);
}
/**
* @ingroup nan_functions
* @brief Compute the standard deviation along the specified axis, excluding nans.
*
* Returns the standard deviation, a measure of the spread of a distribution,
* of the array elements. The standard deviation is computed for the flattened
* array by default, otherwise over the specified axis.
* Excluding NaNs changes the number of elements considered in the statistic.
*
* Note: this function is not yet specialized for complex numbers.
*
* @param e an \ref xexpression
* @param axes the axes along which the standard deviation is computed (optional)
* @param es evaluation strategy to use (lazy (default), or immediate)
* @tparam T the result type. The default is `E::value_type`.
* You can pass `big_promote_value_type_t<E>` to avoid overflow in computation.
* @return an \ref xexpression
*
* @sa nanvar, nanmean
*/
template <
class T = void,
class E,
class X,
class EVS = DEFAULT_STRATEGY_REDUCERS,
XTL_REQUIRES(xtl::negation<is_reducer_options<X>>)>
inline auto nanstd(E&& e, X&& axes, EVS es = EVS())
{
return sqrt(nanvar<T>(std::forward<E>(e), std::forward<X>(axes), es));
}
template <class T = void, class E, class A, std::size_t N, class EVS = DEFAULT_STRATEGY_REDUCERS>
inline auto nanstd(E&& e, const A (&axes)[N], EVS es = EVS())
{
return nanstd<T>(
std::forward<E>(e),
xtl::forward_sequence<std::array<std::size_t, N>, decltype(axes)>(axes),
es
);
}
template <class T = void, class E, class A, std::size_t N, class EVS = DEFAULT_STRATEGY_REDUCERS>
inline auto nanvar(E&& e, const A (&axes)[N], EVS es = EVS())
{
return nanvar<T>(
std::forward<E>(e),
xtl::forward_sequence<std::array<std::size_t, N>, decltype(axes)>(axes),
es
);
}
/**
* @ingroup red_functions
* @brief Calculate the n-th discrete difference along the given axis.
*
* Calculate the n-th discrete difference along the given axis. This function is not lazy (might change in
* the future).
* @param a an \ref xexpression
* @param n The number of times values are differenced. If zero, the input is returned as-is. (optional)
* @param axis The axis along which the difference is taken, default is the last axis.
* @return an xarray
*/
template <class T>
auto diff(const xexpression<T>& a, std::size_t n = 1, std::ptrdiff_t axis = -1)
{
typename std::decay_t<T>::temporary_type ad = a.derived_cast();
std::size_t saxis = normalize_axis(ad.dimension(), axis);
if (n <= ad.size())
{
if (n != std::size_t(0))
{
xstrided_slice_vector slice1(ad.dimension(), all());
xstrided_slice_vector slice2(ad.dimension(), all());
slice1[saxis] = range(1, xnone());
detail::diff_impl<typename T::value_type> impl;
impl(ad, n, slice1, slice2, saxis);
}
}
else
{
auto shape = ad.shape();
shape[saxis] = std::size_t(0);
ad.resize(shape);
}
return ad;
}
/**
* @ingroup red_functions
* @brief Integrate along the given axis using the composite trapezoidal rule.
*
* Returns definite integral as approximated by trapezoidal rule. This function is not lazy (might change
* in the future).
* @param y an \ref xexpression
* @param dx the spacing between sample points (optional)
* @param axis the axis along which to integrate.
* @return an xarray
*/
template <class T>
auto trapz(const xexpression<T>& y, double dx = 1.0, std::ptrdiff_t axis = -1)
{
auto& yd = y.derived_cast();
std::size_t saxis = normalize_axis(yd.dimension(), axis);
xstrided_slice_vector slice1(yd.dimension(), all());
xstrided_slice_vector slice2(yd.dimension(), all());
slice1[saxis] = range(1, xnone());
slice2[saxis] = range(xnone(), yd.shape()[saxis] - 1);
auto trap = dx * (strided_view(yd, slice1) + strided_view(yd, slice2)) * 0.5;
return eval(sum(trap, {saxis}));
}
/**
* @ingroup red_functions
* @brief Integrate along the given axis using the composite trapezoidal rule.
*
* Returns definite integral as approximated by trapezoidal rule. This function is not lazy (might change
* in the future).
* @param y an \ref xexpression
* @param x an \ref xexpression representing the sample points corresponding to the y values.
* @param axis the axis along which to integrate.
* @return an xarray
*/
template <class T, class E>
auto trapz(const xexpression<T>& y, const xexpression<E>& x, std::ptrdiff_t axis = -1)
{
auto& yd = y.derived_cast();
auto& xd = x.derived_cast();
decltype(diff(x)) dx;
std::size_t saxis = normalize_axis(yd.dimension(), axis);
if (xd.dimension() == 1)
{
dx = diff(x);
typename std::decay_t<decltype(yd)>::shape_type shape;
resize_container(shape, yd.dimension());
std::fill(shape.begin(), shape.end(), 1);
shape[saxis] = dx.shape()[0];
dx.reshape(shape);
}
else
{
dx = diff(x, 1, axis);
}
xstrided_slice_vector slice1(yd.dimension(), all());
xstrided_slice_vector slice2(yd.dimension(), all());
slice1[saxis] = range(1, xnone());
slice2[saxis] = range(xnone(), yd.shape()[saxis] - 1);
auto trap = dx * (strided_view(yd, slice1) + strided_view(yd, slice2)) * 0.5;
return eval(sum(trap, {saxis}));
}
/**
* @ingroup basic_functions
* @brief Returns the one-dimensional piecewise linear interpolant to a function with given discrete data
* points (xp, fp), evaluated at x.
*
* @param x The x-coordinates at which to evaluate the interpolated values (sorted).
* @param xp The x-coordinates of the data points (sorted).
* @param fp The y-coordinates of the data points, same length as xp.
* @param left Value to return for x < xp[0].
* @param right Value to return for x > xp[-1]
* @return an one-dimensional xarray, same length as x.
*/
template <class E1, class E2, class E3, typename T>
inline auto interp(const E1& x, const E2& xp, const E3& fp, T left, T right)
{
using size_type = common_size_type_t<E1, E2, E3>;
using value_type = typename E3::value_type;
// basic checks
XTENSOR_ASSERT(xp.dimension() == 1);
XTENSOR_ASSERT(std::is_sorted(x.cbegin(), x.cend()));
XTENSOR_ASSERT(std::is_sorted(xp.cbegin(), xp.cend()));
// allocate output
auto f = xtensor<value_type, 1>::from_shape(x.shape());
// counter in "x": from left
size_type i = 0;
// fill f[i] for x[i] <= xp[0]
for (; i < x.size(); ++i)
{
if (x[i] > xp[0])
{
break;
}
f[i] = static_cast<value_type>(left);
}
// counter in "x": from right
// (index counts one right, to terminate the reverse loop, without risking being negative)
size_type imax = x.size();
// fill f[i] for x[-1] >= xp[-1]
for (; imax > 0; --imax)
{
if (x[imax - 1] < xp[xp.size() - 1])
{
break;
}
f[imax - 1] = static_cast<value_type>(right);
}
// catch edge case: all entries are "right"
if (imax == 0)
{
return f;
}
// set "imax" as actual index
// (counted one right, see above)
--imax;
// counter in "xp"
size_type ip = 1;
// fill f[i] for the interior
for (; i <= imax; ++i)
{
// - search next value in "xp"
while (x[i] > xp[ip])
{
++ip;
}
// - distances as doubles
double dfp = static_cast<double>(fp[ip] - fp[ip - 1]);
double dxp = static_cast<double>(xp[ip] - xp[ip - 1]);
double dx = static_cast<double>(x[i] - xp[ip - 1]);
// - interpolate
f[i] = fp[ip - 1] + static_cast<value_type>(dfp / dxp * dx);
}
return f;
}
namespace detail
{
template <class E1, class E2>
auto calculate_discontinuity(E1&& discontinuity, E2&&)
{
return discontinuity;
}
template <class E2>
auto calculate_discontinuity(xt::placeholders::xtuph, E2&& period)
{
return 0.5 * period;
}
template <class E1, class E2>
auto
calculate_interval(E2&& period, typename std::enable_if<std::is_integral<E1>::value, E1>::type* = 0)
{
auto interval_high = 0.5 * period;
uint64_t remainder = static_cast<uint64_t>(period) % 2;
auto boundary_ambiguous = (remainder == 0);
return std::make_tuple(interval_high, boundary_ambiguous);
}
template <class E1, class E2>
auto
calculate_interval(E2&& period, typename std::enable_if<std::is_floating_point<E1>::value, E1>::type* = 0)
{
auto interval_high = 0.5 * period;
auto boundary_ambiguous = true;
return std::make_tuple(interval_high, boundary_ambiguous);
}
}
/**
* @ingroup basic_functions
* @brief Unwrap by taking the complement of large deltas with respect to the period
* @details https://numpy.org/doc/stable/reference/generated/numpy.unwrap.html
* @param p Input array.
* @param discontinuity
* Maximum discontinuity between values, default is `period / 2`.
* Values below `period / 2` are treated as if they were `period / 2`.
* To have an effect different from the default, use `discontinuity > period / 2`.
* @param axis Axis along which unwrap will operate, default: the last axis.
* @param period Size of the range over which the input wraps. Default: \f$ 2 \pi \f$.
*/
template <class E1, class E2 = xt::placeholders::xtuph, class E3 = double>
inline auto unwrap(
E1&& p,
E2 discontinuity = xnone(),
std::ptrdiff_t axis = -1,
E3 period = 2.0 * xt::numeric_constants<double>::PI
)
{
auto discont = detail::calculate_discontinuity(discontinuity, period);
using value_type = typename std::decay_t<E1>::value_type;
std::size_t saxis = normalize_axis(p.dimension(), axis);
auto dd = diff(p, 1, axis);
xstrided_slice_vector slice(p.dimension(), all());
slice[saxis] = range(1, xnone());
auto interval_tuple = detail::calculate_interval<value_type>(period);
auto interval_high = std::get<0>(interval_tuple);
auto boundary_ambiguous = std::get<1>(interval_tuple);
auto interval_low = -interval_high;
auto ddmod = xt::eval(xt::fmod(xt::fmod(dd - interval_low, period) + period, period) + interval_low);
if (boundary_ambiguous)
{
// for `mask = (abs(dd) == period/2)`, the above line made
//`ddmod[mask] == -period/2`. correct these such that
//`ddmod[mask] == sign(dd[mask])*period/2`.
auto boolmap = xt::equal(ddmod, interval_low) && (xt::greater(dd, 0.0));
ddmod = xt::where(boolmap, interval_high, ddmod);
}
auto ph_correct = xt::eval(ddmod - dd);
ph_correct = xt::where(xt::abs(dd) < discont, 0.0, ph_correct);
E1 up(p);
strided_view(up, slice) = strided_view(p, slice)
+ xt::cumsum(ph_correct, static_cast<std::ptrdiff_t>(saxis));
return up;
}
/**
* @ingroup basic_functions
* @brief Returns the one-dimensional piecewise linear interpolant to a function with given discrete data
* points (xp, fp), evaluated at x.
*
* @param x The x-coordinates at which to evaluate the interpolated values (sorted).
* @param xp The x-coordinates of the data points (sorted).
* @param fp The y-coordinates of the data points, same length as xp.
* @return an one-dimensional xarray, same length as x.
*/
template <class E1, class E2, class E3>
inline auto interp(const E1& x, const E2& xp, const E3& fp)
{
return interp(x, xp, fp, fp[0], fp[fp.size() - 1]);
}
/**
* @brief Returns the covariance matrix
*
* @param x one or two dimensional array
* @param y optional one-dimensional array to build covariance to x
*/
template <class E1>
inline auto cov(const E1& x, const E1& y = E1())
{
using value_type = typename E1::value_type;
if (y.dimension() == 0)
{
auto s = x.shape();
using size_type = std::decay_t<decltype(s[0])>;
if (x.dimension() == 1)
{
auto covar = eval(zeros<value_type>({1, 1}));
auto x_norm = x - eval(mean(x));
covar(0, 0) = std::inner_product(x_norm.begin(), x_norm.end(), x_norm.begin(), 0.0)
/ value_type(s[0] - 1);
return covar;
}
XTENSOR_ASSERT(x.dimension() == 2);
auto covar = eval(zeros<value_type>({s[0], s[0]}));
auto m = eval(mean(x, {1}));
m.reshape({m.shape()[0], 1});
auto x_norm = x - m;
for (size_type i = 0; i < s[0]; i++)
{
auto xi = strided_view(x_norm, {range(i, i + 1), all()});
for (size_type j = i; j < s[0]; j++)
{
auto xj = strided_view(x_norm, {range(j, j + 1), all()});
covar(j, i) = std::inner_product(xi.begin(), xi.end(), xj.begin(), 0.0)
/ value_type(s[1] - 1);
}
}
return eval(covar + transpose(covar) - diag(diagonal(covar)));
}
else
{
return cov(eval(stack(xtuple(x, y))));
}
}
/*
* convolution mode placeholders for selecting the algorithm
* used in computing a 1D convolution.
* Same as NumPy's mode parameter.
*/
namespace convolve_mode
{
struct valid
{
};
struct full
{
};
}
namespace detail
{
template <class E1, class E2>
inline auto convolve_impl(E1&& e1, E2&& e2, convolve_mode::valid)
{
using value_type = typename std::decay<E1>::type::value_type;
const std::size_t na = e1.size();
const std::size_t nv = e2.size();
const std::size_t n = na - nv + 1;
xt::xtensor<value_type, 1> out = xt::zeros<value_type>({n});
for (std::size_t i = 0; i < n; i++)
{
for (std::size_t j = 0; j < nv; j++)
{
out(i) += e1(j) * e2(j + i);
}
}
return out;
}
template <class E1, class E2>
inline auto convolve_impl(E1&& e1, E2&& e2, convolve_mode::full)
{
using value_type = typename std::decay<E1>::type::value_type;
const std::size_t na = e1.size();
const std::size_t nv = e2.size();
const std::size_t n = na + nv - 1;
xt::xtensor<value_type, 1> out = xt::zeros<value_type>({n});
for (std::size_t i = 0; i < n; i++)
{
const std::size_t jmn = (i >= nv - 1) ? i - (nv - 1) : 0;
const std::size_t jmx = (i < na - 1) ? i : na - 1;
for (std::size_t j = jmn; j <= jmx; ++j)
{
out(i) += e1(j) * e2(i - j);
}
}
return out;
}
}
/*
* @brief computes the 1D convolution between two 1D expressions
*
* @param a 1D expression
* @param v 1D expression
* @param mode placeholder Select algorithm #convolve_mode
*
* @detail the algorithm convolves a with v and will incur a copy overhead
* should v be longer than a.
*/
template <class E1, class E2, class E3>
inline auto convolve(E1&& a, E2&& v, E3 mode)
{
if (a.dimension() != 1 || v.dimension() != 1)
{
XTENSOR_THROW(std::runtime_error, "Invalid dimentions convolution arguments must be 1D expressions");
}
XTENSOR_ASSERT(a.size() > 0 && v.size() > 0);
// swap them so a is always the longest one
if (a.size() < v.size())
{
return detail::convolve_impl(std::forward<E2>(v), std::forward<E1>(a), mode);
}
else
{
return detail::convolve_impl(std::forward<E1>(a), std::forward<E2>(v), mode);
}
}
}
#endif
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