/usr/include/xtensor/xbuilder.hpp is in xtensor-dev 0.10.11-1.
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* Copyright (c) 2016, Johan Mabille, Sylvain Corlay and Wolf Vollprecht *
* *
* Distributed under the terms of the BSD 3-Clause License. *
* *
* The full license is in the file LICENSE, distributed with this software. *
****************************************************************************/
/**
* @brief standard mathematical functions for xexpressions
*/
#ifndef XBUILDER_HPP
#define XBUILDER_HPP
#include <array>
#include <cstddef>
#include <cmath>
#include <functional>
#include <utility>
#include <vector>
#include "xbroadcast.hpp"
#include "xfunction.hpp"
#include "xgenerator.hpp"
#ifdef X_OLD_CLANG
#include <initializer_list>
#endif
namespace xt
{
/********
* ones *
********/
/**
* Returns an \ref xexpression containing ones of the specified shape.
* @tparam shape the shape of the returned expression.
*/
template <class T, class S>
inline auto ones(S shape) noexcept
{
return broadcast(T(1), std::forward<S>(shape));
}
#ifdef X_OLD_CLANG
template <class T, class I>
inline auto ones(std::initializer_list<I> shape) noexcept
{
return broadcast(T(1), shape);
}
#else
template <class T, class I, std::size_t L>
inline auto ones(const I (&shape)[L]) noexcept
{
return broadcast(T(1), shape);
}
#endif
/*********
* zeros *
*********/
/**
* Returns an \ref xexpression containing zeros of the specified shape.
* @tparam shape the shape of the returned expression.
*/
template <class T, class S>
inline auto zeros(S shape) noexcept
{
return broadcast(T(0), std::forward<S>(shape));
}
#ifdef X_OLD_CLANG
template <class T, class I>
inline auto zeros(std::initializer_list<I> shape) noexcept
{
return broadcast(T(0), shape);
}
#else
template <class T, class I, std::size_t L>
inline auto zeros(const I (&shape)[L]) noexcept
{
return broadcast(T(0), shape);
}
#endif
namespace detail
{
template <class T>
class arange_impl
{
public:
using value_type = T;
arange_impl(T start, T stop, T step)
: m_start(start), m_stop(stop), m_step(step)
{
}
template <class... Args>
inline T operator()(Args... args) const
{
return access_impl(args...);
}
template <class It>
inline T element(It first, It) const
{
return m_start + m_step * T(*first);
}
private:
value_type m_start;
value_type m_stop;
value_type m_step;
template <class T1, class... Args>
inline T access_impl(T1 t, Args...) const
{
return m_start + m_step * T(t);
}
inline T access_impl() const
{
return m_start;
}
};
template <class F>
class fn_impl
{
public:
using value_type = typename F::value_type;
using size_type = std::size_t;
fn_impl(F&& f)
: m_ft(f)
{
}
inline value_type operator()() const
{
size_type idx[1] = {0ul};
return access_impl(std::begin(idx), std::end(idx));
}
template <class... Args>
inline value_type operator()(Args... args) const
{
size_type idx[sizeof...(Args)] = {static_cast<size_type>(args)...};
return access_impl(std::begin(idx), std::end(idx));
}
template <class It>
inline value_type element(It first, It last) const
{
return access_impl(first, last);
}
private:
F m_ft;
template <class It>
inline value_type access_impl(const It& begin, const It& end) const
{
return m_ft(begin, end);
}
};
template <class T>
class eye_fn
{
public:
using value_type = T;
eye_fn(int k)
: m_k(k)
{
}
template <class It>
inline T operator()(const It& /*begin*/, const It& end) const
{
return *(end - 1) == *(end - 2) + m_k ? T(1) : T(0);
}
private:
int m_k;
};
}
/**
* Generates an array with ones on the diagonal.
* @param shape shape of the resulting expression
* @param k index of the diagonal. 0 (default) refers to the main diagonal,
* a positive value refers to an upper diagonal, and a negative
* value to a lower diagonal.
* @tparam T value_type of xexpression
* @return xgenerator that generates the values on access
*/
template <class T = bool>
inline auto eye(const std::vector<std::size_t>& shape, int k = 0)
{
return detail::make_xgenerator(detail::fn_impl<detail::eye_fn<T>>(detail::eye_fn<T>(k)), shape);
}
/**
* Generates a (n x n) array with ones on the diagonal.
* @param n length of the diagonal.
* @param k index of the diagonal. 0 (default) refers to the main diagonal,
* a positive value refers to an upper diagonal, and a negative
* value to a lower diagonal.
* @tparam T value_type of xexpression
* @return xgenerator that generates the values on access
*/
template <class T = bool>
inline auto eye(std::size_t n, int k = 0)
{
return eye<T>({n, n}, k);
}
/**
* Generates numbers evenly spaced within given half-open interval [start, stop).
* @param start start of the interval
* @param stop stop of the interval
* @param step stepsize
* @tparam T value_type of xexpression
* @return xgenerator that generates the values on access
*/
template <class T>
inline auto arange(T start, T stop, T step = 1) noexcept
{
std::size_t shape = static_cast<std::size_t>(std::ceil((stop - start) / step));
return detail::make_xgenerator(detail::arange_impl<T>(start, stop, step), {shape});
}
/**
* Generate numbers evenly spaced within given half-open interval [0, stop)
* with a step size of 1.
* @param stop stop of the interval
* @tparam T value_type of xexpression
* @return xgenerator that generates the values on access
*/
template <class T>
inline auto arange(T stop) noexcept
{
return arange<T>(T(0), stop, T(1));
}
/**
* Generates @a num_samples evenly spaced numbers over given interval
* @param start start of interval
* @param stop stop of interval
* @param num_samples number of samples (defaults to 50)
* @param endpoint if true, include endpoint (defaults to true)
* @tparam T value_type of xexpression
* @return xgenerator that generates the values on access
*/
template <class T>
inline auto linspace(T start, T stop, std::size_t num_samples = 50, bool endpoint = true) noexcept
{
T step = (stop - start) / T(num_samples - (endpoint ? 1 : 0));
return detail::make_xgenerator(detail::arange_impl<T>(start, stop, step), {num_samples});
}
/**
* Generates @a num_samples numbers evenly spaced on a log scale over given interval
* @param start start of interval (pow(base, start) is the first value).
* @param stop stop of interval (pow(base, stop) is the final value, except if endpoint = false)
* @param num_samples number of samples (defaults to 50)
* @param base the base of the log space.
* @param endpoint if true, include endpoint (defaults to true)
* @tparam T value_type of xexpression
* @return xgenerator that generates the values on access
*/
template <class T>
inline auto logspace(T start, T stop, std::size_t num_samples, T base = 10, bool endpoint = true) noexcept
{
return pow(std::forward<T>(base), linspace(start, stop, num_samples, endpoint));
}
namespace detail
{
template <class... CT>
class concatenate_impl
{
public:
using size_type = std::size_t;
using value_type = std::common_type_t<typename std::decay_t<CT>::value_type...>;
inline concatenate_impl(std::tuple<CT...>&& t, size_type axis)
: m_t(t), m_axis(axis)
{
}
template <class... Args>
inline value_type operator()(Args... args) const
{
// TODO: avoid memory allocation
return access_impl(xindex({{static_cast<size_type>(args)...}}));
}
template <class It>
inline value_type element(It first, It last) const
{
// TODO: avoid memory allocation
return access_impl(xindex(first, last));
}
private:
inline value_type access_impl(xindex idx) const
{
auto match = [this, &idx](auto& arr)
{
if (idx[this->m_axis] >= arr.shape()[this->m_axis])
{
idx[this->m_axis] -= arr.shape()[this->m_axis];
return false;
}
return true;
};
auto get = [&idx](auto& arr)
{
return arr[idx];
};
size_type i = 0;
for (; i < sizeof...(CT); ++i)
{
if (apply<bool>(i, match, m_t))
{
break;
}
}
return apply<value_type>(i, get, m_t);
}
std::tuple<CT...> m_t;
size_type m_axis;
};
template <class... CT>
class stack_impl
{
public:
using size_type = std::size_t;
using value_type = std::common_type_t<typename std::decay_t<CT>::value_type...>;
inline stack_impl(std::tuple<CT...>&& t, size_type axis)
: m_t(t), m_axis(axis)
{
}
template <class... Args>
inline value_type operator()(Args... args) const
{
// TODO: avoid memory allocation
return access_impl(xindex({{static_cast<size_type>(args)...}}));
}
template <class It>
inline value_type element(It first, It last) const
{
// TODO: avoid memory allocation
return access_impl(xindex(first, last));
}
private:
inline value_type access_impl(xindex idx) const
{
auto get_item = [&idx](auto& arr)
{
return arr[idx];
};
size_type i = idx[m_axis];
idx.erase(idx.begin() + m_axis);
return apply<value_type>(i, get_item, m_t);
}
const std::tuple<CT...> m_t;
const size_type m_axis;
};
template <class CT>
class repeat_impl
{
public:
using xexpression_type = std::decay_t<CT>;
using size_type = typename xexpression_type::size_type;
using value_type = typename xexpression_type::value_type;
template <class CTA>
repeat_impl(CTA&& source, size_type axis)
: m_source(std::forward<CTA>(source)), m_axis(axis)
{
}
template <class... Args>
value_type operator()(Args... args) const
{
std::array<size_type, sizeof...(Args)> args_arr = {static_cast<size_type>(args)...};
return m_source(args_arr[m_axis]);
}
template <class It>
inline value_type element(It first, It) const
{
return m_source(*(first + m_axis));
}
private:
CT m_source;
size_type m_axis;
};
}
/**
* @brief Creates tuples from arguments for \ref concatenate and \ref stack.
* Very similar to std::make_tuple.
*/
template <class... Types>
inline auto xtuple(Types&&... args)
{
return std::tuple<const_closure_t<Types>...>(std::forward<Types>(args)...);
}
/**
* @brief Concatenates xexpressions along \em axis.
*
* @param t \ref xtuple of xexpressions to concatenate
* @param axis axis along which elements are concatenated
* @returns xgenerator evaluating to concatenated elements
*
* \code{.cpp}
* xt::xarray<double> a = {{1, 2, 3}};
* xt::xarray<double> b = {{2, 3, 4}};
* xt::xarray<double> c = xt::concatenate(xt::xtuple(a, b)); // => {{1, 2, 3},
* {2, 3, 4}}
* xt::xarray<double> d = xt::concatenate(xt::xtuple(a, b), 1); // => {{1, 2, 3, 2, 3, 4}}
* \endcode
*/
template <class... CT>
inline auto concatenate(std::tuple<CT...>&& t, std::size_t axis = 0)
{
using shape_type = promote_shape_t<typename std::decay_t<CT>::shape_type...>;
shape_type new_shape = forward_sequence<shape_type>(std::get<0>(t).shape());
auto shape_at_axis = [&axis](std::size_t prev, auto& arr) -> std::size_t {
return prev + arr.shape()[axis];
};
new_shape[axis] += accumulate(shape_at_axis, std::size_t(0), t) - new_shape[axis];
return detail::make_xgenerator(detail::concatenate_impl<CT...>(std::forward<std::tuple<CT...>>(t), axis), new_shape);
}
namespace detail
{
template <class T, std::size_t N>
inline std::array<T, N + 1> add_axis(std::array<T, N> arr, std::size_t axis, std::size_t value)
{
std::array<T, N + 1> temp;
std::copy(arr.begin(), arr.begin() + axis, temp.begin());
temp[axis] = value;
std::copy(arr.begin() + axis, arr.end(), temp.begin() + axis + 1);
return temp;
}
template <class T>
inline T add_axis(T arr, std::size_t axis, std::size_t value)
{
T temp(arr);
temp.insert(temp.begin() + axis, value);
return temp;
}
}
/**
* @brief Stack xexpressions along \em axis.
* Stacking always creates a new dimension along which elements are stacked.
*
* @param t \ref xtuple of xexpressions to concatenate
* @param axis axis along which elements are stacked
* @returns xgenerator evaluating to stacked elements
*
* \code{.cpp}
* xt::xarray<double> a = {1, 2, 3};
* xt::xarray<double> b = {5, 6, 7};
* xt::xarray<double> s = xt::stack(xt::xtuple(a, b)); // => {{1, 2, 3},
* {5, 6, 7}}
* xt::xarray<double> t = xt::stack(xt::xtuple(a, b), 1); // => {{1, 5},
* {2, 6},
* {3, 7}}
* \endcode
*/
template <class... CT>
inline auto stack(std::tuple<CT...>&& t, std::size_t axis = 0)
{
using shape_type = promote_shape_t<typename std::decay_t<CT>::shape_type...>;
auto new_shape = detail::add_axis(forward_sequence<shape_type>(std::get<0>(t).shape()), axis, sizeof...(CT));
return detail::make_xgenerator(detail::stack_impl<CT...>(std::forward<std::tuple<CT...>>(t), axis), new_shape);
}
namespace detail
{
template <std::size_t... I, class... E>
inline auto meshgrid_impl(std::index_sequence<I...>, E&&... e) noexcept
{
#if defined X_OLD_CLANG || defined _MSC_VER
const std::array<std::size_t, sizeof...(E)> shape { e.shape()[0]... };
return std::make_tuple(
detail::make_xgenerator(
detail::repeat_impl<xclosure_t<E>>(std::forward<E>(e), I),
shape
)...
);
#else
return std::make_tuple(
detail::make_xgenerator(
detail::repeat_impl<xclosure_t<E>>(std::forward<E>(e), I),
{ e.shape()[0]... }
)...
);
#endif
}
}
/**
* @brief Return coordinate tensors from coordinate vectors.
* Make N-D coordinate tensor expressions for vectorized evaluations of N-D scalar/vector
* fields over N-D grids, given one-dimensional coordinate arrays x1, x2,..., xn.
*
* @param e xexpressions to concatenate
* @returns tuple of xgenerator expressions.
*/
template <class... E>
inline auto meshgrid(E&&... e) noexcept
{
return detail::meshgrid_impl(std::make_index_sequence<sizeof...(E)>(), std::forward<E>(e)...);
}
namespace detail
{
template <class CT>
class diagonal_fn
{
public:
using xexpression_type = std::decay_t<CT>;
using value_type = typename xexpression_type::value_type;
template <class CTA>
diagonal_fn(CTA&& source, int offset, std::size_t axis_1, std::size_t axis_2)
: m_source(std::forward<CTA>(source)), m_offset(offset), m_axis_1(axis_1), m_axis_2(axis_2)
{
}
template <class It>
inline value_type operator()(It begin, It) const
{
xindex idx(m_source.shape().size());
for (std::size_t i = 0; i < idx.size(); i++)
{
if (i != m_axis_1 && i != m_axis_2)
{
idx[i] = *begin++;
}
}
if (m_offset >= 0)
{
idx[m_axis_1] = *(begin);
idx[m_axis_2] = *(begin) + m_offset;
}
else
{
idx[m_axis_1] = *(begin) - m_offset;
idx[m_axis_2] = *(begin);
}
return m_source[idx];
}
private:
CT m_source;
const int m_offset;
const std::size_t m_axis_1;
const std::size_t m_axis_2;
};
template <class CT>
class diag_fn
{
public:
using xexpression_type = std::decay_t<CT>;
using value_type = typename xexpression_type::value_type;
template <class CTA>
diag_fn(CTA&& source, int k)
: m_source(std::forward<CTA>(source)), m_k(k)
{
}
template <class It>
inline value_type operator()(It begin, It) const
{
if (m_k > 0)
{
return *begin + m_k == *(begin + 1) ? m_source(*begin) : value_type(0);
}
else
{
return *begin + m_k == *(begin + 1) ? m_source(*begin + m_k) : value_type(0);
}
}
private:
CT m_source;
const int m_k;
};
template <class CT>
class flip_impl
{
public:
using xexpression_type = std::decay_t<CT>;
using value_type = typename xexpression_type::value_type;
using size_type = typename xexpression_type::size_type;
template <class CTA>
flip_impl(CTA&& source, std::size_t axis)
: m_source(std::forward<CTA>(source)), m_axis(axis), m_shape_at_axis(m_source.shape()[m_axis] - 1)
{
}
template <class... Args>
inline value_type operator()(Args... args) const
{
std::array<size_type, sizeof...(Args)> idx({static_cast<size_type>(args)...});
return access_impl(idx.begin(), idx.end());
}
template <class It>
inline value_type element(It first, It last) const
{
// TODO: avoid memory allocation
xindex idx(first, last);
return access_impl(idx.begin(), idx.end());
}
private:
template <class It>
inline value_type access_impl(It begin, It end) const
{
auto it = begin + m_axis;
*it = m_shape_at_axis - *it;
return m_source.element(begin, end);
}
CT m_source;
const size_type m_axis;
const size_type m_shape_at_axis;
};
template <class CT, class Comp>
class trilu_fn
{
public:
using xexpression_type = std::decay_t<CT>;
using value_type = typename xexpression_type::value_type;
using signed_idx_type = long int;
template <class CTA>
trilu_fn(CTA&& source, int k, Comp comp)
: m_source(std::forward<CTA>(source)), m_k(k), m_comp(comp)
{
}
template <class It>
inline value_type operator()(It begin, It end) const
{
// have to cast to signed int otherwise -1 can lead to overflow
return m_comp(signed_idx_type(*begin) + m_k, signed_idx_type(*(begin + 1))) ? m_source.element(begin, end) : value_type(0);
}
private:
CT m_source;
const signed_idx_type m_k;
const Comp m_comp;
};
}
namespace detail
{
// meta-function returning the shape type for a diagonal
template <class ST, class... S>
struct diagonal_shape_type
{
using type = ST;
};
template <class I, std::size_t L>
struct diagonal_shape_type<std::array<I, L>>
{
using type = std::array<I, L - 1>;
};
}
/**
* @brief Returns the elements on the diagonal of arr
* If arr has more than two dimensions, then the axes specified by
* axis_1 and axis_2 are used to determine the 2-D sub-array whose
* diagonal is returned. The shape of the resulting array can be
* determined by removing axis1 and axis2 and appending an index
* to the right equal to the size of the resulting diagonals.
*
* @param arr the input array
* @param offset offset of the diagonal from the main diagonal. Can
* be positive or negative.
* @param axis_1 Axis to be used as the first axis of the 2-D sub-arrays
* from which the diagonals should be taken.
* @param axis_2 Axis to be used as the second axis of the 2-D sub-arrays
* from which the diagonals should be taken.
* @returns xexpression with values of the diagonal
*
* \code{.cpp}
* xt::xarray<double> a = {{1, 2, 3},
* {4, 5, 6}
* {7, 8, 9}};
* auto b = xt::diagonal(a); // => {1, 5, 9}
* \endcode
*/
template <class E>
inline auto diagonal(E&& arr, int offset = 0, std::size_t axis_1 = 0, std::size_t axis_2 = 1)
{
using CT = xclosure_t<E>;
using shape_type = typename detail::diagonal_shape_type<typename std::decay_t<E>::shape_type>::type;
auto shape = arr.shape();
auto dimension = arr.dimension();
// The following shape calculation code is an almost verbatim adaptation of numpy:
// https://github.com/numpy/numpy/blob/2aabeafb97bea4e1bfa29d946fbf31e1104e7ae0/numpy/core/src/multiarray/item_selection.c#L1799
auto ret_shape = make_sequence<shape_type>(dimension - 1, 0);
std::size_t dim_1 = shape[axis_1];
std::size_t dim_2 = shape[axis_2];
offset >= 0 ? dim_2 -= offset : dim_1 += offset;
auto diag_size = dim_2 < dim_1 ? dim_2 : dim_1;
std::size_t i = 0;
for (std::size_t idim = 0; idim < dimension; ++idim)
{
if (idim != axis_1 && idim != axis_2)
{
ret_shape[i++] = shape[idim];
}
}
ret_shape.back() = diag_size;
return detail::make_xgenerator(detail::fn_impl<detail::diagonal_fn<CT>>(detail::diagonal_fn<CT>(std::forward<E>(arr), offset, axis_1, axis_2)),
ret_shape);
}
/**
* @brief xexpression with values of arr on the diagonal, zeroes otherwise
*
* @param arr the 1D input array of length n
* @param k the offset of the considered diagonal
* @returns xexpression function with shape n x n and arr on the diagonal
*
* \code{.cpp}
* xt::xarray<double> a = {1, 5, 9};
* auto b = xt::diag(a); // => {{1, 0, 0},
* // {0, 5, 0},
* // {0, 0, 9}}
* \endcode
*/
template <class E>
inline auto diag(E&& arr, int k = 0)
{
using CT = xclosure_t<E>;
std::size_t s = arr.shape()[0] + std::abs(k);
return detail::make_xgenerator(detail::fn_impl<detail::diag_fn<CT>>(detail::diag_fn<CT>(std::forward<E>(arr), k)),
{s, s});
}
/**
* @brief Reverse the order of elements in an xexpression along the given axis.
* Note: A NumPy/Matlab style `flipud(arr)` is equivalent to `xt::flip(arr, 0)`,
* `fliplr(arr)` to `xt::flip(arr, 1)`.
*
* @param arr the input xexpression
* @param axis the axis along which elements should be reversed
*
* @return xexpression evaluating to reversed array
*/
template <class E>
inline auto flip(E&& arr, std::size_t axis)
{
using CT = xclosure_t<E>;
auto shape = arr.shape();
return detail::make_xgenerator(detail::flip_impl<CT>(std::forward<E>(arr), axis),
shape);
}
/**
* @brief Extract lower triangular matrix from xexpression. The parameter k selects the
* offset of the diagonal.
*
* @param arr the input array
* @param k the diagonal above which to zero elements. 0 (default) selects the main diagonal,
* k < 0 is below the main diagonal, k > 0 above.
* @returns xexpression containing lower triangle from arr, 0 otherwise
*/
template <class E>
inline auto tril(E&& arr, int k = 0)
{
using CT = xclosure_t<E>;
auto shape = arr.shape();
return detail::make_xgenerator(detail::fn_impl<detail::trilu_fn<CT, std::greater_equal<long int>>>(
detail::trilu_fn<CT, std::greater_equal<long int>>(std::forward<E>(arr), k, std::greater_equal<long int>())),
shape);
}
/**
* @brief Extract upper triangular matrix from xexpression. The parameter k selects the
* offset of the diagonal.
*
* @param arr the input array
* @param k the diagonal below which to zero elements. 0 (default) selects the main diagonal,
* k < 0 is below the main diagonal, k > 0 above.
* @returns xexpression containing lower triangle from arr, 0 otherwise
*/
template <class E>
inline auto triu(E&& arr, int k = 0)
{
using CT = xclosure_t<E>;
auto shape = arr.shape();
return detail::make_xgenerator(detail::fn_impl<detail::trilu_fn<CT, std::less_equal<long int>>>(
detail::trilu_fn<CT, std::less_equal<long int>>(std::forward<E>(arr), k, std::less_equal<long int>())),
shape);
}
}
#endif
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