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// Copyright (c) 2021-2022 Matthew Scroggs and Garth N. Wells
// FEniCS Project
// SPDX-License-Identifier: MIT
#pragma once
#include "mdspan.hpp"
#include "types.h"
#include <algorithm>
#include <stdexcept>
#include <type_traits>
/// Information about finite element maps
namespace basix::maps
{
namespace impl
{
/// @private These structs are used to get the float/value type from a
/// template argument, including support for complex types.
template <typename T, typename = void>
struct scalar_value_type
{
/// @internal
typedef T value_type;
};
/// @private
template <typename T>
struct scalar_value_type<T, std::void_t<typename T::value_type>>
{
typedef typename T::value_type value_type;
};
/// @private Convenience typedef
template <typename T>
using scalar_value_type_t = typename scalar_value_type<T>::value_type;
} // namespace impl
/// Map type
enum class type
{
identity = 0,
L2Piola = 1,
covariantPiola = 2,
contravariantPiola = 3,
doubleCovariantPiola = 4,
doubleContravariantPiola = 5,
};
/// @brief L2 Piola map
template <typename O, typename P, typename Q, typename R>
void l2_piola(O&& r, const P& U, const Q& /*J*/, double detJ, const R& /*K*/)
{
assert(U.extent(0) == r.extent(0));
assert(U.extent(1) == r.extent(1));
for (std::size_t i = 0; i < U.extent(0); ++i)
for (std::size_t j = 0; j < U.extent(1); ++j)
r(i, j) = U(i, j) / detJ;
}
/// @brief Covariant Piola map
template <typename O, typename P, typename Q, typename R>
void covariant_piola(O&& r, const P& U, const Q& /*J*/, double /*detJ*/,
const R& K)
{
using T = typename std::decay_t<O>::value_type;
using Z = typename impl::scalar_value_type_t<T>;
for (std::size_t p = 0; p < U.extent(0); ++p)
{
// r_p = K^T U_p, where p indicates the p-th row
for (std::size_t i = 0; i < r.extent(1); ++i)
{
T acc = 0;
for (std::size_t k = 0; k < K.extent(0); ++k)
acc += static_cast<Z>(K(k, i)) * U(p, k);
r(p, i) = acc;
}
}
}
/// @brief Contravariant Piola map
template <typename O, typename P, typename Q, typename R>
void contravariant_piola(O&& r, const P& U, const Q& J, double detJ,
const R& /*K*/)
{
using T = typename std::decay_t<O>::value_type;
using Z = typename impl::scalar_value_type_t<T>;
for (std::size_t p = 0; p < U.extent(0); ++p)
{
for (std::size_t i = 0; i < r.extent(1); ++i)
{
T acc = 0;
for (std::size_t k = 0; k < J.extent(1); ++k)
acc += static_cast<Z>(J(i, k)) * U(p, k);
r(p, i) = acc;
}
}
std::transform(r.data_handle(), r.data_handle() + r.size(), r.data_handle(),
[detJ](auto ri) { return ri / static_cast<Z>(detJ); });
}
/// @brief Double covariant Piola map
template <typename O, typename P, typename Q, typename R>
void double_covariant_piola(O&& r, const P& U, const Q& /*J*/, double /*detJ*/,
const R& K)
{
using T = typename std::decay_t<O>::value_type;
using Z = typename impl::scalar_value_type_t<T>;
for (std::size_t p = 0; p < U.extent(0); ++p)
{
md::mdspan<const T, md::dextents<std::size_t, 2>> _U(
U.data_handle() + p * U.extent(1), K.extent(0), K.extent(0));
md::mdspan<T, md::dextents<std::size_t, 2>> _r(
r.data_handle() + p * r.extent(1), K.extent(1), K.extent(1));
// _r = K^T _U K
for (std::size_t i = 0; i < _r.extent(0); ++i)
{
for (std::size_t j = 0; j < _r.extent(1); ++j)
{
T acc = 0;
for (std::size_t k = 0; k < K.extent(0); ++k)
for (std::size_t l = 0; l < _U.extent(1); ++l)
acc += static_cast<Z>(K(k, i)) * _U(k, l) * static_cast<Z>(K(l, j));
_r(i, j) = acc;
}
}
}
}
/// @brief Double contravariant Piola map
template <typename O, typename P, typename Q, typename R>
void double_contravariant_piola(O&& r, const P& U, const Q& J, double detJ,
const R& /*K*/)
{
using T = typename std::decay_t<O>::value_type;
using Z = typename impl::scalar_value_type_t<T>;
for (std::size_t p = 0; p < U.extent(0); ++p)
{
md::mdspan<const T, md::dextents<std::size_t, 2>> _U(
U.data_handle() + p * U.extent(1), J.extent(1), J.extent(1));
md::mdspan<T, md::dextents<std::size_t, 2>> _r(
r.data_handle() + p * r.extent(1), J.extent(0), J.extent(0));
// _r = J U J^T
for (std::size_t i = 0; i < _r.extent(0); ++i)
{
for (std::size_t j = 0; j < _r.extent(1); ++j)
{
T acc = 0;
for (std::size_t k = 0; k < J.extent(1); ++k)
for (std::size_t l = 0; l < _U.extent(1); ++l)
acc += static_cast<Z>(J(i, k)) * _U(k, l) * static_cast<Z>(J(j, l));
_r(i, j) = acc;
}
}
}
std::transform(r.data_handle(), r.data_handle() + r.size(), r.data_handle(),
[detJ](auto ri) { return ri / static_cast<Z>(detJ * detJ); });
}
} // namespace basix::maps
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