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/**
* file tensor_algebra.hh
*
* @author Till Junge <till.junge@epfl.ch>
*
* @date 05 Nov 2017
*
* @brief collection of compile-time quantities and algrebraic functions for
* tensor operations
*
* @section LICENCE
*
* Copyright (C) 2017 Till Junge
*
* µSpectre is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation, either version 3, or (at
* your option) any later version.
*
* µSpectre is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with GNU Emacs; see the file COPYING. If not, write to the
* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
* Boston, MA 02111-1307, USA.
*/
#ifndef TENSOR_ALGEBRA_H
#define TENSOR_ALGEBRA_H
#include <type_traits>
#include <Eigen/Dense>
#include <unsupported/Eigen/CXX11/Tensor>
#include "common/T4_map_proxy.hh"
#include "common/common.hh"
#include "common/eigen_tools.hh"
namespace muSpectre {
namespace Tensors {
template<Dim_t dim>
using Tens2_t = Eigen::TensorFixedSize<Real, Eigen::Sizes<dim, dim>>;
template<Dim_t dim>
using Tens4_t = Eigen::TensorFixedSize<Real, Eigen::Sizes<dim, dim, dim, dim>>;
//----------------------------------------------------------------------------//
//! compile-time second-order identity
template<Dim_t dim>
constexpr inline Tens2_t<dim> I2() {
Tens2_t<dim> T;
using Mat_t = Eigen::Matrix<Real, dim, dim>;
Eigen::Map<Mat_t>(&T(0, 0)) = Mat_t::Identity();
return T;
}
/* ---------------------------------------------------------------------- */
//! Check whether a given expression represents a Tensor specified order
template<class T, Dim_t order>
struct is_tensor {
constexpr static bool value = (std::is_convertible
<T, Eigen::Tensor<Real, order>>::value ||
std::is_convertible
<T, Eigen::Tensor<Int, order>>::value ||
std::is_convertible
<T, Eigen::Tensor<Complex, order>>::value);
};
/* ---------------------------------------------------------------------- */
/** compile-time outer tensor product as defined by Curnier
* R_ijkl = A_ij.B_klxx
* 0123 01 23
*/
template<Dim_t dim, typename T1, typename T2>
constexpr inline decltype(auto) outer(T1 && A, T2 && B) {
// Just make sure that the right type of parameters have been given
constexpr Dim_t order{2};
static_assert(is_tensor<T1, order>::value,
"T1 needs to be convertible to a second order Tensor");
static_assert(is_tensor<T2, order>::value,
"T2 needs to be convertible to a second order Tensor");
// actual function
std::array<Eigen::IndexPair<Dim_t>, 0> dims{};
return A.contract(B, dims);
}
/* ---------------------------------------------------------------------- */
/** compile-time underlined outer tensor product as defined by Curnier
* R_ijkl = A_ik.B_jlxx
* 0123 02 13
* 0213 01 23 <- this defines the shuffle order
*/
template<Dim_t dim, typename T1, typename T2>
constexpr inline decltype(auto) outer_under(T1 && A, T2 && B) {
constexpr size_t order{4};
return outer<dim>(A, B).shuffle(std::array<Dim_t, order>{0, 2, 1, 3});
}
/* ---------------------------------------------------------------------- */
/** compile-time overlined outer tensor product as defined by Curnier
* R_ijkl = A_il.B_jkxx
* 0123 03 12
* 0231 01 23 <- this defines the shuffle order
*/
template<Dim_t dim, typename T1, typename T2>
constexpr inline decltype(auto) outer_over(T1 && A, T2 && B) {
constexpr size_t order{4};
return outer<dim>(A, B).shuffle(std::array<Dim_t, order>{0, 2, 3, 1});
}
//! compile-time fourth-order symmetrising identity
template<Dim_t dim>
constexpr inline Tens4_t<dim> I4S() {
auto I = I2<dim>();
return 0.5*(outer_under<dim>(I, I) + outer_over<dim>(I, I));
}
} // Tensors
namespace Matrices {
template<Dim_t dim>
using Tens2_t = Eigen::Matrix<Real, dim, dim>;
template<Dim_t dim>
using Tens4_t = T4Mat<Real, dim>;
//----------------------------------------------------------------------------//
//! compile-time second-order identity
template<Dim_t dim>
constexpr inline Tens2_t<dim> I2() {
return Tens2_t<dim>::Identity();
}
/* ---------------------------------------------------------------------- */
/** compile-time outer tensor product as defined by Curnier
* R_ijkl = A_ij.B_klxx
* 0123 01 23
*/
template<typename T1, typename T2>
constexpr inline decltype(auto) outer(T1 && A, T2 && B) {
// Just make sure that the right type of parameters have been given
constexpr Dim_t dim{EigenCheck::TensorDim(A)};
static_assert((dim == EigenCheck::TensorDim(B)),
"A and B do not have the same dimension");
Tens4_t<dim> product;
for (Dim_t i = 0; i < dim; ++i) {
for (Dim_t j = 0; j < dim; ++j) {
for (Dim_t k = 0; k < dim; ++k) {
for (Dim_t l = 0; l < dim; ++l) {
get(product, i, j, k, l) = A(i, j) * B(k, l);
}
}
}
}
return product;
}
/* ---------------------------------------------------------------------- */
/** compile-time underlined outer tensor product as defined by Curnier
* R_ijkl = A_ik.B_jlxx
* 0123 02 13
* 0213 01 23 <- this defines the shuffle order
*/
template<typename T1, typename T2>
constexpr inline decltype(auto) outer_under(T1 && A, T2 && B) {
// Just make sure that the right type of parameters have been given
constexpr Dim_t dim{EigenCheck::TensorDim(A)};
static_assert((dim == EigenCheck::TensorDim(B)),
"A and B do not have the same dimension");
Tens4_t<dim> product;
for (Dim_t i = 0; i < dim; ++i) {
for (Dim_t j = 0; j < dim; ++j) {
for (Dim_t k = 0; k < dim; ++k) {
for (Dim_t l = 0; l < dim; ++l) {
get(product, i, j, k, l) = A(i, k) * B(j, l);
}
}
}
}
return product;
}
/* ---------------------------------------------------------------------- */
/** compile-time overlined outer tensor product as defined by Curnier
* R_ijkl = A_il.B_jkxx
* 0123 03 12
* 0231 01 23 <- this defines the shuffle order
*/
template<typename T1, typename T2>
constexpr inline decltype(auto) outer_over(T1 && A, T2 && B) {
// Just make sure that the right type of parameters have been given
constexpr Dim_t dim{EigenCheck::TensorDim(A)};
static_assert((dim == EigenCheck::TensorDim(B)),
"A and B do not have the same dimension");
Tens4_t<dim> product;
for (Dim_t i = 0; i < dim; ++i) {
for (Dim_t j = 0; j < dim; ++j) {
for (Dim_t k = 0; k < dim; ++k) {
for (Dim_t l = 0; l < dim; ++l) {
get(product, i, j, k, l) = A(i, l) * B(j, k);
}
}
}
}
return product;
}
/**
* Standart tensor multiplication
*/
template<typename T4, typename T2>
constexpr inline decltype(auto) tensmult(T4 && A, T2 && B) {
constexpr Dim_t dim{EigenCheck::Tensor4Dim(A)};
static_assert((dim == EigenCheck::TensorDim(B)),
"Dimensionality check failed. Expects A to be a fourth-"
"order tensor of dimension dim and B to be a second-order "
"Tensor of same dimension");
Tens2_t<dim> result;
result.setZero();
for (Dim_t i = 0; i < dim; ++i) {
for (Dim_t j = 0; j < dim; ++j) {
for (Dim_t k = 0; k < dim; ++k) {
for (Dim_t l = 0; l < dim; ++l) {
result(i,j) +=get(A, i, j, k, l) * B(k, l);
}
}
}
}
return result;
}
//! compile-time fourth-order tracer
template <Dim_t dim>
constexpr inline Tens4_t<dim> Itrac() {
auto I = I2<dim>();
return outer(I,I);
}
//! compile-time fourth-order identity
template <Dim_t dim>
constexpr inline Tens4_t<dim> Iiden() {
auto I = I2<dim>();
return outer_under(I,I);
}
//! compile-time fourth-order transposer
template <Dim_t dim>
constexpr inline Tens4_t<dim> Itrns() {
auto I = I2<dim>();
return outer_over(I,I);
}
//! compile-time fourth-order symmetriser
template<Dim_t dim>
constexpr inline Tens4_t<dim> Isymm() {
auto I = I2<dim>();
return 0.5*(outer_under(I, I) + outer_over(I, I));
}
} // Matrices
} // muSpectre
#endif /* TENSOR_ALGEBRA_H */
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