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test_goodies.hh
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/**
* @file test_goodies.hh
*
* @author Till Junge <till.junge@epfl.ch>
*
* @date 27 Sep 2017
*
* @brief helpers for testing
*
* Copyright © 2017 Till Junge
*
* µSpectre is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser 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 Lesser General Public License
* along with µSpectre; see the file COPYING. If not, write to the
* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
* * Boston, MA 02111-1307, USA.
*
* Additional permission under GNU GPL version 3 section 7
*
* If you modify this Program, or any covered work, by linking or combining it
* with proprietary FFT implementations or numerical libraries, containing parts
* covered by the terms of those libraries' licenses, the licensors of this
* Program grant you additional permission to convey the resulting work.
*/
#ifndef TESTS_LIBMUGRID_TEST_GOODIES_HH_
#define TESTS_LIBMUGRID_TEST_GOODIES_HH_
#include <libmugrid/grid_common.hh>
#include <libmugrid/tensor_algebra.hh>
#include <boost/mpl/list.hpp>
#include <random>
#include <type_traits>
namespace muGrid {
namespace testGoodies {
template <Dim_t Dim>
struct dimFixture {
constexpr static Dim_t dim{Dim};
};
using dimlist = boost::mpl::list<dimFixture<oneD>, dimFixture<twoD>,
dimFixture<threeD>>;
/* ---------------------------------------------------------------------- */
template <typename T>
class RandRange {
public:
RandRange() : rd(), gen(rd()) {}
template <typename dummyT = T>
std::enable_if_t<std::is_floating_point<dummyT>::value, dummyT>
randval(T && lower, T && upper) {
static_assert(std::is_same<T, dummyT>::value, "SFINAE");
auto distro = std::uniform_real_distribution<T>(lower, upper);
return distro(this->gen);
}
template <typename dummyT = T>
std::enable_if_t<std::is_integral<dummyT>::value, dummyT>
randval(T && lower, T && upper) {
static_assert(std::is_same<T, dummyT>::value, "SFINAE");
auto distro = std::uniform_int_distribution<T>(lower, upper);
return distro(this->gen);
}
private:
std::random_device rd;
std::default_random_engine gen;
};
/**
* explicit computation of linearisation of PK1 stress for an
* objective Hooke's law. This implementation is not meant to be
* efficient, but te reflect exactly the formulation in Curnier
* 2000, "Méthodes numériques en mécanique des solides" for
* reference and testing
*/
template <Dim_t Dim>
decltype(auto) objective_hooke_explicit(Real lambda, Real mu,
const Matrices::Tens2_t<Dim> & F) {
using Matrices::Tens2_t;
using Matrices::Tens4_t;
using Matrices::tensmult;
using T2 = Tens2_t<Dim>;
using T4 = Tens4_t<Dim>;
T2 P;
T2 I = P.Identity();
T4 K;
// See Curnier, 2000, "Méthodes numériques en mécanique des
// solides", p 252, (6.95b)
Real Fjrjr = (F.array() * F.array()).sum();
T2 Fjrjm = F.transpose() * F;
P.setZero();
for (Dim_t i = 0; i < Dim; ++i) {
for (Dim_t m = 0; m < Dim; ++m) {
P(i, m) += lambda / 2 * (Fjrjr - Dim) * F(i, m);
for (Dim_t r = 0; r < Dim; ++r) {
P(i, m) += mu * F(i, r) * (Fjrjm(r, m) - I(r, m));
}
}
}
// See Curnier, 2000, "Méthodes numériques en mécanique des solides", p
// 252
Real Fkrkr = (F.array() * F.array()).sum();
T2 Fkmkn = F.transpose() * F;
T2 Fisjs = F * F.transpose();
K.setZero();
for (Dim_t i = 0; i < Dim; ++i) {
for (Dim_t j = 0; j < Dim; ++j) {
for (Dim_t m = 0; m < Dim; ++m) {
for (Dim_t n = 0; n < Dim; ++n) {
get(K, i, m, j, n) =
(lambda * ((Fkrkr - Dim) / 2 * I(i, j) * I(m, n) +
F(i, m) * F(j, n)) +
mu * (I(i, j) * Fkmkn(m, n) + Fisjs(i, j) * I(m, n) -
I(i, j) * I(m, n) + F(i, n) * F(j, m)));
}
}
}
}
return std::make_tuple(P, K);
}
/**
* takes a 4th-rank tensor and returns a copy with the last two
* dimensions switched. This is particularly useful to check for
* identity between a stiffness tensors computed the regular way
* and the Geers way. For testing, not efficient.
*/
template <class Derived>
inline auto right_transpose(const Eigen::MatrixBase<Derived> & t4)
-> Eigen::Matrix<typename Derived::Scalar, Derived::RowsAtCompileTime,
Derived::ColsAtCompileTime> {
constexpr Dim_t Rows{Derived::RowsAtCompileTime};
constexpr Dim_t Cols{Derived::ColsAtCompileTime};
constexpr Dim_t DimSq{Rows};
using T = typename Derived::Scalar;
static_assert(Rows == Cols, "only square problems");
constexpr Dim_t Dim{ct_sqrt(DimSq)};
static_assert((Dim == twoD) or (Dim == threeD),
"only two- and three-dimensional problems");
static_assert(ipow(Dim, 2) == DimSq,
"The array is not a valid fourth order tensor");
T4Mat<T, Dim> retval{T4Mat<T, Dim>::Zero()};
/**
* Note: this looks like it's doing a left transpose, but in
* reality, np is rowmajor in all directions, so from numpy to
* eigen, we need to transpose left, center, and
* right. Therefore, if we want to right-transpose, then we need
* to transpose once left, once center, and *twice* right, which
* is equal to just left and center transpose. Center-transpose
* happens automatically when eigen parses the input (which is
* naturally written in rowmajor but interpreted into colmajor),
* so all that's left to do is (ironically) the subsequent
* left-transpose
*/
for (int i{0}; i < Dim; ++i) {
for (int j{0}; j < Dim; ++j) {
for (int k{0}; k < Dim; ++k) {
for (int l{0}; l < Dim; ++l) {
get(retval, i, j, k, l) = get(t4, j, i, k, l);
}
}
}
}
return retval;
}
/**
* recomputes a colmajor representation of a fourth-rank rowmajor
* tensor. this is useful when comparing to reference results
* computed in numpy
*/
template <class Derived>
inline auto from_numpy(const Eigen::MatrixBase<Derived> & t4_np)
-> Eigen::Matrix<typename Derived::Scalar, Derived::RowsAtCompileTime,
Derived::ColsAtCompileTime> {
constexpr Dim_t Rows{Derived::RowsAtCompileTime};
constexpr Dim_t Cols{Derived::ColsAtCompileTime};
constexpr Dim_t DimSq{Rows};
using T = typename Derived::Scalar;
static_assert(Rows == Cols, "only square problems");
constexpr Dim_t Dim{ct_sqrt(DimSq)};
static_assert((Dim == twoD) or (Dim == threeD),
"only two- and three-dimensional problems");
static_assert(ipow(Dim, 2) == DimSq,
"The array is not a valid fourth order tensor");
T4Mat<T, Dim> retval{T4Mat<T, Dim>::Zero()};
T4Mat<T, Dim> intermediate{T4Mat<T, Dim>::Zero()};
// transpose rows
for (int row{0}; row < DimSq; ++row) {
for (int i{0}; i < Dim; ++i) {
for (int j{0}; j < Dim; ++j) {
intermediate(row, i + Dim * j) = t4_np(row, i * Dim + j);
}
}
}
// transpose columns
for (int col{0}; col < DimSq; ++col) {
for (int i{0}; i < Dim; ++i) {
for (int j{0}; j < Dim; ++j) {
retval(i + Dim * j, col) = intermediate(i * Dim + j, col);
}
}
}
return retval;
}
} // namespace testGoodies
} // namespace muGrid
#endif // TESTS_LIBMUGRID_TEST_GOODIES_HH_

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