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Matrix.hpp
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/**
Implementation of Matrix.h
\file Matrix.hpp
\copyright Copyright 2017. Tom de Geus. All rights reserved.
\license This project is released under the GNU Public License (GPLv3).
*/
#ifndef GOOSEFEM_MATRIX_HPP
#define GOOSEFEM_MATRIX_HPP
#include "Matrix.h"
namespace GooseFEM {
inline Matrix::Matrix(const xt::xtensor<size_t, 2>& conn, const xt::xtensor<size_t, 2>& dofs)
: m_conn(conn), m_dofs(dofs)
{
m_nelem = m_conn.shape(0);
m_nne = m_conn.shape(1);
m_nnode = m_dofs.shape(0);
m_ndim = m_dofs.shape(1);
m_ndof = xt::amax(m_dofs)() + 1;
m_T.reserve(m_nelem * m_nne * m_ndim * m_nne * m_ndim);
m_A.resize(m_ndof, m_ndof);
GOOSEFEM_ASSERT(xt::amax(m_conn)() + 1 <= m_nnode);
GOOSEFEM_ASSERT(m_ndof <= m_nnode * m_ndim);
}
inline size_t Matrix::nelem() const
{
return m_nelem;
}
inline size_t Matrix::nne() const
{
return m_nne;
}
inline size_t Matrix::nnode() const
{
return m_nnode;
}
inline size_t Matrix::ndim() const
{
return m_ndim;
}
inline size_t Matrix::ndof() const
{
return m_ndof;
}
inline xt::xtensor<size_t, 2> Matrix::dofs() const
{
return m_dofs;
}
inline void Matrix::assemble(const xt::xtensor<double, 3>& elemmat)
{
GOOSEFEM_ASSERT(xt::has_shape(elemmat, {m_nelem, m_nne * m_ndim, m_nne * m_ndim}));
m_T.clear();
for (size_t e = 0; e < m_nelem; ++e) {
for (size_t m = 0; m < m_nne; ++m) {
for (size_t i = 0; i < m_ndim; ++i) {
for (size_t n = 0; n < m_nne; ++n) {
for (size_t j = 0; j < m_ndim; ++j) {
m_T.push_back(Eigen::Triplet<double>(
m_dofs(m_conn(e, m), i),
m_dofs(m_conn(e, n), j),
elemmat(e, m * m_ndim + i, n * m_ndim + j)));
}
}
}
}
}
m_A.setFromTriplets(m_T.begin(), m_T.end());
m_changed = true;
}
inline void Matrix::set(
const xt::xtensor<size_t, 1>& rows,
const xt::xtensor<size_t, 1>& cols,
const xt::xtensor<double, 2>& matrix)
{
GOOSEFEM_ASSERT(rows.size() == matrix.shape(0));
GOOSEFEM_ASSERT(cols.size() == matrix.shape(1));
GOOSEFEM_ASSERT(xt::amax(cols)() < m_ndof);
GOOSEFEM_ASSERT(xt::amax(rows)() < m_ndof);
std::vector<Eigen::Triplet<double>> T;
for (size_t i = 0; i < rows.size(); ++i) {
for (size_t j = 0; j < cols.size(); ++j) {
T.push_back(Eigen::Triplet<double>(rows(i), cols(j), matrix(i, j)));
}
}
m_A.setFromTriplets(T.begin(), T.end());
m_changed = true;
}
inline void Matrix::add(
const xt::xtensor<size_t, 1>& rows,
const xt::xtensor<size_t, 1>& cols,
const xt::xtensor<double, 2>& matrix)
{
GOOSEFEM_ASSERT(rows.size() == matrix.shape(0));
GOOSEFEM_ASSERT(cols.size() == matrix.shape(1));
GOOSEFEM_ASSERT(xt::amax(cols)() < m_ndof);
GOOSEFEM_ASSERT(xt::amax(rows)() < m_ndof);
std::vector<Eigen::Triplet<double>> T;
Eigen::SparseMatrix<double> A(m_ndof, m_ndof);
for (size_t i = 0; i < rows.size(); ++i) {
for (size_t j = 0; j < cols.size(); ++j) {
T.push_back(Eigen::Triplet<double>(rows(i), cols(j), matrix(i, j)));
}
}
A.setFromTriplets(T.begin(), T.end());
m_A += A;
m_changed = true;
}
inline void Matrix::todense(xt::xtensor<double, 2>& ret) const
{
GOOSEFEM_ASSERT(xt::has_shape(ret, {m_ndof, m_ndof}));
ret.fill(0.0);
for (int k = 0; k < m_A.outerSize(); ++k) {
for (Eigen::SparseMatrix<double>::InnerIterator it(m_A, k); it; ++it) {
ret(it.row(), it.col()) = it.value();
}
}
}
inline xt::xtensor<double, 2> Matrix::Todense() const
{
xt::xtensor<double, 2> ret = xt::empty<double>({m_ndof, m_ndof});
this->todense(ret);
return ret;
}
inline void Matrix::dot(const xt::xtensor<double, 2>& x, xt::xtensor<double, 2>& b) const
{
GOOSEFEM_ASSERT(xt::has_shape(b, {m_nnode, m_ndim}));
GOOSEFEM_ASSERT(xt::has_shape(x, {m_nnode, m_ndim}));
this->asNode(m_A * this->AsDofs(x), b);
}
inline void Matrix::dot(const xt::xtensor<double, 1>& x, xt::xtensor<double, 1>& b) const
{
GOOSEFEM_ASSERT(b.size() == m_ndof);
GOOSEFEM_ASSERT(x.size() == m_ndof);
Eigen::Map<Eigen::VectorXd>(b.data(), b.size()).noalias() =
m_A * Eigen::Map<const Eigen::VectorXd>(x.data(), x.size());
}
inline xt::xtensor<double, 2> Matrix::Dot(const xt::xtensor<double, 2>& x) const
{
xt::xtensor<double, 2> b = xt::empty<double>({m_nnode, m_ndim});
this->dot(x, b);
return b;
}
inline xt::xtensor<double, 1> Matrix::Dot(const xt::xtensor<double, 1>& x) const
{
xt::xtensor<double, 1> b = xt::empty<double>({m_ndof});
this->dot(x, b);
return b;
}
inline Eigen::VectorXd Matrix::AsDofs(const xt::xtensor<double, 2>& nodevec) const
{
GOOSEFEM_ASSERT(xt::has_shape(nodevec, {m_nnode, m_ndim}));
Eigen::VectorXd dofval = Eigen::VectorXd::Zero(m_ndof, 1);
#pragma omp parallel for
for (size_t m = 0; m < m_nnode; ++m) {
for (size_t i = 0; i < m_ndim; ++i) {
dofval(m_dofs(m, i)) = nodevec(m, i);
}
}
return dofval;
}
inline void Matrix::asNode(const Eigen::VectorXd& dofval, xt::xtensor<double, 2>& nodevec) const
{
GOOSEFEM_ASSERT(static_cast<size_t>(dofval.size()) == m_ndof);
GOOSEFEM_ASSERT(xt::has_shape(nodevec, {m_nnode, m_ndim}));
#pragma omp parallel for
for (size_t m = 0; m < m_nnode; ++m) {
for (size_t i = 0; i < m_ndim; ++i) {
nodevec(m, i) = dofval(m_dofs(m, i));
}
}
}
template <class Solver>
inline void MatrixSolver<Solver>::factorize(Matrix& matrix)
{
if (!matrix.m_changed && !m_factor) {
return;
}
m_solver.compute(matrix.m_A);
m_factor = false;
matrix.m_changed = false;
}
template <class Solver>
inline void MatrixSolver<Solver>::solve(
Matrix& matrix, const xt::xtensor<double, 2>& b, xt::xtensor<double, 2>& x)
{
GOOSEFEM_ASSERT(xt::has_shape(b, {matrix.m_nnode, matrix.m_ndim}));
GOOSEFEM_ASSERT(xt::has_shape(x, {matrix.m_nnode, matrix.m_ndim}));
this->factorize(matrix);
Eigen::VectorXd X = m_solver.solve(matrix.AsDofs(b));
matrix.asNode(X, x);
}
template <class Solver>
inline void MatrixSolver<Solver>::solve(
Matrix& matrix, const xt::xtensor<double, 1>& b, xt::xtensor<double, 1>& x)
{
GOOSEFEM_ASSERT(b.size() == matrix.m_ndof);
GOOSEFEM_ASSERT(x.size() == matrix.m_ndof);
this->factorize(matrix);
Eigen::Map<Eigen::VectorXd>(x.data(), x.size()).noalias() = m_solver.solve(
Eigen::Map<const Eigen::VectorXd>(b.data(), matrix.m_ndof));
}
template <class Solver>
inline xt::xtensor<double, 2>
MatrixSolver<Solver>::Solve(Matrix& matrix, const xt::xtensor<double, 2>& b)
{
xt::xtensor<double, 2> x = xt::empty<double>({matrix.m_nnode, matrix.m_ndim});
this->solve(matrix, b, x);
return x;
}
template <class Solver>
inline xt::xtensor<double, 1>
MatrixSolver<Solver>::Solve(Matrix& matrix, const xt::xtensor<double, 1>& b)
{
xt::xtensor<double, 1> x = xt::empty<double>({matrix.m_ndof});
this->solve(matrix, b, x);
return x;
}
} // namespace GooseFEM
#endif

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