diff --git a/include/GooseFEM/MatrixPartitioned.h b/include/GooseFEM/MatrixPartitioned.h
index 6136095..17d44d5 100644
--- a/include/GooseFEM/MatrixPartitioned.h
+++ b/include/GooseFEM/MatrixPartitioned.h
@@ -1,176 +1,182 @@
/*
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
*/
#ifndef GOOSEFEM_MATRIXPARTITIONED_H
#define GOOSEFEM_MATRIXPARTITIONED_H
#include "config.h"
#include <Eigen/Eigen>
#include <Eigen/Sparse>
#include <Eigen/SparseCholesky>
namespace GooseFEM {
// forward declaration
template <class> class MatrixPartitionedSolver;
class MatrixPartitioned {
public:
// Constructors
MatrixPartitioned() = default;
MatrixPartitioned(
const xt::xtensor<size_t, 2>& conn,
const xt::xtensor<size_t, 2>& dofs,
const xt::xtensor<size_t, 1>& iip);
// Dimensions
size_t nelem() const; // number of elements
size_t nne() const; // number of nodes per element
size_t nnode() const; // number of nodes
size_t ndim() const; // number of dimensions
size_t ndof() const; // number of DOFs
size_t nnu() const; // number of unknown DOFs
size_t nnp() const; // number of prescribed DOFs
// DOF lists
xt::xtensor<size_t, 2> dofs() const; // DOFs
xt::xtensor<size_t, 1> iiu() const; // unknown DOFs
xt::xtensor<size_t, 1> iip() const; // prescribed DOFs
// Assemble from matrices stored per element [nelem, nne*ndim, nne*ndim]
void assemble(const xt::xtensor<double, 3>& elemmat);
// Overwrite with a dense (sub-) matrix
void set(
const xt::xtensor<size_t, 1>& rows,
const xt::xtensor<size_t, 1>& cols,
const xt::xtensor<double, 2>& matrix);
// Add a dense (sub-) matrix to the current matrix
void add(
const xt::xtensor<size_t, 1>& rows,
const xt::xtensor<size_t, 1>& cols,
const xt::xtensor<double, 2>& matrix);
+
+ // Dot-product:
+ // b_i = A_ij * x_j
+ void dot(const xt::xtensor<double, 2>& x, xt::xtensor<double, 2>& b) const;
+ void dot(const xt::xtensor<double, 1>& x, xt::xtensor<double, 1>& b) const;
+
// Get right-hand-size for corresponding to the prescribed DOFs:
// b_p = A_pu * x_u + A_pp * x_p = A_pp * x_p
void reaction(
const xt::xtensor<double, 2>& x,
xt::xtensor<double, 2>& b) const; // modified with "b_p"
void reaction(
const xt::xtensor<double, 1>& x,
xt::xtensor<double, 1>& b) const; // modified with "b_p"
void reaction_p(
const xt::xtensor<double, 1>& x_u,
const xt::xtensor<double, 1>& x_p,
xt::xtensor<double, 1>& b_p) const;
// Auto-allocation of the functions above
+ xt::xtensor<double, 2> Dot(const xt::xtensor<double, 2>& x) const;
+ xt::xtensor<double, 1> Dot(const xt::xtensor<double, 1>& x) const;
xt::xtensor<double, 2> Reaction(
const xt::xtensor<double, 2>& x, const xt::xtensor<double, 2>& b) const;
-
xt::xtensor<double, 1> Reaction(
const xt::xtensor<double, 1>& x, const xt::xtensor<double, 1>& b) const;
-
xt::xtensor<double, 1> Reaction_p(
const xt::xtensor<double, 1>& x_u, const xt::xtensor<double, 1>& x_p) const;
private:
// The matrix
Eigen::SparseMatrix<double> m_Auu;
Eigen::SparseMatrix<double> m_Aup;
Eigen::SparseMatrix<double> m_Apu;
Eigen::SparseMatrix<double> m_App;
// Matrix entries
std::vector<Eigen::Triplet<double>> m_Tuu;
std::vector<Eigen::Triplet<double>> m_Tup;
std::vector<Eigen::Triplet<double>> m_Tpu;
std::vector<Eigen::Triplet<double>> m_Tpp;
// Signal changes to data compare to the last inverse
bool m_changed = true;
// Bookkeeping
xt::xtensor<size_t, 2> m_conn; // connectivity [nelem, nne ]
xt::xtensor<size_t, 2> m_dofs; // DOF-numbers per node [nnode, ndim]
xt::xtensor<size_t, 2> m_part; // DOF-numbers per node, renumbered [nnode, ndim]
xt::xtensor<size_t, 1> m_iiu; // unknown DOFs [nnu]
xt::xtensor<size_t, 1> m_iip; // prescribed DOFs [nnp]
// Dimensions
size_t m_nelem; // number of elements
size_t m_nne; // number of nodes per element
size_t m_nnode; // number of nodes
size_t m_ndim; // number of dimensions
size_t m_ndof; // number of DOFs
size_t m_nnu; // number of unknown DOFs
size_t m_nnp; // number of prescribed DOFs
// grant access to solver class
template <class> friend class MatrixPartitionedSolver;
// Convert arrays (Eigen version of VectorPartitioned, which contains public functions)
Eigen::VectorXd AsDofs_u(const xt::xtensor<double, 1>& dofval) const;
Eigen::VectorXd AsDofs_u(const xt::xtensor<double, 2>& nodevec) const;
Eigen::VectorXd AsDofs_p(const xt::xtensor<double, 1>& dofval) const;
Eigen::VectorXd AsDofs_p(const xt::xtensor<double, 2>& nodevec) const;
};
template <class Solver = Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>>>
class MatrixPartitionedSolver {
public:
// Constructors
MatrixPartitionedSolver() = default;
// Solve:
// x_u = A_uu \ ( b_u - A_up * x_p )
void solve(
MatrixPartitioned& matrix,
const xt::xtensor<double, 2>& b,
xt::xtensor<double, 2>& x); // modified with "x_u"
void solve(
MatrixPartitioned& matrix,
const xt::xtensor<double, 1>& b,
xt::xtensor<double, 1>& x); // modified with "x_u"
void solve_u(
MatrixPartitioned& matrix,
const xt::xtensor<double, 1>& b_u,
const xt::xtensor<double, 1>& x_p,
xt::xtensor<double, 1>& x_u);
// Auto-allocation of the functions above
xt::xtensor<double, 2> Solve(
MatrixPartitioned& matrix,
const xt::xtensor<double, 2>& b,
const xt::xtensor<double, 2>& x);
xt::xtensor<double, 1> Solve(
MatrixPartitioned& matrix,
const xt::xtensor<double, 1>& b,
const xt::xtensor<double, 1>& x);
xt::xtensor<double, 1> Solve_u(
MatrixPartitioned& matrix,
const xt::xtensor<double, 1>& b_u,
const xt::xtensor<double, 1>& x_p);
private:
Solver m_solver; // solver
bool m_factor = false; // signal to force factorization
void factorize(MatrixPartitioned& matrix); // compute inverse (evaluated by "solve")
};
} // namespace GooseFEM
#include "MatrixPartitioned.hpp"
#endif
diff --git a/include/GooseFEM/MatrixPartitioned.hpp b/include/GooseFEM/MatrixPartitioned.hpp
index 5859bba..4ffce36 100644
--- a/include/GooseFEM/MatrixPartitioned.hpp
+++ b/include/GooseFEM/MatrixPartitioned.hpp
@@ -1,475 +1,525 @@
/*
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
*/
#ifndef GOOSEFEM_MATRIXPARTITIONED_HPP
#define GOOSEFEM_MATRIXPARTITIONED_HPP
#include "MatrixPartitioned.h"
#include "Mesh.h"
namespace GooseFEM {
inline MatrixPartitioned::MatrixPartitioned(
const xt::xtensor<size_t, 2>& conn,
const xt::xtensor<size_t, 2>& dofs,
const xt::xtensor<size_t, 1>& iip)
: m_conn(conn), m_dofs(dofs), m_iip(iip)
{
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_iiu = xt::setdiff1d(dofs, iip);
m_ndof = xt::amax(m_dofs)() + 1;
m_nnp = m_iip.size();
m_nnu = m_iiu.size();
m_part = Mesh::Reorder({m_iiu, m_iip}).get(m_dofs);
m_Tuu.reserve(m_nelem * m_nne * m_ndim * m_nne * m_ndim);
m_Tup.reserve(m_nelem * m_nne * m_ndim * m_nne * m_ndim);
m_Tpu.reserve(m_nelem * m_nne * m_ndim * m_nne * m_ndim);
m_Tpp.reserve(m_nelem * m_nne * m_ndim * m_nne * m_ndim);
m_Auu.resize(m_nnu, m_nnu);
m_Aup.resize(m_nnu, m_nnp);
m_Apu.resize(m_nnp, m_nnu);
m_App.resize(m_nnp, m_nnp);
GOOSEFEM_ASSERT(xt::amax(m_conn)() + 1 <= m_nnode);
GOOSEFEM_ASSERT(xt::amax(m_iip)() <= xt::amax(m_dofs)());
GOOSEFEM_ASSERT(m_ndof <= m_nnode * m_ndim);
}
inline size_t MatrixPartitioned::nelem() const
{
return m_nelem;
}
inline size_t MatrixPartitioned::nne() const
{
return m_nne;
}
inline size_t MatrixPartitioned::nnode() const
{
return m_nnode;
}
inline size_t MatrixPartitioned::ndim() const
{
return m_ndim;
}
inline size_t MatrixPartitioned::ndof() const
{
return m_ndof;
}
inline size_t MatrixPartitioned::nnu() const
{
return m_nnu;
}
inline size_t MatrixPartitioned::nnp() const
{
return m_nnp;
}
inline xt::xtensor<size_t, 2> MatrixPartitioned::dofs() const
{
return m_dofs;
}
inline xt::xtensor<size_t, 1> MatrixPartitioned::iiu() const
{
return m_iiu;
}
inline xt::xtensor<size_t, 1> MatrixPartitioned::iip() const
{
return m_iip;
}
inline void MatrixPartitioned::assemble(const xt::xtensor<double, 3>& elemmat)
{
GOOSEFEM_ASSERT(xt::has_shape(elemmat, {m_nelem, m_nne * m_ndim, m_nne * m_ndim}));
m_Tuu.clear();
m_Tup.clear();
m_Tpu.clear();
m_Tpp.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) {
size_t di = m_part(m_conn(e, m), i);
for (size_t n = 0; n < m_nne; ++n) {
for (size_t j = 0; j < m_ndim; ++j) {
size_t dj = m_part(m_conn(e, n), j);
if (di < m_nnu && dj < m_nnu) {
m_Tuu.push_back(Eigen::Triplet<double>(
di, dj, elemmat(e, m * m_ndim + i, n * m_ndim + j)));
}
else if (di < m_nnu) {
m_Tup.push_back(Eigen::Triplet<double>(
di, dj - m_nnu, elemmat(e, m * m_ndim + i, n * m_ndim + j)));
}
else if (dj < m_nnu) {
m_Tpu.push_back(Eigen::Triplet<double>(
di - m_nnu, dj, elemmat(e, m * m_ndim + i, n * m_ndim + j)));
}
else {
m_Tpp.push_back(Eigen::Triplet<double>(
di - m_nnu,
dj - m_nnu,
elemmat(e, m * m_ndim + i, n * m_ndim + j)));
}
}
}
}
}
}
m_Auu.setFromTriplets(m_Tuu.begin(), m_Tuu.end());
m_Aup.setFromTriplets(m_Tup.begin(), m_Tup.end());
m_Apu.setFromTriplets(m_Tpu.begin(), m_Tpu.end());
m_App.setFromTriplets(m_Tpp.begin(), m_Tpp.end());
m_changed = true;
}
inline void MatrixPartitioned::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>> Tuu;
std::vector<Eigen::Triplet<double>> Tup;
std::vector<Eigen::Triplet<double>> Tpu;
std::vector<Eigen::Triplet<double>> Tpp;
for (size_t i = 0; i < rows.size(); ++i) {
for (size_t j = 0; j < cols.size(); ++j) {
size_t di = rows(i);
size_t dj = cols(j);
double v = matrix(i, j);
if (di < m_nnu && dj < m_nnu) {
Tuu.push_back(Eigen::Triplet<double>(di, dj, v));
}
else if (di < m_nnu) {
Tup.push_back(Eigen::Triplet<double>(di, dj - m_nnu, v));
}
else if (dj < m_nnu) {
Tpu.push_back(Eigen::Triplet<double>(di - m_nnu, dj, v));
}
else {
Tpp.push_back(Eigen::Triplet<double>(di - m_nnu, dj - m_nnu, v));
}
}
}
m_Auu.setFromTriplets(Tuu.begin(), Tuu.end());
m_Aup.setFromTriplets(Tup.begin(), Tup.end());
m_Apu.setFromTriplets(Tpu.begin(), Tpu.end());
m_App.setFromTriplets(Tpp.begin(), Tpp.end());
m_changed = true;
}
inline void MatrixPartitioned::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>> Tuu;
std::vector<Eigen::Triplet<double>> Tup;
std::vector<Eigen::Triplet<double>> Tpu;
std::vector<Eigen::Triplet<double>> Tpp;
- Eigen::SparseMatrix<double> Auu;
- Eigen::SparseMatrix<double> Aup;
- Eigen::SparseMatrix<double> Apu;
- Eigen::SparseMatrix<double> App;
+ Eigen::SparseMatrix<double> Auu(m_nnu, m_nnu);
+ Eigen::SparseMatrix<double> Aup(m_nnu, m_nnp);
+ Eigen::SparseMatrix<double> Apu(m_nnp, m_nnu);
+ Eigen::SparseMatrix<double> App(m_nnp, m_nnp);
for (size_t i = 0; i < rows.size(); ++i) {
for (size_t j = 0; j < cols.size(); ++j) {
size_t di = rows(i);
size_t dj = cols(j);
double v = matrix(i, j);
if (di < m_nnu && dj < m_nnu) {
Tuu.push_back(Eigen::Triplet<double>(di, dj, v));
}
else if (di < m_nnu) {
Tup.push_back(Eigen::Triplet<double>(di, dj - m_nnu, v));
}
else if (dj < m_nnu) {
Tpu.push_back(Eigen::Triplet<double>(di - m_nnu, dj, v));
}
else {
Tpp.push_back(Eigen::Triplet<double>(di - m_nnu, dj - m_nnu, v));
}
}
}
Auu.setFromTriplets(Tuu.begin(), Tuu.end());
Aup.setFromTriplets(Tup.begin(), Tup.end());
Apu.setFromTriplets(Tpu.begin(), Tpu.end());
App.setFromTriplets(Tpp.begin(), Tpp.end());
m_Auu += Auu;
m_Aup += Aup;
m_Apu += Apu;
m_App += App;
m_changed = true;
}
+
+inline void MatrixPartitioned::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}));
+
+ Eigen::VectorXd X_u = this->AsDofs_u(x);
+ Eigen::VectorXd X_p = this->AsDofs_p(x);
+ Eigen::VectorXd B_u = m_Auu * X_u + m_Aup * X_p;
+ Eigen::VectorXd B_p = m_Apu * X_u + m_App * X_p;
+
+ #pragma omp parallel for
+ for (size_t m = 0; m < m_nnode; ++m) {
+ for (size_t i = 0; i < m_ndim; ++i) {
+ if (m_part(m, i) < m_nnu) {
+ b(m, i) = B_u(m_part(m, i));
+ }
+ else{
+ b(m, i) = B_p(m_part(m, i) - m_nnu);
+ }
+ }
+ }
+}
+
+inline void MatrixPartitioned::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::VectorXd X_u = this->AsDofs_u(x);
+ Eigen::VectorXd X_p = this->AsDofs_p(x);
+
+ Eigen::Map<Eigen::VectorXd>(b.data(), m_nnu).noalias() = m_Auu * X_u + m_Aup * X_p;
+ Eigen::Map<Eigen::VectorXd>(b.data() + m_nnu, m_ndof).noalias() = m_Auu * X_u + m_Aup * X_p;
+}
+
+inline xt::xtensor<double, 2> MatrixPartitioned::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> MatrixPartitioned::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 void
MatrixPartitioned::reaction(const xt::xtensor<double, 2>& x, xt::xtensor<double, 2>& b) const
{
GOOSEFEM_ASSERT(xt::has_shape(x, {m_nnode, m_ndim}));
GOOSEFEM_ASSERT(xt::has_shape(b, {m_nnode, m_ndim}));
Eigen::VectorXd X_u = this->AsDofs_u(x);
Eigen::VectorXd X_p = this->AsDofs_p(x);
Eigen::VectorXd B_p = m_Apu * X_u + m_App * X_p;
#pragma omp parallel for
for (size_t m = 0; m < m_nnode; ++m) {
for (size_t i = 0; i < m_ndim; ++i) {
if (m_part(m, i) >= m_nnu) {
b(m, i) = B_p(m_part(m, i) - m_nnu);
}
}
}
}
inline void
MatrixPartitioned::reaction(const xt::xtensor<double, 1>& x, xt::xtensor<double, 1>& b) const
{
GOOSEFEM_ASSERT(x.size() == m_ndof);
GOOSEFEM_ASSERT(b.size() == m_ndof);
Eigen::VectorXd X_u = this->AsDofs_u(x);
Eigen::VectorXd X_p = this->AsDofs_p(x);
Eigen::VectorXd B_p = m_Apu * X_u + m_App * X_p;
#pragma omp parallel for
for (size_t d = 0; d < m_nnp; ++d) {
b(m_iip(d)) = B_p(d);
}
}
inline void MatrixPartitioned::reaction_p(
const xt::xtensor<double, 1>& x_u,
const xt::xtensor<double, 1>& x_p,
xt::xtensor<double, 1>& b_p) const
{
GOOSEFEM_ASSERT(x_u.size() == m_nnu);
GOOSEFEM_ASSERT(x_p.size() == m_nnp);
GOOSEFEM_ASSERT(b_p.size() == m_nnp);
Eigen::Map<Eigen::VectorXd>(b_p.data(), b_p.size()).noalias() =
m_Apu * Eigen::Map<const Eigen::VectorXd>(x_u.data(), x_u.size()) +
m_App * Eigen::Map<const Eigen::VectorXd>(x_p.data(), x_p.size());
}
inline xt::xtensor<double, 2>
MatrixPartitioned::Reaction(const xt::xtensor<double, 2>& x, const xt::xtensor<double, 2>& b) const
{
xt::xtensor<double, 2> ret = b;
this->reaction(x, ret);
return ret;
}
inline xt::xtensor<double, 1>
MatrixPartitioned::Reaction(const xt::xtensor<double, 1>& x, const xt::xtensor<double, 1>& b) const
{
xt::xtensor<double, 1> ret = b;
this->reaction(x, ret);
return ret;
}
inline xt::xtensor<double, 1> MatrixPartitioned::Reaction_p(
const xt::xtensor<double, 1>& x_u, const xt::xtensor<double, 1>& x_p) const
{
xt::xtensor<double, 1> b_p = xt::empty<double>({m_nnp});
this->reaction_p(x_u, x_p, b_p);
return b_p;
}
inline Eigen::VectorXd MatrixPartitioned::AsDofs_u(const xt::xtensor<double, 1>& dofval) const
{
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
Eigen::VectorXd dofval_u(m_nnu, 1);
#pragma omp parallel for
for (size_t d = 0; d < m_nnu; ++d) {
dofval_u(d) = dofval(m_iiu(d));
}
return dofval_u;
}
inline Eigen::VectorXd MatrixPartitioned::AsDofs_u(const xt::xtensor<double, 2>& nodevec) const
{
GOOSEFEM_ASSERT(xt::has_shape(nodevec, {m_nnode, m_ndim}));
Eigen::VectorXd dofval_u = Eigen::VectorXd::Zero(m_nnu, 1);
#pragma omp parallel for
for (size_t m = 0; m < m_nnode; ++m) {
for (size_t i = 0; i < m_ndim; ++i) {
if (m_part(m, i) < m_nnu) {
dofval_u(m_part(m, i)) = nodevec(m, i);
}
}
}
return dofval_u;
}
inline Eigen::VectorXd MatrixPartitioned::AsDofs_p(const xt::xtensor<double, 1>& dofval) const
{
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
Eigen::VectorXd dofval_p(m_nnp, 1);
#pragma omp parallel for
for (size_t d = 0; d < m_nnp; ++d) {
dofval_p(d) = dofval(m_iip(d));
}
return dofval_p;
}
inline Eigen::VectorXd MatrixPartitioned::AsDofs_p(const xt::xtensor<double, 2>& nodevec) const
{
GOOSEFEM_ASSERT(xt::has_shape(nodevec, {m_nnode, m_ndim}));
Eigen::VectorXd dofval_p = Eigen::VectorXd::Zero(m_nnp, 1);
#pragma omp parallel for
for (size_t m = 0; m < m_nnode; ++m) {
for (size_t i = 0; i < m_ndim; ++i) {
if (m_part(m, i) >= m_nnu) {
dofval_p(m_part(m, i) - m_nnu) = nodevec(m, i);
}
}
}
return dofval_p;
}
template <class Solver>
inline void MatrixPartitionedSolver<Solver>::factorize(MatrixPartitioned& matrix)
{
if (!matrix.m_changed && !m_factor) {
return;
}
m_solver.compute(matrix.m_Auu);
m_factor = false;
matrix.m_changed = false;
}
template <class Solver>
inline void MatrixPartitionedSolver<Solver>::solve(
MatrixPartitioned& 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 B_u = matrix.AsDofs_u(b);
Eigen::VectorXd X_p = matrix.AsDofs_p(x);
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - matrix.m_Aup * X_p));
#pragma omp parallel for
for (size_t m = 0; m < matrix.m_nnode; ++m) {
for (size_t i = 0; i < matrix.m_ndim; ++i) {
if (matrix.m_part(m, i) < matrix.m_nnu) {
x(m, i) = X_u(matrix.m_part(m, i));
}
}
}
}
template <class Solver>
inline void MatrixPartitionedSolver<Solver>::solve(
MatrixPartitioned& 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::VectorXd B_u = matrix.AsDofs_u(b);
Eigen::VectorXd X_p = matrix.AsDofs_p(x);
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - matrix.m_Aup * X_p));
#pragma omp parallel for
for (size_t d = 0; d < matrix.m_nnu; ++d) {
x(matrix.m_iiu(d)) = X_u(d);
}
}
template <class Solver>
inline void MatrixPartitionedSolver<Solver>::solve_u(
MatrixPartitioned& matrix,
const xt::xtensor<double, 1>& b_u,
const xt::xtensor<double, 1>& x_p,
xt::xtensor<double, 1>& x_u)
{
GOOSEFEM_ASSERT(b_u.size() == matrix.m_nnu);
GOOSEFEM_ASSERT(x_p.size() == matrix.m_nnp);
GOOSEFEM_ASSERT(x_u.size() == matrix.m_nnu);
this->factorize(matrix);
Eigen::Map<Eigen::VectorXd>(x_u.data(), x_u.size()).noalias() = m_solver.solve(Eigen::VectorXd(
Eigen::Map<const Eigen::VectorXd>(b_u.data(), b_u.size()) -
matrix.m_Aup * Eigen::Map<const Eigen::VectorXd>(x_p.data(), x_p.size())));
}
template <class Solver>
inline xt::xtensor<double, 2> MatrixPartitionedSolver<Solver>::Solve(
MatrixPartitioned& matrix, const xt::xtensor<double, 2>& b, const xt::xtensor<double, 2>& x)
{
xt::xtensor<double, 2> ret = x;
this->solve(matrix, b, ret);
return ret;
}
template <class Solver>
inline xt::xtensor<double, 1> MatrixPartitionedSolver<Solver>::Solve(
MatrixPartitioned& matrix, const xt::xtensor<double, 1>& b, const xt::xtensor<double, 1>& x)
{
xt::xtensor<double, 1> ret = x;
this->solve(matrix, b, ret);
return ret;
}
template <class Solver>
inline xt::xtensor<double, 1> MatrixPartitionedSolver<Solver>::Solve_u(
MatrixPartitioned& matrix, const xt::xtensor<double, 1>& b_u, const xt::xtensor<double, 1>& x_p)
{
xt::xtensor<double, 1> x_u = xt::empty<double>({matrix.m_nnu});
this->solve_u(matrix, b_u, x_p, x_u);
return x_u;
}
} // namespace GooseFEM
#endif
diff --git a/python/MatrixPartitioned.hpp b/python/MatrixPartitioned.hpp
index f0fadf0..5a1b75c 100644
--- a/python/MatrixPartitioned.hpp
+++ b/python/MatrixPartitioned.hpp
@@ -1,124 +1,152 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#include <Eigen/Eigen>
#include <GooseFEM/GooseFEM.h>
#include <pybind11/eigen.h>
#include <pybind11/pybind11.h>
#include <pyxtensor/pyxtensor.hpp>
namespace py = pybind11;
void init_MatrixPartitioned(py::module& m)
{
py::class_<GooseFEM::MatrixPartitioned>(m, "MatrixPartitioned")
.def(
py::init<
const xt::xtensor<size_t, 2>&,
const xt::xtensor<size_t, 2>&,
const xt::xtensor<size_t, 1>&>(),
"Sparse, partitioned, matrix",
py::arg("conn"),
py::arg("dofs"),
py::arg("iip"))
.def("nelem", &GooseFEM::MatrixPartitioned::nelem, "Number of element")
.def("nne", &GooseFEM::MatrixPartitioned::nne, "Number of nodes per element")
.def("nnode", &GooseFEM::MatrixPartitioned::nnode, "Number of nodes")
.def("ndim", &GooseFEM::MatrixPartitioned::ndim, "Number of dimensions")
.def("ndof", &GooseFEM::MatrixPartitioned::ndof, "Number of degrees-of-freedom")
.def("nnu", &GooseFEM::MatrixPartitioned::nnu, "Number of unknown degrees-of-freedom")
.def("nnp", &GooseFEM::MatrixPartitioned::nnp, "Number of prescribed degrees-of-freedom")
.def(
"assemble",
&GooseFEM::MatrixPartitioned::assemble,
"Assemble matrix from 'elemmat",
py::arg("elemmat"))
+ .def(
+ "set",
+ &GooseFEM::MatrixPartitioned::set,
+ "Overwrite with a dense (sub-) matrix",
+ py::arg("rows"),
+ py::arg("cols"),
+ py::arg("matrix"))
+
+ .def(
+ "add",
+ &GooseFEM::MatrixPartitioned::add,
+ "Add a dense (sub-) matrix to the current matrix",
+ py::arg("rows"),
+ py::arg("cols"),
+ py::arg("matrix"))
+
.def("dofs", &GooseFEM::MatrixPartitioned::dofs, "Return degrees-of-freedom")
.def("iiu", &GooseFEM::MatrixPartitioned::iiu, "Return unknown degrees-of-freedom")
.def("iip", &GooseFEM::MatrixPartitioned::iip, "Return prescribed degrees-of-freedom")
.def(
"Reaction",
py::overload_cast<const xt::xtensor<double, 1>&, const xt::xtensor<double, 1>&>(
&GooseFEM::MatrixPartitioned::Reaction, py::const_),
"Reaction",
py::arg("x"),
py::arg("b"))
.def(
"Reaction",
py::overload_cast<const xt::xtensor<double, 2>&, const xt::xtensor<double, 2>&>(
&GooseFEM::MatrixPartitioned::Reaction, py::const_),
"Reaction",
py::arg("x"),
py::arg("b"))
.def(
"Reaction_p",
py::overload_cast<const xt::xtensor<double, 1>&, const xt::xtensor<double, 1>&>(
&GooseFEM::MatrixPartitioned::Reaction_p, py::const_),
"Reaction_p",
py::arg("x_u"),
py::arg("x_p"))
+ .def(
+ "Dot",
+ py::overload_cast<const xt::xtensor<double, 1>&>(&GooseFEM::MatrixPartitioned::Dot, py::const_),
+ "Dot",
+ py::arg("x"))
+
+ .def(
+ "Dot",
+ py::overload_cast<const xt::xtensor<double, 2>&>(&GooseFEM::MatrixPartitioned::Dot, py::const_),
+ "Dot",
+ py::arg("x"))
+
.def("__repr__", [](const GooseFEM::MatrixPartitioned&) {
return "<GooseFEM.MatrixPartitioned>";
});
py::class_<GooseFEM::MatrixPartitionedSolver<>>(m, "MatrixPartitionedSolver")
.def(py::init<>(), "Sparse, partitioned, matrix solver")
.def(
"Solve",
py::overload_cast<
GooseFEM::MatrixPartitioned&,
const xt::xtensor<double, 1>&,
const xt::xtensor<double, 1>&>(&GooseFEM::MatrixPartitionedSolver<>::Solve),
"Solve",
py::arg("matrix"),
py::arg("b"),
py::arg("x"))
.def(
"Solve",
py::overload_cast<
GooseFEM::MatrixPartitioned&,
const xt::xtensor<double, 2>&,
const xt::xtensor<double, 2>&>(&GooseFEM::MatrixPartitionedSolver<>::Solve),
"Solve",
py::arg("matrix"),
py::arg("b"),
py::arg("x"))
.def(
"Solve_u",
py::overload_cast<
GooseFEM::MatrixPartitioned&,
const xt::xtensor<double, 1>&,
const xt::xtensor<double, 1>&>(&GooseFEM::MatrixPartitionedSolver<>::Solve_u),
"Solve_u",
py::arg("matrix"),
py::arg("b_u"),
py::arg("x_p"))
.def("__repr__", [](const GooseFEM::MatrixPartitionedSolver<>&) {
return "<GooseFEM.MatrixPartitionedSolver>";
});
}