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Matrix.h
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/**
* @file
* @copyright Copyright 2017. Tom de Geus. All rights reserved.
* @license This project is released under the GNU Public License (GPLv3).
*/
#ifndef GOOSEFEM_MATRIX_H
#define GOOSEFEM_MATRIX_H
#include "config.h"
#include <Eigen/Eigen>
#include <Eigen/Sparse>
#include <Eigen/SparseCholesky>
namespace GooseFEM {
// forward declaration
template <class>
class MatrixSolver;
/**
* CRTP base class for a solver class.
*/
template <class D>
class MatrixSolverBase {
public:
/**
* Underlying type.
*/
using derived_type = D;
private:
auto derived_cast() -> derived_type&
{
return *static_cast<derived_type*>(this);
}
auto derived_cast() const -> const derived_type&
{
return *static_cast<const derived_type*>(this);
}
public:
/**
* Solve \f$ x = A^{-1} b \f$.
*
* @param A GooseFEM (sparse) matrix, see e.g. GooseFEM::Matrix().
* @param b nodevec [nelem, ndim].
* @param x (overwritten) nodevec [nelem, ndim].
*/
template <class M>
void solve(M& A, const array_type::tensor<double, 2>& b, array_type::tensor<double, 2>& x)
{
GOOSEFEM_ASSERT(xt::has_shape(b, A.shape_nodevec()));
GOOSEFEM_ASSERT(xt::has_shape(x, A.shape_nodevec()));
derived_cast().solve_nodevec_impl(A, b, x);
}
/**
* Solve \f$ x = A^{-1} b \f$.
*
* @param A GooseFEM (sparse) matrix, see e.g. GooseFEM::Matrix().
* @param b dofval [ndof].
* @param x (overwritten) dofval [ndof].
*/
template <class M>
void solve(M& A, const array_type::tensor<double, 1>& b, array_type::tensor<double, 1>& x)
{
GOOSEFEM_ASSERT(xt::has_shape(b, A.shape_dofval()));
GOOSEFEM_ASSERT(xt::has_shape(x, A.shape_dofval()));
derived_cast().solve_dofval_impl(A, b, x);
}
};
/**
* CRTP base class for a solver class.
*/
template <class D>
class MatrixSolverSingleBase {
public:
/**
* Underlying type.
*/
using derived_type = D;
private:
auto derived_cast() -> derived_type&
{
return *static_cast<derived_type*>(this);
}
auto derived_cast() const -> const derived_type&
{
return *static_cast<const derived_type*>(this);
}
public:
/**
* Solve \f$ x = A^{-1} b \f$.
*
* @param A GooseFEM (sparse) matrix, see e.g. GooseFEM::Matrix().
* @param b nodevec [nelem, ndim].
* @return x nodevec [nelem, ndim].
*/
template <class M>
array_type::tensor<double, 2> Solve(M& A, const array_type::tensor<double, 2>& b)
{
GOOSEFEM_ASSERT(xt::has_shape(b, A.shape_nodevec()));
array_type::tensor<double, 2> x = xt::empty_like(b);
derived_cast().solve_nodevec_impl(A, b, x);
return x;
}
/**
* Solve \f$ x = A^{-1} b \f$.
*
* @param A GooseFEM (sparse) matrix, see e.g. GooseFEM::Matrix().
* @param b dofval [ndof].
* @return x dofval [ndof].
*/
template <class M>
array_type::tensor<double, 1> Solve(M& A, const array_type::tensor<double, 1>& b)
{
GOOSEFEM_ASSERT(xt::has_shape(b, A.shape_dofval()));
array_type::tensor<double, 1> x = xt::empty_like(b);
derived_cast().solve_dofval_impl(A, b, x);
return x;
}
};
/**
* CRTP base class for a extra functions for a partitioned solver class.
*/
template <class D>
class MatrixSolverPartitionedBase {
public:
/**
* Underlying type.
*/
using derived_type = D;
private:
auto derived_cast() -> derived_type&
{
return *static_cast<derived_type*>(this);
}
auto derived_cast() const -> const derived_type&
{
return *static_cast<const derived_type*>(this);
}
public:
/**
* Solve \f$ x = A^{-1} b \f$.
*
* @param A GooseFEM (sparse) matrix, see e.g. GooseFEM::Matrix().
* @param b nodevec [nelem, ndim].
* @param x nodevec [nelem, ndim].
* @return x nodevec [nelem, ndim].
*/
template <class M>
array_type::tensor<double, 2>
Solve(M& A, const array_type::tensor<double, 2>& b, const array_type::tensor<double, 2>& x)
{
GOOSEFEM_ASSERT(xt::has_shape(b, A.shape_nodevec()));
GOOSEFEM_ASSERT(xt::has_shape(x, A.shape_nodevec()));
array_type::tensor<double, 2> ret = x;
derived_cast().solve_nodevec_impl(A, b, ret);
return ret;
}
/**
* Solve \f$ x = A^{-1} b \f$.
*
* @param A GooseFEM (sparse) matrix, see e.g. GooseFEM::Matrix().
* @param b dofval [ndof].
* @param x nodevec [nelem, ndim].
* @return x dofval [ndof].
*/
template <class M>
array_type::tensor<double, 1>
Solve(M& A, const array_type::tensor<double, 1>& b, const array_type::tensor<double, 1>& x)
{
GOOSEFEM_ASSERT(xt::has_shape(b, A.shape_dofval()));
GOOSEFEM_ASSERT(xt::has_shape(x, A.shape_dofval()));
array_type::tensor<double, 1> ret = x;
derived_cast().solve_dofval_impl(A, b, ret);
return ret;
}
};
/**
* CRTP base class for a matrix.
*/
template <class D>
class MatrixBase {
protected:
array_type::tensor<size_t, 2> m_conn; ///< Connectivity [#nelem, #nne].
array_type::tensor<size_t, 2> m_dofs; ///< DOF-numbers per node [#nnode, #ndim].
size_t m_nelem; ///< See nelem().
size_t m_nne; ///< See nne().
size_t m_nnode; ///< See nnode().
size_t m_ndim; ///< See ndim().
size_t m_ndof; ///< See ndof().
bool m_changed = true; ///< Signal changes to data.
public:
/**
* Underlying type.
*/
using derived_type = D;
private:
auto derived_cast() -> derived_type&
{
return *static_cast<derived_type*>(this);
}
auto derived_cast() const -> const derived_type&
{
return *static_cast<const derived_type*>(this);
}
public:
/**
* Number of elements.
* @return Unsigned integer.
*/
size_t nelem() const
{
return derived_cast().m_nelem;
}
/**
* Number of nodes per element.
* @return Unsigned integer.
*/
size_t nne() const
{
return derived_cast().m_nne;
}
/**
* Number of nodes.
* @return Unsigned integer.
*/
size_t nnode() const
{
return derived_cast().m_nnode;
}
/**
* Number of dimensions.
* @return Unsigned integer.
*/
size_t ndim() const
{
return derived_cast().m_ndim;
}
/**
* Number of DOFs.
* @return Unsigned integer.
*/
size_t ndof() const
{
return derived_cast().m_ndof;
}
/**
* DOFs per node.
* @return [#nnode, #ndim].
*/
const array_type::tensor<size_t, 2>& dofs() const
{
return derived_cast().m_dofs;
}
/**
* Connectivity.
* @return [#nelem, #nne].
*/
const array_type::tensor<size_t, 2>& conn() const
{
return derived_cast().m_conn;
}
/**
* Shape of "dofval".
* @return [#ndof].
*/
std::array<size_t, 1> shape_dofval() const
{
return std::array<size_t, 1>{derived_cast().m_ndof};
}
/**
* Shape of "nodevec".
* @return [#nnode, #ndim].
*/
std::array<size_t, 2> shape_nodevec() const
{
return std::array<size_t, 2>{derived_cast().m_nnode, derived_cast().m_ndim};
}
/**
* Shape of "elemmat".
* @return [#nelem, #nne * #ndim, #nne * #ndim].
*/
std::array<size_t, 3> shape_elemmat() const
{
return std::array<size_t, 3>{
derived_cast().m_nelem,
derived_cast().m_nne * derived_cast().m_ndim,
derived_cast().m_nne * derived_cast().m_ndim};
}
/**
* Assemble from "elemmat".
* @param elemmat [#nelem, #nne * #ndim, #nne * #ndim].
*/
template <class T>
void assemble(const T& elemmat)
{
GOOSEFEM_ASSERT(xt::has_shape(elemmat, this->shape_elemmat()));
derived_cast().assemble_impl(elemmat);
}
/**
* Copy as dense matrix.
* @return [#ndof, #ndof].
*/
array_type::tensor<double, 2> Todense() const
{
size_t ndof = derived_cast().m_ndof;
array_type::tensor<double, 2> ret = xt::empty<double>({ndof, ndof});
derived_cast().todense_impl(ret);
return ret;
}
/**
* Copy to dense matrix.
* @param ret overwritten [#ndof, #ndof].
*/
template <class T>
void todense(T& ret) const
{
GOOSEFEM_ASSERT(xt::has_shape(ret, {derived_cast().m_ndof, derived_cast().m_ndof}));
derived_cast().todense_impl(ret);
}
/**
* Dot-product \f$ b_i = A_{ij} x_j \f$.
*
* @param x nodevec [#nelem, #ndim].
* @return b nodevec [#nelem, #ndim].
*/
array_type::tensor<double, 2> Dot(const array_type::tensor<double, 2>& x) const
{
GOOSEFEM_ASSERT(xt::has_shape(x, this->shape_nodevec()));
array_type::tensor<double, 2> b = xt::empty_like(x);
derived_cast().dot_nodevec_impl(x, b);
return b;
}
/**
* Dot-product \f$ b_i = A_{ij} x_j \f$.
*
* @param x dofval [#ndof].
* @return b dofval [#ndof].
*/
array_type::tensor<double, 1> Dot(const array_type::tensor<double, 1>& x) const
{
GOOSEFEM_ASSERT(xt::has_shape(x, this->shape_dofval()));
array_type::tensor<double, 1> b = xt::empty_like(x);
derived_cast().dot_dofval_impl(x, b);
return b;
}
/**
* Dot-product \f$ b_i = A_{ij} x_j \f$.
*
* @param x nodevec [#nelem, #ndim].
* @param b (overwritten) nodevec [#nelem, #ndim].
*/
void dot(const array_type::tensor<double, 2>& x, array_type::tensor<double, 2>& b) const
{
GOOSEFEM_ASSERT(xt::has_shape(x, this->shape_nodevec()));
GOOSEFEM_ASSERT(xt::has_shape(b, this->shape_nodevec()));
derived_cast().dot_nodevec_impl(x, b);
}
/**
* Dot-product \f$ b_i = A_{ij} x_j \f$.
*
* @param x dofval [#ndof].
* @param b (overwritten) dofval [#ndof].
*/
void dot(const array_type::tensor<double, 1>& x, array_type::tensor<double, 1>& b) const
{
GOOSEFEM_ASSERT(xt::has_shape(x, this->shape_dofval()));
GOOSEFEM_ASSERT(xt::has_shape(b, this->shape_dofval()));
derived_cast().dot_dofval_impl(x, b);
}
};
/**
* CRTP base class for a partitioned matrix.
*/
template <class D>
class MatrixPartitionedBase : public MatrixBase<D> {
protected:
array_type::tensor<size_t, 1> m_iiu; ///< See iiu()
array_type::tensor<size_t, 1> m_iip; ///< See iip()
size_t m_nnu; ///< See #nnu
size_t m_nnp; ///< See #nnp
public:
/**
* Underlying type.
*/
using derived_type = D;
private:
auto derived_cast() -> derived_type&
{
return *static_cast<derived_type*>(this);
}
auto derived_cast() const -> const derived_type&
{
return *static_cast<const derived_type*>(this);
}
public:
/**
* Number of unknown DOFs.
* @return Unsigned integer.
*/
size_t nnu() const
{
return derived_cast().m_nnu;
}
/**
* Number of prescribed DOFs.
* @return Unsigned integer.
*/
size_t nnp() const
{
return derived_cast().m_nnp;
}
/**
* Unknown DOFs.
* @return [#nnu].
*/
const array_type::tensor<size_t, 1>& iiu() const
{
return derived_cast().m_iiu;
}
/**
* Prescribed DOFs.
* @return [#nnp].
*/
const array_type::tensor<size_t, 1>& iip() const
{
return derived_cast().m_iip;
}
/**
* Right-hand-size for corresponding to the prescribed DOFs:
*
* \f$ b_p = A_{pu} * x_u + A_{pp} * x_p \f$
*
* and assemble them to the appropriate places in "nodevec".
*
* @param x "nodevec" [#nnode, #ndim].
* @param b "nodevec" [#nnode, #ndim].
* @return Copy of `b` with \f$ b_p \f$ overwritten.
*/
array_type::tensor<double, 2>
Reaction(const array_type::tensor<double, 2>& x, const array_type::tensor<double, 2>& b) const
{
GOOSEFEM_ASSERT(xt::has_shape(x, this->shape_nodevec()));
GOOSEFEM_ASSERT(xt::has_shape(b, this->shape_nodevec()));
array_type::tensor<double, 2> ret = b;
derived_cast().reaction_nodevec_impl(x, ret);
return ret;
}
/**
* Same as Reaction(const array_type::tensor<double, 2>&, const array_type::tensor<double, 2>&),
* but of "dofval" input and output.
*
* @param x "dofval" [#ndof].
* @param b "dofval" [#ndof].
* @return Copy of `b` with \f$ b_p \f$ overwritten.
*/
array_type::tensor<double, 1>
Reaction(const array_type::tensor<double, 1>& x, const array_type::tensor<double, 1>& b) const
{
GOOSEFEM_ASSERT(xt::has_shape(x, this->shape_dofval()));
GOOSEFEM_ASSERT(xt::has_shape(b, this->shape_dofval()));
array_type::tensor<double, 1> ret = b;
derived_cast().reaction_dofval_impl(x, ret);
return ret;
}
/**
* Same as Reaction(const array_type::tensor<double, 2>&, const array_type::tensor<double, 2>&),
* but inserting in-place.
*
* @param x "nodevec" [#nnode, #ndim].
* @param b "nodevec" [#nnode, #ndim], \f$ b_p \f$ overwritten.
*/
void reaction(const array_type::tensor<double, 2>& x, array_type::tensor<double, 2>& b) const
{
GOOSEFEM_ASSERT(xt::has_shape(x, this->shape_nodevec()));
GOOSEFEM_ASSERT(xt::has_shape(b, this->shape_nodevec()));
derived_cast().reaction_nodevec_impl(x, b);
}
/**
* Same as Reaction(const array_type::tensor<double, 1>&, const array_type::tensor<double, 1>&),
* but inserting in-place.
*
* @param x "dofval" [#ndof].
* @param b "dofval" [#ndof], \f$ b_p \f$ overwritten.
*/
void reaction(const array_type::tensor<double, 1>& x, array_type::tensor<double, 1>& b) const
{
GOOSEFEM_ASSERT(xt::has_shape(x, this->shape_dofval()));
GOOSEFEM_ASSERT(xt::has_shape(b, this->shape_dofval()));
derived_cast().reaction_dofval_impl(x, b);
}
/**
* Same as Reaction(const array_type::tensor<double, 1>&, const array_type::tensor<double, 1>&),
* but with partitioned input and output.
*
* @param x_u unknown "dofval" [#nnu].
* @param x_p prescribed "dofval" [#nnp].
* @return b_p prescribed "dofval" [#nnp].
*/
array_type::tensor<double, 1> Reaction_p(
const array_type::tensor<double, 1>& x_u,
const array_type::tensor<double, 1>& x_p) const
{
array_type::tensor<double, 1> b_p = xt::empty<double>({m_nnp});
derived_cast().reaction_p_impl(x_u, x_p, b_p);
return b_p;
}
/**
* Same as Reaction_p(const array_type::tensor<double, 1>&, const array_type::tensor<double,
* 1>&), but writing to preallocated output.
*
* @param x_u unknown "dofval" [#nnu].
* @param x_p prescribed "dofval" [#nnp].
* @param b_p (overwritten) prescribed "dofval" [#nnp].
*/
void reaction_p(
const array_type::tensor<double, 1>& x_u,
const array_type::tensor<double, 1>& x_p,
array_type::tensor<double, 1>& b_p) const
{
derived_cast().reaction_p_impl(x_u, x_p, b_p);
}
};
/**
* CRTP base class for a partitioned matrix with tying.
*/
template <class D>
class MatrixPartitionedTyingsBase : public MatrixPartitionedBase<D> {
protected:
array_type::tensor<size_t, 1> m_iii; ///< See iii()
array_type::tensor<size_t, 1> m_iid; ///< See iid()
size_t m_nni; ///< See #nni
size_t m_nnd; ///< See #nnd
public:
/**
* Underlying type.
*/
using derived_type = D;
private:
auto derived_cast() -> derived_type&
{
return *static_cast<derived_type*>(this);
}
auto derived_cast() const -> const derived_type&
{
return *static_cast<const derived_type*>(this);
}
public:
/**
* Number of independent DOFs.
* @return Unsigned integer.
*/
size_t nni() const
{
return derived_cast().m_nni;
}
/**
* Number of dependent DOFs.
* @return Unsigned integer.
*/
size_t nnd() const
{
return derived_cast().m_nnd;
}
/**
* Independent DOFs.
* @return [#nnu].
*/
const array_type::tensor<size_t, 1>& iii() const
{
return derived_cast().m_iii;
}
/**
* Dependent DOFs.
* @return [#nnp].
*/
const array_type::tensor<size_t, 1>& iid() const
{
return derived_cast().m_iid;
}
};
/**
* Sparse matrix.
*
* See GooseFEM::Vector() for bookkeeping definitions.
*/
class Matrix : public MatrixBase<Matrix> {
private:
friend MatrixBase<Matrix>;
private:
bool m_changed = true; ///< Signal changes to data.
Eigen::SparseMatrix<double> m_A; ///< The matrix.
std::vector<Eigen::Triplet<double>> m_T; ///< Matrix entries.
/**
* Class to solve the system (allowing single factorisation for multiple right-hand-sides).
*/
template <class>
friend class MatrixSolver;
public:
Matrix() = default;
/**
* Constructor.
*
* @param conn connectivity [#nelem, #nne].
* @param dofs DOFs per node [#nnode, #ndim].
*/
Matrix(const array_type::tensor<size_t, 2>& conn, const array_type::tensor<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);
}
/**
* Pointer to data.
*/
const Eigen::SparseMatrix<double>& data() const
{
return m_A;
}
private:
template <class T>
void assemble_impl(const T& elemmat)
{
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;
}
public:
/**
* Overwrite matrix.
*
* @param rows Row numbers [m].
* @param cols Column numbers [n].
* @param matrix Data entries `matrix(i, j)` for `rows(i), cols(j)` [m, n].
*/
void
set(const array_type::tensor<size_t, 1>& rows,
const array_type::tensor<size_t, 1>& cols,
const array_type::tensor<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;
}
/**
* Add matrix.
*
* @param rows Row numbers [m].
* @param cols Column numbers [n].
* @param matrix Data entries `matrix(i, j)` for `rows(i), cols(j)` [m, n].
*/
void
add(const array_type::tensor<size_t, 1>& rows,
const array_type::tensor<size_t, 1>& cols,
const array_type::tensor<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;
}
private:
template <class T>
void todense_impl(T& ret) const
{
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();
}
}
}
template <class T>
void dot_nodevec_impl(const T& x, T& b) const
{
this->Eigen_asNode_dofval_nodevec(m_A * this->Eigen_AsDofs_nodevec(x), b);
}
template <class T>
void dot_dofval_impl(const T& x, T& b) const
{
Eigen::Map<Eigen::VectorXd>(b.data(), b.size()).noalias() =
m_A * Eigen::Map<const Eigen::VectorXd>(x.data(), x.size());
}
private:
/**
* Convert "nodevec" to "dofval" (overwrite entries that occur more than once).
*
* @param nodevec input [#nnode, #ndim]
* @return dofval output [#ndof]
*/
template <class T>
Eigen::VectorXd Eigen_AsDofs_nodevec(const T& 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;
}
/**
* Convert "dofval" to "nodevec" (overwrite entries that occur more than once).
*
* @param dofval input [#ndof]
* @param nodevec output [#nnode, #ndim]
*/
template <class T>
void Eigen_asNode_dofval_nodevec(const Eigen::VectorXd& dofval, T& 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));
}
}
}
};
/**
* Solve \f$ x = A^{-1} b \f$, for `A` of the GooseFEM::Matrix() class.
* You can solve for multiple right-hand-sides using one factorisation.
*/
template <class Solver = Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>>>
class MatrixSolver : public MatrixSolverBase<MatrixSolver<Solver>>,
public MatrixSolverSingleBase<MatrixSolver<Solver>> {
private:
friend MatrixSolverBase<MatrixSolver<Solver>>;
friend MatrixSolverSingleBase<MatrixSolver<Solver>>;
public:
MatrixSolver() = default;
private:
template <class T>
void solve_nodevec_impl(Matrix& A, const T& b, T& x)
{
this->factorize(A);
Eigen::VectorXd X = m_solver.solve(A.Eigen_AsDofs_nodevec(b));
A.Eigen_asNode_dofval_nodevec(X, x);
}
template <class T>
void solve_dofval_impl(Matrix& A, const T& b, T& x)
{
this->factorize(A);
Eigen::Map<Eigen::VectorXd>(x.data(), x.size()).noalias() =
m_solver.solve(Eigen::Map<const Eigen::VectorXd>(b.data(), A.m_ndof));
}
private:
Solver m_solver; ///< Solver.
bool m_factor = true; ///< Signal to force factorization.
/**
* Compute inverse (evaluated by "solve").
*/
void factorize(Matrix& A)
{
if (!A.m_changed && !m_factor) {
return;
}
m_solver.compute(A.m_A);
m_factor = false;
A.m_changed = false;
}
};
} // namespace GooseFEM
#endif

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