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Matrix.h
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Thu, May 23, 21:05

Matrix.h
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/*
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
*/
#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;
class Matrix {
public:
// Constructors
Matrix() = default;
Matrix(const xt::xtensor<size_t, 2>& conn, const xt::xtensor<size_t, 2>& dofs);
// 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
// DOF lists
xt::xtensor<size_t, 2> dofs() const; // 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);
// Return as dense matrix
void todense(xt::xtensor<double, 2>& ret) const;
// 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;
// Auto-allocation of the functions above
xt::xtensor<double, 2> Todense() const;
xt::xtensor<double, 2> Dot(const xt::xtensor<double, 2>& x) const;
xt::xtensor<double, 1> Dot(const xt::xtensor<double, 1>& x) const;
private:
// The matrix
Eigen::SparseMatrix<double> m_A;
// Matrix entries
std::vector<Eigen::Triplet<double>> m_T;
// Signal changes to data
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]
// 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
// grant access to solver class
template <class> friend class MatrixSolver;
// Convert arrays (Eigen version of Vector, which contains public functions)
Eigen::VectorXd AsDofs(const xt::xtensor<double, 2>& nodevec) const;
void asNode(const Eigen::VectorXd& dofval, xt::xtensor<double, 2>& nodevec) const;
};
template <class Solver = Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>>>
class MatrixSolver {
public:
// Constructors
MatrixSolver() = default;
// Solve
// x_u = A_uu \ (b_u - A_up * x_p)
void solve(Matrix& matrix, const xt::xtensor<double, 2>& b, xt::xtensor<double, 2>& x);
void solve(Matrix& matrix, const xt::xtensor<double, 1>& b, xt::xtensor<double, 1>& x);
// Auto-allocation of the functions above
xt::xtensor<double, 2> Solve(Matrix& matrix, const xt::xtensor<double, 2>& b);
xt::xtensor<double, 1> Solve(Matrix& matrix, const xt::xtensor<double, 1>& b);
private:
Solver m_solver; // solver
bool m_factor = true; // signal to force factorization
void factorize(Matrix& matrix); // compute inverse (evaluated by "solve")
};
} // namespace GooseFEM
#include "Matrix.hpp"
#endif

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