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MatrixDiagonal.hpp
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/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MATRIXDIAGONAL_CPP
#define GOOSEFEM_MATRIXDIAGONAL_CPP
// -------------------------------------------------------------------------------------------------
#include "MatrixDiagonal.h"
// =========================================== GooseFEM ============================================
namespace GooseFEM {
// ------------------------------------------ constructor ------------------------------------------
inline MatrixDiagonal::MatrixDiagonal(const MatS &conn, const MatS &dofs, const ColS &iip) :
m_conn(conn), m_dofs(dofs), m_iip(iip)
{
// extract mesh dimensions
m_nelem = static_cast<size_t>(m_conn.rows());
m_nne = static_cast<size_t>(m_conn.cols());
m_nnode = static_cast<size_t>(m_dofs.rows());
m_ndim = static_cast<size_t>(m_dofs.cols());
m_ndof = static_cast<size_t>(m_dofs.maxCoeff() + 1);
m_nnp = static_cast<size_t>(m_iip .size());
m_nnu = m_ndof - m_nnp;
// check consistency
assert( m_conn.maxCoeff() + 1 == m_nnode );
assert( m_ndof <= m_nnode * m_ndim );
// reorder DOFs such that they can be used for partitioning; renumber such that
// "iiu" -> beginning
// "iip" -> end
// (otherwise preserving the order)
// this array can be used to assemble to/from partitioned arrays
m_part = Mesh::reorder(m_dofs, m_iip, "end");
// extract unknown DOFs
// - allocate
m_iiu.conservativeResize(m_nnu);
// - set
#pragma omp parallel for
for ( size_t n = 0 ; n < m_nnode ; ++n )
for ( size_t i = 0 ; i < m_ndim ; ++i )
if ( m_part(n,i) < m_nnu )
m_iiu(m_part(n,i)) = m_dofs(n,i);
// allocate matrix and its inverse
m_data.conservativeResize(m_ndof);
m_inv .conservativeResize(m_ndof);
}
// ---------------------------------------- index operator -----------------------------------------
inline double& MatrixDiagonal::operator[](size_t i)
{
m_change = true;
return m_data[i];
}
// ---------------------------------------- index operator -----------------------------------------
inline const double& MatrixDiagonal::operator[](size_t i) const
{
return m_data[i];
}
// ---------------------------------------- index operator -----------------------------------------
inline double& MatrixDiagonal::operator()(size_t a)
{
m_change = true;
return m_data[a];
}
// ---------------------------------------- index operator -----------------------------------------
inline const double& MatrixDiagonal::operator()(size_t a) const
{
return m_data[a];
}
// ---------------------------------------- index operator -----------------------------------------
inline double& MatrixDiagonal::operator()(size_t a, size_t b)
{
assert( a == b );
UNUSED(b);
m_change = true;
return m_data[a];
}
// ---------------------------------------- index operator -----------------------------------------
inline const double& MatrixDiagonal::operator()(size_t a, size_t b) const
{
assert( a == b );
UNUSED(b);
return m_data[a];
}
// -------------------------------------- number of elements ---------------------------------------
inline size_t MatrixDiagonal::nelem() const
{
return m_nelem;
}
// ---------------------------------- number of nodes per element ----------------------------------
inline size_t MatrixDiagonal::nne() const
{
return m_nne;
}
// ---------------------------------------- number of nodes ----------------------------------------
inline size_t MatrixDiagonal::nnode() const
{
return m_nnode;
}
// ------------------------------------- number of dimensions --------------------------------------
inline size_t MatrixDiagonal::ndim() const
{
return m_ndim;
}
// ---------------------------------------- number of DOFs -----------------------------------------
inline size_t MatrixDiagonal::ndof() const
{
return m_ndof;
}
// ------------------------------------ number of unknown DOFs -------------------------------------
inline size_t MatrixDiagonal::nnu() const
{
return m_nnu;
}
// ----------------------------------- number of prescribed DOFs -----------------------------------
inline size_t MatrixDiagonal::nnp() const
{
return m_nnp;
}
// -------------------------------------- return unknown DOFs --------------------------------------
inline ColS MatrixDiagonal::iiu() const
{
return m_iiu;
}
// ------------------------------------ return prescribed DOFs -------------------------------------
inline ColS MatrixDiagonal::iip() const
{
return m_iip;
}
// --------------------------------------- c_i = A_ij * b_j ----------------------------------------
inline ColD MatrixDiagonal::dot(const ColD &b) const
{
// check input
assert( static_cast<size_t>(b.size()) == m_ndof );
// compute product
return m_data.cwiseProduct(b);
}
// --------------------------------------- c_i = A_ij * b_j ----------------------------------------
inline ColD MatrixDiagonal::dot_u(const ColD &b) const
{
// check input
assert( static_cast<size_t>(b.size()) == m_ndof );
// allocate output
ColD c_u(m_nnu);
// compute product
#pragma omp parallel for
for ( size_t i = 0 ; i < m_nnu ; ++i )
c_u(i) = m_data(m_iiu(i)) * b(m_iiu(i));
return c_u;
}
// --------------------------------------- c_i = A_ij * b_j ----------------------------------------
inline ColD MatrixDiagonal::dot_u(const ColD &b_u, const ColD &b_p) const
{
// suppress warning
UNUSED(b_p);
// check input
assert( static_cast<size_t>(b_u.size()) == m_nnu );
assert( static_cast<size_t>(b_p.size()) == m_nnp );
// allocate output
ColD c_u(m_nnu);
// compute product
#pragma omp parallel for
for ( size_t i = 0 ; i < m_nnu ; ++i )
c_u(i) = m_data(m_iiu(i)) * b_u(i);
return c_u;
}
// --------------------------------------- c_i = A_ij * b_j ----------------------------------------
inline ColD MatrixDiagonal::dot_p(const ColD &b) const
{
// check input
assert( static_cast<size_t>(b.size()) == m_ndof );
// allocate output
ColD c_p(m_nnp);
// compute product
#pragma omp parallel for
for ( size_t i = 0 ; i < m_nnp ; ++i )
c_p(i) = m_data(m_iip(i)) * b(m_iip(i));
return c_p;
}
// --------------------------------------- c_i = A_ij * b_j ----------------------------------------
inline ColD MatrixDiagonal::dot_p(const ColD &b_u, const ColD &b_p) const
{
// suppress warning
UNUSED(b_u);
// check input
assert( static_cast<size_t>(b_u.size()) == m_nnu );
assert( static_cast<size_t>(b_p.size()) == m_nnp );
// allocate output
ColD c_p(m_nnp);
// compute product
#pragma omp parallel for
for ( size_t i = 0 ; i < m_nnp ; ++i )
c_p(i) = m_data(m_iip(i)) * b_p(i);
return c_p;
}
// ------------------------ check structure of matrices stored per element -------------------------
inline void MatrixDiagonal::check_diagonal(const ArrD &elemmat) const
{
// check input
assert( elemmat.rank() == 3 );
assert( elemmat.shape(0) == m_nelem );
assert( elemmat.shape(1) == m_nne*m_ndim );
assert( elemmat.shape(2) == m_nne*m_ndim );
// get numerical precision
double eps = std::numeric_limits<double>::epsilon();
// loop over all entries
#pragma omp parallel for
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 )
if ( m*m_ndim+i != n*m_ndim+j )
if ( std::abs(elemmat(e,m*m_ndim+i,n*m_ndim+j)) > eps )
throw std::runtime_error("Element matrices are not diagonal");
}
// ----------------------------- assemble matrices stored per element ------------------------------
inline void MatrixDiagonal::assemble(const ArrD &elemmat)
{
// check input
assert( elemmat.rank() == 3 );
assert( elemmat.shape(0) == m_nelem );
assert( elemmat.shape(1) == m_nne*m_ndim );
assert( elemmat.shape(2) == m_nne*m_ndim );
// zero-initialize matrix
m_data.setZero();
// temporarily disable parallelization by Eigen
Eigen::setNbThreads(1);
// start threads (all variables declared in this scope are local to each thread)
#pragma omp parallel
{
// zero-initialize matrix
ColD t_mat = ColD::Zero(m_ndof);
// assemble
#pragma omp for
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 )
t_mat(m_dofs(m_conn(e,m),i)) += elemmat(e,m*m_ndim+i,m*m_ndim+i);
// reduce: combine result obtained on the different threads
#pragma omp critical
m_data += t_mat;
}
// reset automatic parallelization by Eigen
Eigen::setNbThreads(0);
// signal change
m_change = true;
}
// ------------------------------------- solve: Mat * u = rhs --------------------------------------
inline ColD MatrixDiagonal::solve(const ColD &rhs, const ColD &u_p)
{
// suppress warning
UNUSED(u_p);
// check input
assert( static_cast<size_t>(u_p.size()) == m_nnp );
assert( static_cast<size_t>(rhs.size()) == m_ndof );
// invert if needed
if ( m_change ) m_inv = m_data.cwiseInverse();
// reset signal
m_change = false;
// solve
ColD u = m_inv.cwiseProduct(rhs);
// set prescribed DOFs
for ( size_t i = 0 ; i < m_nnp ; ++i )
u(m_iip(i)) = u_p(i);
return u;
}
// ------------------------------------- solve: Mat * u = rhs --------------------------------------
inline ColD MatrixDiagonal::solve_u(const ColD &rhs_u, const ColD &u_p)
{
// suppress warning
UNUSED(u_p);
// check input
assert( static_cast<size_t>(u_p .size()) == m_nnp );
assert( static_cast<size_t>(rhs_u.size()) == m_nnu );
// invert if needed
if ( m_change ) m_inv = m_data.cwiseInverse();
// reset signal
m_change = false;
// allocate output
ColD u_u(m_nnu);
// solve
#pragma omp parallel for
for ( size_t i = 0 ; i < m_nnu ; ++i )
u_u(i) = m_inv(m_iiu(i)) * rhs_u(i);
return u_u;
}
// ----------------------------------- return as diagonal matrix -----------------------------------
inline ColD MatrixDiagonal::asDiagonal() const
{
return m_data;
}
// --------------------------------------- c_i = A_ij * b_j ----------------------------------------
inline ColD operator* (const MatrixDiagonal &A, const ColD &b)
{
return A.dot(b);
}
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif

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