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MatrixDiagonal.hpp
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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 XGOOSEFEM_MATRIXDIAGONAL_CPP
#define XGOOSEFEM_MATRIXDIAGONAL_CPP
// -------------------------------------------------------------------------------------------------
#include "MatrixDiagonal.h"
// =========================================== GooseFEM ============================================
namespace xGooseFEM {
// ------------------------------------------ constructor ------------------------------------------
inline MatrixDiagonal::MatrixDiagonal(const xt::xtensor<size_t,2> &conn,
const xt::xtensor<size_t,2> &dofs) : m_conn(conn), m_dofs(dofs)
{
// extract mesh dimensions
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)[0] + 1;
m_nnp = 0;
m_nnu = m_ndof;
m_iiu = xt::arange<size_t>(m_ndof);
m_iip = xt::empty<size_t>({0});
// check consistency
assert( xt::amax(m_conn)[0] + 1 == m_nnode );
assert( m_ndof <= m_nnode * m_ndim );
// allocate matrix and its inverse
m_data = xt::empty<double>({m_ndof});
m_inv = xt::empty<double>({m_ndof});
}
// ------------------------------------------ constructor ------------------------------------------
inline MatrixDiagonal::MatrixDiagonal(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)
{
// extract mesh dimensions
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)[0] + 1;
m_nnp = m_iip.size();
m_nnu = m_ndof - m_nnp;
// check consistency
assert( xt::amax(m_conn)[0] + 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 = xt::empty<size_t>({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 = xt::empty<double>({m_ndof});
m_inv = xt::empty<double>({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 xt::xtensor<size_t,1> MatrixDiagonal::iiu() const
{
return m_iiu;
}
// ------------------------------------ return prescribed DOFs -------------------------------------
inline xt::xtensor<size_t,1> MatrixDiagonal::iip() const
{
return m_iip;
}
// --------------------------------------- c_i = A_ij * b_j ----------------------------------------
inline xt::xtensor<double,1> MatrixDiagonal::dot(const xt::xtensor<double,1> &b) const
{
// check input
assert( static_cast<size_t>(b.size()) == m_ndof );
// compute product
return m_data * b;
}
// --------------------------------------- c_i = A_ij * b_j ----------------------------------------
inline xt::xtensor<double,1> MatrixDiagonal::dot_u(const xt::xtensor<double,1> &b) const
{
// check input
assert( static_cast<size_t>(b.size()) == m_ndof );
// allocate output
xt::xtensor<double,1> c_u = xt::empty<double>({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 xt::xtensor<double,1> MatrixDiagonal::dot_u(const xt::xtensor<double,1> &b_u, const xt::xtensor<double,1> &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
xt::xtensor<double,1> c_u = xt::empty<double>({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 xt::xtensor<double,1> MatrixDiagonal::dot_p(const xt::xtensor<double,1> &b) const
{
// check input
assert( static_cast<size_t>(b.size()) == m_ndof );
// allocate output
xt::xtensor<double,1> c_p = xt::empty<double>({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 xt::xtensor<double,1> MatrixDiagonal::dot_p(const xt::xtensor<double,1> &b_u, const xt::xtensor<double,1> &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
xt::xtensor<double,1> c_p = xt::empty<double>({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 xt::xtensor<double,3> &elemmat) const
{
// check input
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 xt::xtensor<double,3> &elemmat)
{
// check input
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 *= 0.0;
// assemble
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 )
m_data(m_dofs(m_conn(e,m),i)) += elemmat(e,m*m_ndim+i,m*m_ndim+i);
// signal change
m_change = true;
}
// ------------------------------------- solve: Mat * u = rhs --------------------------------------
inline xt::xtensor<double,1> MatrixDiagonal::solve(const xt::xtensor<double,1> &rhs)
{
// check input
assert( m_nnp == 0 );
assert( rhs.size() == m_ndof );
// invert if needed
if ( m_change ) {
for ( size_t i = 0 ; i < m_ndof ; ++i ) m_inv(i) = 1. / m_data(i);
}
// reset signal
m_change = false;
// solve
xt::xtensor<double,1> u = m_inv * rhs;
return u;
}
// ------------------------------------- solve: Mat * u = rhs --------------------------------------
inline xt::xtensor<double,1> MatrixDiagonal::solve(const xt::xtensor<double,1> &rhs, const xt::xtensor<double,1> &u_p)
{
// check input
assert( u_p.size() == m_nnp );
assert( rhs.size() == m_ndof );
// invert if needed
if ( m_change ) {
for ( size_t i = 0 ; i < m_ndof ; ++i ) m_inv(i) = 1. / m_data(i);
}
// reset signal
m_change = false;
// solve
xt::xtensor<double,1> u = m_inv * 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 xt::xtensor<double,1> MatrixDiagonal::solve_u(const xt::xtensor<double,1> &rhs_u)
{
// check input
assert( rhs_u.size() == m_nnu );
// invert if needed
if ( m_change ) {
for ( size_t i = 0 ; i < m_ndof ; ++i ) m_inv(i) = 1. / m_data(i);
}
// reset signal
m_change = false;
// allocate output
xt::xtensor<double,1> u_u = xt::empty<double>({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;
}
// ------------------------------------- solve: Mat * u = rhs --------------------------------------
inline xt::xtensor<double,1> MatrixDiagonal::solve_u(const xt::xtensor<double,1> &rhs_u, const xt::xtensor<double,1> &u_p)
{
// suppress warning
UNUSED(u_p);
// check input
assert( u_p .size() == m_nnp );
assert( rhs_u.size() == m_nnu );
// invert if needed
if ( m_change ) {
for ( size_t i = 0 ; i < m_ndof ; ++i ) m_inv(i) = 1. / m_data(i);
}
// reset signal
m_change = false;
// allocate output
xt::xtensor<double,1> u_u = xt::empty<double>({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 xt::xtensor<double,1> MatrixDiagonal::asDiagonal() const
{
return m_data;
}
// --------------------------------------- c_i = A_ij * b_j ----------------------------------------
inline xt::xtensor<double,1> operator* (const MatrixDiagonal &A, const xt::xtensor<double,1> &b)
{
return A.dot(b);
}
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif

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