Exercises_MarkusSchmidt/sheet7/jacobi.template/getmatrix.cpp
Markus Schmidt 4c92446409 Sheet 7
2026-01-06 14:05:44 +01:00

720 lines
21 KiB
C++

#include "getmatrix.h"
#include "userset.h"
#include "omp.h"
#include <algorithm>
#include <cassert>
#include <cmath>
#include <ctime> // contains clock()
#include <iomanip>
#include <iostream>
#include <list>
#include <vector>
using namespace std;
// ####################################################################
Matrix::Matrix(int const nrows, int const ncols)
: _nrows(nrows), _ncols(ncols), _dd(0)
{}
//Matrix::Matrix()
//: Matrix(0,0)
//{}
Matrix::~Matrix()
{}
//vector<double> const & Matrix::GetDiag() const
//{
//if ( 0==_dd.size() )
//{
//_dd.resize(Nrows());
//this->GetDiag(_dd);
//}
//assert( Nrows()==static_cast<int>(_dd.size()) );
//return _dd;
//}
// ####################################################################
CRS_Matrix::CRS_Matrix()
: Matrix(0,0), _nnz(0), _id(0), _ik(0), _sk(0)
{}
CRS_Matrix::~CRS_Matrix()
{}
void CRS_Matrix::Mult(vector<double> &w, vector<double> const &u) const
{
assert( _ncols==static_cast<int>(u.size()) ); // compatibility of inner dimensions
assert( _nrows==static_cast<int>(w.size()) ); // compatibility of outer dimensions
for (int row = 0; row < _nrows; ++row)
{
double wi = 0.0;
for (int ij = _id[row]; ij < _id[row + 1]; ++ij)
{
wi += _sk[ij] * u[ _ik[ij] ];
}
w[row] = wi;
}
return;
}
void CRS_Matrix::Defect(vector<double> &w,
vector<double> const &f, vector<double> const &u) const
{
assert( _ncols==static_cast<int>(u.size()) ); // compatibility of inner dimensions
assert( _nrows==static_cast<int>(w.size()) ); // compatibility of outer dimensions
assert( w.size()==f.size() );
#pragma omp parallel for
for (int row = 0; row < _nrows; ++row)
{
double wi = f[row];
for (int ij = _id[row]; ij < _id[row + 1]; ++ij)
{
wi -= _sk[ij] * u[ _ik[ij] ];
}
w[row] = wi;
}
return;
}
void CRS_Matrix::GetDiag(vector<double> &d) const
{
// be carefull when using a rectangular matrix
int const nm = min(_nrows, _ncols);
assert( nm==static_cast<int>(d.size()) ); // instead of stopping we could resize d and warn the user
for (int row = 0; row < nm; ++row)
{
const int ia = fetch(row, row); // Find diagonal entry of row
assert(ia >= 0);
d[row] = _sk[ia];
}
return;
}
inline
int CRS_Matrix::fetch(int const row, int const col) const
{
int const id2 = _id[row + 1]; // end and
int ip = _id[row]; // start of recent row (global index)
while (ip < id2 && _ik[ip] != col) // find index col (global index)
{
++ip;
}
if (ip >= id2)
{
ip = -1;
#ifndef NDEBUG // compiler option -DNDEBUG switches off the check
cout << "No column " << col << " in row " << row << endl;
assert(ip >= id2);
#endif
}
return ip;
}
void CRS_Matrix::Debug() const
{
// ID points to first entry of row
// no symmetry assumed
cout << "\nMatrix (" << _nrows << " x " << _ncols << " with nnz = " << _id[_nrows] << ")\n";
for (int row = 0; row < _nrows; ++row)
{
cout << "Row " << row << " : ";
int const id1 = _id[row];
int const id2 = _id[row + 1];
for (int j = id1; j < id2; ++j)
{
cout.setf(ios::right, ios::adjustfield);
cout << "[" << setw(2) << _ik[j] << "] " << setw(4) << _sk[j] << " ";
}
cout << endl;
}
return;
}
bool CRS_Matrix::Compare2Old(int nnode, int const id[], int const ik[], double const sk[]) const
{
bool bn = (nnode==_nrows); // number of rows
if (!bn)
{
cout << "######### Error: " << "number of rows" << endl;
}
bool bz = (id[nnode]==_nnz); // number of non zero elements
if (!bz)
{
cout << "######### Error: " << "number of non zero elements" << endl;
}
bool bd = equal(id,id+nnode+1,_id.cbegin()); // row starts
if (!bd)
{
cout << "######### Error: " << "row starts" << endl;
}
bool bk = equal(ik,ik+id[nnode],_ik.cbegin()); // column indices
if (!bk)
{
cout << "######### Error: " << "column indices" << endl;
}
bool bv = equal(sk,sk+id[nnode],_sk.cbegin()); // values
if (!bv)
{
cout << "######### Error: " << "values" << endl;
}
return bn && bz && bd && bk && bv;
}
// ####################################################################
FEM_Matrix::FEM_Matrix(Mesh const & mesh)
: CRS_Matrix(), _mesh(mesh)
{
Derive_Matrix_Pattern();
return;
}
FEM_Matrix::~FEM_Matrix()
{}
void FEM_Matrix::Derive_Matrix_Pattern_fast()
{
cout << "\n############ FEM_Matrix::Derive_Matrix_Pattern ";
double tstart = clock();
int const nelem(_mesh.Nelems());
int const ndof_e(_mesh.NdofsElement());
auto const &ia(_mesh.GetConnectivity());
// Determine the number of matrix rows
_nrows = *max_element(ia.cbegin(), ia.cbegin() + ndof_e * nelem);
++_nrows; // node numberng: 0 ... nnode-1
assert(*min_element(ia.cbegin(), ia.cbegin() + ndof_e * nelem) == 0); // numbering starts with 0 ?
// CSR data allocation
_id.resize(_nrows + 1); // Allocate memory for CSR row pointer
//##########################################################################
auto const v2v=_mesh.Node2NodeGraph();
_nnz=0; // number of connections
_id[0] = 0; // start of matrix row zero
for (size_t v = 0; v<v2v.size(); ++v )
{
_id[v+1] = _id[v] + v2v[v].size();
_nnz += v2v[v].size();
}
assert(_nnz == _id[_nrows]);
_sk.resize(_nnz); // Allocate memory for CSR column index vector
// CSR data allocation
_ik.resize(_nnz); // Allocate memory for CSR column index vector
// Copy column indices
int kk = 0;
for (size_t v = 0; v<v2v.size(); ++v )
{
for (size_t vi=0; vi<v2v[v].size(); ++vi)
{
_ik[kk] = v2v[v][vi];
++kk;
}
}
_ncols = *max_element(_ik.cbegin(), _ik.cend()); // maximal column number
++_ncols; // node numbering: 0 ... nnode-1
//cout << _nrows << " " << _ncols << endl;
assert(_ncols==_nrows);
double duration = (clock() - tstart) / CLOCKS_PER_SEC;
cout << "finished in " << duration << " sec. ########\n";
return;
}
void FEM_Matrix::Derive_Matrix_Pattern_slow()
{
cout << "\n############ FEM_Matrix::Derive_Matrix_Pattern slow ";
double tstart = clock();
int const nelem(_mesh.Nelems());
int const ndof_e(_mesh.NdofsElement());
auto const &ia(_mesh.GetConnectivity());
// Determine the number of matrix rows
_nrows = *max_element(ia.cbegin(), ia.cbegin() + ndof_e * nelem);
++_nrows; // node numberng: 0 ... nnode-1
assert(*min_element(ia.cbegin(), ia.cbegin() + ndof_e * nelem) == 0); // numbering starts with 0 ?
// Collect for each node those nodes it is connected to (multiple entries)
// Detect the neighboring nodes
vector< list<int> > cc(_nrows); // cc[i] is the list of nodes a node i is connected to
for (int i = 0; i < nelem; ++i)
{
int const idx = ndof_e * i;
for (int k = 0; k < ndof_e; ++k)
{
list<int> &cck = cc[ia[idx + k]];
cck.insert( cck.end(), ia.cbegin() + idx, ia.cbegin() + idx + ndof_e );
}
}
// Delete the multiple entries
_nnz = 0;
for (auto &it : cc)
{
it.sort();
it.unique();
_nnz += it.size();
// cout << it.size() << " :: "; copy(it->begin(),it->end(), ostream_iterator<int,char>(cout," ")); cout << endl;
}
// CSR data allocation
_id.resize(_nrows + 1); // Allocate memory for CSR row pointer
_ik.resize(_nnz); // Allocate memory for CSR column index vector
// copy CSR data
_id[0] = 0; // begin of first row
for (size_t i = 0; i < cc.size(); ++i)
{
//cout << i << " " << nid.at(i) << endl;;
const list<int> &ci = cc[i];
const auto nci = static_cast<int>(ci.size());
_id[i + 1] = _id[i] + nci; // begin of next line
copy(ci.begin(), ci.end(), _ik.begin() + _id[i] );
}
assert(_nnz == _id[_nrows]);
_sk.resize(_nnz); // Allocate memory for CSR column index vector
_ncols = *max_element(_ik.cbegin(), _ik.cend()); // maximal column number
++_ncols; // node numbering: 0 ... nnode-1
//cout << _nrows << " " << _ncols << endl;
assert(_ncols==_nrows);
double duration = (clock() - tstart) / CLOCKS_PER_SEC;
cout << "finished in " << duration << " sec. ########\n";
return;
}
void FEM_Matrix::CalculateLaplace(vector<double> &f)
{
cout << "\n############ FEM_Matrix::CalculateLaplace ";
//double tstart = clock();
double tstart = omp_get_wtime(); // OpenMP
assert(_mesh.NdofsElement() == 3); // only for triangular, linear elements
//cout << _nnz << " vs. " << _id[_nrows] << " " << _nrows<< endl;
assert(_nnz == _id[_nrows]);
for (int k = 0; k < _nrows; ++k)
{
_sk[k] = 0.0;
}
for (int k = 0; k < _nrows; ++k)
{
f[k] = 0.0;
}
double ske[3][3], fe[3];
// Loop over all elements
auto const nelem = _mesh.Nelems();
auto const &ia = _mesh.GetConnectivity();
auto const &xc = _mesh.GetCoords();
#pragma omp parallel for private(ske,fe)
for (int i = 0; i < nelem; ++i)
{
CalcElem(ia.data()+3 * i, xc.data(), ske, fe);
//AddElem(ia.data()+3 * i, ske, fe, _id.data(), _ik.data(), _sk.data(), f.data()); // GH: deprecated
AddElem_3(ia.data()+3 * i, ske, fe, f);
}
//double duration = (clock() - tstart) / CLOCKS_PER_SEC;
double duration = omp_get_wtime() - tstart; // OpenMP
cout << "finished in " << duration << " sec. ########\n";
//Debug();
return;
}
//void FEM_Matrix::ApplyDirichletBC(std::vector<double> const &u, std::vector<double> &f)
//{
//double const PENALTY = 1e6;
//auto const idx = _mesh.Index_DirichletNodes();
//int const nidx = idx.size();
//for (int i=0; i<nidx; ++i)
//{
//int const k = idx[i];
//int const id1 = fetch(k, k); // Find diagonal entry of k
//assert(id1 >= 0);
//_sk[id1] += PENALTY; // matrix weighted scaling feasible
//f[k] += PENALTY * u[k];
//}
//return;
//}
void FEM_Matrix::ApplyDirichletBC(std::vector<double> const &u, std::vector<double> &f)
{
auto const idx = _mesh.Index_DirichletNodes();
int const nidx = idx.size();
for (int i=0; i<nidx; ++i)
{
int const row = idx[i];
for (int ij=_id[row]; ij<_id[row+1]; ++ij)
{
int const col=_ik[ij];
if (col==row)
{
_sk[ij] = 1.0;
f[row] = u[row];
}
else
{
int const id1 = fetch(col, row); // Find entry (col,row)
assert(id1 >= 0);
f[col] -= _sk[id1]*u[row];
_sk[id1] = 0.0;
_sk[ij] = 0.0;
}
}
}
return;
}
void FEM_Matrix::AddElem_3(int const ial[3], double const ske[3][3], double const fe[3], vector<double> & f)
{
for (int i = 0; i < 3; ++i)
{
const int ii = ial[i]; // row ii (global index)
for (int j = 0; j < 3; ++j) // no symmetry assumed
{
const int jj = ial[j]; // column jj (global index)
const int ip = fetch(ii,jj); // find column entry jj in row ii
#ifndef NDEBUG // compiler option -DNDEBUG switches off the check
if (ip<0) // no entry found !!
{
cout << "Error in AddElem: (" << ii << "," << jj << ") ["
<< ial[0] << "," << ial[1] << "," << ial[2] << "]\n";
assert(ip>=0);
}
#endif
#pragma omp atomic
_sk[ip] += ske[i][j];
}
#pragma omp atomic
f[ii] += fe[i];
}
}
// ####################################################################
//Prolongation::Prolongation(Mesh const & cmesh, Mesh const & fmesh)
//: CRS_Matrix(), _cmesh(cmesh), _fmesh(fmesh)
//{
//Derive_Matrix_Pattern();
//return;
//}
//void Prolongation::Derive_Matrix_Pattern()
//{
//cout << "\n ***** Subject to ongoing imlementation. *****\n";
//}
// ####################################################################
// *********************************************************************
// general routine for lin. triangular elements
void CalcElem(int const ial[3], double const xc[], double ske[3][3], double fe[3])
//void CalcElem(const int* __restrict__ ial, const double* __restrict__ xc, double* __restrict__ ske[3], double* __restrict__ fe)
{
const int i1 = 2 * ial[0], i2 = 2 * ial[1], i3 = 2 * ial[2];
const double x13 = xc[i3 + 0] - xc[i1 + 0], y13 = xc[i3 + 1] - xc[i1 + 1],
x21 = xc[i1 + 0] - xc[i2 + 0], y21 = xc[i1 + 1] - xc[i2 + 1],
x32 = xc[i2 + 0] - xc[i3 + 0], y32 = xc[i2 + 1] - xc[i3 + 1];
const double jac = fabs(x21 * y13 - x13 * y21);
ske[0][0] = 0.5 / jac * (y32 * y32 + x32 * x32);
ske[0][1] = 0.5 / jac * (y13 * y32 + x13 * x32);
ske[0][2] = 0.5 / jac * (y21 * y32 + x21 * x32);
ske[1][0] = ske[0][1];
ske[1][1] = 0.5 / jac * (y13 * y13 + x13 * x13);
ske[1][2] = 0.5 / jac * (y21 * y13 + x21 * x13);
ske[2][0] = ske[0][2];
ske[2][1] = ske[1][2];
ske[2][2] = 0.5 / jac * (y21 * y21 + x21 * x21);
const double xm = (xc[i1 + 0] + xc[i2 + 0] + xc[i3 + 0]) / 3.0,
ym = (xc[i1 + 1] + xc[i2 + 1] + xc[i3 + 1]) / 3.0;
//fe[0] = fe[1] = fe[2] = 0.5 * jac * FunctF(xm, ym) / 3.0;
fe[0] = fe[1] = fe[2] = 0.5 * jac * fNice(xm, ym) / 3.0;
}
void CalcElem_Masse(int const ial[3], double const xc[], double const cm, double ske[3][3])
{
const int i1 = 2 * ial[0], i2 = 2 * ial[1], i3 = 2 * ial[2];
const double x13 = xc[i3 + 0] - xc[i1 + 0], y13 = xc[i3 + 1] - xc[i1 + 1],
x21 = xc[i1 + 0] - xc[i2 + 0], y21 = xc[i1 + 1] - xc[i2 + 1];
//x32 = xc[i2 + 0] - xc[i3 + 0], y32 = xc[i2 + 1] - xc[i3 + 1];
const double jac = fabs(x21 * y13 - x13 * y21);
ske[0][0] += jac/12.0;
ske[0][1] += jac/24.0;
ske[0][2] += jac/24.0;
ske[1][0] += jac/24.0;
ske[1][1] += jac/12.0;
ske[1][2] += jac/24.0;
ske[2][0] += jac/24.0;
ske[2][1] += jac/24.0;
ske[2][2] += jac/12.0;
return;
}
// general routine for lin. triangular elements,
// non-symm. matrix
// node numbering in element: a s c e n d i n g indices !!
// GH: deprecated
void AddElem(int const ial[3], double const ske[3][3], double const fe[3],
int const id[], int const ik[], double sk[], double f[])
{
for (int i = 0; i < 3; ++i)
{
const int ii = ial[i], // row ii (global index)
id1 = id[ii], // start and
id2 = id[ii + 1]; // end of row ii in matrix
int ip = id1;
for (int j = 0; j < 3; ++j) // no symmetry assumed
{
const int jj = ial[j];
bool not_found = true;
do // find entry jj (global index) in row ii
{
not_found = (ik[ip] != jj);
++ip;
}
while (not_found && ip < id2);
#ifndef NDEBUG // compiler option -DNDEBUG switches off the check
if (not_found) // no entry found !!
{
cout << "Error in AddElem: (" << ii << "," << jj << ") ["
<< ial[0] << "," << ial[1] << "," << ial[2] << "]\n";
assert(!not_found);
}
#endif
sk[ip - 1] += ske[i][j];
}
f[ii] += fe[i];
}
}
// ----------------------------------------------------------------------------
// #####################################################################
BisectInterpolation::BisectInterpolation()
: Matrix( 0, 0 ), _iv(), _vv()
{
}
BisectInterpolation::BisectInterpolation(std::vector<int> const & fathers)
: Matrix( static_cast<int>(fathers.size())/2, 1+*max_element(fathers.cbegin(),fathers.cend()) ),
_iv(fathers), _vv(fathers.size(),0.5)
{
}
BisectInterpolation::~BisectInterpolation()
{}
void BisectInterpolation::GetDiag(vector<double> &d) const
{
assert( Nrows()==static_cast<int>(d.size()) );
for (int k=0; k<Nrows(); ++k)
{
if ( _iv[2*k]==_iv[2*k+1] )
{
d[k] = 1.0;
}
else
{
d[k] = 0.0;
}
}
return;
}
void BisectInterpolation::Mult(vector<double> &wf, vector<double> const &uc) const
{
assert( Nrows()==static_cast<int>(wf.size()) );
assert( Ncols()==static_cast<int>(uc.size()) );
#pragma omp parallel for
for (int k=0; k<Nrows(); ++k)
{
wf[k] = _vv[2*k]*uc[_iv[2*k]] + _vv[2*k+1]*uc[_iv[2*k+1]];
}
return;
}
//void BisectInterpolation::MultT(vector<double> const &wf, vector<double> &uc) const
//{
//assert( Nrows()==static_cast<int>(wf.size()) );
//assert( Ncols()==static_cast<int>(uc.size()) );
//// GH: atomic slows down the code ==> use different storage for MultT operation (CRS-matrix?)
////#pragma omp parallel for
//for (int k=0; k<Ncols(); ++k) uc[k] = 0.0;
//#pragma omp parallel for
//for (int k=0; k<Nrows(); ++k)
//{
//#pragma omp atomic
//uc[_iv[2*k] ] += _vv[2*k ]*wf[k];
//#pragma omp atomic
//uc[_iv[2*k+1]] += _vv[2*k+1]*wf[k];
//}
//return;
//}
void BisectInterpolation::MultT(vector<double> const &wf, vector<double> &uc) const
{
assert( Nrows()==static_cast<int>(wf.size()) );
assert( Ncols()==static_cast<int>(uc.size()) );
// GH: atomic slows down the code ==> use different storage for MultT operation (CRS-matrix?)
//#pragma omp parallel for
for (int k=0; k<Ncols(); ++k) uc[k] = 0.0;
#pragma omp parallel for
for (int k=0; k<Nrows(); ++k)
{
if (_iv[2*k]!=_iv[2*k+1])
{
#pragma omp atomic
uc[_iv[2*k] ] += _vv[2*k ]*wf[k];
#pragma omp atomic
uc[_iv[2*k+1]] += _vv[2*k+1]*wf[k];
}
else
{
#pragma omp atomic
uc[_iv[2*k] ] += 2.0*_vv[2*k ]*wf[k]; // uses a property of class BisectInterpolation
}
}
return;
}
void BisectInterpolation::Defect(vector<double> &w,
vector<double> const &f, vector<double> const &u) const
{
assert( Nrows()==static_cast<int>(w.size()) );
assert( Ncols()==static_cast<int>(u.size()) );
assert( w.size()==f.size() );
for (int k=0; k<Nrows(); ++k)
{
w[k] = f[k] - _vv[2*k]*u[_iv[2*k]] + _vv[2*k+1]*u[_iv[2*k+1]];
}
return;
}
void BisectInterpolation::Debug() const
{
for (int k=0; k<Nrows(); ++k)
{
cout << k << " : fathers(" << _iv[2*k] << "," << _iv[2*k+1] << ") ";
cout << "weights(" << _vv[2*k] << "," << _vv[2*k+1] << endl;
}
cout << endl;
return;
}
int BisectInterpolation::fetch(int row, int col) const
{
int idx(-1);
if (_iv[2*row ] == col) idx = 2*row;
if (_iv[2*row+1] == col) idx = 2*row+1;
assert(idx>=0);
return idx;
}
// #####################################################################
BisectIntDirichlet::BisectIntDirichlet(std::vector<int> const & fathers, std::vector<int> const & idxc_dir)
: BisectInterpolation(fathers)
{
vector<bool> bdir(Ncols(), false); // Indicator for Dirichlet coarse nodes
for (size_t kc=0; kc<idxc_dir.size(); ++kc)
{
bdir.at(idxc_dir[kc]) = true; // Mark Dirichlet node from coarse mesh
}
for (size_t j=0; j<_iv.size(); ++j)
{
if ( bdir.at(_iv[j]) ) _vv[j] = 0.0; // set weight to zero iff (at least) one father is Dirichlet node
}
return;
}
BisectIntDirichlet::~BisectIntDirichlet()
{}
// #####################################################################
void DefectRestrict(CRS_Matrix const & SK, BisectInterpolation const& P,
vector<double> &fc, vector<double> &ff, vector<double> &uf)
{
assert( P.Nrows()==static_cast<int>(ff.size()) );
assert( P.Ncols()==static_cast<int>(fc.size()) );
assert( ff.size()==uf.size() );
assert( P.Nrows()==SK.Nrows() );
//#pragma omp parallel for
for (int k=0; k<P.Ncols(); ++k) fc[k] = 0.0;
// GH: atomic slows down the code ==> use different storage for MultT operation (CRS-matrix?)
#pragma omp parallel for
for (int row = 0; row < SK._nrows; ++row)
{
double wi = ff[row];
for (int ij = SK._id[row]; ij < SK._id[row + 1]; ++ij)
{
wi -= SK._sk[ij] * uf[ SK._ik[ij] ];
}
const int i1=P._iv[2*row];
const int i2=P._iv[2*row+1];
if (i1!=i2)
{
#pragma omp atomic
fc[i1] += P._vv[2*row ]*wi;
#pragma omp atomic
fc[i2] += P._vv[2*row +1]*wi;
}
else
{
#pragma omp atomic
fc[i1] += 2.0*P._vv[2*row ]*wi; // uses a property of class BisectInterpolation
}
}
return;
}