local_system.cc

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#include "local_system.hh"
 
#include <armadillo>
#include "system/asserts.hh"
#include "system/index_types.hh"
 
 
LocalSystem::LocalSystem()
{}
 
 
LocalSystem::LocalSystem(uint nrows, uint ncols)
: row_dofs(nrows),
  col_dofs(ncols),
  matrix(nrows, ncols),
  rhs(nrows),
  sparsity(nrows,ncols),
  elim_rows(nrows),
  elim_cols(ncols),
  solution_rows(nrows),
  solution_cols(ncols),
  diag_rows(nrows)
{
    reset();
}
 
void LocalSystem::set_size(uint nrows, uint ncols)
{
    row_dofs.set_size(nrows);
    col_dofs.set_size(ncols);
    matrix.set_size(nrows, ncols);
    rhs.set_size(nrows);
    elim_rows.set_size(nrows);
    elim_cols.set_size(ncols);
    solution_rows.set_size(nrows);
    solution_cols.set_size(ncols);
    diag_rows.set_size(nrows);
    // destroy previous sparsity pattern
    sparsity.set_size(nrows,ncols);
    sparsity.fill(almost_zero);
}
 
 
void LocalSystem::reset()
{
    // zeros in local system
    matrix.zeros();
    rhs.zeros();
    // drop all dirichlet values
    n_elim_rows=n_elim_cols=0;
}
 
 
void LocalSystem::reset(uint nrows, uint ncols)
{
    if(matrix.n_rows != nrows || matrix.n_cols != ncols)
    {
        set_size(nrows, ncols);
    }
    
    reset();
}
 
 
 
void LocalSystem::reset(const LocDofVec &rdofs, const LocDofVec &cdofs)
{
    if(matrix.n_rows != rdofs.n_rows || matrix.n_cols != cdofs.n_rows)
    {
        set_size(rdofs.n_rows, cdofs.n_rows);
    }
    
    reset();
    row_dofs = rdofs;
    col_dofs = cdofs;
}
 
 
 
void LocalSystem::set_solution(uint loc_dof, double solution, double diag)
{
    // check that dofs are same
    //ASSERT( arma::all(row_dofs == col_dofs) );
    set_solution_row(loc_dof, solution, diag);
    set_solution_col(loc_dof, solution);
}
 
void LocalSystem::set_solution_row(uint loc_row, double solution, double diag) {
    elim_rows[n_elim_rows]=loc_row;
    solution_rows[n_elim_rows] = solution;
    diag_rows[n_elim_rows] = diag;
    n_elim_rows++;
}
 
void LocalSystem::set_solution_col(uint loc_col, double solution) {
    elim_cols[n_elim_cols]=loc_col;
    solution_cols[n_elim_cols] = solution;
    n_elim_cols++;
}
 
void LocalSystem::eliminate_solution()
{
    //if there is solution set, eliminate:
    if (n_elim_rows ||  n_elim_cols )
    {
        //DebugOut().fmt("elim rows: {} elim_cols: {}", n_elim_rows, n_elim_cols);
        
        arma::mat tmp_mat = matrix;
        arma::vec tmp_rhs = rhs;
        
        uint ic, ir, row, col;
 
        // eliminate columns
        for(ic=0; ic < n_elim_cols; ic++) {
            col = elim_cols[ic];
            tmp_rhs -= solution_cols[ic] * tmp_mat.col( col );
            tmp_mat.col( col ).zeros();
        }
 
        // eliminate rows
        for(ir=0; ir < n_elim_rows; ir++) {
            row = elim_rows[ir];
            tmp_rhs( row ) = 0.0;
            tmp_mat.row( row ).zeros();
 
            // fix global diagonal
            for(ic=0; ic < n_elim_cols; ic++) {
                col = elim_cols[ic];
                if (row_dofs[row] == col_dofs[col]) {
                    ASSERT(fabs(solution_rows[ir] - solution_cols[ic]) <1e-12 );
                    // if preferred value is not set, then try using matrix value
                    double new_diagonal = matrix(row, col);
 
                    if (diag_rows[ir] != 0.0)    // if preferred value is set
                        new_diagonal = diag_rows[ir];
                    else if(new_diagonal == 0.0)      // if an assembled value is not available
                        new_diagonal = 1.0;
                    //                     double new_diagonal = fabs(matrix(sol_row,col));
                    //                     if (new_diagonal == 0.0) {
                    //                         if (matrix.is_square()) {
                    //                             new_diagonal = arma::sum( abs(matrix.diag())) / matrix.n_rows;
                    //                         } else {
                    //                             new_diagonal = arma::accu( abs(matrix) ) / matrix.n_elem;
                    //                         }
                    //                     }
                    tmp_mat(row,col) = new_diagonal;
                    tmp_rhs(row) = new_diagonal * solution_rows[ir];
 
                }
            }
        }
 
        matrix = tmp_mat;
        rhs = tmp_rhs;
        n_elim_cols=n_elim_rows=0;
    }
    
    // filling almost_zero according to sparsity pattern
    ASSERT_EQ(matrix.n_rows, sparsity.n_rows);
    ASSERT_EQ(matrix.n_cols, sparsity.n_cols);
    matrix = matrix + sparsity;
    
    //DebugOut() << matrix;
    //DebugOut() << rhs;
}
 
 
void LocalSystem::add_value(uint row, uint col, double mat_val, double rhs_val)
{
    ASSERT(row < matrix.n_rows);
    ASSERT(col < matrix.n_cols);
    ASSERT(sparsity(row,col))(row)(col).error("Violation of sparsity pattern.");
    
    matrix(row, col) += mat_val;
    rhs(row) += rhs_val;
}
 
void LocalSystem::add_value(uint row, uint col, double mat_val)
{
    ASSERT(row < matrix.n_rows);
    ASSERT(col < matrix.n_cols);
    ASSERT(sparsity(row,col))(row)(col).error("Violation of sparsity pattern.");
    
    matrix(row, col) += mat_val;
}
 
void LocalSystem::add_value(uint row, double rhs_val)
{
    ASSERT(row < matrix.n_rows);
    
    rhs(row) += rhs_val;
}
 
 
void LocalSystem::set_matrix(arma::mat m) {
    ASSERT_EQ(matrix.n_rows, m.n_rows);
    ASSERT_EQ(matrix.n_cols, m.n_cols);
    matrix = m;
}
 
void LocalSystem::set_rhs(arma::vec r) {
    ASSERT_EQ(matrix.n_rows, r.n_rows);
    rhs = r;
}
 
void LocalSystem::set_sparsity(const arma::umat & sp)
{
    ASSERT_EQ(sparsity.n_rows, sp.n_rows);
    ASSERT_EQ(sparsity.n_cols, sp.n_cols);
    
    sparsity.zeros();
    for(uint i=0; i < sp.n_rows; i++)
        for(uint j=0; j < sp.n_cols; j++)
            if( sp(i,j) != 0 )
                sparsity(i,j) = almost_zero;
//      sparsity.print("sparsity");
}
 
void LocalSystem::compute_schur_complement(uint offset, LocalSystem& schur, bool negative) const
{
    // only for square matrix
    ASSERT_EQ(matrix.n_rows, matrix.n_cols)("Cannot compute Schur complement for non-square matrix.");
    arma::uword n = matrix.n_rows - 1;
    ASSERT_LT(offset, n)("Schur complement (offset) dimension mismatch.");
 
    // B * invA
    arma::mat BinvA = matrix.submat(offset, 0, n, offset-1) * matrix.submat(0, 0, offset-1, offset-1).i();
    
    // Schur complement S = C - B * invA * Bt
    schur.matrix = matrix.submat(offset, offset, n, n) - BinvA * matrix.submat(0, offset, offset-1, n);
    schur.rhs = rhs.subvec(offset, n) - BinvA * rhs.subvec(0, offset-1);
    
    if(negative)
    {
        schur.matrix = -1.0 * schur.matrix;
        schur.rhs = -1.0 * schur.rhs;
    }
}
 
void LocalSystem::reconstruct_solution_schur(uint offset, const arma::vec &schur_solution, arma::vec& reconstructed_solution) const
{
    // only for square matrix
    ASSERT_EQ(matrix.n_rows, matrix.n_cols)("Cannot compute Schur complement for non-square matrix.");
    arma::uword n = matrix.n_rows - 1;
    ASSERT_LT(offset, n)("Schur complement (offset) dimension mismatch.");
 
    reconstructed_solution.set_size(offset);
    // invA
    arma::mat invA =  matrix.submat(0, 0, offset-1, offset-1).i();
    
    // x = invA*b - invA * Bt * schur_solution
    reconstructed_solution = invA * rhs.subvec(0,offset-1) - invA * matrix.submat(0, offset, offset-1, n) * schur_solution;
}