/usr/include/deal.II/lac/sparse_ilu.templates.h is in libdeal.ii-dev 6.3.1-1.1.
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// Copyright (C) 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2008, 2009 by the deal.II authors
// by the deal.II authors and Stephen "Cheffo" Kolaroff
//
// This file is subject to QPL and may not be distributed
// without copyright and license information. Please refer
// to the file deal.II/doc/license.html for the text and
// further information on this license.
//
//---------------------------------------------------------------------------
#ifndef __deal2__sparse_ilu_templates_h
#define __deal2__sparse_ilu_templates_h
#include <base/config.h>
#include <lac/vector.h>
#include <lac/sparse_ilu.h>
#include <algorithm>
#include <cmath>
DEAL_II_NAMESPACE_OPEN
template <typename number>
SparseILU<number>::SparseILU ()
{}
template <typename number>
SparseILU<number>::SparseILU (const SparsityPattern &sparsity) :
SparseLUDecomposition<number> (sparsity)
{}
template <typename number>
template <typename somenumber>
void SparseILU<number>::initialize (const SparseMatrix<somenumber> &matrix,
const AdditionalData data)
{
SparseLUDecomposition<number>::initialize(matrix, data);
decompose(matrix, data.strengthen_diagonal);
}
template <typename number>
template <typename somenumber>
void SparseILU<number>::decompose (const SparseMatrix<somenumber> &matrix,
const double strengthen_diagonal)
{
Assert (matrix.m()==matrix.n(), ExcNotQuadratic ());
Assert (this->m()==this->n(), ExcNotQuadratic ());
Assert (matrix.m()==this->m(), ExcDimensionMismatch(matrix.m(), this->m()));
Assert (strengthen_diagonal>=0,
ExcInvalidStrengthening (strengthen_diagonal));
SparseLUDecomposition<number>::decompose (matrix, strengthen_diagonal);
if (strengthen_diagonal>0)
this->strengthen_diagonal_impl();
// in the following, we implement
// algorithm 10.4 in the book by
// Saad by translating in essence
// the algorithm given at the end
// of section 10.3.2, using the
// names of variables used there
const SparsityPattern &sparsity = this->get_sparsity_pattern();
const std::size_t * const ia = sparsity.get_rowstart_indices();
const unsigned int * const ja = sparsity.get_column_numbers();
number * luval = this->SparseMatrix<number>::val;
const unsigned int N = this->m();
unsigned int jrow;
std::vector<unsigned int> iw (N, numbers::invalid_unsigned_int);
for (unsigned int k=0; k<N; ++k)
{
const unsigned int j1 = ia[k],
j2 = ia[k+1]-1;
for (unsigned int j=j1; j<=j2; ++j)
iw[ja[j]] = j;
// the algorithm in the book
// works on the elements of row
// k left of the
// diagonal. however, since we
// store the diagonal element
// at the first position, start
// at the element after the
// diagonal and run as long as
// we don't walk into the right
// half
unsigned int j = j1+1;
// pathological case: the current row
// of the matrix has only the
// diagonal entry. then we have
// nothing to do.
if (j > j2)
goto label_200;
label_150:
jrow = ja[j];
if (jrow >= k)
goto label_200;
// actual computations:
{
number t1 = luval[j] * luval[ia[jrow]];
luval[j] = t1;
// jj runs from just right of
// the diagonal to the end of
// the row
unsigned int jj = ia[jrow]+1;
while (ja[jj] < jrow)
++jj;
for (; jj<ia[jrow+1]; ++jj)
{
const unsigned int jw = iw[ja[jj]];
if (jw != numbers::invalid_unsigned_int)
luval[jw] -= t1 * luval[jj];
}
++j;
if (j<=j2)
goto label_150;
}
label_200:
// in the book there is an
// assertion that we have hit
// the diagonal element,
// i.e. that jrow==k. however,
// we store the diagonal
// element at the front, so
// jrow must actually be larger
// than k or j is already in
// the next row
Assert ((jrow > k) || (j==ia[k+1]), ExcInternalError());
// now we have to deal with the
// diagonal element. in the
// book it is located at
// position 'j', but here we
// use the convention of
// storing the diagonal element
// first, so instead of j we
// use uptr[k]=ia[k]
Assert (luval[ia[k]] != 0, ExcInternalError());
luval[ia[k]] = 1./luval[ia[k]];
for (unsigned int j=j1; j<=j2; ++j)
iw[ja[j]] = numbers::invalid_unsigned_int;
}
}
template <typename number>
template <typename somenumber>
void SparseILU<number>::vmult (Vector<somenumber> &dst,
const Vector<somenumber> &src) const
{
Assert (dst.size() == src.size(), ExcDimensionMismatch(dst.size(), src.size()));
Assert (dst.size() == this->m(), ExcDimensionMismatch(dst.size(), this->m()));
const unsigned int N=dst.size();
const std::size_t * const rowstart_indices
= this->get_sparsity_pattern().get_rowstart_indices();
const unsigned int * const column_numbers
= this->get_sparsity_pattern().get_column_numbers();
// solve LUx=b in two steps:
// first Ly = b, then
// Ux = y
//
// first a forward solve. since
// the diagonal values of L are
// one, there holds
// y_i = b_i
// - sum_{j=0}^{i-1} L_{ij}y_j
// we split the y_i = b_i off and
// perform it at the outset of the
// loop
dst = src;
for (unsigned int row=0; row<N; ++row)
{
// get start of this row. skip the
// diagonal element
const unsigned int * const rowstart = &column_numbers[rowstart_indices[row]+1];
// find the position where the part
// right of the diagonal starts
const unsigned int * const first_after_diagonal = this->prebuilt_lower_bound[row];
somenumber dst_row = dst(row);
const number * luval = this->SparseMatrix<number>::val +
(rowstart - column_numbers);
for (const unsigned int * col=rowstart; col!=first_after_diagonal; ++col, ++luval)
dst_row -= *luval * dst(*col);
dst(row) = dst_row;
}
// now the backward solve. same
// procedure, but we need not set
// dst before, since this is already
// done.
//
// note that we need to scale now,
// since the diagonal is not equal to
// one now
for (int row=N-1; row>=0; --row)
{
// get end of this row
const unsigned int * const rowend = &column_numbers[rowstart_indices[row+1]];
// find the position where the part
// right of the diagonal starts
const unsigned int * const first_after_diagonal = this->prebuilt_lower_bound[row];
somenumber dst_row = dst(row);
const number * luval = this->SparseMatrix<number>::val +
(first_after_diagonal - column_numbers);
for (const unsigned int * col=first_after_diagonal; col!=rowend; ++col, ++luval)
dst_row -= *luval * dst(*col);
// scale by the diagonal element.
// note that the diagonal element
// was stored inverted
dst(row) = dst_row * this->diag_element(row);
}
}
template <typename number>
template <typename somenumber>
void SparseILU<number>::Tvmult (Vector<somenumber> &dst,
const Vector<somenumber> &src) const
{
Assert (dst.size() == src.size(), ExcDimensionMismatch(dst.size(), src.size()));
Assert (dst.size() == this->m(), ExcDimensionMismatch(dst.size(), this->m()));
const unsigned int N=dst.size();
const std::size_t * const rowstart_indices
= this->get_sparsity_pattern().get_rowstart_indices();
const unsigned int * const column_numbers
= this->get_sparsity_pattern().get_column_numbers();
// solve (LU)'x=b in two steps:
// first U'y = b, then
// L'x = y
//
// first a forward solve. Due to the
// fact that the transpose of U'
// is not easily accessible, a
// temporary vector is required.
Vector<somenumber> tmp (N);
dst = src;
for (unsigned int row=0; row<N; ++row)
{
dst(row) -= tmp (row);
// scale by the diagonal element.
// note that the diagonal element
// was stored inverted
dst(row) *= this->diag_element(row);
// get end of this row
const unsigned int * const rowend = &column_numbers[rowstart_indices[row+1]];
// find the position where the part
// right of the diagonal starts
const unsigned int * const first_after_diagonal = this->prebuilt_lower_bound[row];
const somenumber dst_row = dst (row);
const number * luval = this->SparseMatrix<number>::val +
(first_after_diagonal - column_numbers);
for (const unsigned int * col=first_after_diagonal; col!=rowend; ++col, ++luval)
tmp(*col) += *luval * dst_row;
}
// now the backward solve. same
// procedure, but we need not set
// dst before, since this is already
// done.
//
// note that we no scaling is required
// now, since the diagonal is one
// now
tmp = 0;
for (int row=N-1; row>=0; --row)
{
dst(row) -= tmp (row);
// get start of this row. skip the
// diagonal element
const unsigned int * const rowstart = &column_numbers[rowstart_indices[row]+1];
// find the position where the part
// right of the diagonal starts
const unsigned int * const first_after_diagonal = this->prebuilt_lower_bound[row];
const somenumber dst_row = dst (row);
const number * luval = this->SparseMatrix<number>::val +
(rowstart - column_numbers);
for (const unsigned int * col=rowstart; col!=first_after_diagonal; ++col, ++luval)
tmp(*col) += *luval * dst_row;
}
}
template <typename number>
unsigned int
SparseILU<number>::memory_consumption () const
{
return SparseLUDecomposition<number>::memory_consumption ();
}
/*---------------------------- sparse_ilu.templates.h ---------------------------*/
DEAL_II_NAMESPACE_CLOSE
#endif
/*---------------------------- sparse_ilu.templates.h ---------------------------*/
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