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// $Id: sparse_ilu.templates.h 30036 2013-07-18 16:55:32Z maier $
//
// Copyright (C) 1999 - 2013 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef __deal2__sparse_ilu_templates_h
#define __deal2__sparse_ilu_templates_h
#include <deal.II/base/config.h>
#include <deal.II/lac/vector.h>
#include <deal.II/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)
{
SparseMatrix<number>::reinit(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.rowstart;
const size_type *const ja = sparsity.colnums;
number *luval = this->SparseMatrix<number>::val;
const size_type N = this->m();
size_type jrow = 0;
std::vector<size_type> iw (N, numbers::invalid_size_type);
for (size_type k=0; k<N; ++k)
{
const size_type j1 = ia[k],
j2 = ia[k+1]-1;
for (size_type 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
size_type 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
size_type jj = ia[jrow]+1;
while (ja[jj] < jrow)
++jj;
for (; jj<ia[jrow+1]; ++jj)
{
const size_type jw = iw[ja[jj]];
if (jw != numbers::invalid_size_type)
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 (size_type j=j1; j<=j2; ++j)
iw[ja[j]] = numbers::invalid_size_type;
}
}
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 size_type N=dst.size();
const std::size_t *const rowstart_indices
= this->get_sparsity_pattern().rowstart;
const size_type *const column_numbers
= this->get_sparsity_pattern().colnums;
// 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 (size_type row=0; row<N; ++row)
{
// get start of this row. skip the
// diagonal element
const size_type *const rowstart = &column_numbers[rowstart_indices[row]+1];
// find the position where the part
// right of the diagonal starts
const size_type *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 size_type *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 size_type *const rowend = &column_numbers[rowstart_indices[row+1]];
// find the position where the part
// right of the diagonal starts
const size_type *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 size_type *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 size_type N=dst.size();
const std::size_t *const rowstart_indices
= this->get_sparsity_pattern().rowstart;
const size_type *const column_numbers
= this->get_sparsity_pattern().colnums;
// 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 (size_type 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 size_type *const rowend = &column_numbers[rowstart_indices[row+1]];
// find the position where the part
// right of the diagonal starts
const size_type *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 size_type *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 size_type *const rowstart = &column_numbers[rowstart_indices[row]+1];
// find the position where the part
// right of the diagonal starts
const size_type *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 size_type *col=rowstart; col!=first_after_diagonal; ++col, ++luval)
tmp(*col) += *luval * dst_row;
}
}
template <typename number>
std::size_t
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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