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// $Id: sparse_mic.templates.h 30036 2013-07-18 16:55:32Z maier $
//
// Copyright (C) 2002 - 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_mic_templates_h
#define __deal2__sparse_mic_templates_h
#include <deal.II/base/memory_consumption.h>
#include <deal.II/lac/sparse_mic.h>
#include <deal.II/lac/vector.h>
DEAL_II_NAMESPACE_OPEN
template <typename number>
SparseMIC<number>::SparseMIC ()
:
diag(0),
inv_diag(0),
inner_sums(0)
{}
template <typename number>
SparseMIC<number>::SparseMIC (const SparsityPattern &sparsity)
:
diag(0),
inv_diag(0),
inner_sums(0)
{
SparseMatrix<number>::reinit (sparsity);
}
template <typename number>
SparseMIC<number>::~SparseMIC()
{
clear();
}
template <typename number>
void SparseMIC<number>::clear()
{
{
std::vector<number> tmp;
tmp.swap (diag);
}
{
std::vector<number> tmp;
tmp.swap (inv_diag);
}
{
std::vector<number> tmp;
tmp.swap (inner_sums);
}
SparseLUDecomposition<number>::clear();
}
template <typename number>
template <typename somenumber>
inline
void SparseMIC<number>::initialize (const SparseMatrix<somenumber> &matrix,
const AdditionalData &data)
{
SparseLUDecomposition<number>::initialize(matrix, data);
decompose(matrix, data.strengthen_diagonal);
}
template <typename number>
void SparseMIC<number>::reinit (const SparsityPattern &sparsity)
{
{
std::vector<number> tmp;
tmp.swap (diag);
}
{
std::vector<number> tmp;
tmp.swap (inv_diag);
}
{
std::vector<number> tmp;
tmp.swap (inner_sums);
}
SparseMatrix<number>::reinit(sparsity);
this->decomposed = false;
}
template <typename number>
template <typename somenumber>
void SparseMIC<number>::decompose (const SparseMatrix<somenumber> &matrix,
const double strengthen_diagonal)
{
SparseLUDecomposition<number>::decompose(matrix, 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));
if (strengthen_diagonal > 0)
this->strengthen_diagonal_impl ();
// MIC implementation: (S. Margenov lectures)
// x[i] = a[i][i] - sum(k=1, i-1,
// a[i][k]/x[k]*sum(j=k+1, N, a[k][j]))
// TODO: for sake of simplicity,
// those are placed here. A better
// implementation would store this
// values in the underlying sparse
// matrix itself.
diag.resize (this->m());
inv_diag.resize (this->m());
inner_sums.resize (this->m());
// precalc sum(j=k+1, N, a[k][j]))
for (size_type row=0; row<this->m(); row++)
inner_sums[row] = get_rowsum(row);
for (size_type row=0; row<this->m(); row++)
{
const number temp = this->begin(row)->value();
number temp1 = 0;
// work on the lower left part of the matrix. we know
// it's symmetric, so we can work with this alone
for (typename SparseMatrix<somenumber>::const_iterator
p = matrix.begin(row)+1;
(p != matrix.end(row)) && (p->column() < row);
++p)
temp1 += p->value() / diag[p->column()] * inner_sums[p->column()];
Assert(temp-temp1 > 0, ExcStrengthenDiagonalTooSmall());
diag[row] = temp - temp1;
inv_diag[row] = 1.0/diag[row];
}
}
template <typename number>
inline number
SparseMIC<number>::get_rowsum (const size_type row) const
{
Assert(this->m()==this->n(), ExcNotQuadratic());
number rowsum = 0;
for (typename SparseMatrix<number>::const_iterator
p = this->begin(row)+1;
p != this->end(row); ++p)
if (p->column() > row)
rowsum += p->value();
return rowsum;
}
template <typename number>
template <typename somenumber>
void
SparseMIC<number>::vmult (Vector<somenumber> &dst,
const Vector<somenumber> &src) const
{
SparseLUDecomposition<number>::vmult (dst, src);
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();
// We assume the underlying matrix A is: A = X - L - U, where -L and -U are
// strictly lower- and upper- diagonal parts of the system.
//
// Solve (X-L)X{-1}(X-U) x = b in 3 steps:
dst = src;
for (size_type row=0; row<N; ++row)
{
// Now: (X-L)u = b
// get start of this row. skip
// the diagonal element
for (typename SparseMatrix<number>::const_iterator
p = this->begin(row)+1;
(p != this->end(row)) && (p->column() < row);
++p)
dst(row) -= p->value() * dst(p->column());
dst(row) *= inv_diag[row];
}
// Now: v = Xu
for (size_type row=0; row<N; row++)
dst(row) *= diag[row];
// x = (X-U)v
for (int row=N-1; row>=0; --row)
{
// get end of this row
for (typename SparseMatrix<number>::const_iterator
p = this->begin(row)+1;
p != this->end(row);
++p)
if (p->column() > static_cast<size_type>(row))
dst(row) -= p->value() * dst(p->column());
dst(row) *= inv_diag[row];
}
}
template <typename number>
std::size_t
SparseMIC<number>::memory_consumption () const
{
return (SparseLUDecomposition<number>::memory_consumption () +
MemoryConsumption::memory_consumption(diag) +
MemoryConsumption::memory_consumption(inv_diag) +
MemoryConsumption::memory_consumption(inner_sums));
}
DEAL_II_NAMESPACE_CLOSE
#endif // __deal2__sparse_mic_templates_h
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