opm-simulators/opm/simulators/linalg/MatrixBlock.hpp

544 lines
20 KiB
C++

/*
Copyright 2016 IRIS AS
Copyright 2019 NORCE
This file is part of the Open Porous Media project (OPM).
OPM is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
OPM is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with OPM. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef OPM_MATRIX_BLOCK_HEADER_INCLUDED
#define OPM_MATRIX_BLOCK_HEADER_INCLUDED
#include <dune/common/fmatrix.hh>
#include <dune/common/fvector.hh>
#include <dune/common/version.hh>
#include <dune/istl/matrixutils.hh>
#include <dune/istl/umfpack.hh>
#include <dune/istl/superlu.hh>
namespace Dune
{
namespace FMatrixHelp {
//! invert 4x4 Matrix without changing the original matrix
template <typename K>
static inline K invertMatrix(const FieldMatrix<K,4,4>& matrix, FieldMatrix<K,4,4>& inverse)
{
inverse[0][0] = matrix[1][1] * matrix[2][2] * matrix[3][3] -
matrix[1][1] * matrix[2][3] * matrix[3][2] -
matrix[2][1] * matrix[1][2] * matrix[3][3] +
matrix[2][1] * matrix[1][3] * matrix[3][2] +
matrix[3][1] * matrix[1][2] * matrix[2][3] -
matrix[3][1] * matrix[1][3] * matrix[2][2];
inverse[1][0] = -matrix[1][0] * matrix[2][2] * matrix[3][3] +
matrix[1][0] * matrix[2][3] * matrix[3][2] +
matrix[2][0] * matrix[1][2] * matrix[3][3] -
matrix[2][0] * matrix[1][3] * matrix[3][2] -
matrix[3][0] * matrix[1][2] * matrix[2][3] +
matrix[3][0] * matrix[1][3] * matrix[2][2];
inverse[2][0] = matrix[1][0] * matrix[2][1] * matrix[3][3] -
matrix[1][0] * matrix[2][3] * matrix[3][1] -
matrix[2][0] * matrix[1][1] * matrix[3][3] +
matrix[2][0] * matrix[1][3] * matrix[3][1] +
matrix[3][0] * matrix[1][1] * matrix[2][3] -
matrix[3][0] * matrix[1][3] * matrix[2][1];
inverse[3][0] = -matrix[1][0] * matrix[2][1] * matrix[3][2] +
matrix[1][0] * matrix[2][2] * matrix[3][1] +
matrix[2][0] * matrix[1][1] * matrix[3][2] -
matrix[2][0] * matrix[1][2] * matrix[3][1] -
matrix[3][0] * matrix[1][1] * matrix[2][2] +
matrix[3][0] * matrix[1][2] * matrix[2][1];
inverse[0][1]= -matrix[0][1] * matrix[2][2] * matrix[3][3] +
matrix[0][1] * matrix[2][3] * matrix[3][2] +
matrix[2][1] * matrix[0][2] * matrix[3][3] -
matrix[2][1] * matrix[0][3] * matrix[3][2] -
matrix[3][1] * matrix[0][2] * matrix[2][3] +
matrix[3][1] * matrix[0][3] * matrix[2][2];
inverse[1][1] = matrix[0][0] * matrix[2][2] * matrix[3][3] -
matrix[0][0] * matrix[2][3] * matrix[3][2] -
matrix[2][0] * matrix[0][2] * matrix[3][3] +
matrix[2][0] * matrix[0][3] * matrix[3][2] +
matrix[3][0] * matrix[0][2] * matrix[2][3] -
matrix[3][0] * matrix[0][3] * matrix[2][2];
inverse[2][1] = -matrix[0][0] * matrix[2][1] * matrix[3][3] +
matrix[0][0] * matrix[2][3] * matrix[3][1] +
matrix[2][0] * matrix[0][1] * matrix[3][3] -
matrix[2][0] * matrix[0][3] * matrix[3][1] -
matrix[3][0] * matrix[0][1] * matrix[2][3] +
matrix[3][0] * matrix[0][3] * matrix[2][1];
inverse[3][1] = matrix[0][0] * matrix[2][1] * matrix[3][2] -
matrix[0][0] * matrix[2][2] * matrix[3][1] -
matrix[2][0] * matrix[0][1] * matrix[3][2] +
matrix[2][0] * matrix[0][2] * matrix[3][1] +
matrix[3][0] * matrix[0][1] * matrix[2][2] -
matrix[3][0] * matrix[0][2] * matrix[2][1];
inverse[0][2] = matrix[0][1] * matrix[1][2] * matrix[3][3] -
matrix[0][1] * matrix[1][3] * matrix[3][2] -
matrix[1][1] * matrix[0][2] * matrix[3][3] +
matrix[1][1] * matrix[0][3] * matrix[3][2] +
matrix[3][1] * matrix[0][2] * matrix[1][3] -
matrix[3][1] * matrix[0][3] * matrix[1][2];
inverse[1][2] = -matrix[0][0] * matrix[1][2] * matrix[3][3] +
matrix[0][0] * matrix[1][3] * matrix[3][2] +
matrix[1][0] * matrix[0][2] * matrix[3][3] -
matrix[1][0] * matrix[0][3] * matrix[3][2] -
matrix[3][0] * matrix[0][2] * matrix[1][3] +
matrix[3][0] * matrix[0][3] * matrix[1][2];
inverse[2][2] = matrix[0][0] * matrix[1][1] * matrix[3][3] -
matrix[0][0] * matrix[1][3] * matrix[3][1] -
matrix[1][0] * matrix[0][1] * matrix[3][3] +
matrix[1][0] * matrix[0][3] * matrix[3][1] +
matrix[3][0] * matrix[0][1] * matrix[1][3] -
matrix[3][0] * matrix[0][3] * matrix[1][1];
inverse[3][2] = -matrix[0][0] * matrix[1][1] * matrix[3][2] +
matrix[0][0] * matrix[1][2] * matrix[3][1] +
matrix[1][0] * matrix[0][1] * matrix[3][2] -
matrix[1][0] * matrix[0][2] * matrix[3][1] -
matrix[3][0] * matrix[0][1] * matrix[1][2] +
matrix[3][0] * matrix[0][2] * matrix[1][1];
inverse[0][3] = -matrix[0][1] * matrix[1][2] * matrix[2][3] +
matrix[0][1] * matrix[1][3] * matrix[2][2] +
matrix[1][1] * matrix[0][2] * matrix[2][3] -
matrix[1][1] * matrix[0][3] * matrix[2][2] -
matrix[2][1] * matrix[0][2] * matrix[1][3] +
matrix[2][1] * matrix[0][3] * matrix[1][2];
inverse[1][3] = matrix[0][0] * matrix[1][2] * matrix[2][3] -
matrix[0][0] * matrix[1][3] * matrix[2][2] -
matrix[1][0] * matrix[0][2] * matrix[2][3] +
matrix[1][0] * matrix[0][3] * matrix[2][2] +
matrix[2][0] * matrix[0][2] * matrix[1][3] -
matrix[2][0] * matrix[0][3] * matrix[1][2];
inverse[2][3] = -matrix[0][0] * matrix[1][1] * matrix[2][3] +
matrix[0][0] * matrix[1][3] * matrix[2][1] +
matrix[1][0] * matrix[0][1] * matrix[2][3] -
matrix[1][0] * matrix[0][3] * matrix[2][1] -
matrix[2][0] * matrix[0][1] * matrix[1][3] +
matrix[2][0] * matrix[0][3] * matrix[1][1];
inverse[3][3] = matrix[0][0] * matrix[1][1] * matrix[2][2] -
matrix[0][0] * matrix[1][2] * matrix[2][1] -
matrix[1][0] * matrix[0][1] * matrix[2][2] +
matrix[1][0] * matrix[0][2] * matrix[2][1] +
matrix[2][0] * matrix[0][1] * matrix[1][2] -
matrix[2][0] * matrix[0][2] * matrix[1][1];
K det = matrix[0][0] * inverse[0][0] + matrix[0][1] * inverse[1][0] +
matrix[0][2] * inverse[2][0] + matrix[0][3] * inverse[3][0];
// return identity for singular or nearly singular matrices.
if (std::abs(det) < 1e-40) {
for (int i = 0; i < 4; ++i){
inverse[i][i] = 1.0;
}
return 1.0;
}
K inv_det = 1.0 / det;
inverse *= inv_det;
return det;
}
template <typename K>
static inline K invertMatrix(const DynamicMatrix<K>& matrix, DynamicMatrix<K>& inverse)
{
// this function is only for 4 X 4 matrix
assert (matrix.rows() == 4);
inverse[0][0] = matrix[1][1] * matrix[2][2] * matrix[3][3] -
matrix[1][1] * matrix[2][3] * matrix[3][2] -
matrix[2][1] * matrix[1][2] * matrix[3][3] +
matrix[2][1] * matrix[1][3] * matrix[3][2] +
matrix[3][1] * matrix[1][2] * matrix[2][3] -
matrix[3][1] * matrix[1][3] * matrix[2][2];
inverse[1][0] = -matrix[1][0] * matrix[2][2] * matrix[3][3] +
matrix[1][0] * matrix[2][3] * matrix[3][2] +
matrix[2][0] * matrix[1][2] * matrix[3][3] -
matrix[2][0] * matrix[1][3] * matrix[3][2] -
matrix[3][0] * matrix[1][2] * matrix[2][3] +
matrix[3][0] * matrix[1][3] * matrix[2][2];
inverse[2][0] = matrix[1][0] * matrix[2][1] * matrix[3][3] -
matrix[1][0] * matrix[2][3] * matrix[3][1] -
matrix[2][0] * matrix[1][1] * matrix[3][3] +
matrix[2][0] * matrix[1][3] * matrix[3][1] +
matrix[3][0] * matrix[1][1] * matrix[2][3] -
matrix[3][0] * matrix[1][3] * matrix[2][1];
inverse[3][0] = -matrix[1][0] * matrix[2][1] * matrix[3][2] +
matrix[1][0] * matrix[2][2] * matrix[3][1] +
matrix[2][0] * matrix[1][1] * matrix[3][2] -
matrix[2][0] * matrix[1][2] * matrix[3][1] -
matrix[3][0] * matrix[1][1] * matrix[2][2] +
matrix[3][0] * matrix[1][2] * matrix[2][1];
inverse[0][1]= -matrix[0][1] * matrix[2][2] * matrix[3][3] +
matrix[0][1] * matrix[2][3] * matrix[3][2] +
matrix[2][1] * matrix[0][2] * matrix[3][3] -
matrix[2][1] * matrix[0][3] * matrix[3][2] -
matrix[3][1] * matrix[0][2] * matrix[2][3] +
matrix[3][1] * matrix[0][3] * matrix[2][2];
inverse[1][1] = matrix[0][0] * matrix[2][2] * matrix[3][3] -
matrix[0][0] * matrix[2][3] * matrix[3][2] -
matrix[2][0] * matrix[0][2] * matrix[3][3] +
matrix[2][0] * matrix[0][3] * matrix[3][2] +
matrix[3][0] * matrix[0][2] * matrix[2][3] -
matrix[3][0] * matrix[0][3] * matrix[2][2];
inverse[2][1] = -matrix[0][0] * matrix[2][1] * matrix[3][3] +
matrix[0][0] * matrix[2][3] * matrix[3][1] +
matrix[2][0] * matrix[0][1] * matrix[3][3] -
matrix[2][0] * matrix[0][3] * matrix[3][1] -
matrix[3][0] * matrix[0][1] * matrix[2][3] +
matrix[3][0] * matrix[0][3] * matrix[2][1];
inverse[3][1] = matrix[0][0] * matrix[2][1] * matrix[3][2] -
matrix[0][0] * matrix[2][2] * matrix[3][1] -
matrix[2][0] * matrix[0][1] * matrix[3][2] +
matrix[2][0] * matrix[0][2] * matrix[3][1] +
matrix[3][0] * matrix[0][1] * matrix[2][2] -
matrix[3][0] * matrix[0][2] * matrix[2][1];
inverse[0][2] = matrix[0][1] * matrix[1][2] * matrix[3][3] -
matrix[0][1] * matrix[1][3] * matrix[3][2] -
matrix[1][1] * matrix[0][2] * matrix[3][3] +
matrix[1][1] * matrix[0][3] * matrix[3][2] +
matrix[3][1] * matrix[0][2] * matrix[1][3] -
matrix[3][1] * matrix[0][3] * matrix[1][2];
inverse[1][2] = -matrix[0][0] * matrix[1][2] * matrix[3][3] +
matrix[0][0] * matrix[1][3] * matrix[3][2] +
matrix[1][0] * matrix[0][2] * matrix[3][3] -
matrix[1][0] * matrix[0][3] * matrix[3][2] -
matrix[3][0] * matrix[0][2] * matrix[1][3] +
matrix[3][0] * matrix[0][3] * matrix[1][2];
inverse[2][2] = matrix[0][0] * matrix[1][1] * matrix[3][3] -
matrix[0][0] * matrix[1][3] * matrix[3][1] -
matrix[1][0] * matrix[0][1] * matrix[3][3] +
matrix[1][0] * matrix[0][3] * matrix[3][1] +
matrix[3][0] * matrix[0][1] * matrix[1][3] -
matrix[3][0] * matrix[0][3] * matrix[1][1];
inverse[3][2] = -matrix[0][0] * matrix[1][1] * matrix[3][2] +
matrix[0][0] * matrix[1][2] * matrix[3][1] +
matrix[1][0] * matrix[0][1] * matrix[3][2] -
matrix[1][0] * matrix[0][2] * matrix[3][1] -
matrix[3][0] * matrix[0][1] * matrix[1][2] +
matrix[3][0] * matrix[0][2] * matrix[1][1];
inverse[0][3] = -matrix[0][1] * matrix[1][2] * matrix[2][3] +
matrix[0][1] * matrix[1][3] * matrix[2][2] +
matrix[1][1] * matrix[0][2] * matrix[2][3] -
matrix[1][1] * matrix[0][3] * matrix[2][2] -
matrix[2][1] * matrix[0][2] * matrix[1][3] +
matrix[2][1] * matrix[0][3] * matrix[1][2];
inverse[1][3] = matrix[0][0] * matrix[1][2] * matrix[2][3] -
matrix[0][0] * matrix[1][3] * matrix[2][2] -
matrix[1][0] * matrix[0][2] * matrix[2][3] +
matrix[1][0] * matrix[0][3] * matrix[2][2] +
matrix[2][0] * matrix[0][2] * matrix[1][3] -
matrix[2][0] * matrix[0][3] * matrix[1][2];
inverse[2][3] = -matrix[0][0] * matrix[1][1] * matrix[2][3] +
matrix[0][0] * matrix[1][3] * matrix[2][1] +
matrix[1][0] * matrix[0][1] * matrix[2][3] -
matrix[1][0] * matrix[0][3] * matrix[2][1] -
matrix[2][0] * matrix[0][1] * matrix[1][3] +
matrix[2][0] * matrix[0][3] * matrix[1][1];
inverse[3][3] = matrix[0][0] * matrix[1][1] * matrix[2][2] -
matrix[0][0] * matrix[1][2] * matrix[2][1] -
matrix[1][0] * matrix[0][1] * matrix[2][2] +
matrix[1][0] * matrix[0][2] * matrix[2][1] +
matrix[2][0] * matrix[0][1] * matrix[1][2] -
matrix[2][0] * matrix[0][2] * matrix[1][1];
K det = matrix[0][0] * inverse[0][0] + matrix[0][1] * inverse[1][0] +
matrix[0][2] * inverse[2][0] + matrix[0][3] * inverse[3][0];
// return identity for singular or nearly singular matrices.
if (std::abs(det) < 1e-40) {
for (int i = 0; i < 4; ++i){
inverse[i][i] = 1.0;
}
return 1.0;
}
K inv_det = 1.0 / det;
inverse *= inv_det;
return det;
}
} // end FMatrixHelp
namespace ISTLUtility {
//! invert matrix by calling FMatrixHelp::invert
template <typename K>
static inline void invertMatrix(FieldMatrix<K,1,1>& matrix)
{
FieldMatrix<K,1,1> A ( matrix );
FMatrixHelp::invertMatrix(A, matrix );
}
//! invert matrix by calling FMatrixHelp::invert
template <typename K>
static inline void invertMatrix(FieldMatrix<K,2,2>& matrix)
{
FieldMatrix<K,2,2> A ( matrix );
FMatrixHelp::invertMatrix(A, matrix );
}
//! invert matrix by calling FMatrixHelp::invert
template <typename K>
static inline void invertMatrix(FieldMatrix<K,3,3>& matrix)
{
FieldMatrix<K,3,3> A ( matrix );
FMatrixHelp::invertMatrix(A, matrix );
}
//! invert matrix by calling FMatrixHelp::invert
template <typename K>
static inline void invertMatrix(FieldMatrix<K,4,4>& matrix)
{
FieldMatrix<K,4,4> A ( matrix );
FMatrixHelp::invertMatrix(A, matrix );
}
//! invert matrix by calling matrix.invert
template <typename K, int n>
static inline void invertMatrix(FieldMatrix<K,n,n>& matrix)
{
#if ! DUNE_VERSION_NEWER( DUNE_COMMON, 2, 7 )
Dune::FMatrixPrecision<K>::set_singular_limit(1.e-20);
#endif
matrix.invert();
}
//! invert matrix by calling matrix.invert
template <typename K>
static inline void invertMatrix(Dune::DynamicMatrix<K>& matrix)
{
// for 4 X 4 matrix, using the invertMatrix() function above
// it is for temporary usage, mainly to reduce the huge burden of testing
// what algorithm should be used to invert 4 X 4 matrix will be handled
// as a seperate issue
if (matrix.rows() == 4) {
Dune::DynamicMatrix<K> A = matrix;
FMatrixHelp::invertMatrix(A, matrix);
return;
}
#if ! DUNE_VERSION_NEWER( DUNE_COMMON, 2, 7 )
Dune::FMatrixPrecision<K>::set_singular_limit(1.e-30);
#endif
matrix.invert();
}
} // end ISTLUtility
template <class Scalar, int n, int m>
class MatrixBlock : public Dune::FieldMatrix<Scalar, n, m>
{
public:
typedef Dune::FieldMatrix<Scalar, n, m> BaseType;
using BaseType :: operator= ;
using BaseType :: rows;
using BaseType :: cols;
explicit MatrixBlock( const Scalar scalar = 0 ) : BaseType( scalar ) {}
void invert()
{
ISTLUtility::invertMatrix( *this );
}
const BaseType& asBase() const { return static_cast< const BaseType& > (*this); }
BaseType& asBase() { return static_cast< BaseType& > (*this); }
};
template<class K, int n, int m>
void
print_row(std::ostream& s, const MatrixBlock<K,n,m>& A,
typename FieldMatrix<K,n,m>::size_type I,
typename FieldMatrix<K,n,m>::size_type J,
typename FieldMatrix<K,n,m>::size_type therow, int width,
int precision)
{
print_row(s, A.asBase(), I, J, therow, width, precision);
}
template<class K, int n, int m>
K& firstmatrixelement(MatrixBlock<K,n,m>& A)
{
return firstmatrixelement( A.asBase() );
}
template<typename Scalar, int n, int m>
struct MatrixDimension< MatrixBlock< Scalar, n, m > >
: public MatrixDimension< typename MatrixBlock< Scalar, n, m >::BaseType >
{
};
#if HAVE_UMFPACK
/// \brief UMFPack specialization for MatrixBlock to make AMG happy
///
/// Without this the empty default implementation would be used.
template<typename T, typename A, int n, int m>
class UMFPack<BCRSMatrix<MatrixBlock<T,n,m>, A> >
: public UMFPack<BCRSMatrix<FieldMatrix<T,n,m>, A> >
{
typedef UMFPack<BCRSMatrix<FieldMatrix<T,n,m>, A> > Base;
typedef BCRSMatrix<FieldMatrix<T,n,m>, A> Matrix;
public:
typedef BCRSMatrix<MatrixBlock<T,n,m>, A> RealMatrix;
UMFPack(const RealMatrix& matrix, int verbose, bool)
: Base(reinterpret_cast<const Matrix&>(matrix), verbose)
{}
};
#endif
#if HAVE_SUPERLU
/// \brief SuperLU specialization for MatrixBlock to make AMG happy
///
/// Without this the empty default implementation would be used.
template<typename T, typename A, int n, int m>
class SuperLU<BCRSMatrix<MatrixBlock<T,n,m>, A> >
: public SuperLU<BCRSMatrix<FieldMatrix<T,n,m>, A> >
{
typedef SuperLU<BCRSMatrix<FieldMatrix<T,n,m>, A> > Base;
typedef BCRSMatrix<FieldMatrix<T,n,m>, A> Matrix;
public:
typedef BCRSMatrix<MatrixBlock<T,n,m>, A> RealMatrix;
SuperLU(const RealMatrix& matrix, int verbose, bool reuse=true)
: Base(reinterpret_cast<const Matrix&>(matrix), verbose, reuse)
{}
};
#endif
} // end namespace Dune
namespace Opm
{
namespace Detail
{
//! calculates ret = sign * (A^T * B)
//! TA, TB, and TC are not necessarily FieldMatrix, but those should
//! follow the Dune::DenseMatrix interface.
template< class TA, class TB, class TC, class PositiveSign >
static inline void multMatrixTransposedImpl ( const TA &A, // n x m
const TB &B, // n x p
TC &ret, // m x p
const PositiveSign )
{
typedef typename TA :: size_type size_type;
typedef typename TA :: field_type K;
assert( A.N() == B.N() );
assert( A.M() == ret.N() );
assert( B.M() == ret.M() );
const size_type n = A.N();
const size_type m = ret.N();
const size_type p = B.M();
for( size_type i = 0; i < m; ++i )
{
for( size_type j = 0; j < p; ++j )
{
K sum = 0;
for( size_type k = 0; k < n; ++k )
{
sum += A[ k ][ i ] * B[ k ][ j ];
}
// set value depending on given sign
ret[ i ][ j ] = PositiveSign::value ? sum : -sum;
}
}
}
//! calculates ret = A^T * B
template <class DenseMatrixA, class DenseMatrixB, class DenseMatrixC>
static inline void multMatrixTransposed(const DenseMatrixA& A,
const DenseMatrixB& B,
DenseMatrixC& ret)
{
multMatrixTransposedImpl( A, B, ret, std::true_type() );
}
//! calculates ret = -A^T * B
template <class DenseMatrixA, class DenseMatrixB, class DenseMatrixC>
static inline void negativeMultMatrixTransposed(const DenseMatrixA& A,
const DenseMatrixB& B,
DenseMatrixC& ret)
{
multMatrixTransposedImpl( A, B, ret, std::false_type() );
}
//! calculates ret = A * B
template< class K>
static inline void multMatrix(const Dune::DynamicMatrix<K>& A,
const Dune::DynamicMatrix<K>& B,
Dune::DynamicMatrix<K>& ret )
{
typedef typename Dune::DynamicMatrix<K> :: size_type size_type;
const size_type m = A.rows();
const size_type n = A.cols();
assert(n == B.rows() );
const size_type p = B.cols();
ret.resize(m, p);
for( size_type i = 0; i < m; ++i )
{
for( size_type j = 0; j < p; ++j )
{
ret[ i ][ j ] = K( 0 );
for( size_type k = 0; k < n; ++k )
ret[ i ][ j ] += A[ i ][ k ] * B[ k ][ j ];
}
}
}
} // namespace Detail
} // namespace Opm
#endif