void OneD_Node_Mesh<_Type, _Xtype>::set_nodes_vars( const std::size_t node, const DenseVector<_Type>& U )
{
#ifdef PARANOID
if ( U.size() != NV )
{
std::string problem;
problem = " The OneD_Node_Mesh.set_node method is trying to add \n";
problem += " an NVector of variables of a different size to that \n";
problem += " stored at other nodal points. \n";
throw ExceptionGeom( problem, NV, U.size() );
}
#endif
for ( std::size_t var = 0; var < U.size(); ++var )
{
VARS[ node * NV + var ] = U[ var ];
}
}
void DenseLinearEigenSystem<double>::eigensolve_lapack_without_vectors()
{
#ifndef LAPACK
std::string problem;
problem = "The DenseLinearEigenSystem::eigensolve_lapack_without_vectors method has been called\n";
problem += "but the compiler option -DLAPACK was not provided when\n";
problem += "the library was built.";
throw ExceptionExternal( problem );
#else
std::size_t N = p_A -> nrows();
// Cache issues of varying significance plague problems of size 2^j + 2^k + ...
// when LDA = N, so this is my shameless 'tweak' to maintain predictable
// performance, at least for N <=1024 or so.
int padding( 0 );
if ( ( N % 2 == 0 ) && ( N > 127 ) )
{
padding = 1;
}
#ifdef PARANOID
if ( ( p_A -> nrows() != p_B -> nrows() ) ||
( p_A -> ncols() != p_B -> ncols() ) )
{
std::string problem( "The DenseLinearEigenSystem::eigensolve_lapack_without_vectors method has detected a failure \n" );
throw ExceptionGeom( problem, p_A -> nrows(), p_A -> ncols(),
p_B -> nrows(), p_B -> ncols() );
}
#endif
FortranData Af( *p_A, true, padding );
FortranData Bf( *p_B, true, padding );
// eigenvalue storage
DenseVector<double> alpha_r( N, 0.0 );
DenseVector<double> alpha_i( N, 0.0 );
DenseVector<double> beta( N, 0.0 );
// eigenvector storage
DenseVector<double> vec_left( 1, 0.0 );
DenseVector<double> vec_right( 1, 0.0 );
// some workspace for the LAPACK routine
DenseVector<double> work( 1, 0.0 );
int info( 0 );
// Call FORTRAN LAPACK to get the required workspace
LAPACK_DGGEV( ( char* ) "N", ( char* ) "N", N, Af.base(), N + padding, Bf.base(), N + padding, &alpha_r[ 0 ], &alpha_i[ 0 ], &beta[ 0 ], &vec_left[ 0 ], 1, &vec_right[ 0 ], 1, &work[ 0 ], -1, info );
int required_workspace = ( int ) work[ 0 ];
#ifdef DEBUG
std::cout << " [DEBUG] DenseLinearEigenSystem::eigensolve_lapack_without_vectors is requesting \n";
std::cout << " [DEBUG] a workspace vector of size " << required_workspace << "\n";
#endif
work.resize( required_workspace );
// call FORTRAN LAPACK again with the optimum workspace
LAPACK_DGGEV( ( char* ) "N", ( char* ) "N", N, Af.base(), N + padding, Bf.base(), N + padding, &alpha_r[ 0 ], &alpha_i[ 0 ], &beta[ 0 ], &vec_left[ 0 ], 1, &vec_right[ 0 ], 1, &work[ 0 ], required_workspace, info );
if ( 0 != info )
{
std::string problem( "The DenseLinearEigenSystem::eigensolve_lapack_without_vectors method has detected a failure. \n" );
throw ExceptionExternal( problem, info );
}
// create a complex eigenvalue vector
EIGENVALUES_ALPHA = DenseVector<D_complex>( N, 0.0 );
for ( std::size_t i = 0; i < N; ++i )
{
const D_complex eye( 0.0, 1.0 );
EIGENVALUES_ALPHA[ i ] = alpha_r[ i ] + alpha_i[ i ] * eye;
}
// set the eigenvalue member data
EIGENVALUES_BETA = beta;
#endif
}
void DenseLinearEigenSystem< double >::eigensolve_lapack_with_vectors()
{
#ifndef LAPACK
std::string problem;
problem = "The DenseLinearEigenSystem::eigensolve_lapack_with_vectors method has been called\n";
problem += "but the compiler option -DLAPACK was not provided when\n";
problem += "the library was built.";
throw ExceptionExternal( problem );
#else
std::size_t N = p_A -> nrows();
// Cache contention issues of varying significance plague problems of size 2^j + 2^k + ...
// when LDA = N, so this is my shameless 'tweak' to maintain predictable
// performance, at least for N <=1024 or so.
int padding( 0 );
if ( ( N % 2 == 0 ) && ( N > 127 ) )
{
padding = 1;
}
#ifdef PARANOID
if ( ( p_A -> nrows() != p_B -> nrows() ) ||
( p_A -> ncols() != p_B -> ncols() ) )
{
std::string problem( "The DenseLinearEigenSystem::eigensolve_lapack_with_vectors method has detected a failure. \n" );
throw ExceptionGeom( problem, p_A -> nrows(), p_A -> ncols(),
p_B -> nrows(), p_B -> ncols() );
}
#endif
// Convert to fortran data incl. a transpose of the
// input matrices so they are in column_major format then include padding
FortranData Af( *p_A, true, padding );
FortranData Bf( *p_B, true, padding );
// eigenvalue storage
DenseVector<double> alpha_r( N, 0.0 );
DenseVector<double> alpha_i( N, 0.0 );
DenseVector<double> beta( N, 0.0 );
// new the right eigenvector storage
DenseVector<double> vec_left( 1, 0.0 );
DenseVector<double> vec_right( N * N, 0.0 );
// some workspace for the LAPACK routine
DenseVector<double> work( 1, 0.0 );
// return integer for LAPACK
int info( 0 );
// Call FORTRAN LAPACK to get the required workspace
LAPACK_DGGEV( ( char* ) "N", ( char* ) "V", N, Af.base(), N + padding, Bf.base(), N + padding, &alpha_r[ 0 ], &alpha_i[ 0 ], &beta[ 0 ], &vec_left[ 0 ], 1, &vec_right[ 0 ], N, &work[ 0 ], -1, info );
int required_workspace = 4 * int( work[ 0 ] );
#ifdef DEBUG
std::cout << "[DEBUG] DenseLinearEigenSystem::eigensolve_lapack_with_vectors is requesting \n";
std::cout << "[DEBUG] a workspace vector of size " << required_workspace << "\n";
#endif
work.resize( required_workspace );
// call FORTRAN LAPACK again with the optimum workspace
LAPACK_DGGEV( ( char* ) "N", ( char* ) "V", N, Af.base(), N + padding, Bf.base(), N + padding, &alpha_r[ 0 ], &alpha_i[ 0 ], &beta[ 0 ], &vec_left[ 0 ], 1, &vec_right[ 0 ], N, &work[ 0 ], required_workspace, info );
if ( 0 != info )
{
std::string problem( "The DenseLinearEigenSystem::eigensolve_lapack_with_vectors method has detected a failure.\n" );
throw ExceptionExternal( problem, info );
}
// create a complex eigenvalue vector
EIGENVALUES_ALPHA = DenseVector<D_complex>( N, 0.0 );
// complex eigenvector matrix
ALL_EIGENVECTORS = DenseMatrix<D_complex>( N, N, 0.0 );
// step through the eigenvalues
for ( std::size_t i = 0; i < N; ++i )
{
const D_complex eye( 0.0, 1.0 );
// make the complex vector of alpha
EIGENVALUES_ALPHA[ i ] = alpha_r[ i ] + alpha_i[ i ] * eye;
if ( std::abs( alpha_i[ i ] ) > 0.0 )
{
// eigenvector is complex
for ( std::size_t k = 0; k < N; ++k )
{
ALL_EIGENVECTORS[ i ][ k ] = vec_right[ i * N + k ] + eye * vec_right[ ( i + 1 ) * N + k ];
// store the conjugate too for completeness
ALL_EIGENVECTORS[ i + 1 ][ k ] = vec_right[ i * N + k ] - eye * vec_right[ ( i + 1 ) * N + k ];
}
++i;
}
else // eigenvector is real
{
for ( std::size_t k = 0; k < N; ++k )
{
ALL_EIGENVECTORS( i, k ) = vec_right[ i * N + k ];
}
}
}
// set the eigenvalue member data
EIGENVALUES_BETA = beta;
#endif
}
