Namespace holding implementation details for linear algebra routines. Usually not of interest for a library user. More...

Namespaces
	amg
	Implementation namespace for algebraic multigrid preconditioner.

	fft

	spai
	Implementation namespace for sparse approximate inverse preconditioner.

Classes
class	FastMatrix
	Internal helper class representing a row-major dense matrix used for the QR method for the purpose of computing eigenvalues. More...

class	ilu_vector_range
	Helper range class for representing a subvector of a larger buffer. More...

struct	ilut_sparse_vector
	Helper struct for holding a sparse vector in linear memory. For internal use only. More...

struct	InputData
	In this class the input matrix is stored. More...

struct	op_applier
	Worker class for decomposing expression templates. More...

struct	op_executor
	Worker class for decomposing expression templates. More...

struct	ResultDataLarge
	In this class the data of the result for large matrices is stored. More...

struct	ResultDataSmall
	In this class the data of the result for small matrices is stored. More...

class	z_handler
	handles the no_precond case at minimal overhead More...

class	z_handler< VectorT, viennacl::linalg::no_precond >

Enumerations
enum	row_info_types { SPARSE_ROW_NORM_INF = 0, SPARSE_ROW_NORM_1, SPARSE_ROW_NORM_2, SPARSE_ROW_DIAGONAL }

Functions
template<typename NumericT >
void	amg_galerkin_prod (compressed_matrix< NumericT > &A_fine, compressed_matrix< NumericT > &P, compressed_matrix< NumericT > &R, compressed_matrix< NumericT > &A_coarse)
	Sparse Galerkin product: Calculates A_coarse = trans(P)A_fineP = RA_fineP. More...

template<typename NumericT , typename AMGContextListT >
vcl_size_t	amg_setup (std::vector< compressed_matrix< NumericT > > &list_of_A, std::vector< compressed_matrix< NumericT > > &list_of_P, std::vector< compressed_matrix< NumericT > > &list_of_R, AMGContextListT &list_of_amg_level_context, amg_tag &tag)
	Setup AMG preconditioner. More...

template<typename MatrixT , typename InternalT1 , typename InternalT2 >
void	amg_init (MatrixT const &mat, InternalT1 &list_of_A, InternalT1 &list_of_P, InternalT1 &list_of_R, InternalT2 &list_of_amg_level_context, amg_tag &tag)
	Initialize AMG preconditioner. More...

template<typename InternalVectorT , typename SparseMatrixT >
void	amg_setup_apply (InternalVectorT &result, InternalVectorT &result_backup, InternalVectorT &rhs, InternalVectorT &residual, SparseMatrixT const &A, vcl_size_t coarse_levels, amg_tag const &tag)
	Setup data structures for precondition phase for later use on the GPU. More...

template<typename NumericT , typename SparseMatrixT >
void	amg_lu (viennacl::matrix< NumericT > &op, SparseMatrixT const &A, amg_tag const &tag)
	Pre-compute LU factorization for direct solve (ublas library). More...

template<typename MatrixT , typename NumericT >
viennacl::vector< NumericT >	pipelined_solve (MatrixT const &A, viennacl::vector_base< NumericT > const &rhs, bicgstab_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Implementation of a pipelined stabilized Bi-conjugate gradient solver. More...

template<typename NumericT >
viennacl::vector< NumericT >	solve_impl (viennacl::compressed_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, bicgstab_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. More...

template<typename NumericT >
viennacl::vector< NumericT >	solve_impl (viennacl::coordinate_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, bicgstab_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. More...

template<typename NumericT >
viennacl::vector< NumericT >	solve_impl (viennacl::ell_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, bicgstab_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. More...

template<typename NumericT >
viennacl::vector< NumericT >	solve_impl (viennacl::sliced_ell_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, bicgstab_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. More...

template<typename NumericT >
viennacl::vector< NumericT >	solve_impl (viennacl::hyb_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, bicgstab_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. More...

template<typename MatrixT , typename VectorT >
VectorT	solve_impl (MatrixT const &matrix, VectorT const &rhs, bicgstab_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(VectorT const &, typename viennacl::result_of::cpu_value_type< typename viennacl::result_of::value_type< VectorT >::type >::type, void )=NULL, void *monitor_data=NULL)
	Implementation of the unpreconditioned stabilized Bi-conjugate gradient solver. More...

template<typename MatrixT , typename VectorT , typename PreconditionerT >
VectorT	solve_impl (MatrixT const &matrix, VectorT const &rhs, bicgstab_tag const &tag, PreconditionerT const &precond, bool(monitor)(VectorT const &, typename viennacl::result_of::cpu_value_type< typename viennacl::result_of::value_type< VectorT >::type >::type, void )=NULL, void *monitor_data=NULL)
	Implementation of the preconditioned stabilized Bi-conjugate gradient solver. More...

template<typename NumericT , typename OtherVectorT >
void	copy_vec_to_vec (viennacl::vector< NumericT > const &src, OtherVectorT &dest)
	overloaded function for copying vectors More...

template<typename OtherVectorT , typename NumericT >
void	copy_vec_to_vec (OtherVectorT const &src, viennacl::vector< NumericT > &dest)

template<typename VectorT1 , typename VectorT2 >
void	copy_vec_to_vec (VectorT1 const &src, VectorT2 &dest)

template<typename MatrixT , typename NumericT >
viennacl::vector< NumericT >	pipelined_solve (MatrixT const &A, viennacl::vector< NumericT > const &rhs, cg_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Implementation of a pipelined conjugate gradient algorithm (no preconditioner), specialized for ViennaCL types. More...

template<typename NumericT >
viennacl::vector< NumericT >	solve_impl (viennacl::compressed_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, cg_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. More...

template<typename NumericT >
viennacl::vector< NumericT >	solve_impl (viennacl::coordinate_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, cg_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. More...

template<typename NumericT >
viennacl::vector< NumericT >	solve_impl (viennacl::ell_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, cg_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. More...

template<typename NumericT >
viennacl::vector< NumericT >	solve_impl (viennacl::sliced_ell_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, cg_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. More...

template<typename NumericT >
viennacl::vector< NumericT >	solve_impl (viennacl::hyb_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, cg_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. More...

template<typename MatrixT , typename VectorT , typename PreconditionerT >
VectorT	solve_impl (MatrixT const &matrix, VectorT const &rhs, cg_tag const &tag, PreconditionerT const &precond, bool(monitor)(VectorT const &, typename viennacl::result_of::cpu_value_type< typename viennacl::result_of::value_type< VectorT >::type >::type, void )=NULL, void *monitor_data=NULL)

template<typename NumericT >
void	bisectSmall (const InputData< NumericT > &input, ResultDataSmall< NumericT > &result, const unsigned int mat_size, const NumericT lg, const NumericT ug, const NumericT precision)

template<typename NumericT >
void	bisectLarge (const InputData< NumericT > &input, ResultDataLarge< NumericT > &result, const unsigned int mat_size, const NumericT lg, const NumericT ug, const NumericT precision)

template<typename NumericT >
void	bisectLarge_OneIntervals (const InputData< NumericT > &input, ResultDataLarge< NumericT > &result, const unsigned int mat_size, const NumericT precision)

template<typename NumericT >
void	bisectLarge_MultIntervals (const InputData< NumericT > &input, ResultDataLarge< NumericT > &result, const unsigned int mat_size, const NumericT precision)

template<typename NumericT >
void	computeEigenvaluesLargeMatrix (InputData< NumericT > &input, ResultDataLarge< NumericT > &result, const unsigned int mat_size, const NumericT lg, const NumericT ug, const NumericT precision)

template<typename NumericT >
bool	processResultDataLargeMatrix (ResultDataLarge< NumericT > &result, const unsigned int mat_size)

template<typename NumericT >
void	computeEigenvaluesSmallMatrix (const InputData< NumericT > &input, ResultDataSmall< NumericT > &result, const unsigned int mat_size, const NumericT lg, const NumericT ug, const NumericT precision)

template<typename NumericT >
void	processResultSmallMatrix (ResultDataSmall< NumericT > &result, const unsigned int mat_size)

template<typename NumericT >
void	computeGerschgorin (std::vector< NumericT > &d, std::vector< NumericT > &s, unsigned int n, NumericT &lg, NumericT &ug)

template<class T >
T	min (const T &lhs, const T &rhs)
	Minimum. More...

template<class T >
T	max (const T &lhs, const T &rhs)
	Maximum. More...

float	sign_f (const float &val)
	Sign of number (float) More...

double	sign_d (const double &val)
	Sign of number (double) More...

unsigned int	getNumBlocksLinear (const unsigned int num_threads, const unsigned int num_threads_block)

template<typename NumericT >
void	extract_block_matrix (viennacl::compressed_matrix< NumericT > const &A, viennacl::compressed_matrix< NumericT > &diagonal_block_A, vcl_size_t start_index, vcl_size_t stop_index)
	Extracts a diagonal block from a larger system matrix. More...

template<typename NumericT >
void	precondition (viennacl::compressed_matrix< NumericT > const &A, viennacl::compressed_matrix< NumericT > &L, viennacl::vector< NumericT > &diag_L, viennacl::compressed_matrix< NumericT > &L_trans, chow_patel_tag const &tag)
	Implementation of the parallel ICC0 factorization, Algorithm 3 in Chow-Patel paper. More...

template<typename NumericT >
void	precondition (viennacl::compressed_matrix< NumericT > const &A, viennacl::compressed_matrix< NumericT > &L, viennacl::vector< NumericT > &diag_L, viennacl::compressed_matrix< NumericT > &U, viennacl::vector< NumericT > &diag_U, chow_patel_tag const &tag)
	Implementation of the parallel ILU0 factorization, Algorithm 2 in Chow-Patel paper. More...

template<typename NumericT , unsigned int AlignmentV>
void	level_scheduling_setup_impl (viennacl::compressed_matrix< NumericT, AlignmentV > const &LU, viennacl::vector< NumericT > const &diagonal_LU, std::list< viennacl::backend::mem_handle > &row_index_arrays, std::list< viennacl::backend::mem_handle > &row_buffers, std::list< viennacl::backend::mem_handle > &col_buffers, std::list< viennacl::backend::mem_handle > &element_buffers, std::list< vcl_size_t > &row_elimination_num_list, bool setup_U)

template<typename NumericT , unsigned int AlignmentV>
void	level_scheduling_setup_L (viennacl::compressed_matrix< NumericT, AlignmentV > const &LU, viennacl::vector< NumericT > const &diagonal_LU, std::list< viennacl::backend::mem_handle > &row_index_arrays, std::list< viennacl::backend::mem_handle > &row_buffers, std::list< viennacl::backend::mem_handle > &col_buffers, std::list< viennacl::backend::mem_handle > &element_buffers, std::list< vcl_size_t > &row_elimination_num_list)

template<typename NumericT , unsigned int AlignmentV>
void	level_scheduling_setup_U (viennacl::compressed_matrix< NumericT, AlignmentV > const &LU, viennacl::vector< NumericT > const &diagonal_LU, std::list< viennacl::backend::mem_handle > &row_index_arrays, std::list< viennacl::backend::mem_handle > &row_buffers, std::list< viennacl::backend::mem_handle > &col_buffers, std::list< viennacl::backend::mem_handle > &element_buffers, std::list< vcl_size_t > &row_elimination_num_list)

template<typename NumericT >
void	level_scheduling_substitute (viennacl::vector< NumericT > &vec, std::list< viennacl::backend::mem_handle > const &row_index_arrays, std::list< viennacl::backend::mem_handle > const &row_buffers, std::list< viennacl::backend::mem_handle > const &col_buffers, std::list< viennacl::backend::mem_handle > const &element_buffers, std::list< vcl_size_t > const &row_elimination_num_list)

template<typename IndexT , typename NumericT >
IndexT	merge_subtract_sparse_rows (IndexT const w_coords, NumericT const w_elements, IndexT w_size, IndexT const u_coords, NumericT const u_elements, IndexT u_size, NumericT alpha, IndexT z_coords, NumericT z_elements)
	Subtracts a scaled sparse vector u from a sparse vector w and writes the output to z: z = w - alpha * u. More...

template<typename SizeT , typename NumericT >
void	insert_with_value_sort (std::vector< std::pair< SizeT, NumericT > > &map, SizeT index, NumericT value)

template<typename NumericT , typename B >
bool	op_aliasing (vector_base< NumericT > const &, B const &)

template<typename NumericT >
bool	op_aliasing (vector_base< NumericT > const &lhs, vector_base< NumericT > const &b)

template<typename NumericT , typename LhsT , typename RhsT , typename OpT >
bool	op_aliasing (vector_base< NumericT > const &lhs, vector_expression< const LhsT, const RhsT, OpT > const &rhs)

template<typename NumericT , typename B >
bool	op_aliasing (matrix_base< NumericT > const &, B const &)

template<typename NumericT >
bool	op_aliasing (matrix_base< NumericT > const &lhs, matrix_base< NumericT > const &b)

template<typename NumericT , typename LhsT , typename RhsT , typename OpT >
bool	op_aliasing (matrix_base< NumericT > const &lhs, matrix_expression< const LhsT, const RhsT, OpT > const &rhs)

template<typename NumericT , typename SolverTagT >
void	inplace_solve_kernel (const matrix_base< NumericT > &A, const matrix_base< NumericT > &B, SolverTagT)
	Direct inplace solver for dense triangular systems using a single kernel launch. Matlab notation: A \ B. More...

template<typename NumericT , typename SolverTagT >
void	inplace_solve_vec_kernel (const matrix_base< NumericT > &mat, const vector_base< NumericT > &vec, SolverTagT)

template<typename MatrixT1 , typename MatrixT2 , typename SolverTagT >
void	inplace_solve_lower_impl (MatrixT1 const &A, MatrixT2 &B, SolverTagT)

template<typename MatrixT1 , typename MatrixT2 >
void	inplace_solve_impl (MatrixT1 const &A, MatrixT2 &B, viennacl::linalg::lower_tag)

template<typename MatrixT1 , typename MatrixT2 >
void	inplace_solve_impl (MatrixT1 const &A, MatrixT2 &B, viennacl::linalg::unit_lower_tag)

template<typename MatrixT1 , typename MatrixT2 , typename SolverTagT >
void	inplace_solve_upper_impl (MatrixT1 const &A, MatrixT2 &B, SolverTagT)

template<typename MatrixT1 , typename MatrixT2 >
void	inplace_solve_impl (MatrixT1 const &A, MatrixT2 &B, viennacl::linalg::upper_tag)

template<typename MatrixT1 , typename MatrixT2 >
void	inplace_solve_impl (MatrixT1 const &A, MatrixT2 &B, viennacl::linalg::unit_upper_tag)

template<typename MatrixT1 , typename VectorT , typename SolverTagT >
void	inplace_solve_lower_vec_impl (MatrixT1 const &A, VectorT &b, SolverTagT)

template<typename MatrixT1 , typename VectorT >
void	inplace_solve_vec_impl (MatrixT1 const &A, VectorT &B, viennacl::linalg::lower_tag)

template<typename MatrixT1 , typename VectorT >
void	inplace_solve_vec_impl (MatrixT1 const &A, VectorT &B, viennacl::linalg::unit_lower_tag)

template<typename MatrixT1 , typename VectorT , typename SolverTagT >
void	inplace_solve_upper_vec_impl (MatrixT1 const &A, VectorT &b, SolverTagT)

template<typename MatrixT1 , typename VectorT >
void	inplace_solve_vec_impl (MatrixT1 const &A, VectorT &b, viennacl::linalg::upper_tag)

template<typename MatrixT1 , typename VectorT >
void	inplace_solve_vec_impl (MatrixT1 const &A, VectorT &b, viennacl::linalg::unit_upper_tag)

template<typename SrcVectorT , typename DestVectorT >
void	gmres_copy_helper (SrcVectorT const &src, DestVectorT &dest, vcl_size_t len, vcl_size_t start=0)

template<typename NumericT , typename DestVectorT >
void	gmres_copy_helper (viennacl::vector< NumericT > const &src, DestVectorT &dest, vcl_size_t len, vcl_size_t start=0)

template<typename VectorT , typename NumericT >
void	gmres_setup_householder_vector (VectorT const &input_vec, VectorT &hh_vec, NumericT &beta, NumericT &mu, vcl_size_t j)
	Computes the householder vector 'hh_vec' which rotates 'input_vec' such that all entries below the j-th entry of 'v' become zero. More...

template<typename VectorT , typename NumericT >
void	gmres_householder_reflect (VectorT &x, VectorT const &h, NumericT beta)

template<typename MatrixType , typename ScalarType >
viennacl::vector< ScalarType >	pipelined_solve (MatrixType const &A, viennacl::vector< ScalarType > const &rhs, gmres_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< ScalarType > const &, ScalarType, void )=NULL, void *monitor_data=NULL)
	Implementation of a pipelined GMRES solver without preconditioner. More...

template<typename NumericT >
viennacl::vector< NumericT >	solve_impl (viennacl::compressed_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, gmres_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. More...

template<typename NumericT >
viennacl::vector< NumericT >	solve_impl (viennacl::coordinate_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, gmres_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. More...

template<typename NumericT >
viennacl::vector< NumericT >	solve_impl (viennacl::ell_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, gmres_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. More...

template<typename NumericT >
viennacl::vector< NumericT >	solve_impl (viennacl::sliced_ell_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, gmres_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. More...

template<typename NumericT >
viennacl::vector< NumericT >	solve_impl (viennacl::hyb_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, gmres_tag const &tag, viennacl::linalg::no_precond, bool(monitor)(viennacl::vector< NumericT > const &, NumericT, void )=NULL, void *monitor_data=NULL)
	Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. More...

template<typename MatrixT , typename VectorT , typename PreconditionerT >
VectorT	solve_impl (MatrixT const &matrix, VectorT const &rhs, gmres_tag const &tag, PreconditionerT const &precond, bool(monitor)(VectorT const &, typename viennacl::result_of::cpu_value_type< typename viennacl::result_of::value_type< VectorT >::type >::type, void )=NULL, void *monitor_data=NULL)
	Implementation of the GMRES solver. More...

template<typename NumericT >
void	inverse_iteration (std::vector< NumericT > const &alphas, std::vector< NumericT > const &betas, NumericT &eigenvalue, std::vector< NumericT > &eigenvector)
	Inverse iteration for finding an eigenvector for an eigenvalue. More...

template<typename MatrixT , typename DenseMatrixT , typename NumericT >
std::vector< NumericT >	lanczosPRO (MatrixT const &A, vector_base< NumericT > &r, DenseMatrixT &eigenvectors_A, vcl_size_t size, lanczos_tag const &tag, bool compute_eigenvectors)
	Implementation of the Lanczos PRO algorithm (partial reorthogonalization) More...

template<typename MatrixT , typename DenseMatrixT , typename NumericT >
std::vector< NumericT >	lanczos (MatrixT const &A, vector_base< NumericT > &r, DenseMatrixT &eigenvectors_A, vcl_size_t krylov_dim, lanczos_tag const &tag, bool compute_eigenvectors)
	Implementation of the Lanczos FRO algorithm. More...

template<typename ScalarType >
void	level_scheduling_substitute (vector< ScalarType > &vec, viennacl::backend::mem_handle const &row_index_array, viennacl::backend::mem_handle const &row_buffer, viennacl::backend::mem_handle const &col_buffer, viennacl::backend::mem_handle const &element_buffer, vcl_size_t num_rows)

template<typename SCALARTYPE >
SCALARTYPE	pythag (SCALARTYPE a, SCALARTYPE b)

template<typename SCALARTYPE >
SCALARTYPE	sign (SCALARTYPE val)

template<typename VectorType >
VectorType::value_type	norm_lcl (VectorType const &x, vcl_size_t size)

template<typename VectorType >
void	normalize (VectorType &x, vcl_size_t size)

template<typename VectorType >
void	householder_vector (VectorType &v, vcl_size_t start)

template<typename SCALARTYPE >
void	transpose (matrix_base< SCALARTYPE > &A)

template<typename T >
void	cdiv (T xr, T xi, T yr, T yi, T &cdivr, T &cdivi)

template<typename SCALARTYPE >
void	prepare_householder_vector (matrix_base< SCALARTYPE > &A, vector_base< SCALARTYPE > &D, vcl_size_t size, vcl_size_t row_start, vcl_size_t col_start, vcl_size_t start, bool is_column)

template<typename SCALARTYPE >
void	final_iter_update_gpu (matrix_base< SCALARTYPE > &A, int n, int last_n, SCALARTYPE q, SCALARTYPE p)

template<typename SCALARTYPE , typename VectorType >
void	update_float_QR_column_gpu (matrix_base< SCALARTYPE > &A, const VectorType &buf, viennacl::vector< SCALARTYPE > &buf_vcl, int m, int n, int last_n, bool)

template<typename SCALARTYPE , typename MatrixT >
void	final_iter_update (MatrixT &A, int n, int last_n, SCALARTYPE q, SCALARTYPE p)

template<typename SCALARTYPE , typename MatrixT >
void	update_float_QR_column (MatrixT &A, const std::vector< SCALARTYPE > &buf, int m, int n, int last_i, bool is_triangular)

template<typename SCALARTYPE , typename VectorType >
void	hqr2 (viennacl::matrix< SCALARTYPE > &vcl_H, viennacl::matrix< SCALARTYPE > &V, VectorType &d, VectorType &e)

template<typename SCALARTYPE >
bool	householder_twoside (matrix_base< SCALARTYPE > &A, matrix_base< SCALARTYPE > &Q, vector_base< SCALARTYPE > &D, vcl_size_t start)

template<typename SCALARTYPE >
void	tridiagonal_reduction (matrix_base< SCALARTYPE > &A, matrix_base< SCALARTYPE > &Q)

template<typename SCALARTYPE >
void	qr_method (viennacl::matrix< SCALARTYPE > &A, viennacl::matrix< SCALARTYPE > &Q, std::vector< SCALARTYPE > &D, std::vector< SCALARTYPE > &E, bool is_symmetric=true)

template<typename MatrixType , typename VectorType >
MatrixType::value_type	setup_householder_vector_ublas (MatrixType const &A, VectorType &v, MatrixType &matrix_1x1, vcl_size_t j)

template<typename MatrixType , typename VectorType >
viennacl::result_of::cpu_value_type < typename MatrixType::value_type >::type	setup_householder_vector_viennacl (MatrixType const &A, VectorType &v, MatrixType &matrix_1x1, vcl_size_t j)

template<typename MatrixType , typename VectorType , typename ScalarType >
void	householder_reflect (MatrixType &A, VectorType &v, ScalarType beta, vcl_size_t j, vcl_size_t k)

template<typename MatrixType , typename VectorType , typename ScalarType >
void	householder_reflect_ublas (MatrixType &A, VectorType &v, MatrixType &matrix_1x1, ScalarType beta, vcl_size_t j, vcl_size_t k)

template<typename MatrixType , typename VectorType , typename ScalarType >
void	householder_reflect_viennacl (MatrixType &A, VectorType &v, MatrixType &matrix_1x1, ScalarType beta, vcl_size_t j, vcl_size_t k)

template<typename MatrixType , typename VectorType , typename ScalarType >
void	householder_reflect (MatrixType &A, VectorType &v, ScalarType beta, vcl_size_t j)

template<typename MatrixType , typename VectorType >
void	write_householder_to_A (MatrixType &A, VectorType const &v, vcl_size_t j)

template<typename MatrixType , typename VectorType >
void	write_householder_to_A_ublas (MatrixType &A, VectorType const &v, vcl_size_t j)

template<typename MatrixType , typename VectorType >
void	write_householder_to_A_viennacl (MatrixType &A, VectorType const &v, vcl_size_t j)

template<typename MatrixType >
std::vector< typename MatrixType::value_type >	inplace_qr_ublas (MatrixType &A, vcl_size_t block_size=32)
	Implementation of inplace-QR factorization for a general Boost.uBLAS compatible matrix A. More...

template<typename MatrixType >
std::vector< typename viennacl::result_of::cpu_value_type < typename MatrixType::value_type >::type >	inplace_qr_viennacl (MatrixType &A, vcl_size_t block_size=16)
	Implementation of a OpenCL-only QR factorization for GPUs (or multi-core CPU). DEPRECATED! Use only if you're curious and interested in playing a bit with a GPU-only implementation. More...

template<typename MatrixType >
std::vector< typename viennacl::result_of::cpu_value_type < typename MatrixType::value_type >::type >	inplace_qr_hybrid (MatrixType &A, vcl_size_t block_size=16)
	Implementation of a hybrid QR factorization using uBLAS on the CPU and ViennaCL for GPUs (or multi-core CPU) More...

template<typename SparseMatrixType , typename SCALARTYPE , unsigned int VEC_ALIGNMENT>
viennacl::enable_if < viennacl::is_any_sparse_matrix < SparseMatrixType >::value > ::type	row_info (SparseMatrixType const &mat, vector< SCALARTYPE, VEC_ALIGNMENT > &vec, row_info_types info_selector)

template<typename SparseMatrixType , class ScalarType , typename SOLVERTAG >
viennacl::enable_if < viennacl::is_any_sparse_matrix < SparseMatrixType >::value > ::type	block_inplace_solve (const matrix_expression< const SparseMatrixType, const SparseMatrixType, op_trans > &mat, viennacl::backend::mem_handle const &block_index_array, vcl_size_t num_blocks, viennacl::vector_base< ScalarType > const &mat_diagonal, viennacl::vector_base< ScalarType > &vec, SOLVERTAG tag)

template<typename MatrixType , typename VectorType >
void	givens_prev (MatrixType &matrix, VectorType &tmp1, VectorType &tmp2, int n, int l, int k)

template<typename MatrixType , typename VectorType >
void	change_signs (MatrixType &matrix, VectorType &signs, int n)

template<typename MatrixType , typename CPU_VectorType >
void	svd_qr_shift (MatrixType &vcl_u, MatrixType &vcl_v, CPU_VectorType &q, CPU_VectorType &e)

template<typename SCALARTYPE , unsigned int ALIGNMENT>
bool	householder_c (viennacl::matrix< SCALARTYPE, row_major, ALIGNMENT > &A, viennacl::matrix< SCALARTYPE, row_major, ALIGNMENT > &Q, viennacl::vector< SCALARTYPE, ALIGNMENT > &D, vcl_size_t row_start, vcl_size_t col_start)

template<typename SCALARTYPE , unsigned int ALIGNMENT>
bool	householder_r (viennacl::matrix< SCALARTYPE, row_major, ALIGNMENT > &A, viennacl::matrix< SCALARTYPE, row_major, ALIGNMENT > &Q, viennacl::vector< SCALARTYPE, ALIGNMENT > &D, vcl_size_t row_start, vcl_size_t col_start)

template<typename SCALARTYPE , unsigned int ALIGNMENT>
void	bidiag (viennacl::matrix< SCALARTYPE, row_major, ALIGNMENT > &Ai, viennacl::matrix< SCALARTYPE, row_major, ALIGNMENT > &QL, viennacl::matrix< SCALARTYPE, row_major, ALIGNMENT > &QR)

Detailed Description

Namespace holding implementation details for linear algebra routines. Usually not of interest for a library user.

Enumeration Type Documentation

enum viennacl::linalg::detail::row_info_types

Enumerator
SPARSE_ROW_NORM_INF
SPARSE_ROW_NORM_1
SPARSE_ROW_NORM_2
SPARSE_ROW_DIAGONAL

Definition at line 837 of file forwards.h.

Function Documentation

template<typename NumericT >

void viennacl::linalg::detail::amg_galerkin_prod	(	compressed_matrix< NumericT > &	A_fine,
		compressed_matrix< NumericT > &	P,
		compressed_matrix< NumericT > &	R,
		compressed_matrix< NumericT > &	A_coarse
	)

Sparse Galerkin product: Calculates A_coarse = trans(P)*A_fine*P = R*A_fine*P.

Parameters

A_fine	Operator matrix on fine grid (quadratic)
P	Prolongation/Interpolation matrix
R	Restriction matrix
A_coarse	Result matrix on coarse grid (Galerkin operator)

Definition at line 78 of file amg.hpp.

template<typename MatrixT , typename InternalT1 , typename InternalT2 >

void viennacl::linalg::detail::amg_init	(	MatrixT const &	mat,
		InternalT1 &	list_of_A,
		InternalT1 &	list_of_P,
		InternalT1 &	list_of_R,
		InternalT2 &	list_of_amg_level_context,
		amg_tag &	tag
	)

Initialize AMG preconditioner.

Parameters

mat	System matrix
list_of_A	Operator matrices on all levels
list_of_P	Prolongation/Interpolation operators on all levels
list_of_R	Restriction operators on all levels
list_of_amg_level_context	Auxiliary datastructures for managing the grid hierarchy (coarse nodes, etc.)
tag	AMG preconditioner tag

Definition at line 169 of file amg.hpp.

template<typename NumericT , typename SparseMatrixT >

void viennacl::linalg::detail::amg_lu	(	viennacl::matrix< NumericT > &	op,
		SparseMatrixT const &	A,
		amg_tag const &	tag
	)

Pre-compute LU factorization for direct solve (ublas library).

Speeds up precondition phase as this is computed only once overall instead of once per iteration.

Parameters

op	Operator matrix for direct solve
A	Operator matrix on coarsest level
tag	AMG preconditioner tag

Definition at line 236 of file amg.hpp.

template<typename NumericT , typename AMGContextListT >

vcl_size_t viennacl::linalg::detail::amg_setup	(	std::vector< compressed_matrix< NumericT > > &	list_of_A,
		std::vector< compressed_matrix< NumericT > > &	list_of_P,
		std::vector< compressed_matrix< NumericT > > &	list_of_R,
		AMGContextListT &	list_of_amg_level_context,
		amg_tag &	tag
	)

Setup AMG preconditioner.

Parameters

list_of_A	Operator matrices on all levels
list_of_P	Prolongation/Interpolation operators on all levels
list_of_R	Restriction operators on all levels
list_of_amg_level_context	Auxiliary datastructures for managing the grid hierarchy (coarse nodes, etc.)
tag	AMG preconditioner tag

Definition at line 105 of file amg.hpp.

template<typename InternalVectorT , typename SparseMatrixT >

void viennacl::linalg::detail::amg_setup_apply	(	InternalVectorT &	result,
		InternalVectorT &	result_backup,
		InternalVectorT &	rhs,
		InternalVectorT &	residual,
		SparseMatrixT const &	A,
		vcl_size_t	coarse_levels,
		amg_tag const &	tag
	)

Setup data structures for precondition phase for later use on the GPU.

Parameters

result	Result vector on all levels
result_backup	Copy of result vector on all levels
rhs	RHS vector on all levels
residual	Residual vector on all levels
A	Operators matrices on all levels from setup phase
coarse_levels	Number of coarse levels for which the datastructures should be set up.
tag	AMG preconditioner tag

Definition at line 199 of file amg.hpp.

template<typename SCALARTYPE , unsigned int ALIGNMENT>

void viennacl::linalg::detail::bidiag	(	viennacl::matrix< SCALARTYPE, row_major, ALIGNMENT > &	Ai,
		viennacl::matrix< SCALARTYPE, row_major, ALIGNMENT > &	QL,
		viennacl::matrix< SCALARTYPE, row_major, ALIGNMENT > &	QR
	)

Definition at line 459 of file svd.hpp.

template<typename NumericT >

void viennacl::linalg::detail::bisectLarge	(	const InputData< NumericT > &	input,
		ResultDataLarge< NumericT > &	result,
		const unsigned int	mat_size,
		const NumericT	lg,
		const NumericT	ug,
		const NumericT	precision
	)

Definition at line 93 of file bisect_kernel_calls.hpp.

template<typename NumericT >

void viennacl::linalg::detail::bisectLarge_MultIntervals	(	const InputData< NumericT > &	input,
		ResultDataLarge< NumericT > &	result,
		const unsigned int	mat_size,
		const NumericT	precision
	)

Definition at line 160 of file bisect_kernel_calls.hpp.

template<typename NumericT >

void viennacl::linalg::detail::bisectLarge_OneIntervals	(	const InputData< NumericT > &	input,
		ResultDataLarge< NumericT > &	result,
		const unsigned int	mat_size,
		const NumericT	precision
	)

Definition at line 128 of file bisect_kernel_calls.hpp.

template<typename NumericT >

void viennacl::linalg::detail::bisectSmall	(	const InputData< NumericT > &	input,
		ResultDataSmall< NumericT > &	result,
		const unsigned int	mat_size,
		const NumericT	lg,
		const NumericT	ug,
		const NumericT	precision
	)

Definition at line 59 of file bisect_kernel_calls.hpp.

template<typename SparseMatrixType , class ScalarType , typename SOLVERTAG >

viennacl::enable_if< viennacl::is_any_sparse_matrix<SparseMatrixType>::value>::type viennacl::linalg::detail::block_inplace_solve	(	const matrix_expression< const SparseMatrixType, const SparseMatrixType, op_trans > &	mat,
		viennacl::backend::mem_handle const &	block_index_array,
		vcl_size_t	num_blocks,
		viennacl::vector_base< ScalarType > const &	mat_diagonal,
		viennacl::vector_base< ScalarType > &	vec,
		SOLVERTAG	tag
	)

Definition at line 332 of file sparse_matrix_operations.hpp.

template<typename T >

void viennacl::linalg::detail::cdiv	(	T	xr,
		T	xi,
		T	yr,
		T	yi,
		T &	cdivr,
		T &	cdivi
	)

Definition at line 142 of file qr-method-common.hpp.

template<typename MatrixType , typename VectorType >

void viennacl::linalg::detail::change_signs	(	MatrixType &	matrix,
		VectorType &	signs,
		int	n
	)

Definition at line 78 of file svd.hpp.

template<typename NumericT >

void viennacl::linalg::detail::computeEigenvaluesLargeMatrix	(	InputData< NumericT > &	input,
		ResultDataLarge< NumericT > &	result,
		const unsigned int	mat_size,
		const NumericT	lg,
		const NumericT	ug,
		const NumericT	precision
	)

Run the kernels to compute the eigenvalues for large matrices

Parameters

input	handles to input data
result	handles to result data
mat_size	matrix size
precision	desired precision of eigenvalues
lg	lower limit of Gerschgorin interval
ug	upper limit of Gerschgorin interval

Definition at line 60 of file bisect_large.hpp.

template<typename NumericT >

void viennacl::linalg::detail::computeEigenvaluesSmallMatrix	(	const InputData< NumericT > &	input,
		ResultDataSmall< NumericT > &	result,
		const unsigned int	mat_size,
		const NumericT	lg,
		const NumericT	ug,
		const NumericT	precision
	)

Determine eigenvalues for matrices smaller than MAX_SMALL_MATRIX

Parameters

input	handles to input data of kernel
result	handles to result of kernel
mat_size	matrix size
lg	lower limit of Gerschgorin interval
ug	upper limit of Gerschgorin interval
precision	desired precision of eigenvalues

Definition at line 61 of file bisect_small.hpp.

template<typename NumericT >

void viennacl::linalg::detail::computeGerschgorin	(	std::vector< NumericT > &	d,
		std::vector< NumericT > &	s,
		unsigned int	n,
		NumericT &	lg,
		NumericT &	ug
	)

Compute Gerschgorin interval for symmetric, tridiagonal matrix

Parameters

d	diagonal elements
s	superdiagonal elements
n	size of matrix
lg	lower limit of Gerschgorin interval
ug	upper limit of Gerschgorin interval

Definition at line 55 of file gerschgorin.hpp.

template<typename NumericT , typename OtherVectorT >

void viennacl::linalg::detail::copy_vec_to_vec	(	viennacl::vector< NumericT > const &	src,
		OtherVectorT &	dest
	)

overloaded function for copying vectors

Definition at line 44 of file bisect.hpp.

template<typename OtherVectorT , typename NumericT >

void viennacl::linalg::detail::copy_vec_to_vec	(	OtherVectorT const &	src,
		viennacl::vector< NumericT > &	dest
	)

Definition at line 50 of file bisect.hpp.

template<typename VectorT1 , typename VectorT2 >

void viennacl::linalg::detail::copy_vec_to_vec	(	VectorT1 const &	src,
		VectorT2 &	dest
	)

Definition at line 56 of file bisect.hpp.

template<typename NumericT >

void viennacl::linalg::detail::extract_block_matrix	(	viennacl::compressed_matrix< NumericT > const &	A,
		viennacl::compressed_matrix< NumericT > &	diagonal_block_A,
		vcl_size_t	start_index,
		vcl_size_t	stop_index
	)

Extracts a diagonal block from a larger system matrix.

Parameters

A	The full matrix
diagonal_block_A	The output matrix, to which the extracted block is written to
start_index	First row- and column-index of the block
stop_index	First row- and column-index beyond the block

Definition at line 79 of file block_ilu.hpp.

template<typename SCALARTYPE , typename MatrixT >

void viennacl::linalg::detail::final_iter_update	(	MatrixT &	A,
		int	n,
		int	last_n,
		SCALARTYPE	q,
		SCALARTYPE	p
	)

Definition at line 128 of file qr-method.hpp.

template<typename SCALARTYPE >

void viennacl::linalg::detail::final_iter_update_gpu	(	matrix_base< SCALARTYPE > &	A,
		int	n,
		int	last_n,
		SCALARTYPE	q,
		SCALARTYPE	p
	)

Definition at line 42 of file qr-method.hpp.

unsigned int viennacl::linalg::detail::getNumBlocksLinear	(	const unsigned int	num_threads,
		const unsigned int	num_threads_block
	)

inline

Get the number of blocks that are required to process num_threads with num_threads_blocks threads per block

Definition at line 96 of file util.hpp.

template<typename MatrixType , typename VectorType >

void viennacl::linalg::detail::givens_prev	(	MatrixType &	matrix,
		VectorType &	tmp1,
		VectorType &	tmp2,
		int	n,
		int	l,
		int	k
	)

Definition at line 48 of file svd.hpp.

template<typename SrcVectorT , typename DestVectorT >

void viennacl::linalg::detail::gmres_copy_helper	(	SrcVectorT const &	src,
		DestVectorT &	dest,
		vcl_size_t	len,
		vcl_size_t	start = `0`
	)

Definition at line 107 of file gmres.hpp.

template<typename NumericT , typename DestVectorT >

void viennacl::linalg::detail::gmres_copy_helper	(	viennacl::vector< NumericT > const &	src,
		DestVectorT &	dest,
		vcl_size_t	len,
		vcl_size_t	start = `0`
	)

Definition at line 114 of file gmres.hpp.

template<typename VectorT , typename NumericT >

void viennacl::linalg::detail::gmres_householder_reflect	(	VectorT &	x,
		VectorT const &	h,
		NumericT	beta
	)

Definition at line 162 of file gmres.hpp.

template<typename VectorT , typename NumericT >

void viennacl::linalg::detail::gmres_setup_householder_vector	(	VectorT const &	input_vec,
		VectorT &	hh_vec,
		NumericT &	beta,
		NumericT &	mu,
		vcl_size_t	j
	)

Computes the householder vector 'hh_vec' which rotates 'input_vec' such that all entries below the j-th entry of 'v' become zero.

Parameters

input_vec	The input vector
hh_vec	The householder vector defining the relection (I - beta * hh_vec * hh_vec^T)
beta	The coefficient beta in (I - beta * hh_vec * hh_vec^T)
mu	The norm of the input vector part relevant for the reflection: norm_2(input_vec[j:size])
j	Index of the last nonzero index in 'input_vec' after applying the reflection

Definition at line 131 of file gmres.hpp.

template<typename SCALARTYPE , unsigned int ALIGNMENT>

bool viennacl::linalg::detail::householder_c	(	viennacl::matrix< SCALARTYPE, row_major, ALIGNMENT > &	A,
		viennacl::matrix< SCALARTYPE, row_major, ALIGNMENT > &	Q,
		viennacl::vector< SCALARTYPE, ALIGNMENT > &	D,
		vcl_size_t	row_start,
		vcl_size_t	col_start
	)

Definition at line 328 of file svd.hpp.

template<typename SCALARTYPE , unsigned int ALIGNMENT>

bool viennacl::linalg::detail::householder_r	(	viennacl::matrix< SCALARTYPE, row_major, ALIGNMENT > &	A,
		viennacl::matrix< SCALARTYPE, row_major, ALIGNMENT > &	Q,
		viennacl::vector< SCALARTYPE, ALIGNMENT > &	D,
		vcl_size_t	row_start,
		vcl_size_t	col_start
	)

Definition at line 415 of file svd.hpp.

template<typename MatrixType , typename VectorType , typename ScalarType >

void viennacl::linalg::detail::householder_reflect	(	MatrixType &	A,
		VectorType &	v,
		ScalarType	beta,
		vcl_size_t	j,
		vcl_size_t	k
	)

Definition at line 134 of file qr.hpp.

template<typename MatrixType , typename VectorType , typename ScalarType >

void viennacl::linalg::detail::householder_reflect	(	MatrixType &	A,
		VectorType &	v,
		ScalarType	beta,
		vcl_size_t	j
	)

Definition at line 184 of file qr.hpp.

template<typename MatrixType , typename VectorType , typename ScalarType >

void viennacl::linalg::detail::householder_reflect_ublas	(	MatrixType &	A,
		VectorType &	v,
		MatrixType &	matrix_1x1,
		ScalarType	beta,
		vcl_size_t	j,
		vcl_size_t	k
	)

Definition at line 147 of file qr.hpp.

template<typename MatrixType , typename VectorType , typename ScalarType >

void viennacl::linalg::detail::householder_reflect_viennacl	(	MatrixType &	A,
		VectorType &	v,
		MatrixType &	matrix_1x1,
		ScalarType	beta,
		vcl_size_t	j,
		vcl_size_t	k
	)

Definition at line 161 of file qr.hpp.

template<typename SCALARTYPE >

bool viennacl::linalg::detail::householder_twoside	(	matrix_base< SCALARTYPE > &	A,
		matrix_base< SCALARTYPE > &	Q,
		vector_base< SCALARTYPE > &	D,
		vcl_size_t	start
	)

Definition at line 694 of file qr-method.hpp.

template<typename VectorType >

void viennacl::linalg::detail::householder_vector	(	VectorType &	v,
		vcl_size_t	start
	)

Definition at line 97 of file qr-method-common.hpp.

template<typename SCALARTYPE , typename VectorType >

void viennacl::linalg::detail::hqr2	(	viennacl::matrix< SCALARTYPE > &	vcl_H,
		viennacl::matrix< SCALARTYPE > &	V,
		VectorType &	d,
		VectorType &	e
	)

Definition at line 236 of file qr-method.hpp.

template<typename MatrixType >

std::vector< typename viennacl::result_of::cpu_value_type< typename MatrixType::value_type >::type > viennacl::linalg::detail::inplace_qr_hybrid	(	MatrixType &	A,
		vcl_size_t	block_size = `16`
	)

Implementation of a hybrid QR factorization using uBLAS on the CPU and ViennaCL for GPUs (or multi-core CPU)

Prefer the use of the convenience interface inplace_qr()

Parameters

A	A dense ViennaCL matrix to be factored
block_size	The block size to be used. The number of columns of A must be a multiple of block_size

Definition at line 426 of file qr.hpp.

template<typename MatrixType >

std::vector<typename MatrixType::value_type> viennacl::linalg::detail::inplace_qr_ublas	(	MatrixType &	A,
		vcl_size_t	block_size = `32`
	)

Implementation of inplace-QR factorization for a general Boost.uBLAS compatible matrix A.

Parameters

A	A dense compatible to Boost.uBLAS
block_size	The block size to be used. The number of columns of A must be a multiple of block_size

Definition at line 228 of file qr.hpp.

template<typename MatrixType >

std::vector< typename viennacl::result_of::cpu_value_type< typename MatrixType::value_type >::type > viennacl::linalg::detail::inplace_qr_viennacl	(	MatrixType &	A,
		vcl_size_t	block_size = `16`
	)

Implementation of a OpenCL-only QR factorization for GPUs (or multi-core CPU). DEPRECATED! Use only if you're curious and interested in playing a bit with a GPU-only implementation.

Performance is rather poor at small matrix sizes. Prefer the use of the hybrid version, which is automatically chosen using the interface function inplace_qr()

Parameters

A	A dense ViennaCL matrix to be factored
block_size	The block size to be used. The number of columns of A must be a multiple of block_size

Definition at line 322 of file qr.hpp.

template<typename MatrixT1 , typename MatrixT2 >

void viennacl::linalg::detail::inplace_solve_impl	(	MatrixT1 const &	A,
		MatrixT2 &	B,
		viennacl::linalg::lower_tag
	)

Definition at line 155 of file direct_solve.hpp.

template<typename MatrixT1 , typename MatrixT2 >

void viennacl::linalg::detail::inplace_solve_impl	(	MatrixT1 const &	A,
		MatrixT2 &	B,
		viennacl::linalg::unit_lower_tag
	)

Definition at line 161 of file direct_solve.hpp.

template<typename MatrixT1 , typename MatrixT2 >

void viennacl::linalg::detail::inplace_solve_impl	(	MatrixT1 const &	A,
		MatrixT2 &	B,
		viennacl::linalg::upper_tag
	)

Definition at line 198 of file direct_solve.hpp.

template<typename MatrixT1 , typename MatrixT2 >

void viennacl::linalg::detail::inplace_solve_impl	(	MatrixT1 const &	A,
		MatrixT2 &	B,
		viennacl::linalg::unit_upper_tag
	)

Definition at line 204 of file direct_solve.hpp.

template<typename NumericT , typename SolverTagT >

void viennacl::linalg::detail::inplace_solve_kernel	(	const matrix_base< NumericT > &	A,
		const matrix_base< NumericT > &	B,
		SolverTagT
	)

Direct inplace solver for dense triangular systems using a single kernel launch. Matlab notation: A \ B.

Parameters

A	The system matrix
B	The matrix of row vectors, where the solution is directly written to

Definition at line 62 of file direct_solve.hpp.

template<typename MatrixT1 , typename MatrixT2 , typename SolverTagT >

void viennacl::linalg::detail::inplace_solve_lower_impl	(	MatrixT1 const &	A,
		MatrixT2 &	B,
		SolverTagT
	)

Definition at line 125 of file direct_solve.hpp.

template<typename MatrixT1 , typename VectorT , typename SolverTagT >

void viennacl::linalg::detail::inplace_solve_lower_vec_impl	(	MatrixT1 const &	A,
		VectorT &	b,
		SolverTagT
	)

Definition at line 369 of file direct_solve.hpp.

template<typename MatrixT1 , typename MatrixT2 , typename SolverTagT >

void viennacl::linalg::detail::inplace_solve_upper_impl	(	MatrixT1 const &	A,
		MatrixT2 &	B,
		SolverTagT
	)

Definition at line 167 of file direct_solve.hpp.

template<typename MatrixT1 , typename VectorT , typename SolverTagT >

void viennacl::linalg::detail::inplace_solve_upper_vec_impl	(	MatrixT1 const &	A,
		VectorT &	b,
		SolverTagT
	)

Definition at line 407 of file direct_solve.hpp.

template<typename MatrixT1 , typename VectorT >

void viennacl::linalg::detail::inplace_solve_vec_impl	(	MatrixT1 const &	A,
		VectorT &	B,
		viennacl::linalg::lower_tag
	)

Definition at line 395 of file direct_solve.hpp.

template<typename MatrixT1 , typename VectorT >

void viennacl::linalg::detail::inplace_solve_vec_impl	(	MatrixT1 const &	A,
		VectorT &	B,
		viennacl::linalg::unit_lower_tag
	)

Definition at line 401 of file direct_solve.hpp.

template<typename MatrixT1 , typename VectorT >

void viennacl::linalg::detail::inplace_solve_vec_impl	(	MatrixT1 const &	A,
		VectorT &	b,
		viennacl::linalg::upper_tag
	)

Definition at line 433 of file direct_solve.hpp.

template<typename MatrixT1 , typename VectorT >

void viennacl::linalg::detail::inplace_solve_vec_impl	(	MatrixT1 const &	A,
		VectorT &	b,
		viennacl::linalg::unit_upper_tag
	)

Definition at line 439 of file direct_solve.hpp.

template<typename NumericT , typename SolverTagT >

void viennacl::linalg::detail::inplace_solve_vec_kernel	(	const matrix_base< NumericT > &	mat,
		const vector_base< NumericT > &	vec,
		SolverTagT
	)

Definition at line 94 of file direct_solve.hpp.

template<typename SizeT , typename NumericT >

void viennacl::linalg::detail::insert_with_value_sort	(	std::vector< std::pair< SizeT, NumericT > > &	map,
		SizeT	index,
		NumericT	value
	)

Definition at line 164 of file ilut.hpp.

template<typename NumericT >

void viennacl::linalg::detail::inverse_iteration	(	std::vector< NumericT > const &	alphas,
		std::vector< NumericT > const &	betas,
		NumericT &	eigenvalue,
		std::vector< NumericT > &	eigenvector
	)

Inverse iteration for finding an eigenvector for an eigenvalue.

beta[0] to be ignored for consistency.

Definition at line 109 of file lanczos.hpp.

template<typename MatrixT , typename DenseMatrixT , typename NumericT >

std::vector<NumericT> viennacl::linalg::detail::lanczos	(	MatrixT const &	A,
		vector_base< NumericT > &	r,
		DenseMatrixT &	eigenvectors_A,
		vcl_size_t	krylov_dim,
		lanczos_tag const &	tag,
		bool	compute_eigenvectors
	)

Implementation of the Lanczos FRO algorithm.

Parameters

A	The system matrix
r	Random start vector
eigenvectors_A	A dense matrix in which the eigenvectors of A will be stored. Both row- and column-major matrices are supported.
krylov_dim	Size of krylov-space
tag	The Lanczos tag holding tolerances, etc.
compute_eigenvectors	Boolean flag. If true, eigenvectors are computed. Otherwise the routine returns after calculating eigenvalues.

Returns: Returns the eigenvalues (number of eigenvalues equals size of krylov-space)

Definition at line 345 of file lanczos.hpp.

template<typename MatrixT , typename DenseMatrixT , typename NumericT >

std::vector<NumericT> viennacl::linalg::detail::lanczosPRO	(	MatrixT const &	A,
		vector_base< NumericT > &	r,
		DenseMatrixT &	eigenvectors_A,
		vcl_size_t	size,
		lanczos_tag const &	tag,
		bool	compute_eigenvectors
	)

Implementation of the Lanczos PRO algorithm (partial reorthogonalization)

Parameters

A	The system matrix
r	Random start vector
eigenvectors_A	Dense matrix holding the eigenvectors of A (one eigenvector per column)
size	Size of krylov-space
tag	Lanczos_tag with several options for the algorithm
compute_eigenvectors	Boolean flag. If true, eigenvectors are computed. Otherwise the routine returns after calculating eigenvalues.

Returns: Returns the eigenvalues (number of eigenvalues equals size of krylov-space)

Definition at line 158 of file lanczos.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::detail::level_scheduling_setup_impl	(	viennacl::compressed_matrix< NumericT, AlignmentV > const &	LU,
		viennacl::vector< NumericT > const &	diagonal_LU,
		std::list< viennacl::backend::mem_handle > &	row_index_arrays,
		std::list< viennacl::backend::mem_handle > &	row_buffers,
		std::list< viennacl::backend::mem_handle > &	col_buffers,
		std::list< viennacl::backend::mem_handle > &	element_buffers,
		std::list< vcl_size_t > &	row_elimination_num_list,
		bool	setup_U
	)

Definition at line 51 of file common.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::detail::level_scheduling_setup_L	(	viennacl::compressed_matrix< NumericT, AlignmentV > const &	LU,
		viennacl::vector< NumericT > const &	diagonal_LU,
		std::list< viennacl::backend::mem_handle > &	row_index_arrays,
		std::list< viennacl::backend::mem_handle > &	row_buffers,
		std::list< viennacl::backend::mem_handle > &	col_buffers,
		std::list< viennacl::backend::mem_handle > &	element_buffers,
		std::list< vcl_size_t > &	row_elimination_num_list
	)

Definition at line 191 of file common.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::detail::level_scheduling_setup_U	(	viennacl::compressed_matrix< NumericT, AlignmentV > const &	LU,
		viennacl::vector< NumericT > const &	diagonal_LU,
		std::list< viennacl::backend::mem_handle > &	row_index_arrays,
		std::list< viennacl::backend::mem_handle > &	row_buffers,
		std::list< viennacl::backend::mem_handle > &	col_buffers,
		std::list< viennacl::backend::mem_handle > &	element_buffers,
		std::list< vcl_size_t > &	row_elimination_num_list
	)

Definition at line 208 of file common.hpp.

template<typename ScalarType >

void viennacl::linalg::detail::level_scheduling_substitute	(	vector< ScalarType > &	vec,
		viennacl::backend::mem_handle const &	row_index_array,
		viennacl::backend::mem_handle const &	row_buffer,
		viennacl::backend::mem_handle const &	col_buffer,
		viennacl::backend::mem_handle const &	element_buffer,
		vcl_size_t	num_rows
	)

Definition at line 49 of file misc_operations.hpp.

template<typename NumericT >

void viennacl::linalg::detail::level_scheduling_substitute	(	viennacl::vector< NumericT > &	vec,
		std::list< viennacl::backend::mem_handle > const &	row_index_arrays,
		std::list< viennacl::backend::mem_handle > const &	row_buffers,
		std::list< viennacl::backend::mem_handle > const &	col_buffers,
		std::list< viennacl::backend::mem_handle > const &	element_buffers,
		std::list< vcl_size_t > const &	row_elimination_num_list
	)

Definition at line 224 of file common.hpp.

template<class T >

T viennacl::linalg::detail::max	(	const T &	lhs,
		const T &	rhs
	)

Maximum.

Examples:: bandwidth-reduction.cpp.

Definition at line 59 of file util.hpp.

template<typename IndexT , typename NumericT >

IndexT viennacl::linalg::detail::merge_subtract_sparse_rows	(	IndexT const *	w_coords,
		NumericT const *	w_elements,
		IndexT	w_size,
		IndexT const *	u_coords,
		NumericT const *	u_elements,
		IndexT	u_size,
		NumericT	alpha,
		IndexT *	z_coords,
		NumericT *	z_elements
	)

Subtracts a scaled sparse vector u from a sparse vector w and writes the output to z: z = w - alpha * u.

Sparsity pattern of u and w are usually different.

Returns: Length of new vector

Definition at line 120 of file ilut.hpp.

template<class T >

T viennacl::linalg::detail::min	(	const T &	lhs,
		const T &	rhs
	)

Minimum.

Definition at line 45 of file util.hpp.

template<typename VectorType >

VectorType::value_type viennacl::linalg::detail::norm_lcl	(	VectorType const &	x,
		vcl_size_t	size
	)

Definition at line 78 of file qr-method-common.hpp.

template<typename VectorType >

void viennacl::linalg::detail::normalize	(	VectorType &	x,
		vcl_size_t	size
	)

Definition at line 87 of file qr-method-common.hpp.

template<typename NumericT , typename B >

bool viennacl::linalg::detail::op_aliasing	(	vector_base< NumericT > const &	,
		B const &
	)

Definition at line 36 of file op_executor.hpp.

template<typename NumericT >

bool viennacl::linalg::detail::op_aliasing	(	vector_base< NumericT > const &	lhs,
		vector_base< NumericT > const &	b
	)

Definition at line 42 of file op_executor.hpp.

template<typename NumericT , typename LhsT , typename RhsT , typename OpT >

bool viennacl::linalg::detail::op_aliasing	(	vector_base< NumericT > const &	lhs,
		vector_expression< const LhsT, const RhsT, OpT > const &	rhs
	)

Definition at line 48 of file op_executor.hpp.

template<typename NumericT , typename B >

bool viennacl::linalg::detail::op_aliasing	(	matrix_base< NumericT > const &	,
		B const &
	)

Definition at line 55 of file op_executor.hpp.

template<typename NumericT >

bool viennacl::linalg::detail::op_aliasing	(	matrix_base< NumericT > const &	lhs,
		matrix_base< NumericT > const &	b
	)

Definition at line 61 of file op_executor.hpp.

template<typename NumericT , typename LhsT , typename RhsT , typename OpT >

bool viennacl::linalg::detail::op_aliasing	(	matrix_base< NumericT > const &	lhs,
		matrix_expression< const LhsT, const RhsT, OpT > const &	rhs
	)

Definition at line 67 of file op_executor.hpp.

template<typename MatrixT , typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::pipelined_solve	(	MatrixT const &	A,
		viennacl::vector_base< NumericT > const &	rhs,
		bicgstab_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Implementation of a pipelined stabilized Bi-conjugate gradient solver.

Definition at line 98 of file bicgstab.hpp.

template<typename MatrixT , typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::pipelined_solve	(	MatrixT const &	A,
		viennacl::vector< NumericT > const &	rhs,
		cg_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Implementation of a pipelined conjugate gradient algorithm (no preconditioner), specialized for ViennaCL types.

Pipelined version from A. T. Chronopoulos and C. W. Gear, J. Comput. Appl. Math. 25(2), 153–168 (1989)

Parameters

A	The system matrix
rhs	The load vector
tag	Solver configuration tag
monitor	A callback routine which is called at each GMRES restart
monitor_data	Data pointer to be passed to the callback routine to pass on user-specific data

Returns: The result vector

Definition at line 129 of file cg.hpp.

template<typename MatrixType , typename ScalarType >

viennacl::vector<ScalarType> viennacl::linalg::detail::pipelined_solve	(	MatrixType const &	A,
		viennacl::vector< ScalarType > const &	rhs,
		gmres_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< ScalarType > const &, ScalarType, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Implementation of a pipelined GMRES solver without preconditioner.

Following algorithm 2.1 proposed by Walker in "A Simpler GMRES", but uses classical Gram-Schmidt instead of modified Gram-Schmidt for better parallelization. Uses some pipelining techniques for minimizing host-device transfer

Parameters

A	The system matrix
rhs	The load vector
tag	Solver configuration tag
monitor	A callback routine which is called at each GMRES restart
monitor_data	Data pointer to be passed to the callback routine to pass on user-specific data

Returns: The result vector

Definition at line 182 of file gmres.hpp.

template<typename NumericT >

void viennacl::linalg::detail::precondition	(	viennacl::compressed_matrix< NumericT > const &	A,
		viennacl::compressed_matrix< NumericT > &	L,
		viennacl::vector< NumericT > &	diag_L,
		viennacl::compressed_matrix< NumericT > &	L_trans,
		chow_patel_tag const &	tag
	)

Implementation of the parallel ICC0 factorization, Algorithm 3 in Chow-Patel paper.

Rather than dealing with a column-major upper triangular matrix U, we use the lower-triangular matrix L such that A is approximately given by LL^T. The advantage is that L is readily available in row-major format.

Definition at line 77 of file chow_patel_ilu.hpp.

template<typename NumericT >

void viennacl::linalg::detail::precondition	(	viennacl::compressed_matrix< NumericT > const &	A,
		viennacl::compressed_matrix< NumericT > &	L,
		viennacl::vector< NumericT > &	diag_L,
		viennacl::compressed_matrix< NumericT > &	U,
		viennacl::vector< NumericT > &	diag_U,
		chow_patel_tag const &	tag
	)

Implementation of the parallel ILU0 factorization, Algorithm 2 in Chow-Patel paper.

Definition at line 110 of file chow_patel_ilu.hpp.

template<typename SCALARTYPE >

void viennacl::linalg::detail::prepare_householder_vector	(	matrix_base< SCALARTYPE > &	A,
		vector_base< SCALARTYPE > &	D,
		vcl_size_t	size,
		vcl_size_t	row_start,
		vcl_size_t	col_start,
		vcl_size_t	start,
		bool	is_column
	)

Definition at line 165 of file qr-method-common.hpp.

template<typename NumericT >

bool viennacl::linalg::detail::processResultDataLargeMatrix	(	ResultDataLarge< NumericT > &	result,
		const unsigned int	mat_size
	)

Process the result, that is obtain result from device and do simple sanity checking

Parameters

result	handles to result data
mat_size	matrix size

Definition at line 88 of file bisect_large.hpp.

template<typename NumericT >

void viennacl::linalg::detail::processResultSmallMatrix	(	ResultDataSmall< NumericT > &	result,
		const unsigned int	mat_size
	)

Process the result obtained on the device, that is transfer to host and perform basic sanity checking

Parameters

result	handles to result data
mat_size	matrix size

Definition at line 78 of file bisect_small.hpp.

template<typename SCALARTYPE >

SCALARTYPE viennacl::linalg::detail::pythag	(	SCALARTYPE	a,
		SCALARTYPE	b
	)

Definition at line 65 of file qr-method-common.hpp.

template<typename SCALARTYPE >

void viennacl::linalg::detail::qr_method	(	viennacl::matrix< SCALARTYPE > &	A,
		viennacl::matrix< SCALARTYPE > &	Q,
		std::vector< SCALARTYPE > &	D,
		std::vector< SCALARTYPE > &	E,
		bool	is_symmetric = `true`
	)

Definition at line 728 of file qr-method.hpp.

template<typename SparseMatrixType , typename SCALARTYPE , unsigned int VEC_ALIGNMENT>

viennacl::enable_if< viennacl::is_any_sparse_matrix<SparseMatrixType>::value >::type viennacl::linalg::detail::row_info	(	SparseMatrixType const &	mat,
		vector< SCALARTYPE, VEC_ALIGNMENT > &	vec,
		row_info_types	info_selector
	)

Definition at line 50 of file sparse_matrix_operations.hpp.

template<typename MatrixType , typename VectorType >

MatrixType::value_type viennacl::linalg::detail::setup_householder_vector_ublas	(	MatrixType const &	A,
		VectorType &	v,
		MatrixType &	matrix_1x1,
		vcl_size_t	j
	)

Definition at line 53 of file qr.hpp.

template<typename MatrixType , typename VectorType >

viennacl::result_of::cpu_value_type< typename MatrixType::value_type >::type viennacl::linalg::detail::setup_householder_vector_viennacl	(	MatrixType const &	A,
		VectorType &	v,
		MatrixType &	matrix_1x1,
		vcl_size_t	j
	)

Definition at line 93 of file qr.hpp.

template<typename SCALARTYPE >

SCALARTYPE viennacl::linalg::detail::sign ( SCALARTYPE val )

Definition at line 71 of file qr-method-common.hpp.

double viennacl::linalg::detail::sign_d ( const double & val )

inline

Sign of number (double)

Definition at line 84 of file util.hpp.

float viennacl::linalg::detail::sign_f ( const float & val )

inline

Sign of number (float)

Definition at line 72 of file util.hpp.

template<typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::solve_impl	(	viennacl::compressed_matrix< NumericT > const &	A,
		viennacl::vector< NumericT > const &	rhs,
		cg_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Overload for the pipelined CG implementation for the ViennaCL sparse matrix types.

Definition at line 192 of file cg.hpp.

template<typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::solve_impl	(	viennacl::coordinate_matrix< NumericT > const &	A,
		viennacl::vector< NumericT > const &	rhs,
		cg_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Overload for the pipelined CG implementation for the ViennaCL sparse matrix types.

Definition at line 205 of file cg.hpp.

template<typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::solve_impl	(	viennacl::ell_matrix< NumericT > const &	A,
		viennacl::vector< NumericT > const &	rhs,
		cg_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Overload for the pipelined CG implementation for the ViennaCL sparse matrix types.

Definition at line 219 of file cg.hpp.

template<typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::solve_impl	(	viennacl::compressed_matrix< NumericT > const &	A,
		viennacl::vector< NumericT > const &	rhs,
		bicgstab_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Overload for the pipelined CG implementation for the ViennaCL sparse matrix types.

Definition at line 219 of file bicgstab.hpp.

template<typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::solve_impl	(	viennacl::coordinate_matrix< NumericT > const &	A,
		viennacl::vector< NumericT > const &	rhs,
		bicgstab_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Overload for the pipelined CG implementation for the ViennaCL sparse matrix types.

Definition at line 232 of file bicgstab.hpp.

template<typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::solve_impl	(	viennacl::sliced_ell_matrix< NumericT > const &	A,
		viennacl::vector< NumericT > const &	rhs,
		cg_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Overload for the pipelined CG implementation for the ViennaCL sparse matrix types.

Definition at line 233 of file cg.hpp.

template<typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::solve_impl	(	viennacl::hyb_matrix< NumericT > const &	A,
		viennacl::vector< NumericT > const &	rhs,
		cg_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Overload for the pipelined CG implementation for the ViennaCL sparse matrix types.

Definition at line 246 of file cg.hpp.

template<typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::solve_impl	(	viennacl::ell_matrix< NumericT > const &	A,
		viennacl::vector< NumericT > const &	rhs,
		bicgstab_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Overload for the pipelined CG implementation for the ViennaCL sparse matrix types.

Definition at line 246 of file bicgstab.hpp.

template<typename MatrixT , typename VectorT , typename PreconditionerT >

VectorT viennacl::linalg::detail::solve_impl	(	MatrixT const &	matrix,
		VectorT const &	rhs,
		cg_tag const &	tag,
		PreconditionerT const &	precond,
		bool()(VectorT const &, typename viennacl::result_of::cpu_value_type< typename viennacl::result_of::value_type< VectorT >::type >::type, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Definition at line 258 of file cg.hpp.

template<typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::solve_impl	(	viennacl::sliced_ell_matrix< NumericT > const &	A,
		viennacl::vector< NumericT > const &	rhs,
		bicgstab_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Overload for the pipelined CG implementation for the ViennaCL sparse matrix types.

Definition at line 260 of file bicgstab.hpp.

template<typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::solve_impl	(	viennacl::hyb_matrix< NumericT > const &	A,
		viennacl::vector< NumericT > const &	rhs,
		bicgstab_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Overload for the pipelined CG implementation for the ViennaCL sparse matrix types.

Definition at line 273 of file bicgstab.hpp.

template<typename MatrixT , typename VectorT >

VectorT viennacl::linalg::detail::solve_impl	(	MatrixT const &	matrix,
		VectorT const &	rhs,
		bicgstab_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(VectorT const &, typename viennacl::result_of::cpu_value_type< typename viennacl::result_of::value_type< VectorT >::type >::type, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Implementation of the unpreconditioned stabilized Bi-conjugate gradient solver.

Following the description in "Iterative Methods for Sparse Linear Systems" by Y. Saad

Parameters

matrix	The system matrix
rhs	The load vector
tag	Solver configuration tag
monitor	A callback routine which is called at each GMRES restart
monitor_data	Data pointer to be passed to the callback routine to pass on user-specific data

Returns: The result vector

Definition at line 296 of file bicgstab.hpp.

template<typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::solve_impl	(	viennacl::compressed_matrix< NumericT > const &	A,
		viennacl::vector< NumericT > const &	rhs,
		gmres_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Overload for the pipelined CG implementation for the ViennaCL sparse matrix types.

Definition at line 371 of file gmres.hpp.

template<typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::solve_impl	(	viennacl::coordinate_matrix< NumericT > const &	A,
		viennacl::vector< NumericT > const &	rhs,
		gmres_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Overload for the pipelined CG implementation for the ViennaCL sparse matrix types.

Definition at line 384 of file gmres.hpp.

template<typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::solve_impl	(	viennacl::ell_matrix< NumericT > const &	A,
		viennacl::vector< NumericT > const &	rhs,
		gmres_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Overload for the pipelined CG implementation for the ViennaCL sparse matrix types.

Definition at line 398 of file gmres.hpp.

template<typename MatrixT , typename VectorT , typename PreconditionerT >

VectorT viennacl::linalg::detail::solve_impl	(	MatrixT const &	matrix,
		VectorT const &	rhs,
		bicgstab_tag const &	tag,
		PreconditionerT const &	precond,
		bool()(VectorT const &, typename viennacl::result_of::cpu_value_type< typename viennacl::result_of::value_type< VectorT >::type >::type, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Implementation of the preconditioned stabilized Bi-conjugate gradient solver.

Following the description of the unpreconditioned case in "Iterative Methods for Sparse Linear Systems" by Y. Saad

Parameters

matrix	The system matrix
rhs	The load vector
tag	Solver configuration tag
precond	A preconditioner. Precondition operation is done via member function apply()
monitor	A callback routine which is called at each GMRES restart
monitor_data	Data pointer to be passed to the callback routine to pass on user-specific data

Returns: The result vector

Definition at line 399 of file bicgstab.hpp.

template<typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::solve_impl	(	viennacl::sliced_ell_matrix< NumericT > const &	A,
		viennacl::vector< NumericT > const &	rhs,
		gmres_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Overload for the pipelined CG implementation for the ViennaCL sparse matrix types.

Definition at line 412 of file gmres.hpp.

template<typename NumericT >

viennacl::vector<NumericT> viennacl::linalg::detail::solve_impl	(	viennacl::hyb_matrix< NumericT > const &	A,
		viennacl::vector< NumericT > const &	rhs,
		gmres_tag const &	tag,
		viennacl::linalg::no_precond	,
		bool()(viennacl::vector< NumericT > const &, NumericT, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Overload for the pipelined CG implementation for the ViennaCL sparse matrix types.

Definition at line 425 of file gmres.hpp.

template<typename MatrixT , typename VectorT , typename PreconditionerT >

VectorT viennacl::linalg::detail::solve_impl	(	MatrixT const &	matrix,
		VectorT const &	rhs,
		gmres_tag const &	tag,
		PreconditionerT const &	precond,
		bool()(VectorT const &, typename viennacl::result_of::cpu_value_type< typename viennacl::result_of::value_type< VectorT >::type >::type, void )	monitor = `NULL`,
		void *	monitor_data = `NULL`
	)

Implementation of the GMRES solver.

Following the algorithm proposed by Walker in "A Simpler GMRES"

Parameters

matrix	The system matrix
rhs	The load vector
tag	Solver configuration tag
precond	A preconditioner. Precondition operation is done via member function apply()
monitor	A callback routine which is called at each GMRES restart
monitor_data	Data pointer to be passed to the callback routine to pass on user-specific data

Returns: The result vector

Definition at line 450 of file gmres.hpp.

template<typename MatrixType , typename CPU_VectorType >

void viennacl::linalg::detail::svd_qr_shift	(	MatrixType &	vcl_u,
		MatrixType &	vcl_v,
		CPU_VectorType &	q,
		CPU_VectorType &	e
	)

Definition at line 101 of file svd.hpp.

template<typename SCALARTYPE >

void viennacl::linalg::detail::transpose ( matrix_base< SCALARTYPE > & A )

Definition at line 107 of file qr-method-common.hpp.

template<typename SCALARTYPE >

void viennacl::linalg::detail::tridiagonal_reduction	(	matrix_base< SCALARTYPE > &	A,
		matrix_base< SCALARTYPE > &	Q
	)

Definition at line 713 of file qr-method.hpp.

template<typename SCALARTYPE , typename MatrixT >

void viennacl::linalg::detail::update_float_QR_column	(	MatrixT &	A,
		const std::vector< SCALARTYPE > &	buf,
		int	m,
		int	n,
		int	last_i,
		bool	is_triangular
	)

Definition at line 145 of file qr-method.hpp.

template<typename SCALARTYPE , typename VectorType >

void viennacl::linalg::detail::update_float_QR_column_gpu	(	matrix_base< SCALARTYPE > &	A,
		const VectorType &	buf,
		viennacl::vector< SCALARTYPE > &	buf_vcl,
		int	m,
		int	n,
		int	last_n,
		bool
	)

Definition at line 82 of file qr-method.hpp.

template<typename MatrixType , typename VectorType >

void viennacl::linalg::detail::write_householder_to_A	(	MatrixType &	A,
		VectorType const &	v,
		vcl_size_t	j
	)

Definition at line 194 of file qr.hpp.

template<typename MatrixType , typename VectorType >

void viennacl::linalg::detail::write_householder_to_A_ublas	(	MatrixType &	A,
		VectorType const &	v,
		vcl_size_t	j
	)

Definition at line 201 of file qr.hpp.

template<typename MatrixType , typename VectorType >

void viennacl::linalg::detail::write_householder_to_A_viennacl	(	MatrixType &	A,
		VectorType const &	v,
		vcl_size_t	j
	)

Definition at line 211 of file qr.hpp.

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