ViennaCL - The Vienna Computing Library: viennacl::linalg::detail Namespace Reference

ViennaCL - The Vienna Computing Library 1.7.1 Free open-source GPU-accelerated linear algebra and solver library. |

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viennacl::linalg::detail Namespace Reference

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_fine*P = R*A_fine*P. 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.