viennacl::linalg::detail::spai Namespace Reference

Implementation namespace for sparse approximate inverse preconditioner. More...

Classes
class	block_matrix
	Represents contigious matrices on GPU. More...
class	block_vector
	Represents a contiguous vector on the GPU to represent a concatentation of small vectors. More...
struct	CompareSecond
	Helper functor for comparing std::pair<> based on the second member. More...
class	fspai_tag
	A tag for FSPAI. Experimental. More...
class	spai_tag
	A tag for SPAI. More...
class	sparse_vector
	Represents a sparse vector based on std::map<unsigned int, NumericT> More...

Functions
template<typename MatrixT , typename NumericT >
void	sym_sparse_matrix_to_stl (MatrixT const &A, std::vector< std::map< unsigned int, NumericT > > &STL_A)
template<typename MatrixT >
void	generateJ (MatrixT const &A, std::vector< std::vector< vcl_size_t > > &J)
template<typename NumericT , typename MatrixT , typename VectorT >
void	fill_blocks (std::vector< std::map< unsigned int, NumericT > > &A, std::vector< MatrixT > &blocks, std::vector< std::vector< vcl_size_t > > const &J, std::vector< VectorT > &Y)
template<typename MatrixT >
void	cholesky_decompose (MatrixT &A)
template<typename MatrixT , typename VectorT >
void	cholesky_solve (MatrixT const &L, VectorT &b)
template<typename MatrixT , typename VectorT >
void	computeL (MatrixT const &A, MatrixT &L, MatrixT &L_trans, std::vector< VectorT > &Y, std::vector< std::vector< vcl_size_t > > &J)
template<typename MatrixT >
void	computeFSPAI (MatrixT const &A, MatrixT const &PatternA, MatrixT &L, MatrixT &L_trans, fspai_tag)
template<typename T , typename InputIteratorT >
void	Print (std::ostream &ostr, InputIteratorT it_begin, InputIteratorT it_end)
template<typename VectorT , typename MatrixT >
void	write_to_block (VectorT &con_A_I_J, unsigned int start_ind, std::vector< unsigned int > const &I, std::vector< unsigned int > const &J, MatrixT &m)
template<typename VectorT >
void	print_continious_matrix (VectorT &con_A_I_J, std::vector< cl_uint > &blocks_ind, std::vector< std::vector< unsigned int > > const &g_I, std::vector< std::vector< unsigned int > > const &g_J)
template<typename VectorT >
void	print_continious_vector (VectorT &con_v, std::vector< cl_uint > &block_ind, std::vector< std::vector< unsigned int > > const &g_J)
void	compute_blocks_size (std::vector< std::vector< unsigned int > > const &g_I, std::vector< std::vector< unsigned int > > const &g_J, unsigned int &sz, std::vector< cl_uint > &blocks_ind, std::vector< cl_uint > &matrix_dims)
	**************************************** BLOCK FUNCTIONS ************************************// More...
template<typename SizeT >
void	get_size (std::vector< std::vector< SizeT > > const &inds, SizeT &size)
	Computes size of particular container of index set. More...
template<typename SizeT >
void	init_start_inds (std::vector< std::vector< SizeT > > const &inds, std::vector< cl_uint > &start_inds)
	Initializes start indices of particular index set. More...
template<typename MatrixT , typename NumericT >
void	dot_prod (MatrixT const &A, unsigned int beg_ind, NumericT &res)
	Dot prod of particular column of martix A with it's self starting at a certain index beg_ind. More...
template<typename MatrixT , typename VectorT , typename NumericT >
void	custom_inner_prod (MatrixT const &A, VectorT const &v, unsigned int col_ind, unsigned int start_ind, NumericT &res)
	Dot prod of particular matrix column with arbitrary vector: A(:, col_ind) More...
template<typename MatrixT , typename VectorT >
void	copy_vector (MatrixT const &A, VectorT &v, unsigned int beg_ind)
	Copying part of matrix column. More...
template<typename MatrixT , typename VectorT , typename NumericT >
void	householder_vector (MatrixT const &A, unsigned int j, VectorT &v, NumericT &b)
	Computation of Householder vector, householder reflection c.f. Gene H. Golub, Charles F. Van Loan "Matrix Computations" 3rd edition p.210. More...
template<typename MatrixT , typename VectorT , typename NumericT >
void	apply_householder_reflection (MatrixT &A, unsigned int iter_cnt, VectorT &v, NumericT b)
	Inplace application of Householder vector to a matrix A. More...
template<typename MatrixT , typename VectorT >
void	store_householder_vector (MatrixT &A, unsigned int ind, VectorT &v)
	Storage of vector v in column(A, ind), starting from ind-1 index of a column. More...
template<typename MatrixT , typename VectorT >
void	single_qr (MatrixT &R, VectorT &b_v)
	Inplace QR factorization via Householder reflections c.f. Gene H. Golub, Charles F. Van Loan "Matrix Computations" 3rd edition p.224. More...
template<typename SizeT >
void	get_max_block_size (std::vector< std::vector< SizeT > > const &inds, SizeT &max_size)
	Getting max size of rows/columns from container of index set. More...
template<typename MatrixT , typename VectorT , typename NumericT >
void	custom_dot_prod (MatrixT const &A, VectorT const &v, unsigned int ind, NumericT &res)
	Dot_prod(column(A, ind), v) starting from index ind+1. More...
template<typename MatrixT , typename VectorT >
void	apply_q_trans_vec (MatrixT const &R, VectorT const &b_v, VectorT &y)
	Recovery Q from matrix R and vector of betas b_v. More...
template<typename MatrixT , typename VectorT >
void	apply_q_trans_mat (MatrixT const &R, VectorT const &b_v, MatrixT &A)
	Multiplication of Q'*A, where Q is in implicit for lower part of R and vector of betas - b_v. More...
template<typename NumericT >
void	block_qr (std::vector< std::vector< unsigned int > > &g_I, std::vector< std::vector< unsigned int > > &g_J, block_matrix &g_A_I_J_vcl, block_vector &g_bv_vcl, std::vector< cl_uint > &g_is_update, viennacl::context ctx)
	Inplace QR factorization via Householder reflections c.f. Gene H. Golub, Charles F. Van Loan "Matrix Computations" 3rd edition p.224 performed on GPU. More...
template<typename MatrixT >
void	make_rotation_matrix (MatrixT &mat, vcl_size_t new_size, vcl_size_t off_diagonal_distance=4)
template<typename MatrixT >
double	determinant (boost::numeric::ublas::matrix_expression< MatrixT > const &mat_r)
template<typename MatrixT >
void	composeNewR (MatrixT const &A, MatrixT const &R_n, MatrixT &R)
	Composition of new matrix R, that is going to be used in Least Square problem solving. More...
template<typename VectorT >
void	composeNewVector (VectorT const &v_n, VectorT &v)
	Composition of new vector of coefficients beta from QR factorizations(necessary for Q recovery) More...
template<typename SparseVectorT , typename NumericT >
void	sparse_norm_2 (SparseVectorT const &v, NumericT &norm)
	Computation of Euclidean norm for sparse vector. More...
template<typename SparseVectorT , typename NumericT >
void	sparse_inner_prod (SparseVectorT const &v1, SparseVectorT const &v2, NumericT &res_v)
	Dot product of two sparse vectors. More...
template<typename SparseVectorT , typename NumericT >
bool	buildAugmentedIndexSet (std::vector< SparseVectorT > const &A_v_c, SparseVectorT const &res, std::vector< unsigned int > &J, std::vector< unsigned int > &J_u, spai_tag const &tag)
	Building a new set of column indices J_u, cf. Kallischko dissertation p.31. More...
template<typename SparseVectorT >
void	buildNewRowSet (std::vector< SparseVectorT > const &A_v_c, std::vector< unsigned int > const &I, std::vector< unsigned int > const &J_n, std::vector< unsigned int > &I_n)
	Building a new indices to current set of row indices I_n, cf. Kallischko dissertation p.32. More...
template<typename MatrixT >
void	QRBlockComposition (MatrixT const &A_I_J, MatrixT const &A_I_J_u, MatrixT &A_I_u_J_u)
	Composition of new block for QR factorization cf. Kallischko dissertation p.82, figure 4.7. More...
template<typename SparseMatrixT , typename SparseVectorT , typename DenseMatrixT , typename VectorT >
void	block_update (SparseMatrixT const &A, std::vector< SparseVectorT > const &A_v_c, std::vector< SparseVectorT > &g_res, std::vector< bool > &g_is_update, std::vector< std::vector< unsigned int > > &g_I, std::vector< std::vector< unsigned int > > &g_J, std::vector< VectorT > &g_b_v, std::vector< DenseMatrixT > &g_A_I_J, spai_tag const &tag)
	CPU-based dynamic update for SPAI preconditioner. More...
template<typename NumericT >
void	block_q_multiplication (std::vector< std::vector< unsigned int > > const &g_J_u, std::vector< std::vector< unsigned int > > const &g_I, block_matrix &g_A_I_J_vcl, block_vector &g_bv_vcl, block_matrix &g_A_I_J_u_vcl, std::vector< cl_uint > &g_is_update, viennacl::context ctx)
	Performs multiplication Q'*A(I, \tilde J) on GPU. More...
template<typename SizeT >
void	assemble_qr_row_inds (std::vector< std::vector< SizeT > > const &g_I, std::vector< std::vector< SizeT > > const &g_J, std::vector< std::vector< SizeT > > const &g_I_u, std::vector< std::vector< SizeT > > &g_I_q)
	Assembly of container of index row sets: I_q, row indices for new "QR block". More...
template<typename NumericT >
void	assemble_qr_block (std::vector< std::vector< unsigned int > > const &g_J, std::vector< std::vector< unsigned int > > const &g_I, std::vector< std::vector< unsigned int > > const &g_J_u, std::vector< std::vector< unsigned int > > const &g_I_u, std::vector< std::vector< unsigned int > > &g_I_q, block_matrix &g_A_I_J_u_vcl, viennacl::ocl::handle< cl_mem > &matrix_dimensions, block_matrix &g_A_I_u_J_u_vcl, std::vector< cl_uint > &g_is_update, bool is_empty_block, viennacl::context ctx)
	Performs assembly for new QR block. More...
template<typename NumericT >
void	assemble_r (std::vector< std::vector< unsigned int > > &g_I, std::vector< std::vector< unsigned int > > &g_J, block_matrix &g_A_I_J_vcl, block_matrix &g_A_I_J_u_vcl, block_matrix &g_A_I_u_J_u_vcl, block_vector &g_bv_vcl, block_vector &g_bv_vcl_u, std::vector< cl_uint > &g_is_update, viennacl::context ctx)
	Performs assembly for new R matrix on GPU. More...
template<typename NumericT , unsigned int AlignmentV, typename SparseVectorT >
void	block_update (viennacl::compressed_matrix< NumericT, AlignmentV > const &A, std::vector< SparseVectorT > const &A_v_c, std::vector< cl_uint > &g_is_update, std::vector< SparseVectorT > &g_res, std::vector< std::vector< unsigned int > > &g_J, std::vector< std::vector< unsigned int > > &g_I, block_matrix &g_A_I_J_vcl, block_vector &g_bv_vcl, spai_tag const &tag)
	GPU-based block update. More...
template<typename SizeT >
bool	isInIndexSet (std::vector< SizeT > const &J, SizeT ind)
	Determines if element ind is in set {J}. More...
template<typename VectorT , typename SparseVectorT >
void	fanOutVector (VectorT const &m_in, std::vector< unsigned int > const &J, SparseVectorT &m)
	Projects solution of LS problem onto original column m. More...
template<typename MatrixT , typename VectorT >
void	backwardSolve (MatrixT const &R, VectorT const &y, VectorT &x)
	Solution of linear:R*x=y system by backward substitution. More...
template<typename VectorT , typename NumericT >
void	projectI (std::vector< unsigned int > const &I, VectorT &y, unsigned int ind)
	Perform projection of set I on the unit-vector. More...
template<typename SparseVectorT >
void	buildColumnIndexSet (SparseVectorT const &v, std::vector< unsigned int > &J)
	Builds index set of projected columns for current column of preconditioner. More...
template<typename SparseMatrixT >
void	initPreconditioner (SparseMatrixT const &A, SparseMatrixT &M)
	Initialize preconditioner with sparcity pattern = p(A) More...
template<typename SparseVectorT >
void	projectRows (std::vector< SparseVectorT > const &A_v_c, std::vector< unsigned int > const &J, std::vector< unsigned int > &I)
	Row projection for matrix A(:,J) -> A(I,J), building index set of non-zero rows. More...
template<typename SparseVectorT >
void	print_sparse_vector (SparseVectorT const &v)
template<typename DenseMatrixT >
void	print_matrix (DenseMatrixT &m)
template<typename SparseVectorT , typename NumericT >
void	add_sparse_vectors (SparseVectorT const &v, NumericT b, SparseVectorT &res_v)
	Add two sparse vectors res_v = b*v. More...
template<typename SparseVectorT , typename NumericT >
void	compute_spai_residual (std::vector< SparseVectorT > const &A_v_c, SparseVectorT const &v, unsigned int ind, SparseVectorT &res)
	Computation of residual res = A*v - e. More...
template<typename SparseVectorT >
void	build_index_set (std::vector< SparseVectorT > const &A_v_c, SparseVectorT const &v, std::vector< unsigned int > &J, std::vector< unsigned int > &I)
	Setting up index set of columns and rows for certain column. More...
template<typename SparseMatrixT , typename DenseMatrixT >
void	initProjectSubMatrix (SparseMatrixT const &A_in, std::vector< unsigned int > const &J, std::vector< unsigned int > &I, DenseMatrixT &A_out)
	Initializes a dense matrix from a sparse one. More...
template<typename SparseMatrixT , typename DenseMatrixT , typename SparseVectorT , typename VectorT >
void	block_set_up (SparseMatrixT const &A, std::vector< SparseVectorT > const &A_v_c, std::vector< SparseVectorT > const &M_v, std::vector< std::vector< unsigned int > > &g_I, std::vector< std::vector< unsigned int > > &g_J, std::vector< DenseMatrixT > &g_A_I_J, std::vector< VectorT > &g_b_v)
	Setting up blocks and QR factorizing them on CPU. More...
template<typename SparseVectorT >
void	index_set_up (std::vector< SparseVectorT > const &A_v_c, std::vector< SparseVectorT > const &M_v, std::vector< std::vector< unsigned int > > &g_J, std::vector< std::vector< unsigned int > > &g_I)
	Setting up index set of columns and rows for all columns. More...
template<typename NumericT , unsigned int AlignmentV, typename SparseVectorT >
void	block_set_up (viennacl::compressed_matrix< NumericT, AlignmentV > const &A, std::vector< SparseVectorT > const &A_v_c, std::vector< SparseVectorT > const &M_v, std::vector< cl_uint > g_is_update, std::vector< std::vector< unsigned int > > &g_I, std::vector< std::vector< unsigned int > > &g_J, block_matrix &g_A_I_J, block_vector &g_bv)
	Setting up blocks and QR factorizing them on GPU. More...
template<typename NumericT , typename SparseVectorT >
void	custom_fan_out (std::vector< NumericT > const &m_in, unsigned int start_m_ind, std::vector< unsigned int > const &J, SparseVectorT &m)
	Elicitation of sparse vector m for particular column from m_in - contigious vector for all columns. More...
template<typename SparseVectorT , typename NumericT >
void	least_square_solve (std::vector< SparseVectorT > &A_v_c, std::vector< SparseVectorT > &M_v, std::vector< std::vector< unsigned int > > &g_I, std::vector< std::vector< unsigned int > > &g_J, block_matrix &g_A_I_J_vcl, block_vector &g_bv_vcl, std::vector< SparseVectorT > &g_res, std::vector< cl_uint > &g_is_update, const spai_tag &tag, viennacl::context ctx)
	Solution of Least square problem on GPU. More...
template<typename SparseVectorT , typename DenseMatrixT , typename VectorT >
void	least_square_solve (std::vector< SparseVectorT > const &A_v_c, std::vector< DenseMatrixT > &g_R, std::vector< VectorT > &g_b_v, std::vector< std::vector< unsigned int > > &g_I, std::vector< std::vector< unsigned int > > &g_J, std::vector< SparseVectorT > &g_res, std::vector< bool > &g_is_update, std::vector< SparseVectorT > &M_v, spai_tag const &tag)
	Solution of Least square problem on CPU. More...
template<typename VectorType >
bool	is_all_update (VectorType &parallel_is_update)
template<typename SparseMatrixT , typename SparseVectorT >
void	vectorize_column_matrix (SparseMatrixT const &M_in, std::vector< SparseVectorT > &M_v)
	Solution of Least square problem on CPU. More...
template<typename SparseMatrixT , typename SparseVectorT >
void	vectorize_row_matrix (SparseMatrixT const &M_in, std::vector< SparseVectorT > &M_v)
template<typename SizeT >
void	write_set_to_array (std::vector< std::vector< SizeT > > const &ind_set, std::vector< cl_uint > &a)
template<typename NumericT , unsigned int AlignmentV>
void	block_assembly (viennacl::compressed_matrix< NumericT, AlignmentV > const &A, std::vector< std::vector< unsigned int > > const &g_J, std::vector< std::vector< unsigned int > > const &g_I, block_matrix &g_A_I_J_vcl, std::vector< cl_uint > &g_is_update, bool &is_empty_block)
	Assembly of blocks on GPU by a gived set of row indices: g_I and column indices: g_J. More...
template<typename SparseMatrixT , typename SparseVectorT >
void	insert_sparse_columns (std::vector< SparseVectorT > const &M_v, SparseMatrixT &M, bool is_right)
	Insertion of vectorized matrix column into original sparse matrix. More...
template<typename MatrixT >
void	sparse_transpose (MatrixT const &A_in, MatrixT &A)
	Transposition of sparse matrix. More...
template<typename MatrixT >
void	computeSPAI (MatrixT const &A, MatrixT &M, spai_tag &tag)
	Construction of SPAI preconditioner on CPU. More...
template<typename NumericT , unsigned int AlignmentV>
void	computeSPAI (viennacl::compressed_matrix< NumericT, AlignmentV > const &A, boost::numeric::ublas::compressed_matrix< NumericT > const &cpu_A, boost::numeric::ublas::compressed_matrix< NumericT > &cpu_M, viennacl::compressed_matrix< NumericT, AlignmentV > &M, spai_tag const &tag)
	Construction of SPAI preconditioner on GPU. More...

Detailed Description

Implementation namespace for sparse approximate inverse preconditioner.

Function Documentation

template<typename SparseVectorT , typename NumericT >

void viennacl::linalg::detail::spai::add_sparse_vectors	(	SparseVectorT const &	v,
		NumericT	b,
		SparseVectorT &	res_v
	)

Add two sparse vectors res_v = b*v.

Parameters

v	initial sparse vector
b	scalar
res_v	output vector

Definition at line 105 of file spai.hpp.

template<typename MatrixT , typename VectorT , typename NumericT >

void viennacl::linalg::detail::spai::apply_householder_reflection	(	MatrixT &	A,
		unsigned int	iter_cnt,
		VectorT &	v,
		NumericT	b
	)

Inplace application of Householder vector to a matrix A.

Parameters

A	init matrix
iter_cnt	current iteration
v	Householder vector
b	beta

Definition at line 271 of file qr.hpp.

template<typename MatrixT , typename VectorT >

void viennacl::linalg::detail::spai::apply_q_trans_mat	(	MatrixT const &	R,
		VectorT const &	b_v,
		MatrixT &	A
	)

Multiplication of Q'*A, where Q is in implicit for lower part of R and vector of betas - b_v.

Parameters

R	input matrix
b_v	vector of betas
A	output matrix

Definition at line 404 of file qr.hpp.

template<typename MatrixT , typename VectorT >

void viennacl::linalg::detail::spai::apply_q_trans_vec	(	MatrixT const &	R,
		VectorT const &	b_v,
		VectorT &	y
	)

Recovery Q from matrix R and vector of betas b_v.

Parameters

R	input matrix
b_v	vector of betas
y	output vector

Definition at line 377 of file qr.hpp.

template<typename NumericT >

void viennacl::linalg::detail::spai::assemble_qr_block	(	std::vector< std::vector< unsigned int > > const &	g_J,
		std::vector< std::vector< unsigned int > > const &	g_I,
		std::vector< std::vector< unsigned int > > const &	g_J_u,
		std::vector< std::vector< unsigned int > > const &	g_I_u,
		std::vector< std::vector< unsigned int > > &	g_I_q,
		block_matrix &	g_A_I_J_u_vcl,
		viennacl::ocl::handle< cl_mem > &	matrix_dimensions,
		block_matrix &	g_A_I_u_J_u_vcl,
		std::vector< cl_uint > &	g_is_update,
		bool	is_empty_block,
		viennacl::context	ctx
	)

Performs assembly for new QR block.

Parameters

g_J	container of column indices
g_I	container of row indices
g_J_u	container of new column indices
g_I_u	container of new row indices
g_I_q	container of row indices for new QR blocks
g_A_I_J_u_vcl	blocks of Q'*A(I, \tilde J)
matrix_dimensions	array with matrix dimensions for all blocks
g_A_I_u_J_u_vcl	blocks A(\tilde I, \tilde J)
g_is_update	container with update indicators
is_empty_block	indicator if all previous blocks A(\tilde I, \tilde J) - are empty, in case if they are empty kernel with smaller number of arguments is used
ctx	Optional context in which the matrix is created (one out of multiple OpenCL contexts, CUDA, host)

Definition at line 439 of file spai-dynamic.hpp.

template<typename SizeT >

void viennacl::linalg::detail::spai::assemble_qr_row_inds	(	std::vector< std::vector< SizeT > > const &	g_I,
		std::vector< std::vector< SizeT > > const &	g_J,
		std::vector< std::vector< SizeT > > const &	g_I_u,
		std::vector< std::vector< SizeT > > &	g_I_q
	)

Assembly of container of index row sets: I_q, row indices for new "QR block".

Parameters

g_I	container of row indices
g_J	container of column indices
g_I_u	container of new row indices
g_I_q	container of row indices for new QR blocks

Definition at line 406 of file spai-dynamic.hpp.

template<typename NumericT >

void viennacl::linalg::detail::spai::assemble_r	(	std::vector< std::vector< unsigned int > > &	g_I,
		std::vector< std::vector< unsigned int > > &	g_J,
		block_matrix &	g_A_I_J_vcl,
		block_matrix &	g_A_I_J_u_vcl,
		block_matrix &	g_A_I_u_J_u_vcl,
		block_vector &	g_bv_vcl,
		block_vector &	g_bv_vcl_u,
		std::vector< cl_uint > &	g_is_update,
		viennacl::context	ctx
	)

Performs assembly for new R matrix on GPU.

Parameters

g_I	container of row indices
g_J	container of column indices
g_A_I_J_vcl	container of block matrices from previous update
g_A_I_J_u_vcl	container of block matrices Q'*A(I, \tilde J)
g_A_I_u_J_u_vcl	container of block matrices QR factored on current iteration
g_bv_vcl	block of beta vectors from previous iteration
g_bv_vcl_u	block of updated beta vectors got after recent QR factorization
g_is_update	container with identificators that shows which block should be modified
ctx	Optional context in which the auxiliary data is created (one out of multiple OpenCL contexts, CUDA, host)

Definition at line 533 of file spai-dynamic.hpp.

template<typename MatrixT , typename VectorT >

void viennacl::linalg::detail::spai::backwardSolve	(	MatrixT const &	R,
		VectorT const &	y,
		VectorT &	x
	)

Solution of linear:R*x=y system by backward substitution.

Parameters

R	uppertriangular matrix
y	right handside vector
x	solution vector

Definition at line 102 of file spai-static.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::detail::spai::block_assembly	(	viennacl::compressed_matrix< NumericT, AlignmentV > const &	A,
		std::vector< std::vector< unsigned int > > const &	g_J,
		std::vector< std::vector< unsigned int > > const &	g_I,
		block_matrix &	g_A_I_J_vcl,
		std::vector< cl_uint > &	g_is_update,
		bool &	is_empty_block
	)

Assembly of blocks on GPU by a gived set of row indices: g_I and column indices: g_J.

Parameters

A	intial sparse matrix
g_J	container of column index set
g_I	container of row index set
g_A_I_J_vcl	contigious blocks A(I, J) using GPU memory
g_is_update	container with indicators which blocks are active
is_empty_block	parameter that indicates if no block were assembled

Definition at line 507 of file spai.hpp.

template<typename NumericT >

void viennacl::linalg::detail::spai::block_q_multiplication	(	std::vector< std::vector< unsigned int > > const &	g_J_u,
		std::vector< std::vector< unsigned int > > const &	g_I,
		block_matrix &	g_A_I_J_vcl,
		block_vector &	g_bv_vcl,
		block_matrix &	g_A_I_J_u_vcl,
		std::vector< cl_uint > &	g_is_update,
		viennacl::context	ctx
	)

Performs multiplication Q'*A(I, \tilde J) on GPU.

Parameters

g_J_u	container of sets of new column indices
g_I	container of row indices
g_A_I_J_vcl	block matrix composed from previous blocks, they are blocks of R
g_bv_vcl	block of beta vectors
g_A_I_J_u_vcl	block of matrices A(I, \tilde J)
g_is_update	indicators, that show if a certain block should be processed
ctx	Optional context in which the auxiliary data is created (one out of multiple OpenCL contexts, CUDA, host)

Definition at line 361 of file spai-dynamic.hpp.

template<typename NumericT >

void viennacl::linalg::detail::spai::block_qr	(	std::vector< std::vector< unsigned int > > &	g_I,
		std::vector< std::vector< unsigned int > > &	g_J,
		block_matrix &	g_A_I_J_vcl,
		block_vector &	g_bv_vcl,
		std::vector< cl_uint > &	g_is_update,
		viennacl::context	ctx
	)

Inplace QR factorization via Householder reflections c.f. Gene H. Golub, Charles F. Van Loan "Matrix Computations" 3rd edition p.224 performed on GPU.

Parameters

g_I	container of row indices
g_J	container of column indices
g_A_I_J_vcl	contigious matrices, GPU memory is used
g_bv_vcl	contigiuos vectors beta, GPU memory is used
g_is_update	container of indicators that show active blocks
ctx	Optional context in which the auxiliary data is created (one out of multiple OpenCL contexts, CUDA, host)

Definition at line 428 of file qr.hpp.

template<typename SparseMatrixT , typename DenseMatrixT , typename SparseVectorT , typename VectorT >

void viennacl::linalg::detail::spai::block_set_up	(	SparseMatrixT const &	A,
		std::vector< SparseVectorT > const &	A_v_c,
		std::vector< SparseVectorT > const &	M_v,
		std::vector< std::vector< unsigned int > > &	g_I,
		std::vector< std::vector< unsigned int > > &	g_J,
		std::vector< DenseMatrixT > &	g_A_I_J,
		std::vector< VectorT > &	g_b_v
	)

Setting up blocks and QR factorizing them on CPU.

Parameters

A	initial sparse matrix
A_v_c	column major vectorized initial sparse matrix
M_v	initialized preconditioner
g_I	container of row indices
g_J	container of column indices
g_A_I_J	container of dense matrices -> R matrices after QR factorization
g_b_v	container of vectors beta, necessary for Q recovery

Definition at line 181 of file spai.hpp.

template<typename NumericT , unsigned int AlignmentV, typename SparseVectorT >

void viennacl::linalg::detail::spai::block_set_up	(	viennacl::compressed_matrix< NumericT, AlignmentV > const &	A,
		std::vector< SparseVectorT > const &	A_v_c,
		std::vector< SparseVectorT > const &	M_v,
		std::vector< cl_uint >	g_is_update,
		std::vector< std::vector< unsigned int > > &	g_I,
		std::vector< std::vector< unsigned int > > &	g_J,
		block_matrix &	g_A_I_J,
		block_vector &	g_bv
	)

Setting up blocks and QR factorizing them on GPU.

Parameters

A	initial sparse matrix
A_v_c	column major vectorized initial sparse matrix
M_v	initialized preconditioner
g_is_update	container that indicates which blocks are active
g_I	container of row indices
g_J	container of column indices
g_A_I_J	container of dense matrices -> R matrices after QR factorization
g_bv	container of vectors beta, necessary for Q recovery

Definition at line 240 of file spai.hpp.

template<typename SparseMatrixT , typename SparseVectorT , typename DenseMatrixT , typename VectorT >

void viennacl::linalg::detail::spai::block_update	(	SparseMatrixT const &	A,
		std::vector< SparseVectorT > const &	A_v_c,
		std::vector< SparseVectorT > &	g_res,
		std::vector< bool > &	g_is_update,
		std::vector< std::vector< unsigned int > > &	g_I,
		std::vector< std::vector< unsigned int > > &	g_J,
		std::vector< VectorT > &	g_b_v,
		std::vector< DenseMatrixT > &	g_A_I_J,
		spai_tag const &	tag
	)

CPU-based dynamic update for SPAI preconditioner.

Parameters

A	initial sparse matrix
A_v_c	vectorized column-wise initial matrix
g_res	container of residuals for all columns
g_is_update	container with identificators that shows which block should be modified
g_I	container of row index sets for all columns
g_J	container of column index sets for all columns
g_b_v	container of vectors of beta for Q recovery(cf. Golub Van Loan "Matrix Computations", 3rd edition p.211)
g_A_I_J	container of block matrices from previous update
tag	SPAI configuration tag

Definition at line 291 of file spai-dynamic.hpp.

template<typename NumericT , unsigned int AlignmentV, typename SparseVectorT >

void viennacl::linalg::detail::spai::block_update	(	viennacl::compressed_matrix< NumericT, AlignmentV > const &	A,
		std::vector< SparseVectorT > const &	A_v_c,
		std::vector< cl_uint > &	g_is_update,
		std::vector< SparseVectorT > &	g_res,
		std::vector< std::vector< unsigned int > > &	g_J,
		std::vector< std::vector< unsigned int > > &	g_I,
		block_matrix &	g_A_I_J_vcl,
		block_vector &	g_bv_vcl,
		spai_tag const &	tag
	)

GPU-based block update.

Parameters

A	sparse matrix
A_v_c	vectorized column-wise initial matrix
g_is_update	container with identificators that shows which block should be modified
g_res	container of residuals for all columns
g_J	container of column index sets for all columns
g_I	container of row index sets for all columns
g_A_I_J_vcl	container of block matrices from previous update
g_bv_vcl	block of beta vectors from previous iteration
tag	SPAI configuration tag

Definition at line 625 of file spai-dynamic.hpp.

template<typename SparseVectorT >

void viennacl::linalg::detail::spai::build_index_set	(	std::vector< SparseVectorT > const &	A_v_c,
		SparseVectorT const &	v,
		std::vector< unsigned int > &	J,
		std::vector< unsigned int > &	I
	)

Setting up index set of columns and rows for certain column.

Parameters

A_v_c	column major vectorized initial sparse matrix
v	current column of preconditioner matrix
J	set of column indices
I	set of row indices

Definition at line 139 of file spai.hpp.

template<typename SparseVectorT , typename NumericT >

bool viennacl::linalg::detail::spai::buildAugmentedIndexSet	(	std::vector< SparseVectorT > const &	A_v_c,
		SparseVectorT const &	res,
		std::vector< unsigned int > &	J,
		std::vector< unsigned int > &	J_u,
		spai_tag const &	tag
	)

Building a new set of column indices J_u, cf. Kallischko dissertation p.31.

Parameters

A_v_c	vectorized column-wise initial matrix
res	residual vector
J	set of column indices
J_u	set of new column indices
tag	SPAI tag with parameters

Definition at line 188 of file spai-dynamic.hpp.

template<typename SparseVectorT >

void viennacl::linalg::detail::spai::buildColumnIndexSet	(	SparseVectorT const &	v,
		std::vector< unsigned int > &	J
	)

Builds index set of projected columns for current column of preconditioner.

Parameters

v	current column of preconditioner
J	output - index set of non-zero columns

Definition at line 140 of file spai-static.hpp.

template<typename SparseVectorT >

void viennacl::linalg::detail::spai::buildNewRowSet	(	std::vector< SparseVectorT > const &	A_v_c,
		std::vector< unsigned int > const &	I,
		std::vector< unsigned int > const &	J_n,
		std::vector< unsigned int > &	I_n
	)

Building a new indices to current set of row indices I_n, cf. Kallischko dissertation p.32.

Parameters

A_v_c	vectorized column-wise initial matrix
I	set of previous determined row indices
J_n	set of new column indices
I_n	set of new indices

Definition at line 228 of file spai-dynamic.hpp.

template<typename MatrixT >

void viennacl::linalg::detail::spai::cholesky_decompose

(

MatrixT &

A

)

Definition at line 210 of file fspai.hpp.

template<typename MatrixT , typename VectorT >

void viennacl::linalg::detail::spai::cholesky_solve	(	MatrixT const &	L,
		VectorT &	b
	)

Definition at line 238 of file fspai.hpp.

template<typename MatrixT >

void viennacl::linalg::detail::spai::composeNewR	(	MatrixT const &	A,
		MatrixT const &	R_n,
		MatrixT &	R
	)

Composition of new matrix R, that is going to be used in Least Square problem solving.

Parameters

A	matrix Q'*A(I, \tilde J), where \tilde J - set of new column indices
R_n	matrix A_Iu_J_u after QR factorization
R	previously composed matrix R

Definition at line 94 of file spai-dynamic.hpp.

template<typename VectorT >

void viennacl::linalg::detail::spai::composeNewVector	(	VectorT const &	v_n,
		VectorT &	v
	)

Composition of new vector of coefficients beta from QR factorizations(necessary for Q recovery)

Parameters

v_n	new vector from last QR factorization
v	composition of previous vectors from QR factorizations

Definition at line 124 of file spai-dynamic.hpp.

void viennacl::linalg::detail::spai::compute_blocks_size ( std::vector< std::vector< unsigned int > > const &  g_I, std::vector< std::vector< unsigned int > > const &  g_J, unsigned int &  sz, std::vector< cl_uint > &  blocks_ind, std::vector< cl_uint > &  matrix_dims  )

inline

**************************************** BLOCK FUNCTIONS ************************************//

Computes size of elements, start indices and matrix dimensions for a certain block

Parameters

g_I	container of row indices
g_J	container of column indices
sz	general size for all elements in a certain block
blocks_ind	start indices in a certain
matrix_dims	matrix dimensions for each block

Definition at line 129 of file qr.hpp.

template<typename SparseVectorT , typename NumericT >

void viennacl::linalg::detail::spai::compute_spai_residual	(	std::vector< SparseVectorT > const &	A_v_c,
		SparseVectorT const &	v,
		unsigned int	ind,
		SparseVectorT &	res
	)

Computation of residual res = A*v - e.

Parameters

A_v_c	column major vectorized input sparse matrix
v	sparse vector, in this case new column of preconditioner matrix
ind	index for current column
res	residual

Definition at line 120 of file spai.hpp.

template<typename MatrixT >

void viennacl::linalg::detail::spai::computeFSPAI	(	MatrixT const &	A,
		MatrixT const &	PatternA,
		MatrixT &	L,
		MatrixT &	L_trans,
		fspai_tag
	)

Definition at line 313 of file fspai.hpp.

template<typename MatrixT , typename VectorT >

void viennacl::linalg::detail::spai::computeL	(	MatrixT const &	A,
		MatrixT &	L,
		MatrixT &	L_trans,
		std::vector< VectorT > &	Y,
		std::vector< std::vector< vcl_size_t > > &	J
	)

Definition at line 266 of file fspai.hpp.

template<typename MatrixT >

void viennacl::linalg::detail::spai::computeSPAI	(	MatrixT const &	A,
		MatrixT &	M,
		spai_tag &	tag
	)

Construction of SPAI preconditioner on CPU.

Parameters

A	initial sparse matrix
M	output preconditioner
tag	spai tag

Definition at line 686 of file spai.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::detail::spai::computeSPAI	(	viennacl::compressed_matrix< NumericT, AlignmentV > const &	A,
		boost::numeric::ublas::compressed_matrix< NumericT > const &	cpu_A,
		boost::numeric::ublas::compressed_matrix< NumericT > &	cpu_M,
		viennacl::compressed_matrix< NumericT, AlignmentV > &	M,
		spai_tag const &	tag
	)

Construction of SPAI preconditioner on GPU.

Parameters

A	initial sparse matrix
cpu_A	copy of initial matrix on CPU
cpu_M	output preconditioner on CPU
M	output preconditioner
tag	SPAI tag class with parameters

Definition at line 775 of file spai.hpp.

template<typename MatrixT , typename VectorT >

void viennacl::linalg::detail::spai::copy_vector	(	MatrixT const &	A,
		VectorT &	v,
		unsigned int	beg_ind
	)

Copying part of matrix column.

Parameters

A	init matrix
v	output vector
beg_ind	start index for copying

Definition at line 218 of file qr.hpp.

template<typename MatrixT , typename VectorT , typename NumericT >

void viennacl::linalg::detail::spai::custom_dot_prod	(	MatrixT const &	A,
		VectorT const &	v,
		unsigned int	ind,
		NumericT &	res
	)

Dot_prod(column(A, ind), v) starting from index ind+1.

Parameters

A	input matrix
v	input vector
ind	index
res	result value

Definition at line 355 of file qr.hpp.

template<typename NumericT , typename SparseVectorT >

void viennacl::linalg::detail::spai::custom_fan_out	(	std::vector< NumericT > const &	m_in,
		unsigned int	start_m_ind,
		std::vector< unsigned int > const &	J,
		SparseVectorT &	m
	)

Elicitation of sparse vector m for particular column from m_in - contigious vector for all columns.

Parameters

m_in	contigious sparse vector for all columns
start_m_ind	start index of particular vector
J	column index set
m	sparse vector for particular column

Definition at line 271 of file spai.hpp.

template<typename MatrixT , typename VectorT , typename NumericT >

void viennacl::linalg::detail::spai::custom_inner_prod	(	MatrixT const &	A,
		VectorT const &	v,
		unsigned int	col_ind,
		unsigned int	start_ind,
		NumericT &	res
	)

Dot prod of particular matrix column with arbitrary vector: A(:, col_ind)

Parameters

A	init matrix
v	input vector
col_ind	starting column index
start_ind	starting index inside column
res	result of dot product

Definition at line 200 of file qr.hpp.

template<typename MatrixT >

double viennacl::linalg::detail::spai::determinant

(

boost::numeric::ublas::matrix_expression< MatrixT > const &

mat_r

)

Definition at line 84 of file small_matrix.hpp.

template<typename MatrixT , typename NumericT >

void viennacl::linalg::detail::spai::dot_prod	(	MatrixT const &	A,
		unsigned int	beg_ind,
		NumericT &	res
	)

Dot prod of particular column of martix A with it's self starting at a certain index beg_ind.

Parameters

A	init matrix
beg_ind	starting index
res	result of dot product

Definition at line 182 of file qr.hpp.

template<typename VectorT , typename SparseVectorT >

void viennacl::linalg::detail::spai::fanOutVector	(	VectorT const &	m_in,
		std::vector< unsigned int > const &	J,
		SparseVectorT &	m
	)

Projects solution of LS problem onto original column m.

Parameters

m_in	solution of LS
J	set of non-zero columns
m	original column of M

Definition at line 88 of file spai-static.hpp.

template<typename NumericT , typename MatrixT , typename VectorT >

void viennacl::linalg::detail::spai::fill_blocks	(	std::vector< std::map< unsigned int, NumericT > > &	A,
		std::vector< MatrixT > &	blocks,
		std::vector< std::vector< vcl_size_t > > const &	J,
		std::vector< VectorT > &	Y
	)

Definition at line 172 of file fspai.hpp.

template<typename MatrixT >

void viennacl::linalg::detail::spai::generateJ	(	MatrixT const &	A,
		std::vector< std::vector< vcl_size_t > > &	J
	)

Definition at line 145 of file fspai.hpp.

template<typename SizeT >

void viennacl::linalg::detail::spai::get_max_block_size	(	std::vector< std::vector< SizeT > > const &	inds,
		SizeT &	max_size
	)

Getting max size of rows/columns from container of index set.

Parameters

inds	container of index set
max_size	max size that corresponds to that container

Definition at line 338 of file qr.hpp.

template<typename SizeT >

void viennacl::linalg::detail::spai::get_size	(	std::vector< std::vector< SizeT > > const &	inds,
		SizeT &	size
	)

Computes size of particular container of index set.

Parameters

inds	container of index sets
size	output size

Definition at line 151 of file qr.hpp.

template<typename MatrixT , typename VectorT , typename NumericT >

void viennacl::linalg::detail::spai::householder_vector	(	MatrixT const &	A,
		unsigned int	j,
		VectorT &	v,
		NumericT &	b
	)

Computation of Householder vector, householder reflection c.f. Gene H. Golub, Charles F. Van Loan "Matrix Computations" 3rd edition p.210.

Parameters

A	init matrix
j	start index for computations
v	output Householder vector
b	beta

Definition at line 236 of file qr.hpp.

template<typename SparseVectorT >

void viennacl::linalg::detail::spai::index_set_up	(	std::vector< SparseVectorT > const &	A_v_c,
		std::vector< SparseVectorT > const &	M_v,
		std::vector< std::vector< unsigned int > > &	g_J,
		std::vector< std::vector< unsigned int > > &	g_I
	)

Setting up index set of columns and rows for all columns.

Parameters

A_v_c	column major vectorized initial sparse matrix
M_v	initialized preconditioner
g_J	container of column indices
g_I	container of row indices

Definition at line 211 of file spai.hpp.

template<typename SizeT >

void viennacl::linalg::detail::spai::init_start_inds	(	std::vector< std::vector< SizeT > > const &	inds,
		std::vector< cl_uint > &	start_inds
	)

Initializes start indices of particular index set.

Parameters

inds	container of index sets
start_inds	output index set

Definition at line 165 of file qr.hpp.

template<typename SparseMatrixT >

void viennacl::linalg::detail::spai::initPreconditioner	(	SparseMatrixT const &	A,
		SparseMatrixT &	M
	)

Initialize preconditioner with sparcity pattern = p(A)

Parameters

A	input matrix
M	output matrix - initialized preconditioner

Definition at line 154 of file spai-static.hpp.

template<typename SparseMatrixT , typename DenseMatrixT >

void viennacl::linalg::detail::spai::initProjectSubMatrix	(	SparseMatrixT const &	A_in,
		std::vector< unsigned int > const &	J,
		std::vector< unsigned int > &	I,
		DenseMatrixT &	A_out
	)

Initializes a dense matrix from a sparse one.

Parameters

A_in	Oiginal sparse matrix
J	Set of column indices
I	Set of row indices
A_out	dense matrix output

Definition at line 156 of file spai.hpp.

template<typename SparseMatrixT , typename SparseVectorT >

void viennacl::linalg::detail::spai::insert_sparse_columns	(	std::vector< SparseVectorT > const &	M_v,
		SparseMatrixT &	M,
		bool	is_right
	)

Insertion of vectorized matrix column into original sparse matrix.

Parameters

M_v	column-major vectorized matrix
M	original sparse matrix
is_right	indicates if matrix should be transposed in the output

Definition at line 616 of file spai.hpp.

template<typename VectorType >

bool viennacl::linalg::detail::spai::is_all_update

(

VectorType &

parallel_is_update

)

Definition at line 443 of file spai.hpp.

template<typename SizeT >

bool viennacl::linalg::detail::spai::isInIndexSet	(	std::vector< SizeT > const &	J,
		SizeT	ind
	)

Determines if element ind is in set {J}.

Parameters

J	current set
ind	current element

Definition at line 72 of file spai-static.hpp.

template<typename SparseVectorT , typename NumericT >

void viennacl::linalg::detail::spai::least_square_solve	(	std::vector< SparseVectorT > &	A_v_c,
		std::vector< SparseVectorT > &	M_v,
		std::vector< std::vector< unsigned int > > &	g_I,
		std::vector< std::vector< unsigned int > > &	g_J,
		block_matrix &	g_A_I_J_vcl,
		block_vector &	g_bv_vcl,
		std::vector< SparseVectorT > &	g_res,
		std::vector< cl_uint > &	g_is_update,
		const spai_tag &	tag,
		viennacl::context	ctx
	)

Solution of Least square problem on GPU.

Parameters

A_v_c	column-major vectorized initial sparse matrix
M_v	column-major vectorized sparse preconditioner matrix
g_I	container of row set indices
g_J	container of column set indices
g_A_I_J_vcl	contigious matrix that consists of blocks A(I_k, J_k)
g_bv_vcl	contigious vector that consists of betas, necessary for Q recovery
g_res	container of residuals
g_is_update	container with indicators which blocks are active
tag	spai tag
ctx	Optional context in which the auxiliary data is created (one out of multiple OpenCL contexts, CUDA, host)

Definition at line 298 of file spai.hpp.

template<typename SparseVectorT , typename DenseMatrixT , typename VectorT >

void viennacl::linalg::detail::spai::least_square_solve	(	std::vector< SparseVectorT > const &	A_v_c,
		std::vector< DenseMatrixT > &	g_R,
		std::vector< VectorT > &	g_b_v,
		std::vector< std::vector< unsigned int > > &	g_I,
		std::vector< std::vector< unsigned int > > &	g_J,
		std::vector< SparseVectorT > &	g_res,
		std::vector< bool > &	g_is_update,
		std::vector< SparseVectorT > &	M_v,
		spai_tag const &	tag
	)

Solution of Least square problem on CPU.

Parameters

A_v_c	column-major vectorized initial sparse matrix
g_R	blocks for least square solution
g_b_v	vectors beta, necessary for Q recovery
g_I	container of row index set for all columns of matrix M
g_J	container of column index set for all columns of matrix M
g_res	container of residuals
g_is_update	container with indicators which blocks are active
M_v	column-major vectorized sparse matrix, final preconditioner
tag	spai tag

Definition at line 398 of file spai.hpp.

template<typename MatrixT >

void viennacl::linalg::detail::spai::make_rotation_matrix	(	MatrixT &	mat,
		vcl_size_t	new_size,
		vcl_size_t	off_diagonal_distance = 4
	)

Definition at line 61 of file small_matrix.hpp.

template<typename T , typename InputIteratorT >

void viennacl::linalg::detail::spai::Print	(	std::ostream &	ostr,
		InputIteratorT	it_begin,
		InputIteratorT	it_end
	)

Definition at line 63 of file qr.hpp.

template<typename VectorT >

void viennacl::linalg::detail::spai::print_continious_matrix	(	VectorT &	con_A_I_J,
		std::vector< cl_uint > &	blocks_ind,
		std::vector< std::vector< unsigned int > > const &	g_I,
		std::vector< std::vector< unsigned int > > const &	g_J
	)

Definition at line 85 of file qr.hpp.

template<typename VectorT >

void viennacl::linalg::detail::spai::print_continious_vector	(	VectorT &	con_v,
		std::vector< cl_uint > &	block_ind,
		std::vector< std::vector< unsigned int > > const &	g_J
	)

Definition at line 101 of file qr.hpp.

template<typename DenseMatrixT >

void viennacl::linalg::detail::spai::print_matrix

(

DenseMatrixT &

m

)

Definition at line 88 of file spai.hpp.

template<typename SparseVectorT >

void viennacl::linalg::detail::spai::print_sparse_vector

(

SparseVectorT const &

v

)

Definition at line 81 of file spai.hpp.

template<typename VectorT , typename NumericT >

void viennacl::linalg::detail::spai::projectI	(	std::vector< unsigned int > const &	I,
		VectorT &	y,
		unsigned int	ind
	)

Perform projection of set I on the unit-vector.

Parameters

I	set of non-zero rows
y	result vector
ind	index of unit vector

Definition at line 122 of file spai-static.hpp.

template<typename SparseVectorT >

void viennacl::linalg::detail::spai::projectRows	(	std::vector< SparseVectorT > const &	A_v_c,
		std::vector< unsigned int > const &	J,
		std::vector< unsigned int > &	I
	)

Row projection for matrix A(:,J) -> A(I,J), building index set of non-zero rows.

Parameters

A_v_c	input matrix
J	set of non-zero rows
I	output matrix

Definition at line 171 of file spai-static.hpp.

template<typename MatrixT >

void viennacl::linalg::detail::spai::QRBlockComposition	(	MatrixT const &	A_I_J,
		MatrixT const &	A_I_J_u,
		MatrixT &	A_I_u_J_u
	)

Composition of new block for QR factorization cf. Kallischko dissertation p.82, figure 4.7.

Parameters

A_I_J	previously composed block
A_I_J_u	matrix Q'*A(I, \tilde J), where \tilde J - set of new column indices
A_I_u_J_u	is composition of lower part A(I, \tilde J) and A(\tilde I, \tilde J) - new block for QR decomposition

Definition at line 250 of file spai-dynamic.hpp.

template<typename MatrixT , typename VectorT >

void viennacl::linalg::detail::spai::single_qr	(	MatrixT &	R,
		VectorT &	b_v
	)

Inplace QR factorization via Householder reflections c.f. Gene H. Golub, Charles F. Van Loan "Matrix Computations" 3rd edition p.224.

Parameters

R	input matrix
b_v	vector of betas

Definition at line 311 of file qr.hpp.

template<typename SparseVectorT , typename NumericT >

void viennacl::linalg::detail::spai::sparse_inner_prod	(	SparseVectorT const &	v1,
		SparseVectorT const &	v2,
		NumericT &	res_v
	)

Dot product of two sparse vectors.

Parameters

v1	initial sparse vector
v2	initial sparse vector
res_v	scalar that represents dot product result

Definition at line 157 of file spai-dynamic.hpp.

template<typename SparseVectorT , typename NumericT >

void viennacl::linalg::detail::spai::sparse_norm_2	(	SparseVectorT const &	v,
		NumericT &	norm
	)

Computation of Euclidean norm for sparse vector.

Parameters

v	initial sparse vector
norm	scalar that represents Euclidean norm

Definition at line 141 of file spai-dynamic.hpp.

template<typename MatrixT >

void viennacl::linalg::detail::spai::sparse_transpose	(	MatrixT const &	A_in,
		MatrixT &	A
	)

Transposition of sparse matrix.

Parameters

A_in	intial sparse matrix
A	output transposed matrix

Definition at line 640 of file spai.hpp.

template<typename MatrixT , typename VectorT >

void viennacl::linalg::detail::spai::store_householder_vector	(	MatrixT &	A,
		unsigned int	ind,
		VectorT &	v
	)

Storage of vector v in column(A, ind), starting from ind-1 index of a column.

Parameters

A	init matrix
ind	index of a column
v	vector that should be stored

Definition at line 295 of file qr.hpp.

template<typename MatrixT , typename NumericT >

void viennacl::linalg::detail::spai::sym_sparse_matrix_to_stl	(	MatrixT const &	A,
		std::vector< std::map< unsigned int, NumericT > > &	STL_A
	)

Definition at line 121 of file fspai.hpp.

template<typename SparseMatrixT , typename SparseVectorT >

void viennacl::linalg::detail::spai::vectorize_column_matrix	(	SparseMatrixT const &	M_in,
		std::vector< SparseVectorT > &	M_v
	)

Solution of Least square problem on CPU.

Parameters

M_in	input sparse, boost::numeric::ublas::compressed_matrix
M_v	array of sparse vectors

Definition at line 462 of file spai.hpp.

template<typename SparseMatrixT , typename SparseVectorT >

void viennacl::linalg::detail::spai::vectorize_row_matrix	(	SparseMatrixT const &	M_in,
		std::vector< SparseVectorT > &	M_v
	)

Definition at line 472 of file spai.hpp.

template<typename SizeT >

void viennacl::linalg::detail::spai::write_set_to_array	(	std::vector< std::vector< SizeT > > const &	ind_set,
		std::vector< cl_uint > &	a
	)

Definition at line 484 of file spai.hpp.

template<typename VectorT , typename MatrixT >

void viennacl::linalg::detail::spai::write_to_block	(	VectorT &	con_A_I_J,
		unsigned int	start_ind,
		std::vector< unsigned int > const &	I,
		std::vector< unsigned int > const &	J,
		MatrixT &	m
	)

Definition at line 72 of file qr.hpp.