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viennacl::linalg::host_based Namespace Reference

Holds all compute kernels with conventional host-based execution (buffers in CPU RAM). More...

## Namespaces

| amg
| detail
| Helper functions for the host-based linear algebra backend.

## Classes

struct | spgemm_output_write_disabled
struct | spgemm_output_write_enabled

## Functions

template<typename NumericT , typename SolverTagT >
void | inplace_solve (matrix_base< NumericT > const &A, matrix_base< NumericT > &B, SolverTagT)
| Direct inplace solver for triangular systems with multiple right hand sides, i.e. A \ B (MATLAB notation) More...
template<typename NumericT , typename SolverTagT >
void | inplace_solve (matrix_base< NumericT > const &mat, vector_base< NumericT > &vec, SolverTagT)
template<typename NumericT >
void | fft_direct (std::complex< NumericT > *input_complex, std::complex< NumericT > *output, vcl_size_t size, vcl_size_t stride, vcl_size_t batch_num, NumericT sign, viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER data_order=viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR)
| Direct algoritm kenrnel. More...
template<typename NumericT , unsigned int AlignmentV>
void | direct (viennacl::vector< NumericT, AlignmentV > const &in, viennacl::vector< NumericT, AlignmentV > &out, vcl_size_t size, vcl_size_t stride, vcl_size_t batch_num, NumericT sign=NumericT(-1), viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER data_order=viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR)
| Direct 1D algorithm for computing Fourier transformation. More...
template<typename NumericT , unsigned int AlignmentV>
void | direct (viennacl::matrix< NumericT, viennacl::row_major, AlignmentV > const &in, viennacl::matrix< NumericT, viennacl::row_major, AlignmentV > &out, vcl_size_t size, vcl_size_t stride, vcl_size_t batch_num, NumericT sign=NumericT(-1), viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER data_order=viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR)
| Direct 2D algorithm for computing Fourier transformation. More...
template<typename NumericT , unsigned int AlignmentV>
void | reorder (viennacl::vector< NumericT, AlignmentV > &in, vcl_size_t size, vcl_size_t stride, vcl_size_t bits_datasize, vcl_size_t batch_num, viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER data_order=viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR)
template<typename NumericT , unsigned int AlignmentV>
void | reorder (viennacl::matrix< NumericT, viennacl::row_major, AlignmentV > &in, vcl_size_t size, vcl_size_t stride, vcl_size_t bits_datasize, vcl_size_t batch_num, viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER data_order=viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR)
template<typename NumericT >
void | fft_radix2 (std::complex< NumericT > *input_complex, vcl_size_t batch_num, vcl_size_t bit_size, vcl_size_t size, vcl_size_t stride, NumericT sign, viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER data_order=viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR)
| Radix-2 algorithm for computing Fourier transformation. Kernel for computing smaller amount of data. More...
template<typename NumericT >
void | fft_radix2_local (std::complex< NumericT > *input_complex, std::complex< NumericT > *lcl_input, vcl_size_t batch_num, vcl_size_t bit_size, vcl_size_t size, vcl_size_t stride, NumericT sign, viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER data_order=viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR)
| Radix-2 algorithm for computing Fourier transformation. Kernel for computing bigger amount of data. More...
template<typename NumericT , unsigned int AlignmentV>
void | radix2 (viennacl::vector< NumericT, AlignmentV > &in, vcl_size_t size, vcl_size_t stride, vcl_size_t batch_num, NumericT sign=NumericT(-1), viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER data_order=viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR)
| Radix-2 1D algorithm for computing Fourier transformation. More...
template<typename NumericT , unsigned int AlignmentV>
void | radix2 (viennacl::matrix< NumericT, viennacl::row_major, AlignmentV > &in, vcl_size_t size, vcl_size_t stride, vcl_size_t batch_num, NumericT sign=NumericT(-1), viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER data_order=viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR)
| Radix-2 2D algorithm for computing Fourier transformation. More...
template<typename NumericT , unsigned int AlignmentV>
void | bluestein (viennacl::vector< NumericT, AlignmentV > &in, viennacl::vector< NumericT, AlignmentV > &out, vcl_size_t)
| Bluestein's algorithm for computing Fourier transformation. More...
template<typename NumericT , unsigned int AlignmentV>
void | normalize (viennacl::vector< NumericT, AlignmentV > &input)
| Normalize vector with his own size. More...
template<typename NumericT , unsigned int AlignmentV>
void | multiply_complex (viennacl::vector< NumericT, AlignmentV > const &input1, viennacl::vector< NumericT, AlignmentV > const &input2, viennacl::vector< NumericT, AlignmentV > &output)
| Complex multiplikation of two vectors. More...
template<typename NumericT , unsigned int AlignmentV>
void | transpose (viennacl::matrix< NumericT, viennacl::row_major, AlignmentV > &input)
| Inplace transpose of matrix. More...
template<typename NumericT , unsigned int AlignmentV>
void | transpose (viennacl::matrix< NumericT, viennacl::row_major, AlignmentV > const &input, viennacl::matrix< NumericT, viennacl::row_major, AlignmentV > &output)
| Transpose matrix. More...
template<typename NumericT >
void | real_to_complex (viennacl::vector_base< NumericT > const &in, viennacl::vector_base< NumericT > &out, vcl_size_t size)
| Create complex vector from real vector (even elements(2*k) = real part, odd elements(2*k+1) = imaginary part) More...
template<typename NumericT >
void | complex_to_real (viennacl::vector_base< NumericT > const &in, viennacl::vector_base< NumericT > &out, vcl_size_t size)
| Create real vector from complex vector (even elements(2*k) = real part, odd elements(2*k+1) = imaginary part) More...
template<typename NumericT >
void | reverse (viennacl::vector_base< NumericT > &in)
| Reverse vector to opposite order and save it in input vector. More...
template<typename NumericT >
void | extract_L (compressed_matrix< NumericT > const &A, compressed_matrix< NumericT > &L)
template<typename NumericT >
void | icc_scale (compressed_matrix< NumericT > const &A, compressed_matrix< NumericT > &L)
| Scales the values extracted from A such that A' = DAD has unit diagonal. Updates values from A in L and U accordingly. More...
template<typename NumericT >
void | icc_chow_patel_sweep (compressed_matrix< NumericT > &L, vector< NumericT > &aij_L)
| Performs one nonlinear relaxation step in the Chow-Patel-ICC using OpenMP (cf. Algorithm 3 in paper, but for L rather than U) More...
template<typename NumericT >
void | extract_LU (compressed_matrix< NumericT > const &A, compressed_matrix< NumericT > &L, compressed_matrix< NumericT > &U)
template<typename NumericT >
void | ilu_scale (compressed_matrix< NumericT > const &A, compressed_matrix< NumericT > &L, compressed_matrix< NumericT > &U)
| Scales the values extracted from A such that A' = DAD has unit diagonal. Updates values from A in L and U accordingly. More...
template<typename NumericT >
void | ilu_transpose (compressed_matrix< NumericT > const &A, compressed_matrix< NumericT > &B)
template<typename NumericT >
void | ilu_chow_patel_sweep (compressed_matrix< NumericT > &L, vector< NumericT > const &aij_L, compressed_matrix< NumericT > &U_trans, vector< NumericT > const &aij_U_trans)
| Performs one nonlinear relaxation step in the Chow-Patel-ILU using OpenMP (cf. Algorithm 2 in paper) More...
template<typename NumericT >
void | ilu_form_neumann_matrix (compressed_matrix< NumericT > &R, vector< NumericT > &diag_R)
template<typename NumericT >
void | pipelined_cg_vector_update (vector_base< NumericT > &result, NumericT alpha, vector_base< NumericT > &p, vector_base< NumericT > &r, vector_base< NumericT > const &Ap, NumericT beta, vector_base< NumericT > &inner_prod_buffer)
| Performs a joint vector update operation needed for an efficient pipelined CG algorithm. More...
template<typename NumericT >
void | pipelined_cg_prod (compressed_matrix< NumericT > const &A, vector_base< NumericT > const &p, vector_base< NumericT > &Ap, vector_base< NumericT > &inner_prod_buffer)
| Performs a fused matrix-vector product with a compressed_matrix for an efficient pipelined CG algorithm. More...
template<typename NumericT >
void | pipelined_cg_prod (coordinate_matrix< NumericT > const &A, vector_base< NumericT > const &p, vector_base< NumericT > &Ap, vector_base< NumericT > &inner_prod_buffer)
| Performs a fused matrix-vector product with a coordinate_matrix for an efficient pipelined CG algorithm. More...
template<typename NumericT >
void | pipelined_cg_prod (ell_matrix< NumericT > const &A, vector_base< NumericT > const &p, vector_base< NumericT > &Ap, vector_base< NumericT > &inner_prod_buffer)
| Performs a fused matrix-vector product with an ell_matrix for an efficient pipelined CG algorithm. More...
template<typename NumericT , typename IndexT >
void | pipelined_cg_prod (sliced_ell_matrix< NumericT, IndexT > const &A, vector_base< NumericT > const &p, vector_base< NumericT > &Ap, vector_base< NumericT > &inner_prod_buffer)
| Performs a fused matrix-vector product with an sliced_ell_matrix for an efficient pipelined CG algorithm. More...
template<typename NumericT >
void | pipelined_cg_prod (hyb_matrix< NumericT > const &A, vector_base< NumericT > const &p, vector_base< NumericT > &Ap, vector_base< NumericT > &inner_prod_buffer)
| Performs a fused matrix-vector product with an hyb_matrix for an efficient pipelined CG algorithm. More...
template<typename NumericT >
void | pipelined_bicgstab_update_s (vector_base< NumericT > &s, vector_base< NumericT > &r, vector_base< NumericT > const &Ap, vector_base< NumericT > &inner_prod_buffer, vcl_size_t buffer_chunk_size, vcl_size_t buffer_chunk_offset)
| Performs a joint vector update operation needed for an efficient pipelined BiCGStab algorithm. More...
template<typename NumericT >
void | pipelined_bicgstab_vector_update (vector_base< NumericT > &result, NumericT alpha, vector_base< NumericT > &p, NumericT omega, vector_base< NumericT > const &s, vector_base< NumericT > &residual, vector_base< NumericT > const &As, NumericT beta, vector_base< NumericT > const &Ap, vector_base< NumericT > const &r0star, vector_base< NumericT > &inner_prod_buffer, vcl_size_t buffer_chunk_size)
| Performs a joint vector update operation needed for an efficient pipelined BiCGStab algorithm. More...
template<typename NumericT >
void | pipelined_bicgstab_prod (compressed_matrix< NumericT > const &A, vector_base< NumericT > const &p, vector_base< NumericT > &Ap, vector_base< NumericT > const &r0star, vector_base< NumericT > &inner_prod_buffer, vcl_size_t buffer_chunk_size, vcl_size_t buffer_chunk_offset)
| Performs a fused matrix-vector product with a compressed_matrix for an efficient pipelined BiCGStab algorithm. More...
template<typename NumericT >
void | pipelined_bicgstab_prod (coordinate_matrix< NumericT > const &A, vector_base< NumericT > const &p, vector_base< NumericT > &Ap, vector_base< NumericT > const &r0star, vector_base< NumericT > &inner_prod_buffer, vcl_size_t buffer_chunk_size, vcl_size_t buffer_chunk_offset)
| Performs a fused matrix-vector product with a coordinate_matrix for an efficient pipelined BiCGStab algorithm. More...
template<typename NumericT >
void | pipelined_bicgstab_prod (ell_matrix< NumericT > const &A, vector_base< NumericT > const &p, vector_base< NumericT > &Ap, vector_base< NumericT > const &r0star, vector_base< NumericT > &inner_prod_buffer, vcl_size_t buffer_chunk_size, vcl_size_t buffer_chunk_offset)
| Performs a fused matrix-vector product with an ell_matrix for an efficient pipelined BiCGStab algorithm. More...
template<typename NumericT , typename IndexT >
void | pipelined_bicgstab_prod (sliced_ell_matrix< NumericT, IndexT > const &A, vector_base< NumericT > const &p, vector_base< NumericT > &Ap, vector_base< NumericT > const &r0star, vector_base< NumericT > &inner_prod_buffer, vcl_size_t buffer_chunk_size, vcl_size_t buffer_chunk_offset)
| Performs a fused matrix-vector product with a sliced_ell_matrix for an efficient pipelined BiCGStab algorithm. More...
template<typename NumericT >
void | pipelined_bicgstab_prod (hyb_matrix< NumericT > const &A, vector_base< NumericT > const &p, vector_base< NumericT > &Ap, vector_base< NumericT > const &r0star, vector_base< NumericT > &inner_prod_buffer, vcl_size_t buffer_chunk_size, vcl_size_t buffer_chunk_offset)
| Performs a fused matrix-vector product with a hyb_matrix for an efficient pipelined BiCGStab algorithm. More...
template<typename T >
void | pipelined_gmres_normalize_vk (vector_base< T > &v_k, vector_base< T > const &residual, vector_base< T > &R_buffer, vcl_size_t offset_in_R, vector_base< T > const &inner_prod_buffer, vector_base< T > &r_dot_vk_buffer, vcl_size_t buffer_chunk_size, vcl_size_t buffer_chunk_offset)
| Performs a vector normalization needed for an efficient pipelined GMRES algorithm. More...
template<typename T >
void | pipelined_gmres_gram_schmidt_stage1 (vector_base< T > const &device_krylov_basis, vcl_size_t v_k_size, vcl_size_t v_k_internal_size, vcl_size_t k, vector_base< T > &vi_in_vk_buffer, vcl_size_t buffer_chunk_size)
| Computes first reduction stage for multiple inner products <v_i, v_k>, i=0..k-1. More...
template<typename T >
void | pipelined_gmres_gram_schmidt_stage2 (vector_base< T > &device_krylov_basis, vcl_size_t v_k_size, vcl_size_t v_k_internal_size, vcl_size_t k, vector_base< T > const &vi_in_vk_buffer, vector_base< T > &R_buffer, vcl_size_t krylov_dim, vector_base< T > &inner_prod_buffer, vcl_size_t buffer_chunk_size)
| Computes the second reduction stage for multiple inner products <v_i, v_k>, i=0..k-1, then updates v_k -= <v_i, v_k> v_i and computes the first reduction stage for ||v_k||. More...
template<typename T >
void | pipelined_gmres_update_result (vector_base< T > &result, vector_base< T > const &residual, vector_base< T > const &krylov_basis, vcl_size_t v_k_size, vcl_size_t v_k_internal_size, vector_base< T > const &coefficients, vcl_size_t k)
| Computes x += eta_0 r + sum_{i=1}^{k-1} eta_i v_{i-1}. More...
template<typename MatrixType , typename T >
void | pipelined_gmres_prod (MatrixType const &A, vector_base< T > const &p, vector_base< T > &Ap, vector_base< T > &inner_prod_buffer)
template<typename DestNumericT , typename SrcNumericT >
void | convert (matrix_base< DestNumericT > &mat1, matrix_base< SrcNumericT > const &mat2)
template<typename NumericT , typename SizeT , typename DistanceT >
void | trans (const matrix_expression< const matrix_base< NumericT, SizeT, DistanceT >, const matrix_base< NumericT, SizeT, DistanceT >, op_trans > &proxy, matrix_base< NumericT > &temp_trans)
template<typename NumericT , typename ScalarT1 >
void | am (matrix_base< NumericT > &mat1, matrix_base< NumericT > const &mat2, ScalarT1 const &alpha, vcl_size_t, bool reciprocal_alpha, bool flip_sign_alpha)
template<typename NumericT , typename ScalarT1 , typename ScalarT2 >
void | ambm (matrix_base< NumericT > &mat1, matrix_base< NumericT > const &mat2, ScalarT1 const &alpha, vcl_size_t, bool reciprocal_alpha, bool flip_sign_alpha, matrix_base< NumericT > const &mat3, ScalarT2 const &beta, vcl_size_t, bool reciprocal_beta, bool flip_sign_beta)
template<typename NumericT , typename ScalarT1 , typename ScalarT2 >
void | ambm_m (matrix_base< NumericT > &mat1, matrix_base< NumericT > const &mat2, ScalarT1 const &alpha, vcl_size_t, bool reciprocal_alpha, bool flip_sign_alpha, matrix_base< NumericT > const &mat3, ScalarT2 const &beta, vcl_size_t, bool reciprocal_beta, bool flip_sign_beta)
template<typename NumericT >
void | matrix_assign (matrix_base< NumericT > &mat, NumericT s, bool clear=false)
template<typename NumericT >
void | matrix_diagonal_assign (matrix_base< NumericT > &mat, NumericT s)
template<typename NumericT >
void | matrix_diag_from_vector (const vector_base< NumericT > &vec, int k, matrix_base< NumericT > &mat)
template<typename NumericT >
void | matrix_diag_to_vector (const matrix_base< NumericT > &mat, int k, vector_base< NumericT > &vec)
template<typename NumericT >
void | matrix_row (const matrix_base< NumericT > &mat, unsigned int i, vector_base< NumericT > &vec)
template<typename NumericT >
void | matrix_column (const matrix_base< NumericT > &mat, unsigned int j, vector_base< NumericT > &vec)
template<typename NumericT , typename OpT >
void | element_op (matrix_base< NumericT > &A, matrix_expression< const matrix_base< NumericT >, const matrix_base< NumericT >, op_element_binary< OpT > > const &proxy)
| Implementation of the element-wise operations A = B .* C and A = B ./ C (using MATLAB syntax) More...
template<typename NumericT , typename OpT >
void | element_op (matrix_base< NumericT > &A, matrix_expression< const matrix_base< NumericT >, const matrix_base< NumericT >, op_element_unary< OpT > > const &proxy)
template<typename NumericT >
void | prod_impl (const matrix_base< NumericT > &mat, bool trans, const vector_base< NumericT > &vec, vector_base< NumericT > &result)
| Carries out matrix-vector multiplication. More...
template<typename NumericT , typename ScalarT1 , typename ScalarT2 >
void | prod_impl (const matrix_base< NumericT > &A, bool trans_A, const matrix_base< NumericT > &B, bool trans_B, matrix_base< NumericT > &C, ScalarT1 alpha, ScalarT2 beta)
| Carries out matrix-matrix multiplication. More...
template<typename NumericT , typename ScalarT >
void | scaled_rank_1_update (matrix_base< NumericT > &mat1, ScalarT const &alpha, vcl_size_t, bool reciprocal_alpha, bool flip_sign_alpha, const vector_base< NumericT > &vec1, const vector_base< NumericT > &vec2)
| The implementation of the operation mat += alpha * vec1 * vec2^T, i.e. a scaled rank 1 update. More...
template<typename NumericT , typename S1 >
void | bidiag_pack_impl (matrix_base< NumericT > &A, vector_base< S1 > &D, vector_base< S1 > &S)
| This function stores the diagonal and the superdiagonal of a matrix in two vectors. More...
template<typename NumericT , typename VectorType >
void | bidiag_pack (matrix_base< NumericT > &A, VectorType &dh, VectorType &sh)
template<typename NumericT >
void | house_update_A_left (matrix_base< NumericT > &A, vector_base< NumericT > &D, vcl_size_t start)
| This function applies a householder transformation to a matrix. A <- P * A with a householder reflection P. More...
template<typename NumericT >
void | house_update_A_right (matrix_base< NumericT > &A, vector_base< NumericT > &D)
| This function applies a householder transformation to a matrix: A <- A * P with a householder reflection P. More...
template<typename NumericT >
void | house_update_QL (matrix_base< NumericT > &Q, vector_base< NumericT > &D, vcl_size_t A_size1)
| This function updates the matrix Q, which is needed for the computation of the eigenvectors. More...
template<typename NumericT >
void | givens_next (matrix_base< NumericT > &Q, vector_base< NumericT > &tmp1, vector_base< NumericT > &tmp2, int l, int m)
| This function updates the matrix Q. It is part of the tql2 algorithm. More...
template<typename NumericT , typename S1 >
void | copy_vec (matrix_base< NumericT > &A, vector_base< S1 > &V, vcl_size_t row_start, vcl_size_t col_start, bool copy_col)
| This function copies a row or a column from a matrix to a vector. More...
template<typename NumericT >
void | el_wise_mul_div (NumericT *matrix1, NumericT const *matrix2, NumericT const *matrix3, vcl_size_t size)
| Missing OpenMP kernel for nonnegative matrix factorization of a dense matrices. More...
template<typename NumericT >
void | nmf (viennacl::matrix_base< NumericT > const &V, viennacl::matrix_base< NumericT > &W, viennacl::matrix_base< NumericT > &H, viennacl::linalg::nmf_config const &conf)
| The nonnegative matrix factorization (approximation) algorithm as suggested by Lee and Seung. Factorizes a matrix V with nonnegative entries into matrices W and H such that ||V - W*H|| is minimized. More...
template<typename ScalarT1 , typename ScalarT2 , typename FactorT >
viennacl::enable_if < viennacl::is_scalar < ScalarT1 >::value &&viennacl::is_scalar < ScalarT2 >::value &&viennacl::is_any_scalar < FactorT >::value >::type | as (ScalarT1 &s1, ScalarT2 const &s2, FactorT const &alpha, vcl_size_t, bool reciprocal_alpha, bool flip_sign_alpha)
template<typename ScalarT1 , typename ScalarT2 , typename FactorT2 , typename ScalarT3 , typename FactorT3 >

viennacl::enable_if
< viennacl::is_scalar
< ScalarT1 >::value
&&viennacl::is_scalar
< ScalarT2 >::value
&&viennacl::is_scalar
< ScalarT3 >::value
&&viennacl::is_any_scalar
< FactorT2 >::value
&&viennacl::is_any_scalar
< FactorT3 >::value >::type

asbs (ScalarT1 &s1, ScalarT2 const &s2, FactorT2 const &alpha, vcl_size_t, bool reciprocal_alpha, bool flip_sign_alpha, ScalarT3 const &s3, FactorT3 const &beta, vcl_size_t, bool reciprocal_beta, bool flip_sign_beta)

template<typename ScalarT1 , typename ScalarT2 , typename FactorT2 , typename ScalarT3 , typename FactorT3 >

viennacl::enable_if
< viennacl::is_scalar
< ScalarT1 >::value
&&viennacl::is_scalar
< ScalarT2 >::value
&&viennacl::is_scalar
< ScalarT3 >::value
&&viennacl::is_any_scalar
< FactorT2 >::value
&&viennacl::is_any_scalar
< FactorT3 >::value >::type

asbs_s (ScalarT1 &s1, ScalarT2 const &s2, FactorT2 const &alpha, vcl_size_t, bool reciprocal_alpha, bool flip_sign_alpha, ScalarT3 const &s3, FactorT3 const &beta, vcl_size_t, bool reciprocal_beta, bool flip_sign_beta)

template<typename ScalarT1 , typename ScalarT2 >
viennacl::enable_if < viennacl::is_scalar < ScalarT1 >::value &&viennacl::is_scalar < ScalarT2 >::value >::type | swap (ScalarT1 &s1, ScalarT2 &s2)
| Swaps the contents of two scalars, data is copied. More...
template<typename NumericT , unsigned int AlignmentV>
void | prod_impl (const viennacl::compressed_matrix< NumericT, AlignmentV > &mat, const viennacl::vector_base< NumericT > &vec, NumericT alpha, viennacl::vector_base< NumericT > &result, NumericT beta)
| Carries out matrix-vector multiplication with a compressed_matrix. More...
template<typename NumericT , unsigned int AlignmentV>
void | prod_impl (const viennacl::compressed_matrix< NumericT, AlignmentV > &sp_mat, const viennacl::matrix_base< NumericT > &d_mat, viennacl::matrix_base< NumericT > &result)
| Carries out sparse_matrix-matrix multiplication first matrix being compressed. More...
template<typename NumericT , unsigned int AlignmentV>
void | prod_impl (const viennacl::compressed_matrix< NumericT, AlignmentV > &sp_mat, const viennacl::matrix_expression< const viennacl::matrix_base< NumericT >, const viennacl::matrix_base< NumericT >, viennacl::op_trans > &d_mat, viennacl::matrix_base< NumericT > &result)
| Carries out matrix-trans(matrix) multiplication first matrix being compressed and the second transposed. More...
template<typename NumericT , unsigned int AlignmentV>
void | prod_impl (viennacl::compressed_matrix< NumericT, AlignmentV > const &A, viennacl::compressed_matrix< NumericT, AlignmentV > const &B, viennacl::compressed_matrix< NumericT, AlignmentV > &C)
| Carries out sparse_matrix-sparse_matrix multiplication for CSR matrices. More...
template<typename NumericT , unsigned int AlignmentV>
void | inplace_solve (compressed_matrix< NumericT, AlignmentV > const &L, vector_base< NumericT > &vec, viennacl::linalg::unit_lower_tag tag)
| Inplace solution of a lower triangular compressed_matrix with unit diagonal. Typically used for LU substitutions. More...
template<typename NumericT , unsigned int AlignmentV>
void | inplace_solve (compressed_matrix< NumericT, AlignmentV > const &L, vector_base< NumericT > &vec, viennacl::linalg::lower_tag tag)
| Inplace solution of a lower triangular compressed_matrix. Typically used for LU substitutions. More...
template<typename NumericT , unsigned int AlignmentV>
void | inplace_solve (compressed_matrix< NumericT, AlignmentV > const &U, vector_base< NumericT > &vec, viennacl::linalg::unit_upper_tag tag)
| Inplace solution of a upper triangular compressed_matrix with unit diagonal. Typically used for LU substitutions. More...
template<typename NumericT , unsigned int AlignmentV>
void | inplace_solve (compressed_matrix< NumericT, AlignmentV > const &U, vector_base< NumericT > &vec, viennacl::linalg::upper_tag tag)
| Inplace solution of a upper triangular compressed_matrix. Typically used for LU substitutions. More...
template<typename NumericT , unsigned int AlignmentV>
void | inplace_solve (matrix_expression< const compressed_matrix< NumericT, AlignmentV >, const compressed_matrix< NumericT, AlignmentV >, op_trans > const &proxy, vector_base< NumericT > &vec, viennacl::linalg::unit_lower_tag tag)
| Inplace solution of a lower triangular compressed_matrix with unit diagonal. Typically used for LU substitutions. More...
template<typename NumericT , unsigned int AlignmentV>
void | inplace_solve (matrix_expression< const compressed_matrix< NumericT, AlignmentV >, const compressed_matrix< NumericT, AlignmentV >, op_trans > const &proxy, vector_base< NumericT > &vec, viennacl::linalg::lower_tag tag)
| Inplace solution of a lower triangular compressed_matrix. Typically used for LU substitutions. More...
template<typename NumericT , unsigned int AlignmentV>
void | inplace_solve (matrix_expression< const compressed_matrix< NumericT, AlignmentV >, const compressed_matrix< NumericT, AlignmentV >, op_trans > const &proxy, vector_base< NumericT > &vec, viennacl::linalg::unit_upper_tag tag)
| Inplace solution of a upper triangular compressed_matrix with unit diagonal. Typically used for LU substitutions. More...
template<typename NumericT , unsigned int AlignmentV>
void | inplace_solve (matrix_expression< const compressed_matrix< NumericT, AlignmentV >, const compressed_matrix< NumericT, AlignmentV >, op_trans > const &proxy, vector_base< NumericT > &vec, viennacl::linalg::upper_tag tag)
| Inplace solution of a upper triangular compressed_matrix with unit diagonal. Typically used for LU substitutions. More...
template<typename NumericT >
void | prod_impl (const viennacl::compressed_compressed_matrix< NumericT > &mat, const viennacl::vector_base< NumericT > &vec, NumericT alpha, viennacl::vector_base< NumericT > &result, NumericT beta)
| Carries out matrix-vector multiplication with a compressed_matrix. More...
template<typename NumericT , unsigned int AlignmentV>
void | prod_impl (const viennacl::coordinate_matrix< NumericT, AlignmentV > &mat, const viennacl::vector_base< NumericT > &vec, NumericT alpha, viennacl::vector_base< NumericT > &result, NumericT beta)
| Carries out matrix-vector multiplication with a coordinate_matrix. More...
template<typename NumericT , unsigned int AlignmentV>
void | prod_impl (const viennacl::coordinate_matrix< NumericT, AlignmentV > &sp_mat, const viennacl::matrix_base< NumericT > &d_mat, viennacl::matrix_base< NumericT > &result)
| Carries out Compressed Matrix(COO)-Dense Matrix multiplication. More...
template<typename NumericT , unsigned int AlignmentV>
void | prod_impl (const viennacl::coordinate_matrix< NumericT, AlignmentV > &sp_mat, const viennacl::matrix_expression< const viennacl::matrix_base< NumericT >, const viennacl::matrix_base< NumericT >, viennacl::op_trans > &d_mat, viennacl::matrix_base< NumericT > &result)
| Carries out Compressed Matrix(COO)-Dense Transposed Matrix multiplication. More...
template<typename NumericT , unsigned int AlignmentV>
void | prod_impl (const viennacl::ell_matrix< NumericT, AlignmentV > &mat, const viennacl::vector_base< NumericT > &vec, NumericT alpha, viennacl::vector_base< NumericT > &result, NumericT beta)
| Carries out matrix-vector multiplication with a ell_matrix. More...
template<typename NumericT , unsigned int AlignmentV>
void | prod_impl (const viennacl::ell_matrix< NumericT, AlignmentV > &sp_mat, const viennacl::matrix_base< NumericT > &d_mat, viennacl::matrix_base< NumericT > &result)
| Carries out ell_matrix-d_matrix multiplication. More...
template<typename NumericT , unsigned int AlignmentV>
void | prod_impl (const viennacl::ell_matrix< NumericT, AlignmentV > &sp_mat, const viennacl::matrix_expression< const viennacl::matrix_base< NumericT >, const viennacl::matrix_base< NumericT >, viennacl::op_trans > &d_mat, viennacl::matrix_base< NumericT > &result)
| Carries out matrix-trans(matrix) multiplication first matrix being sparse ell and the second dense transposed. More...
template<typename NumericT , typename IndexT >
void | prod_impl (const viennacl::sliced_ell_matrix< NumericT, IndexT > &mat, const viennacl::vector_base< NumericT > &vec, NumericT alpha, viennacl::vector_base< NumericT > &result, NumericT beta)
| Carries out matrix-vector multiplication with a sliced_ell_matrix. More...
template<typename NumericT , unsigned int AlignmentV>
void | prod_impl (const viennacl::hyb_matrix< NumericT, AlignmentV > &mat, const viennacl::vector_base< NumericT > &vec, NumericT alpha, viennacl::vector_base< NumericT > &result, NumericT beta)
| Carries out matrix-vector multiplication with a hyb_matrix. More...
template<typename NumericT , unsigned int AlignmentV>
void | prod_impl (const viennacl::hyb_matrix< NumericT, AlignmentV > &mat, const viennacl::matrix_base< NumericT > &d_mat, viennacl::matrix_base< NumericT > &result)
| Carries out sparse-matrix-dense-matrix multiplication with a hyb_matrix. More...
template<typename NumericT , unsigned int AlignmentV>
void | prod_impl (const viennacl::hyb_matrix< NumericT, AlignmentV > &mat, const viennacl::matrix_expression< const viennacl::matrix_base< NumericT >, const viennacl::matrix_base< NumericT >, viennacl::op_trans > &d_mat, viennacl::matrix_base< NumericT > &result)
| Carries out sparse-matrix-transposed-dense-matrix multiplication with a hyb_matrix. More...
template<unsigned int IndexNum>
unsigned int | row_C_scan_symbolic_vector_N (unsigned int const *row_indices_B, unsigned int const *B_row_buffer, unsigned int const *B_col_buffer, unsigned int B_size2, unsigned int const *row_C_vector_input, unsigned int const *row_C_vector_input_end, unsigned int *row_C_vector_output)
| Merges up to IndexNum rows from B into the result buffer. More...
template<typename OutputWriterT >
unsigned int | row_C_scan_symbolic_vector_1 (unsigned int const *input1_begin, unsigned int const *input1_end, unsigned int const *input2_begin, unsigned int const *input2_end, unsigned int termination_index, unsigned int *output_begin)
unsigned int | row_C_scan_symbolic_vector (unsigned int row_start_A, unsigned int row_end_A, unsigned int const *A_col_buffer, unsigned int const *B_row_buffer, unsigned int const *B_col_buffer, unsigned int B_size2, unsigned int *row_C_vector_1, unsigned int *row_C_vector_2, unsigned int *row_C_vector_3)
template<unsigned int IndexNum, typename NumericT >

unsigned int

row_C_scan_numeric_vector_N (unsigned int const *row_indices_B, NumericT const *val_A, unsigned int const *B_row_buffer, unsigned int const *B_col_buffer, NumericT const *B_elements, unsigned int B_size2, unsigned int const *row_C_vector_input, unsigned int const *row_C_vector_input_end, NumericT *row_C_vector_input_values, unsigned int *row_C_vector_output, NumericT *row_C_vector_output_values)

| Merges up to IndexNum rows from B into the result buffer. More...
template<typename NumericT >

unsigned int

row_C_scan_numeric_vector_1 (unsigned int const *input1_index_begin, unsigned int const *input1_index_end, NumericT const *input1_values_begin, NumericT factor1, unsigned int const *input2_index_begin, unsigned int const *input2_index_end, NumericT const *input2_values_begin, NumericT factor2, unsigned int termination_index, unsigned int *output_index_begin, NumericT *output_values_begin)

template<typename NumericT >

void

row_C_scan_numeric_vector (unsigned int row_start_A, unsigned int row_end_A, unsigned int const *A_col_buffer, NumericT const *A_elements, unsigned int const *B_row_buffer, unsigned int const *B_col_buffer, NumericT const *B_elements, unsigned int B_size2, unsigned int row_start_C, unsigned int row_end_C, unsigned int *C_col_buffer, NumericT *C_elements, unsigned int *row_C_vector_1, NumericT *row_C_vector_1_values, unsigned int *row_C_vector_2, NumericT *row_C_vector_2_values, unsigned int *row_C_vector_3, NumericT *row_C_vector_3_values)

template<typename DestNumericT , typename SrcNumericT >
void | convert (vector_base< DestNumericT > &dest, vector_base< SrcNumericT > const &src)
template<typename NumericT , typename ScalarT1 >
void | av (vector_base< NumericT > &vec1, vector_base< NumericT > const &vec2, ScalarT1 const &alpha, vcl_size_t, bool reciprocal_alpha, bool flip_sign_alpha)
template<typename NumericT , typename ScalarT1 , typename ScalarT2 >
void | avbv (vector_base< NumericT > &vec1, vector_base< NumericT > const &vec2, ScalarT1 const &alpha, vcl_size_t, bool reciprocal_alpha, bool flip_sign_alpha, vector_base< NumericT > const &vec3, ScalarT2 const &beta, vcl_size_t, bool reciprocal_beta, bool flip_sign_beta)
template<typename NumericT , typename ScalarT1 , typename ScalarT2 >
void | avbv_v (vector_base< NumericT > &vec1, vector_base< NumericT > const &vec2, ScalarT1 const &alpha, vcl_size_t, bool reciprocal_alpha, bool flip_sign_alpha, vector_base< NumericT > const &vec3, ScalarT2 const &beta, vcl_size_t, bool reciprocal_beta, bool flip_sign_beta)
template<typename NumericT >
void | vector_assign (vector_base< NumericT > &vec1, const NumericT &alpha, bool up_to_internal_size=false)
| Assign a constant value to a vector (-range/-slice) More...
template<typename NumericT >
void | vector_swap (vector_base< NumericT > &vec1, vector_base< NumericT > &vec2)
| Swaps the contents of two vectors, data is copied. More...
template<typename NumericT , typename OpT >
void | element_op (vector_base< NumericT > &vec1, vector_expression< const vector_base< NumericT >, const vector_base< NumericT >, op_element_binary< OpT > > const &proxy)
| Implementation of the element-wise operation v1 = v2 .* v3 and v1 = v2 ./ v3 (using MATLAB syntax) More...
template<typename NumericT , typename OpT >
void | element_op (vector_base< NumericT > &vec1, vector_expression< const vector_base< NumericT >, const vector_base< NumericT >, op_element_unary< OpT > > const &proxy)
| Implementation of the element-wise operation v1 = v2 .* v3 and v1 = v2 ./ v3 (using MATLAB syntax) More...
template<typename NumericT , typename ScalarT >
void | inner_prod_impl (vector_base< NumericT > const &vec1, vector_base< NumericT > const &vec2, ScalarT &result)
| Computes the inner product of two vectors - implementation. Library users should call inner_prod(vec1, vec2). More...
template<typename NumericT >
void | inner_prod_impl (vector_base< NumericT > const &x, vector_tuple< NumericT > const &vec_tuple, vector_base< NumericT > &result)
template<typename NumericT , typename ScalarT >
void | norm_1_impl (vector_base< NumericT > const &vec1, ScalarT &result)
| Computes the l^1-norm of a vector. More...
template<typename NumericT , typename ScalarT >
void | norm_2_impl (vector_base< NumericT > const &vec1, ScalarT &result)
| Computes the l^2-norm of a vector - implementation. More...
template<typename NumericT , typename ScalarT >
void | norm_inf_impl (vector_base< NumericT > const &vec1, ScalarT &result)
| Computes the supremum-norm of a vector. More...
template<typename NumericT >
vcl_size_t | index_norm_inf (vector_base< NumericT > const &vec1)
| Computes the index of the first entry that is equal to the supremum-norm in modulus. More...
template<typename NumericT , typename ScalarT >
void | max_impl (vector_base< NumericT > const &vec1, ScalarT &result)
| Computes the maximum of a vector. More...
template<typename NumericT , typename ScalarT >
void | min_impl (vector_base< NumericT > const &vec1, ScalarT &result)
| Computes the minimum of a vector. More...
template<typename NumericT , typename ScalarT >
void | sum_impl (vector_base< NumericT > const &vec1, ScalarT &result)
| Computes the sum of all elements from the vector. More...
template<typename NumericT >
void | plane_rotation (vector_base< NumericT > &vec1, vector_base< NumericT > &vec2, NumericT alpha, NumericT beta)
| Computes a plane rotation of two vectors. More...
template<typename NumericT >
void | inclusive_scan (vector_base< NumericT > const &vec1, vector_base< NumericT > &vec2)
| This function implements an inclusive scan on the host using OpenMP. More...
template<typename NumericT >
void | exclusive_scan (vector_base< NumericT > const &vec1, vector_base< NumericT > &vec2)
| This function implements an exclusive scan on the host using OpenMP. More...

## Detailed Description

Holds all compute kernels with conventional host-based execution (buffers in CPU RAM).

## Function Documentation

template<typename NumericT , typename ScalarT1 >

void viennacl::linalg::host_based::am | ( | matrix_base< NumericT > & | mat1,
|  | matrix_base< NumericT > const & | mat2,
|  | ScalarT1 const & | alpha,
|  | vcl_size_t | ,
|  | bool | reciprocal_alpha,
|  | bool | flip_sign_alpha
| ) |  |

Definition at line 231 of file matrix_operations.hpp.

template<typename NumericT , typename ScalarT1 , typename ScalarT2 >

void viennacl::linalg::host_based::ambm | ( | matrix_base< NumericT > & | mat1,
|  | matrix_base< NumericT > const & | mat2,
|  | ScalarT1 const & | alpha,
|  | vcl_size_t | ,
|  | bool | reciprocal_alpha,
|  | bool | flip_sign_alpha,
|  | matrix_base< NumericT > const & | mat3,
|  | ScalarT2 const & | beta,
|  | vcl_size_t | ,
|  | bool | reciprocal_beta,
|  | bool | flip_sign_beta
| ) |  |

Definition at line 314 of file matrix_operations.hpp.

template<typename NumericT , typename ScalarT1 , typename ScalarT2 >

void viennacl::linalg::host_based::ambm_m | ( | matrix_base< NumericT > & | mat1,
|  | matrix_base< NumericT > const & | mat2,
|  | ScalarT1 const & | alpha,
|  | vcl_size_t | ,
|  | bool | reciprocal_alpha,
|  | bool | flip_sign_alpha,
|  | matrix_base< NumericT > const & | mat3,
|  | ScalarT2 const & | beta,
|  | vcl_size_t | ,
|  | bool | reciprocal_beta,
|  | bool | flip_sign_beta
| ) |  |

Definition at line 449 of file matrix_operations.hpp.

template<typename ScalarT1 , typename ScalarT2 , typename FactorT >

viennacl::enable_if< viennacl::is_scalar<ScalarT1>::value && viennacl::is_scalar<ScalarT2>::value && viennacl::is_any_scalar<FactorT>::value >::type viennacl::linalg::host_based::as | ( | ScalarT1 & | s1,
|  | ScalarT2 const & | s2,
|  | FactorT const & | alpha,
|  | vcl_size_t | ,
|  | bool | reciprocal_alpha,
|  | bool | flip_sign_alpha
| ) |  |

Definition at line 46 of file scalar_operations.hpp.

template<typename ScalarT1 , typename ScalarT2 , typename FactorT2 , typename ScalarT3 , typename FactorT3 >

viennacl::enable_if< viennacl::is_scalar<ScalarT1>::value && viennacl::is_scalar<ScalarT2>::value && viennacl::is_scalar<ScalarT3>::value && viennacl::is_any_scalar<FactorT2>::value && viennacl::is_any_scalar<FactorT3>::value >::type viennacl::linalg::host_based::asbs | ( | ScalarT1 & | s1,
|  | ScalarT2 const & | s2,
|  | FactorT2 const & | alpha,
|  | vcl_size_t | ,
|  | bool | reciprocal_alpha,
|  | bool | flip_sign_alpha,
|  | ScalarT3 const & | s3,
|  | FactorT3 const & | beta,
|  | vcl_size_t | ,
|  | bool | reciprocal_beta,
|  | bool | flip_sign_beta
| ) |  |

Definition at line 73 of file scalar_operations.hpp.

template<typename ScalarT1 , typename ScalarT2 , typename FactorT2 , typename ScalarT3 , typename FactorT3 >

viennacl::enable_if< viennacl::is_scalar<ScalarT1>::value && viennacl::is_scalar<ScalarT2>::value && viennacl::is_scalar<ScalarT3>::value && viennacl::is_any_scalar<FactorT2>::value && viennacl::is_any_scalar<FactorT3>::value >::type viennacl::linalg::host_based::asbs_s | ( | ScalarT1 & | s1,
|  | ScalarT2 const & | s2,
|  | FactorT2 const & | alpha,
|  | vcl_size_t | ,
|  | bool | reciprocal_alpha,
|  | bool | flip_sign_alpha,
|  | ScalarT3 const & | s3,
|  | FactorT3 const & | beta,
|  | vcl_size_t | ,
|  | bool | reciprocal_beta,
|  | bool | flip_sign_beta
| ) |  |

Definition at line 108 of file scalar_operations.hpp.

template<typename NumericT , typename ScalarT1 >

void viennacl::linalg::host_based::av | ( | vector_base< NumericT > & | vec1,
|  | vector_base< NumericT > const & | vec2,
|  | ScalarT1 const & | alpha,
|  | vcl_size_t | ,
|  | bool | reciprocal_alpha,
|  | bool | flip_sign_alpha
| ) |  |

Definition at line 88 of file vector_operations.hpp.

template<typename NumericT , typename ScalarT1 , typename ScalarT2 >

void viennacl::linalg::host_based::avbv | ( | vector_base< NumericT > & | vec1,
|  | vector_base< NumericT > const & | vec2,
|  | ScalarT1 const & | alpha,
|  | vcl_size_t | ,
|  | bool | reciprocal_alpha,
|  | bool | flip_sign_alpha,
|  | vector_base< NumericT > const & | vec3,
|  | ScalarT2 const & | beta,
|  | vcl_size_t | ,
|  | bool | reciprocal_beta,
|  | bool | flip_sign_beta
| ) |  |

Definition at line 127 of file vector_operations.hpp.

template<typename NumericT , typename ScalarT1 , typename ScalarT2 >

void viennacl::linalg::host_based::avbv_v | ( | vector_base< NumericT > & | vec1,
|  | vector_base< NumericT > const & | vec2,
|  | ScalarT1 const & | alpha,
|  | vcl_size_t | ,
|  | bool | reciprocal_alpha,
|  | bool | flip_sign_alpha,
|  | vector_base< NumericT > const & | vec3,
|  | ScalarT2 const & | beta,
|  | vcl_size_t | ,
|  | bool | reciprocal_beta,
|  | bool | flip_sign_beta
| ) |  |

Definition at line 197 of file vector_operations.hpp.

template<typename NumericT , typename VectorType >

void viennacl::linalg::host_based::bidiag_pack | ( | matrix_base< NumericT > & | A,
|  | VectorType & | dh,
|  | VectorType & | sh
| ) |  |

Definition at line 1722 of file matrix_operations.hpp.

template<typename NumericT , typename S1 >

void viennacl::linalg::host_based::bidiag_pack_impl | ( | matrix_base< NumericT > & | A,
|  | vector_base< S1 > & | D,
|  | vector_base< S1 > & | S
| ) |  |

This function stores the diagonal and the superdiagonal of a matrix in two vectors.

Parameters

  A | The matrix from which the vectors will be extracted of.
  D | The vector in which the diagonal of the matrix will be stored in.
  S | The vector in which the superdiagonal of the matrix will be stored in.

Definition at line 1661 of file matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::bluestein | ( | viennacl::vector< NumericT, AlignmentV > & | in,
|  | viennacl::vector< NumericT, AlignmentV > & | out,
|  | vcl_size_t |
| ) |  |

Bluestein's algorithm for computing Fourier transformation.

Currently, Works only for sizes of input data which less than 2^16. Uses a lot of additional memory, but should be fast for any size of data. Serial implementation has something about o(n * lg n) complexity

Definition at line 599 of file fft_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::complex_to_real | ( | viennacl::vector_base< NumericT > const & | in,
|  | viennacl::vector_base< NumericT > & | out,
|  | vcl_size_t | size
| ) |  |

Create real vector from complex vector (even elements(2*k) = real part, odd elements(2*k+1) = imaginary part)

Definition at line 818 of file fft_operations.hpp.

template<typename DestNumericT , typename SrcNumericT >

void viennacl::linalg::host_based::convert | ( | matrix_base< DestNumericT > & | mat1,
|  | matrix_base< SrcNumericT > const & | mat2
| ) |  |

Definition at line 58 of file matrix_operations.hpp.

template<typename DestNumericT , typename SrcNumericT >

void viennacl::linalg::host_based::convert | ( | vector_base< DestNumericT > & | dest,
|  | vector_base< SrcNumericT > const & | src
| ) |  |

Definition at line 68 of file vector_operations.hpp.

template<typename NumericT , typename S1 >

void viennacl::linalg::host_based::copy_vec | ( | matrix_base< NumericT > & | A,
|  | vector_base< S1 > & | V,
|  | vcl_size_t | row_start,
|  | vcl_size_t | col_start,
|  | bool | copy_col
| ) |  |

This function copies a row or a column from a matrix to a vector.

Parameters

  A | The matrix where to copy from.
  V | The vector to fill with data.
  row_start | The number of the first row to copy.
  col_start | The number of the first column to copy.
  copy_col | Set to TRUE to copy a column, FALSE to copy a row.

Definition at line 1983 of file matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::direct | ( | viennacl::vector< NumericT, AlignmentV > const & | in,
|  | viennacl::vector< NumericT, AlignmentV > & | out,
|  | vcl_size_t | size,
|  | vcl_size_t | stride,
|  | vcl_size_t | batch_num,
|  | NumericT | sign = `NumericT(-1)`,
|  | viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER | data_order = `viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR`
| ) |  |

Direct 1D algorithm for computing Fourier transformation.

Works on any sizes of data. Serial implementation has o(n^2) complexity

Definition at line 251 of file fft_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::direct | ( | viennacl::matrix< NumericT, viennacl::row_major, AlignmentV > const & | in,
|  | viennacl::matrix< NumericT, viennacl::row_major, AlignmentV > & | out,
|  | vcl_size_t | size,
|  | vcl_size_t | stride,
|  | vcl_size_t | batch_num,
|  | NumericT | sign = `NumericT(-1)`,
|  | viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER | data_order = `viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR`
| ) |  |

Direct 2D algorithm for computing Fourier transformation.

Works on any sizes of data. Serial implementation has o(n^2) complexity

Definition at line 274 of file fft_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::el_wise_mul_div | ( | NumericT * | matrix1,
|  | NumericT const * | matrix2,
|  | NumericT const * | matrix3,
|  | vcl_size_t | size
| ) |  |

Missing OpenMP kernel for nonnegative matrix factorization of a dense matrices.

Definition at line 132 of file nmf_operations.hpp.

template<typename NumericT , typename OpT >

void viennacl::linalg::host_based::element_op | ( | vector_base< NumericT > & | vec1,
|  | vector_expression< const vector_base< NumericT >, const vector_base< NumericT >, op_element_binary< OpT > > const & | proxy
| ) |  |

Implementation of the element-wise operation v1 = v2 .* v3 and v1 = v2 ./ v3 (using MATLAB syntax)

Parameters

  vec1 | The result vector (or -range, or -slice)
  proxy | The proxy object holding v2, v3 and the operation

Definition at line 336 of file vector_operations.hpp.

template<typename NumericT , typename OpT >

void viennacl::linalg::host_based::element_op | ( | vector_base< NumericT > & | vec1,
|  | vector_expression< const vector_base< NumericT >, const vector_base< NumericT >, op_element_unary< OpT > > const & | proxy
| ) |  |

Implementation of the element-wise operation v1 = v2 .* v3 and v1 = v2 ./ v3 (using MATLAB syntax)

Parameters

  vec1 | The result vector (or -range, or -slice)
  proxy | The proxy object holding v2, v3 and the operation

Definition at line 369 of file vector_operations.hpp.

template<typename NumericT , typename OpT >

void viennacl::linalg::host_based::element_op | ( | matrix_base< NumericT > & | A,
|  | matrix_expression< const matrix_base< NumericT >, const matrix_base< NumericT >, op_element_binary< OpT > > const & | proxy
| ) |  |

Implementation of the element-wise operations A = B .* C and A = B ./ C (using MATLAB syntax)

Parameters

  A | The result matrix (or -range, or -slice)
  proxy | The proxy object holding B, C, and the operation

Definition at line 848 of file matrix_operations.hpp.

template<typename NumericT , typename OpT >

void viennacl::linalg::host_based::element_op | ( | matrix_base< NumericT > & | A,
|  | matrix_expression< const matrix_base< NumericT >, const matrix_base< NumericT >, op_element_unary< OpT > > const & | proxy
| ) |  |

Definition at line 922 of file matrix_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::exclusive_scan | ( | vector_base< NumericT > const & | vec1,
|  | vector_base< NumericT > & | vec2
| ) |  |

This function implements an exclusive scan on the host using OpenMP.

Given an element vector (x_0, x_1, ..., x_{n-1}), this routine computes (0, x_0, x_0 + x_1, ..., x_0 + x_1 + ... + x_{n-2})

Parameters

  vec1 | Input vector: Gets overwritten by the routine.
  vec2 | The output vector. Either idential to vec1 or non-overlapping.

Definition at line 1176 of file vector_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::extract_L | ( | compressed_matrix< NumericT > const & | A,
|  | compressed_matrix< NumericT > & | L
| ) |  |

Definition at line 53 of file ilu_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::extract_LU | ( | compressed_matrix< NumericT > const & | A,
|  | compressed_matrix< NumericT > & | L,
|  | compressed_matrix< NumericT > & | U
| ) |  |

Definition at line 258 of file ilu_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::fft_direct | ( | std::complex< NumericT > * | input_complex,
|  | std::complex< NumericT > * | output,
|  | vcl_size_t | size,
|  | vcl_size_t | stride,
|  | vcl_size_t | batch_num,
|  | NumericT | sign,
|  | viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER | data_order = `viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR`
| ) |  |

Direct algoritm kenrnel.

Definition at line 205 of file fft_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::fft_radix2 | ( | std::complex< NumericT > * | input_complex,
|  | vcl_size_t | batch_num,
|  | vcl_size_t | bit_size,
|  | vcl_size_t | size,
|  | vcl_size_t | stride,
|  | NumericT | sign,
|  | viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER | data_order = `viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR`
| ) |  |

Radix-2 algorithm for computing Fourier transformation. Kernel for computing smaller amount of data.

Definition at line 389 of file fft_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::fft_radix2_local | ( | std::complex< NumericT > * | input_complex,
|  | std::complex< NumericT > * | lcl_input,
|  | vcl_size_t | batch_num,
|  | vcl_size_t | bit_size,
|  | vcl_size_t | size,
|  | vcl_size_t | stride,
|  | NumericT | sign,
|  | viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER | data_order = `viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR`
| ) |  |

Radix-2 algorithm for computing Fourier transformation. Kernel for computing bigger amount of data.

Definition at line 447 of file fft_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::givens_next | ( | matrix_base< NumericT > & | Q,
|  | vector_base< NumericT > & | tmp1,
|  | vector_base< NumericT > & | tmp2,
|  | int | l,
|  | int | m
| ) |  |

This function updates the matrix Q. It is part of the tql2 algorithm.

Parameters

  Q | The matrix to be updated.
  tmp1 | Vector with data from the tql2 algorithm.
  tmp2 | Vector with data from the tql2 algorithm.
  l | Data from the tql2 algorithm.
  m | Data from the tql2 algorithm.

Definition at line 1896 of file matrix_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::house_update_A_left | ( | matrix_base< NumericT > & | A,
|  | vector_base< NumericT > & | D,
|  | vcl_size_t | start
| ) |  |

This function applies a householder transformation to a matrix. A <- P * A with a householder reflection P.

Parameters

  A | The matrix to be updated.
  D | The normalized householder vector.
  start | The repetition counter.

Definition at line 1739 of file matrix_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::house_update_A_right | ( | matrix_base< NumericT > & | A,
|  | vector_base< NumericT > & | D
| ) |  |

This function applies a householder transformation to a matrix: A <- A * P with a householder reflection P.

Parameters

  A | The matrix to be updated.
  D | The normalized householder vector.

Definition at line 1804 of file matrix_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::house_update_QL | ( | matrix_base< NumericT > & | Q,
|  | vector_base< NumericT > & | D,
|  | vcl_size_t | A_size1
| ) |  |

This function updates the matrix Q, which is needed for the computation of the eigenvectors.

Parameters

  Q | The matrix to be updated.
  D | The householder vector.
  A_size1 | size1 of matrix A

Definition at line 1870 of file matrix_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::icc_chow_patel_sweep | ( | compressed_matrix< NumericT > & | L,
|  | vector< NumericT > & | aij_L
| ) |  |

Performs one nonlinear relaxation step in the Chow-Patel-ICC using OpenMP (cf. Algorithm 3 in paper, but for L rather than U)

Definition at line 185 of file ilu_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::icc_scale | ( | compressed_matrix< NumericT > const & | A,
|  | compressed_matrix< NumericT > & | L
| ) |  |

Scales the values extracted from A such that A' = DAD has unit diagonal. Updates values from A in L and U accordingly.

Definition at line 124 of file ilu_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::ilu_chow_patel_sweep | ( | compressed_matrix< NumericT > & | L,
|  | vector< NumericT > const & | aij_L,
|  | compressed_matrix< NumericT > & | U_trans,
|  | vector< NumericT > const & | aij_U_trans
| ) |  |

Performs one nonlinear relaxation step in the Chow-Patel-ILU using OpenMP (cf. Algorithm 2 in paper)

Definition at line 503 of file ilu_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::ilu_form_neumann_matrix | ( | compressed_matrix< NumericT > & | R,
|  | vector< NumericT > & | diag_R
| ) |  |

Definition at line 626 of file ilu_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::ilu_scale | ( | compressed_matrix< NumericT > const & | A,
|  | compressed_matrix< NumericT > & | L,
|  | compressed_matrix< NumericT > & | U
| ) |  |

Scales the values extracted from A such that A' = DAD has unit diagonal. Updates values from A in L and U accordingly.

Definition at line 349 of file ilu_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::ilu_transpose | ( | compressed_matrix< NumericT > const & | A,
|  | compressed_matrix< NumericT > & | B
| ) |  |

Definition at line 431 of file ilu_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::inclusive_scan | ( | vector_base< NumericT > const & | vec1,
|  | vector_base< NumericT > & | vec2
| ) |  |

This function implements an inclusive scan on the host using OpenMP.

Given an element vector (x_0, x_1, ..., x_{n-1}), this routine computes (x_0, x_0 + x_1, ..., x_0 + x_1 + ... + x_{n-1})

Parameters

  vec1 | Input vector: Gets overwritten by the routine.
  vec2 | The output vector. Either idential to vec1 or non-overlapping.

Definition at line 1161 of file vector_operations.hpp.

template<typename NumericT >

vcl_size_t viennacl::linalg::host_based::index_norm_inf | ( | vector_base< NumericT > const & | vec1 | ) |

Computes the index of the first entry that is equal to the supremum-norm in modulus.

Parameters

  vec1 | The vector

Returns
  The result. Note that the result must be a CPU scalar (unsigned int), since gpu scalars are floating point types.

Definition at line 831 of file vector_operations.hpp.

template<typename NumericT , typename ScalarT >

void viennacl::linalg::host_based::inner_prod_impl | ( | vector_base< NumericT > const & | vec1,
|  | vector_base< NumericT > const & | vec2,
|  | ScalarT & | result
| ) |  |

Computes the inner product of two vectors - implementation. Library users should call inner_prod(vec1, vec2).

Parameters

  vec1 | The first vector
  vec2 | The second vector
  result | The result scalar (on the gpu)

Definition at line 497 of file vector_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::inner_prod_impl | ( | vector_base< NumericT > const & | x,
|  | vector_tuple< NumericT > const & | vec_tuple,
|  | vector_base< NumericT > & | result
| ) |  |

Definition at line 518 of file vector_operations.hpp.

template<typename NumericT , typename SolverTagT >

void viennacl::linalg::host_based::inplace_solve | ( | matrix_base< NumericT > const & | A,
|  | matrix_base< NumericT > & | B,
|  | SolverTagT |
| ) |  |

Direct inplace solver for triangular systems with multiple right hand sides, i.e. A \ B (MATLAB notation)

Parameters

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

Definition at line 130 of file direct_solve.hpp.

template<typename NumericT , typename SolverTagT >

void viennacl::linalg::host_based::inplace_solve | ( | matrix_base< NumericT > const & | mat,
|  | vector_base< NumericT > & | vec,
|  | SolverTagT |
| ) |  |

Definition at line 266 of file direct_solve.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::inplace_solve | ( | compressed_matrix< NumericT, AlignmentV > const & | L,
|  | vector_base< NumericT > & | vec,
|  | viennacl::linalg::unit_lower_tag | tag
| ) |  |

Inplace solution of a lower triangular compressed_matrix with unit diagonal. Typically used for LU substitutions.

Parameters

  L | The matrix
  vec | The vector holding the right hand side. Is overwritten by the solution.
  tag | The solver tag identifying the respective triangular solver

Definition at line 613 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::inplace_solve | ( | compressed_matrix< NumericT, AlignmentV > const & | L,
|  | vector_base< NumericT > & | vec,
|  | viennacl::linalg::lower_tag | tag
| ) |  |

Inplace solution of a lower triangular compressed_matrix. Typically used for LU substitutions.

Parameters

  L | The matrix
  vec | The vector holding the right hand side. Is overwritten by the solution.
  tag | The solver tag identifying the respective triangular solver

Definition at line 632 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::inplace_solve | ( | compressed_matrix< NumericT, AlignmentV > const & | U,
|  | vector_base< NumericT > & | vec,
|  | viennacl::linalg::unit_upper_tag | tag
| ) |  |

Inplace solution of a upper triangular compressed_matrix with unit diagonal. Typically used for LU substitutions.

Parameters

  U | The matrix
  vec | The vector holding the right hand side. Is overwritten by the solution.
  tag | The solver tag identifying the respective triangular solver

Definition at line 652 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::inplace_solve | ( | compressed_matrix< NumericT, AlignmentV > const & | U,
|  | vector_base< NumericT > & | vec,
|  | viennacl::linalg::upper_tag | tag
| ) |  |

Inplace solution of a upper triangular compressed_matrix. Typically used for LU substitutions.

Parameters

  U | The matrix
  vec | The vector holding the right hand side. Is overwritten by the solution.
  tag | The solver tag identifying the respective triangular solver

Definition at line 671 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::inplace_solve | ( | matrix_expression< const compressed_matrix< NumericT, AlignmentV >, const compressed_matrix< NumericT, AlignmentV >, op_trans > const & | proxy,
|  | vector_base< NumericT > & | vec,
|  | viennacl::linalg::unit_lower_tag | tag
| ) |  |

Inplace solution of a lower triangular compressed_matrix with unit diagonal. Typically used for LU substitutions.

Parameters

  proxy | Proxy object for a transposed CSR-matrix
  vec | The right hand side vector
  tag | The solver tag identifying the respective triangular solver

Definition at line 968 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::inplace_solve | ( | matrix_expression< const compressed_matrix< NumericT, AlignmentV >, const compressed_matrix< NumericT, AlignmentV >, op_trans > const & | proxy,
|  | vector_base< NumericT > & | vec,
|  | viennacl::linalg::lower_tag | tag
| ) |  |

Inplace solution of a lower triangular compressed_matrix. Typically used for LU substitutions.

Parameters

  proxy | Proxy object for a transposed CSR-matrix
  vec | The right hand side vector
  tag | The solver tag identifying the respective triangular solver

Definition at line 989 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::inplace_solve | ( | matrix_expression< const compressed_matrix< NumericT, AlignmentV >, const compressed_matrix< NumericT, AlignmentV >, op_trans > const & | proxy,
|  | vector_base< NumericT > & | vec,
|  | viennacl::linalg::unit_upper_tag | tag
| ) |  |

Inplace solution of a upper triangular compressed_matrix with unit diagonal. Typically used for LU substitutions.

Parameters

  proxy | Proxy object for a transposed CSR-matrix
  vec | The right hand side vector
  tag | The solver tag identifying the respective triangular solver

Definition at line 1011 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::inplace_solve | ( | matrix_expression< const compressed_matrix< NumericT, AlignmentV >, const compressed_matrix< NumericT, AlignmentV >, op_trans > const & | proxy,
|  | vector_base< NumericT > & | vec,
|  | viennacl::linalg::upper_tag | tag
| ) |  |

Inplace solution of a upper triangular compressed_matrix with unit diagonal. Typically used for LU substitutions.

Parameters

  proxy | Proxy object for a transposed CSR-matrix
  vec | The right hand side vector
  tag | The solver tag identifying the respective triangular solver

Definition at line 1033 of file sparse_matrix_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::matrix_assign | ( | matrix_base< NumericT > & | mat,
|  | NumericT | s,
|  | bool | clear = `false`
| ) |  |

Definition at line 585 of file matrix_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::matrix_column | ( | const matrix_base< NumericT > & | mat,
|  | unsigned int | j,
|  | vector_base< NumericT > & | vec
| ) |  |

Definition at line 800 of file matrix_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::matrix_diag_from_vector | ( | const vector_base< NumericT > & | vec,
|  | int | k,
|  | matrix_base< NumericT > & | mat
| ) |  |

Definition at line 671 of file matrix_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::matrix_diag_to_vector | ( | const matrix_base< NumericT > & | mat,
|  | int | k,
|  | vector_base< NumericT > & | vec
| ) |  |

Definition at line 718 of file matrix_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::matrix_diagonal_assign | ( | matrix_base< NumericT > & | mat,
|  | NumericT | s
| ) |  |

Definition at line 632 of file matrix_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::matrix_row | ( | const matrix_base< NumericT > & | mat,
|  | unsigned int | i,
|  | vector_base< NumericT > & | vec
| ) |  |

Definition at line 763 of file matrix_operations.hpp.

template<typename NumericT , typename ScalarT >

void viennacl::linalg::host_based::max_impl | ( | vector_base< NumericT > const & | vec1,
|  | ScalarT & | result
| ) |  |

Computes the maximum of a vector.

Parameters

  vec1 | The vector
  result | The result scalar

Definition at line 891 of file vector_operations.hpp.

template<typename NumericT , typename ScalarT >

void viennacl::linalg::host_based::min_impl | ( | vector_base< NumericT > const & | vec1,
|  | ScalarT & | result
| ) |  |

Computes the minimum of a vector.

Parameters

  vec1 | The vector
  result | The result scalar

Definition at line 940 of file vector_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::multiply_complex | ( | viennacl::vector< NumericT, AlignmentV > const & | input1,
|  | viennacl::vector< NumericT, AlignmentV > const & | input2,
|  | viennacl::vector< NumericT, AlignmentV > & | output
| ) |  |

Complex multiplikation of two vectors.

Definition at line 697 of file fft_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::nmf | ( | viennacl::matrix_base< NumericT > const & | V,
|  | viennacl::matrix_base< NumericT > & | W,
|  | viennacl::matrix_base< NumericT > & | H,
|  | viennacl::linalg::nmf_config const & | conf
| ) |  |

The nonnegative matrix factorization (approximation) algorithm as suggested by Lee and Seung. Factorizes a matrix V with nonnegative entries into matrices W and H such that ||V - W*H|| is minimized.

Parameters

  V | Input matrix
  W | First factor
  H | Second factor
  conf | A configuration object holding tolerances and the like

Definition at line 156 of file nmf_operations.hpp.

template<typename NumericT , typename ScalarT >

void viennacl::linalg::host_based::norm_1_impl | ( | vector_base< NumericT > const & | vec1,
|  | ScalarT & | result
| ) |  |

Computes the l^1-norm of a vector.

Parameters

  vec1 | The vector
  result | The result scalar

Definition at line 648 of file vector_operations.hpp.

template<typename NumericT , typename ScalarT >

void viennacl::linalg::host_based::norm_2_impl | ( | vector_base< NumericT > const & | vec1,
|  | ScalarT & | result
| ) |  |

Computes the l^2-norm of a vector - implementation.

Parameters

  vec1 | The vector
  result | The result scalar

Definition at line 761 of file vector_operations.hpp.

template<typename NumericT , typename ScalarT >

void viennacl::linalg::host_based::norm_inf_impl | ( | vector_base< NumericT > const & | vec1,
|  | ScalarT & | result
| ) |  |

Computes the supremum-norm of a vector.

Parameters

  vec1 | The vector
  result | The result scalar

Definition at line 781 of file vector_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::normalize | ( | viennacl::vector< NumericT, AlignmentV > & | input | ) |

Normalize vector with his own size.

Definition at line 684 of file fft_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::pipelined_bicgstab_prod | ( | compressed_matrix< NumericT > const & | A,
|  | vector_base< NumericT > const & | p,
|  | vector_base< NumericT > & | Ap,
|  | vector_base< NumericT > const & | r0star,
|  | vector_base< NumericT > & | inner_prod_buffer,
|  | vcl_size_t | buffer_chunk_size,
|  | vcl_size_t | buffer_chunk_offset
| ) |  |

Performs a fused matrix-vector product with a compressed_matrix for an efficient pipelined BiCGStab algorithm.

This routines computes for a matrix A and vectors 'p', 'Ap', and 'r0': Ap = prod(A, p); and computes the two reduction stages for computing inner_prod(p,Ap), inner_prod(Ap,Ap), inner_prod(Ap, r0)

Definition at line 607 of file iterative_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::pipelined_bicgstab_prod | ( | coordinate_matrix< NumericT > const & | A,
|  | vector_base< NumericT > const & | p,
|  | vector_base< NumericT > & | Ap,
|  | vector_base< NumericT > const & | r0star,
|  | vector_base< NumericT > & | inner_prod_buffer,
|  | vcl_size_t | buffer_chunk_size,
|  | vcl_size_t | buffer_chunk_offset
| ) |  |

Performs a fused matrix-vector product with a coordinate_matrix for an efficient pipelined BiCGStab algorithm.

This routines computes for a matrix A and vectors 'p', 'Ap', and 'r0': Ap = prod(A, p); and computes the two reduction stages for computing inner_prod(p,Ap), inner_prod(Ap,Ap), inner_prod(Ap, r0)

Definition at line 627 of file iterative_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::pipelined_bicgstab_prod | ( | ell_matrix< NumericT > const & | A,
|  | vector_base< NumericT > const & | p,
|  | vector_base< NumericT > & | Ap,
|  | vector_base< NumericT > const & | r0star,
|  | vector_base< NumericT > & | inner_prod_buffer,
|  | vcl_size_t | buffer_chunk_size,
|  | vcl_size_t | buffer_chunk_offset
| ) |  |

Performs a fused matrix-vector product with an ell_matrix for an efficient pipelined BiCGStab algorithm.

This routines computes for a matrix A and vectors 'p', 'Ap', and 'r0': Ap = prod(A, p); and computes the two reduction stages for computing inner_prod(p,Ap), inner_prod(Ap,Ap), inner_prod(Ap, r0)

Definition at line 647 of file iterative_operations.hpp.

template<typename NumericT , typename IndexT >

void viennacl::linalg::host_based::pipelined_bicgstab_prod | ( | sliced_ell_matrix< NumericT, IndexT > const & | A,
|  | vector_base< NumericT > const & | p,
|  | vector_base< NumericT > & | Ap,
|  | vector_base< NumericT > const & | r0star,
|  | vector_base< NumericT > & | inner_prod_buffer,
|  | vcl_size_t | buffer_chunk_size,
|  | vcl_size_t | buffer_chunk_offset
| ) |  |

Performs a fused matrix-vector product with a sliced_ell_matrix for an efficient pipelined BiCGStab algorithm.

This routines computes for a matrix A and vectors 'p', 'Ap', and 'r0': Ap = prod(A, p); and computes the two reduction stages for computing inner_prod(p,Ap), inner_prod(Ap,Ap), inner_prod(Ap, r0)

Definition at line 667 of file iterative_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::pipelined_bicgstab_prod | ( | hyb_matrix< NumericT > const & | A,
|  | vector_base< NumericT > const & | p,
|  | vector_base< NumericT > & | Ap,
|  | vector_base< NumericT > const & | r0star,
|  | vector_base< NumericT > & | inner_prod_buffer,
|  | vcl_size_t | buffer_chunk_size,
|  | vcl_size_t | buffer_chunk_offset
| ) |  |

Performs a fused matrix-vector product with a hyb_matrix for an efficient pipelined BiCGStab algorithm.

This routines computes for a matrix A and vectors 'p', 'Ap', and 'r0': Ap = prod(A, p); and computes the two reduction stages for computing inner_prod(p,Ap), inner_prod(Ap,Ap), inner_prod(Ap, r0)

Definition at line 687 of file iterative_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::pipelined_bicgstab_update_s | ( | vector_base< NumericT > & | s,
|  | vector_base< NumericT > & | r,
|  | vector_base< NumericT > const & | Ap,
|  | vector_base< NumericT > & | inner_prod_buffer,
|  | vcl_size_t | buffer_chunk_size,
|  | vcl_size_t | buffer_chunk_offset
| ) |  |

Performs a joint vector update operation needed for an efficient pipelined BiCGStab algorithm.

This routines computes for vectors 's', 'r', 'Ap': s = r - alpha * Ap with alpha obtained from a reduction step on the 0th and the 3rd out of 6 chunks in inner_prod_buffer and runs the parallel reduction stage for computing inner_prod(s,s)

Definition at line 504 of file iterative_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::pipelined_bicgstab_vector_update | ( | vector_base< NumericT > & | result,
|  | NumericT | alpha,
|  | vector_base< NumericT > & | p,
|  | NumericT | omega,
|  | vector_base< NumericT > const & | s,
|  | vector_base< NumericT > & | residual,
|  | vector_base< NumericT > const & | As,
|  | NumericT | beta,
|  | vector_base< NumericT > const & | Ap,
|  | vector_base< NumericT > const & | r0star,
|  | vector_base< NumericT > & | inner_prod_buffer,
|  | vcl_size_t | buffer_chunk_size
| ) |  |

Performs a joint vector update operation needed for an efficient pipelined BiCGStab algorithm.

x_{j+1} = x_j + alpha * p_j + omega * s_j r_{j+1} = s_j - omega * t_j p_{j+1} = r_{j+1} + beta * (p_j - omega * q_j) and compute first stage of r_dot_r0 = <r_{j+1}, r_o^*> for use in next iteration

Definition at line 554 of file iterative_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::pipelined_cg_prod | ( | compressed_matrix< NumericT > const & | A,
|  | vector_base< NumericT > const & | p,
|  | vector_base< NumericT > & | Ap,
|  | vector_base< NumericT > & | inner_prod_buffer
| ) |  |

Performs a fused matrix-vector product with a compressed_matrix for an efficient pipelined CG algorithm.

This routines computes for a matrix A and vectors 'p' and 'Ap': Ap = prod(A, p); and computes the two reduction stages for computing inner_prod(p,Ap), inner_prod(Ap,Ap)

Definition at line 413 of file iterative_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::pipelined_cg_prod | ( | coordinate_matrix< NumericT > const & | A,
|  | vector_base< NumericT > const & | p,
|  | vector_base< NumericT > & | Ap,
|  | vector_base< NumericT > & | inner_prod_buffer
| ) |  |

Performs a fused matrix-vector product with a coordinate_matrix for an efficient pipelined CG algorithm.

This routines computes for a matrix A and vectors 'p' and 'Ap': Ap = prod(A, p); and computes the two reduction stages for computing inner_prod(p,Ap), inner_prod(Ap,Ap)

Definition at line 431 of file iterative_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::pipelined_cg_prod | ( | ell_matrix< NumericT > const & | A,
|  | vector_base< NumericT > const & | p,
|  | vector_base< NumericT > & | Ap,
|  | vector_base< NumericT > & | inner_prod_buffer
| ) |  |

Performs a fused matrix-vector product with an ell_matrix for an efficient pipelined CG algorithm.

This routines computes for a matrix A and vectors 'p' and 'Ap': Ap = prod(A, p); and computes the two reduction stages for computing inner_prod(p,Ap), inner_prod(Ap,Ap)

Definition at line 448 of file iterative_operations.hpp.

template<typename NumericT , typename IndexT >

void viennacl::linalg::host_based::pipelined_cg_prod | ( | sliced_ell_matrix< NumericT, IndexT > const & | A,
|  | vector_base< NumericT > const & | p,
|  | vector_base< NumericT > & | Ap,
|  | vector_base< NumericT > & | inner_prod_buffer
| ) |  |

Performs a fused matrix-vector product with an sliced_ell_matrix for an efficient pipelined CG algorithm.

This routines computes for a matrix A and vectors 'p' and 'Ap': Ap = prod(A, p); and computes the two reduction stages for computing inner_prod(p,Ap), inner_prod(Ap,Ap)

Definition at line 465 of file iterative_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::pipelined_cg_prod | ( | hyb_matrix< NumericT > const & | A,
|  | vector_base< NumericT > const & | p,
|  | vector_base< NumericT > & | Ap,
|  | vector_base< NumericT > & | inner_prod_buffer
| ) |  |

Performs a fused matrix-vector product with an hyb_matrix for an efficient pipelined CG algorithm.

This routines computes for a matrix A and vectors 'p' and 'Ap': Ap = prod(A, p); and computes the two reduction stages for computing inner_prod(p,Ap), inner_prod(Ap,Ap)

Definition at line 484 of file iterative_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::pipelined_cg_vector_update | ( | vector_base< NumericT > & | result,
|  | NumericT | alpha,
|  | vector_base< NumericT > & | p,
|  | vector_base< NumericT > & | r,
|  | vector_base< NumericT > const & | Ap,
|  | NumericT | beta,
|  | vector_base< NumericT > & | inner_prod_buffer
| ) |  |

Performs a joint vector update operation needed for an efficient pipelined CG algorithm.

This routines computes for vectors 'result', 'p', 'r', 'Ap': result += alpha * p; r -= alpha * Ap; p = r + beta * p; and runs the parallel reduction stage for computing inner_prod(r,r)

Definition at line 367 of file iterative_operations.hpp.

template<typename T >

void viennacl::linalg::host_based::pipelined_gmres_gram_schmidt_stage1 | ( | vector_base< T > const & | device_krylov_basis,
|  | vcl_size_t | v_k_size,
|  | vcl_size_t | v_k_internal_size,
|  | vcl_size_t | k,
|  | vector_base< T > & | vi_in_vk_buffer,
|  | vcl_size_t | buffer_chunk_size
| ) |  |

Computes first reduction stage for multiple inner products <v_i, v_k>, i=0..k-1.

All vectors v_i are stored column-major in the array 'device_krylov_basis', where each vector has an actual length 'v_k_size', but might be padded to have 'v_k_internal_size'

Definition at line 760 of file iterative_operations.hpp.

template<typename T >

void viennacl::linalg::host_based::pipelined_gmres_gram_schmidt_stage2 | ( | vector_base< T > & | device_krylov_basis,
|  | vcl_size_t | v_k_size,
|  | vcl_size_t | v_k_internal_size,
|  | vcl_size_t | k,
|  | vector_base< T > const & | vi_in_vk_buffer,
|  | vector_base< T > & | R_buffer,
|  | vcl_size_t | krylov_dim,
|  | vector_base< T > & | inner_prod_buffer,
|  | vcl_size_t | buffer_chunk_size
| ) |  |

Computes the second reduction stage for multiple inner products <v_i, v_k>, i=0..k-1, then updates v_k -= <v_i, v_k> v_i and computes the first reduction stage for ||v_k||.

All vectors v_i are stored column-major in the array 'device_krylov_basis', where each vector has an actual length 'v_k_size', but might be padded to have 'v_k_internal_size'

Definition at line 792 of file iterative_operations.hpp.

template<typename T >

void viennacl::linalg::host_based::pipelined_gmres_normalize_vk | ( | vector_base< T > & | v_k,
|  | vector_base< T > const & | residual,
|  | vector_base< T > & | R_buffer,
|  | vcl_size_t | offset_in_R,
|  | vector_base< T > const & | inner_prod_buffer,
|  | vector_base< T > & | r_dot_vk_buffer,
|  | vcl_size_t | buffer_chunk_size,
|  | vcl_size_t | buffer_chunk_offset
| ) |  |

Performs a vector normalization needed for an efficient pipelined GMRES algorithm.

This routines computes for vectors 'r', 'v_k': Second reduction step for ||v_k|| v_k /= ||v_k|| First reduction step for <r, v_k>

Definition at line 711 of file iterative_operations.hpp.

template<typename MatrixType , typename T >

void viennacl::linalg::host_based::pipelined_gmres_prod | ( | MatrixType const & | A,
|  | vector_base< T > const & | p,
|  | vector_base< T > & | Ap,
|  | vector_base< T > & | inner_prod_buffer
| ) |  |

Definition at line 866 of file iterative_operations.hpp.

template<typename T >

void viennacl::linalg::host_based::pipelined_gmres_update_result | ( | vector_base< T > & | result,
|  | vector_base< T > const & | residual,
|  | vector_base< T > const & | krylov_basis,
|  | vcl_size_t | v_k_size,
|  | vcl_size_t | v_k_internal_size,
|  | vector_base< T > const & | coefficients,
|  | vcl_size_t | k
| ) |  |

Computes x += eta_0 r + sum_{i=1}^{k-1} eta_i v_{i-1}.

Definition at line 836 of file iterative_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::plane_rotation | ( | vector_base< NumericT > & | vec1,
|  | vector_base< NumericT > & | vec2,
|  | NumericT | alpha,
|  | NumericT | beta
| ) |  |

Computes a plane rotation of two vectors.

Computes (x,y) <- (alpha * x + beta * y, -beta * x + alpha * y)

Parameters

  vec1 | The first vector
  vec2 | The second vector
  alpha | The first transformation coefficient
  beta | The second transformation coefficient

Definition at line 1020 of file vector_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::prod_impl | ( | const viennacl::compressed_matrix< NumericT, AlignmentV > & | mat,
|  | const viennacl::vector_base< NumericT > & | vec,
|  | NumericT | alpha,
|  | viennacl::vector_base< NumericT > & | result,
|  | NumericT | beta
| ) |  |

Carries out matrix-vector multiplication with a compressed_matrix.

Implementation of the convenience expression result = prod(mat, vec);

Parameters

  mat | The matrix
  vec | The vector
  result | The result vector

Definition at line 111 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::prod_impl | ( | const viennacl::compressed_matrix< NumericT, AlignmentV > & | sp_mat,
|  | const viennacl::matrix_base< NumericT > & | d_mat,
|  | viennacl::matrix_base< NumericT > & | result
| ) |  |

Carries out sparse_matrix-matrix multiplication first matrix being compressed.

Implementation of the convenience expression result = prod(sp_mat, d_mat);

Parameters

  sp_mat | The sparse matrix
  d_mat | The dense matrix
  result | The result matrix

Definition at line 153 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::prod_impl | ( | const viennacl::compressed_matrix< NumericT, AlignmentV > & | sp_mat,
|  | const viennacl::matrix_expression< const viennacl::matrix_base< NumericT >, const viennacl::matrix_base< NumericT >, viennacl::op_trans > & | d_mat,
|  | viennacl::matrix_base< NumericT > & | result
| ) |  |

Carries out matrix-trans(matrix) multiplication first matrix being compressed and the second transposed.

Implementation of the convenience expression result = prod(sp_mat, trans(d_mat));

Parameters

  sp_mat | The sparse matrix
  d_mat | The transposed dense matrix
  result | The result matrix

Definition at line 239 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::prod_impl | ( | viennacl::compressed_matrix< NumericT, AlignmentV > const & | A,
|  | viennacl::compressed_matrix< NumericT, AlignmentV > const & | B,
|  | viennacl::compressed_matrix< NumericT, AlignmentV > & | C
| ) |  |

Carries out sparse_matrix-sparse_matrix multiplication for CSR matrices.

Implementation of the convenience expression C = prod(A, B); Based on computing C(i, :) = A(i, :) * B via merging the respective rows of B

Parameters

  A | Left factor
  B | Right factor
  C | Result matrix

Definition at line 328 of file sparse_matrix_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::prod_impl | ( | const matrix_base< NumericT > & | mat,
|  | bool | trans,
|  | const vector_base< NumericT > & | vec,
|  | vector_base< NumericT > & | result
| ) |  |

Carries out matrix-vector multiplication.

Implementation of the convenience expression result = prod(mat, vec);

Parameters

  mat | The matrix
  trans | Flag whether mat is to be transposed
  vec | The vector
  result | The result vector

Definition at line 993 of file matrix_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::prod_impl | ( | const viennacl::compressed_compressed_matrix< NumericT > & | mat,
|  | const viennacl::vector_base< NumericT > & | vec,
|  | NumericT | alpha,
|  | viennacl::vector_base< NumericT > & | result,
|  | NumericT | beta
| ) |  |

Carries out matrix-vector multiplication with a compressed_matrix.

Implementation of the convenience expression result = prod(mat, vec);

Parameters

  mat | The matrix
  vec | The vector
  result | The result vector

Definition at line 1062 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::prod_impl | ( | const viennacl::coordinate_matrix< NumericT, AlignmentV > & | mat,
|  | const viennacl::vector_base< NumericT > & | vec,
|  | NumericT | alpha,
|  | viennacl::vector_base< NumericT > & | result,
|  | NumericT | beta
| ) |  |

Carries out matrix-vector multiplication with a coordinate_matrix.

Implementation of the convenience expression result = prod(mat, vec);

Parameters

  mat | The matrix
  vec | The vector
  result | The result vector

Definition at line 1178 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::prod_impl | ( | const viennacl::coordinate_matrix< NumericT, AlignmentV > & | sp_mat,
|  | const viennacl::matrix_base< NumericT > & | d_mat,
|  | viennacl::matrix_base< NumericT > & | result
| ) |  |

Carries out Compressed Matrix(COO)-Dense Matrix multiplication.

Implementation of the convenience expression result = prod(sp_mat, d_mat);

Parameters

  sp_mat | The Sparse Matrix (Coordinate format)
  d_mat | The Dense Matrix
  result | The Result Matrix

Definition at line 1214 of file sparse_matrix_operations.hpp.

template<typename NumericT , typename ScalarT1 , typename ScalarT2 >

void viennacl::linalg::host_based::prod_impl | ( | const matrix_base< NumericT > & | A,
|  | bool | trans_A,
|  | const matrix_base< NumericT > & | B,
|  | bool | trans_B,
|  | matrix_base< NumericT > & | C,
|  | ScalarT1 | alpha,
|  | ScalarT2 | beta
| ) |  |

Carries out matrix-matrix multiplication.

Implementation of C = prod(A, B);

Definition at line 1239 of file matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::prod_impl | ( | const viennacl::coordinate_matrix< NumericT, AlignmentV > & | sp_mat,
|  | const viennacl::matrix_expression< const viennacl::matrix_base< NumericT >, const viennacl::matrix_base< NumericT >, viennacl::op_trans > & | d_mat,
|  | viennacl::matrix_base< NumericT > & | result
| ) |  |

Carries out Compressed Matrix(COO)-Dense Transposed Matrix multiplication.

Implementation of the convenience expression result = prod(sp_mat, trans(d_mat));

Parameters

  sp_mat | The Sparse Matrix (Coordinate format)
  d_mat | The Dense Transposed Matrix
  result | The Result Matrix

Definition at line 1328 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::prod_impl | ( | const viennacl::ell_matrix< NumericT, AlignmentV > & | mat,
|  | const viennacl::vector_base< NumericT > & | vec,
|  | NumericT | alpha,
|  | viennacl::vector_base< NumericT > & | result,
|  | NumericT | beta
| ) |  |

Carries out matrix-vector multiplication with a ell_matrix.

Implementation of the convenience expression result = prod(mat, vec);

Parameters

  mat | The matrix
  vec | The vector
  result | The result vector

Definition at line 1459 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::prod_impl | ( | const viennacl::ell_matrix< NumericT, AlignmentV > & | sp_mat,
|  | const viennacl::matrix_base< NumericT > & | d_mat,
|  | viennacl::matrix_base< NumericT > & | result
| ) |  |

Carries out ell_matrix-d_matrix multiplication.

Implementation of the convenience expression result = prod(sp_mat, d_mat);

Parameters

  sp_mat | The sparse(ELL) matrix
  d_mat | The dense matrix
  result | The result dense matrix

Definition at line 1505 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::prod_impl | ( | const viennacl::ell_matrix< NumericT, AlignmentV > & | sp_mat,
|  | const viennacl::matrix_expression< const viennacl::matrix_base< NumericT >, const viennacl::matrix_base< NumericT >, viennacl::op_trans > & | d_mat,
|  | viennacl::matrix_base< NumericT > & | result
| ) |  |

Carries out matrix-trans(matrix) multiplication first matrix being sparse ell and the second dense transposed.

Implementation of the convenience expression result = prod(sp_mat, trans(d_mat));

Parameters

  sp_mat | The sparse matrix
  d_mat | The transposed dense matrix
  result | The result matrix

Definition at line 1627 of file sparse_matrix_operations.hpp.

template<typename NumericT , typename IndexT >

void viennacl::linalg::host_based::prod_impl | ( | const viennacl::sliced_ell_matrix< NumericT, IndexT > & | mat,
|  | const viennacl::vector_base< NumericT > & | vec,
|  | NumericT | alpha,
|  | viennacl::vector_base< NumericT > & | result,
|  | NumericT | beta
| ) |  |

Carries out matrix-vector multiplication with a sliced_ell_matrix.

Implementation of the convenience expression result = prod(mat, vec);

Parameters

  mat | The matrix
  vec | The vector
  result | The result vector

Definition at line 1753 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::prod_impl | ( | const viennacl::hyb_matrix< NumericT, AlignmentV > & | mat,
|  | const viennacl::vector_base< NumericT > & | vec,
|  | NumericT | alpha,
|  | viennacl::vector_base< NumericT > & | result,
|  | NumericT | beta
| ) |  |

Carries out matrix-vector multiplication with a hyb_matrix.

Implementation of the convenience expression result = prod(mat, vec);

Parameters

  mat | The matrix
  vec | The vector
  result | The result vector

Definition at line 1829 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::prod_impl | ( | const viennacl::hyb_matrix< NumericT, AlignmentV > & | mat,
|  | const viennacl::matrix_base< NumericT > & | d_mat,
|  | viennacl::matrix_base< NumericT > & | result
| ) |  |

Carries out sparse-matrix-dense-matrix multiplication with a hyb_matrix.

Implementation of the convenience expression C = prod(A, B);

Parameters

  mat | The sparse matrix A
  d_mat | The dense matrix B
  result | The dense result matrix C

Definition at line 1897 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::prod_impl | ( | const viennacl::hyb_matrix< NumericT, AlignmentV > & | mat,
|  | const viennacl::matrix_expression< const viennacl::matrix_base< NumericT >, const viennacl::matrix_base< NumericT >, viennacl::op_trans > & | d_mat,
|  | viennacl::matrix_base< NumericT > & | result
| ) |  |

Carries out sparse-matrix-transposed-dense-matrix multiplication with a hyb_matrix.

Implementation of the convenience expression C = prod(A, trans(B));

Parameters

  mat | The sparse matrix A
  d_mat | The dense matrix B
  result | The dense result matrix C

Definition at line 1990 of file sparse_matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::radix2 | ( | viennacl::vector< NumericT, AlignmentV > & | in,
|  | vcl_size_t | size,
|  | vcl_size_t | stride,
|  | vcl_size_t | batch_num,
|  | NumericT | sign = `NumericT(-1)`,
|  | viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER | data_order = `viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR`
| ) |  |

Radix-2 1D algorithm for computing Fourier transformation.

Works only on power-of-two sizes of data. Serial implementation has o(n * lg n) complexity. This is a Cooley-Tukey algorithm

Definition at line 525 of file fft_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::radix2 | ( | viennacl::matrix< NumericT, viennacl::row_major, AlignmentV > & | in,
|  | vcl_size_t | size,
|  | vcl_size_t | stride,
|  | vcl_size_t | batch_num,
|  | NumericT | sign = `NumericT(-1)`,
|  | viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER | data_order = `viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR`
| ) |  |

Radix-2 2D algorithm for computing Fourier transformation.

Works only on power-of-two sizes of data. Serial implementation has o(n * lg n) complexity. This is a Cooley-Tukey algorithm

Definition at line 558 of file fft_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::real_to_complex | ( | viennacl::vector_base< NumericT > const & | in,
|  | viennacl::vector_base< NumericT > & | out,
|  | vcl_size_t | size
| ) |  |

Create complex vector from real vector (even elements(2*k) = real part, odd elements(2*k+1) = imaginary part)

Definition at line 797 of file fft_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::reorder | ( | viennacl::vector< NumericT, AlignmentV > & | in,
|  | vcl_size_t | size,
|  | vcl_size_t | stride,
|  | vcl_size_t | bits_datasize,
|  | vcl_size_t | batch_num,
|  | viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER | data_order = `viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR`
| ) |  |

Definition at line 302 of file fft_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::reorder | ( | viennacl::matrix< NumericT, viennacl::row_major, AlignmentV > & | in,
|  | vcl_size_t | size,
|  | vcl_size_t | stride,
|  | vcl_size_t | bits_datasize,
|  | vcl_size_t | batch_num,
|  | viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::DATA_ORDER | data_order = `viennacl::linalg::host_based::detail::fft::FFT_DATA_ORDER::ROW_MAJOR`
| ) |  |

Definition at line 342 of file fft_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::reverse | ( | viennacl::vector_base< NumericT > & | in | ) |

Reverse vector to opposite order and save it in input vector.

Definition at line 835 of file fft_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::row_C_scan_numeric_vector | ( | unsigned int | row_start_A,
|  | unsigned int | row_end_A,
|  | unsigned int const * | A_col_buffer,
|  | NumericT const * | A_elements,
|  | unsigned int const * | B_row_buffer,
|  | unsigned int const * | B_col_buffer,
|  | NumericT const * | B_elements,
|  | unsigned int | B_size2,
|  | unsigned int | row_start_C,
|  | unsigned int | row_end_C,
|  | unsigned int * | C_col_buffer,
|  | NumericT * | C_elements,
|  | unsigned int * | row_C_vector_1,
|  | NumericT * | row_C_vector_1_values,
|  | unsigned int * | row_C_vector_2,
|  | NumericT * | row_C_vector_2_values,
|  | unsigned int * | row_C_vector_3,
|  | NumericT * | row_C_vector_3_values
| ) |  |

Definition at line 567 of file spgemm_vector.hpp.

template<typename NumericT >

unsigned int viennacl::linalg::host_based::row_C_scan_numeric_vector_1 | ( | unsigned int const * | input1_index_begin,
|  | unsigned int const * | input1_index_end,
|  | NumericT const * | input1_values_begin,
|  | NumericT | factor1,
|  | unsigned int const * | input2_index_begin,
|  | unsigned int const * | input2_index_end,
|  | NumericT const * | input2_values_begin,
|  | NumericT | factor2,
|  | unsigned int | termination_index,
|  | unsigned int * | output_index_begin,
|  | NumericT * | output_values_begin
| ) |  |

Definition at line 520 of file spgemm_vector.hpp.

template<unsigned int IndexNum, typename NumericT >

unsigned int viennacl::linalg::host_based::row_C_scan_numeric_vector_N | ( | unsigned int const * | row_indices_B,
|  | NumericT const * | val_A,
|  | unsigned int const * | B_row_buffer,
|  | unsigned int const * | B_col_buffer,
|  | NumericT const * | B_elements,
|  | unsigned int | B_size2,
|  | unsigned int const * | row_C_vector_input,
|  | unsigned int const * | row_C_vector_input_end,
|  | NumericT * | row_C_vector_input_values,
|  | unsigned int * | row_C_vector_output,
|  | NumericT * | row_C_vector_output_values
| ) |  |

Merges up to IndexNum rows from B into the result buffer.

Because the input buffer also needs to be considered, this routine actually works on an index front of length (IndexNum+1)

Definition at line 327 of file spgemm_vector.hpp.

unsigned int viennacl::linalg::host_based::row_C_scan_symbolic_vector | ( | unsigned int | row_start_A,
|  | unsigned int | row_end_A,
|  | unsigned int const * | A_col_buffer,
|  | unsigned int const * | B_row_buffer,
|  | unsigned int const * | B_col_buffer,
|  | unsigned int | B_size2,
|  | unsigned int * | row_C_vector_1,
|  | unsigned int * | row_C_vector_2,
|  | unsigned int * | row_C_vector_3
| ) |  |

inline

Definition at line 206 of file spgemm_vector.hpp.

template<typename OutputWriterT >

unsigned int viennacl::linalg::host_based::row_C_scan_symbolic_vector_1 | ( | unsigned int const * | input1_begin,
|  | unsigned int const * | input1_end,
|  | unsigned int const * | input2_begin,
|  | unsigned int const * | input2_end,
|  | unsigned int | termination_index,
|  | unsigned int * | output_begin
| ) |  |

Definition at line 169 of file spgemm_vector.hpp.

template<unsigned int IndexNum>

unsigned int viennacl::linalg::host_based::row_C_scan_symbolic_vector_N | ( | unsigned int const * | row_indices_B,
|  | unsigned int const * | B_row_buffer,
|  | unsigned int const * | B_col_buffer,
|  | unsigned int | B_size2,
|  | unsigned int const * | row_C_vector_input,
|  | unsigned int const * | row_C_vector_input_end,
|  | unsigned int * | row_C_vector_output
| ) |  |

Merges up to IndexNum rows from B into the result buffer.

Because the input buffer also needs to be considered, this routine actually works on an index front of length (IndexNum+1)

Definition at line 113 of file spgemm_vector.hpp.

template<typename NumericT , typename ScalarT >

void viennacl::linalg::host_based::scaled_rank_1_update | ( | matrix_base< NumericT > & | mat1,
|  | ScalarT const & | alpha,
|  | vcl_size_t | ,
|  | bool | reciprocal_alpha,
|  | bool | flip_sign_alpha,
|  | const vector_base< NumericT > & | vec1,
|  | const vector_base< NumericT > & | vec2
| ) |  |

The implementation of the operation mat += alpha * vec1 * vec2^T, i.e. a scaled rank 1 update.

Implementation of the convenience expression result += alpha * outer_prod(vec1, vec2);

Parameters

  mat1 | The matrix to be updated
  alpha | The scaling factor (either a viennacl::scalar<>, float, or double)
  reciprocal_alpha | Use 1/alpha instead of alpha
  flip_sign_alpha | Use -alpha instead of alpha
  vec1 | The first vector
  vec2 | The second vector

Definition at line 1566 of file matrix_operations.hpp.

template<typename NumericT , typename ScalarT >

void viennacl::linalg::host_based::sum_impl | ( | vector_base< NumericT > const & | vec1,
|  | ScalarT & | result
| ) |  |

Computes the sum of all elements from the vector.

Parameters

  vec1 | The vector
  result | The result scalar

Definition at line 989 of file vector_operations.hpp.

template<typename ScalarT1 , typename ScalarT2 >

viennacl::enable_if< viennacl::is_scalar<ScalarT1>::value && viennacl::is_scalar<ScalarT2>::value >::type viennacl::linalg::host_based::swap | ( | ScalarT1 & | s1,
|  | ScalarT2 & | s2
| ) |  |

Swaps the contents of two scalars, data is copied.

Parameters

  s1 | The first scalar
  s2 | The second scalar

Definition at line 143 of file scalar_operations.hpp.

template<typename NumericT , typename SizeT , typename DistanceT >

void viennacl::linalg::host_based::trans | ( | const matrix_expression< const matrix_base< NumericT, SizeT, DistanceT >, const matrix_base< NumericT, SizeT, DistanceT >, op_trans > & | proxy,
|  | matrix_base< NumericT > & | temp_trans
| ) |  |

Definition at line 111 of file matrix_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::transpose | ( | viennacl::matrix< NumericT, viennacl::row_major, AlignmentV > & | input | ) |

Inplace transpose of matrix.

Definition at line 727 of file fft_operations.hpp.

template<typename NumericT , unsigned int AlignmentV>

void viennacl::linalg::host_based::transpose | ( | viennacl::matrix< NumericT, viennacl::row_major, AlignmentV > const & | input,
|  | viennacl::matrix< NumericT, viennacl::row_major, AlignmentV > & | output
| ) |  |

Transpose matrix.

Definition at line 764 of file fft_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::vector_assign | ( | vector_base< NumericT > & | vec1,
|  | const NumericT & | alpha,
|  | bool | up_to_internal_size = `false`
| ) |  |

Assign a constant value to a vector (-range/-slice)

Parameters

  vec1 | The vector to which the value should be assigned
  alpha | The value to be assigned
  up_to_internal_size | Specifies whether alpha should also be written to padded memory (mostly used for clearing the whole buffer).

Definition at line 275 of file vector_operations.hpp.

template<typename NumericT >

void viennacl::linalg::host_based::vector_swap | ( | vector_base< NumericT > & | vec1,
|  | vector_base< NumericT > & | vec2
| ) |  |

Swaps the contents of two vectors, data is copied.

Parameters

  vec1 | The first vector (or -range, or -slice)
  vec2 | The second vector (or -range, or -slice)

Definition at line 302 of file vector_operations.hpp.