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blas2_interface.h
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/***************************************************************************
*
* @license
* Copyright (C) Codeplay Software Limited
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* For your convenience, a copy of the License has been included in this
* repository.
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
* SYCL-BLAS: BLAS implementation using SYCL
*
* @filename blas2_interface.h
*
**************************************************************************/
#ifndef SYCL_BLAS_BLAS2_INTERFACE_H
#define SYCL_BLAS_BLAS2_INTERFACE_H
#include "operations/blas2_trees.h"
namespace blas {
namespace internal {
/*!
@brief Generalised matrix vector product with a rectangular non-symmetric
matrix.
Generalised matrix vector product with a rectangular non-symmetric matrix, i.e.
computing the mathematical operation:
y = alpha*A*x + beta*y
See the netlib blas interface documentation for more details of the high level
interface: http://www.netlib.org/lapack/explore-html/db/d58/sgemv_8f.html
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename container_1_t, typename increment_t,
typename container_2_t>
typename sb_handle_t::event_t _gemv(
sb_handle_t& sb_handle, // sb_handle_t (sycl, parallel, serial, etc)
char _trans, // The transposition of the matrix ('n', 't', 'c')
index_t _M, // The size of dimension M of the matrix (rows)
index_t _N, // The size of dimension N of the matrix (columns)
element_t _alpha, // Scalar parameter Alpha
container_0_t _mA, // An array (LDA,N), with the first m*n elements
index_t _lda, // Specifies the first dimension of a, max(1, m)
container_1_t _vx, // An array of dimension at least: (1+(n-1)*abs(incx))
// when trans = 'n' and (1+(m-1)*abs(incx) otherwise,
// containing the vector "x"
increment_t _incx, // The increment for elements in x (nonzero).
element_t _beta, // Scalar parameter Beta
container_2_t _vy, // An array of dimension at least: (1+(m-1)*abs(incy))
// when trans = "n" and (1+(n-1)*abs(incy) otherwise,
// containing the vector "y" (if beta is nonzero). When
// finished, y is overwritten with the updated vector.
increment_t _incy // The increment for elements in y (nonzero).
);
/*!
* @brief Prototype for the internal implementation of the GEMV operation. See
* documentation in the blas2_interface.hpp file for details.
*/
template <uint32_t local_range, uint32_t cache_line_size,
gemv_memory_t memory_type, transpose_type trn, typename SB_Handle,
typename index_t, typename element_t, typename container_t0,
typename container_t1, typename increment_t, typename container_t2>
typename SB_Handle::event_t _gemv_impl(SB_Handle& sb_handle, index_t _M,
index_t _N, element_t _alpha,
container_t0 _mA, index_t _lda,
container_t1 _vx, increment_t _incx,
element_t _beta, container_t2 _vy,
increment_t _incy);
/*!
@brief Generalised matrix vector product with a triangular symmetric matrix.
Generalised matrix vector product with a triangular symmetric matrix, i.e.
computing the mathematical operation:
x = A*x
See the netlib blas interface documentation for more details of the high level
interface: http://www.netlib.org/lapack/explore-html/de/d45/strmv_8f.html
*/
template <typename sb_handle_t, typename index_t, typename container_0_t,
typename container_1_t, typename increment_t>
typename sb_handle_t::event_t _trmv(
sb_handle_t& sb_handle, // sb_handle_t (sycl, parallel, serial, etc)
char _Uplo, // Whether the matrix is upper/lower ('u', 'l')
char _trans, // Whether the matrix is transposed ('n', 't', 'c')
char _Diag, // Whether the matrix is unit triangular ('u', 'n')
index_t _N, // >0 The order of matrix A
container_0_t _mA, // (_lda, _N) The input matrix
index_t _lda, // >max(1, _N) The first dimension of _mA
container_1_t _vx, // (1 + (_N-1)*abs(_incx)), output vector X
increment_t _incx // !=0 The increment for the elements of X
);
/**
* @brief Linear system solver for triangular matrices.
*
* Linear system solver for triangular matrices, i.e., computing x s.t.
*
* op(A)*x = x
*
* See the netlib blas interface documentation for more details of the
* interface: https://netlib.org/lapack/explore-html/d0/d2a/strsv_8f.html
*
* @param sb_handle SB_handle
* @param _Uplo Specifies if A is upper or lower triangular
* @param _trans Transposition operation applied to A ('n', 't', 'c')
* @param _Diag Specifies if A unit triangular or not
* @param _N Number of rows and columns of A
* @param _mA A buffer (_LDA,_N) containing the coefficient of A
* @param _lda Leading dimension _mA at least _N
* @param _vx Buffer containing x of at least (1+(_N-1)*abs(_incx)) elements
* @param _incx Increment for _vx (nonzero)
*/
template <typename sb_handle_t, typename index_t, typename container_0_t,
typename container_1_t, typename increment_t>
typename sb_handle_t::event_t _trsv(sb_handle_t& sb_handle, char _Uplo,
char _trans, char _Diag, index_t _N,
container_0_t _mA, index_t _lda,
container_1_t _vx, increment_t _incx);
template <uint32_t subgroup_size, uint32_t subgroups, uplo_type uplo,
transpose_type trn, diag_type diag, typename sb_handle_t,
typename index_t, typename container_t0, typename container_t1,
typename increment_t>
typename sb_handle_t::event_t _trsv_impl(sb_handle_t& sb_handle, index_t _N,
container_t0 _mA, index_t _lda,
container_t1 _vx, increment_t _incx);
/*!
@brief Generalised matrix vector product with a square symmetric matrix,
followed by a vector sum.
Generalised matrix vector product with a square symmetric matrix, followed by
a vector sum, i.e. computing the mathematical operation:
x = alpha*A*x + beta*y
See the netlib blas interface documentation for more details of the high level
interface: http://www.netlib.org/lapack/explore-html/d2/d94/ssymv_8f.html
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename container_1_t, typename increment_t,
typename container_2_t>
typename sb_handle_t::event_t _symv(
sb_handle_t& sb_handle, // sb_handle_t (sycl, parallel, serial, etc)
char _Uplo, // Whether the matrix is upper/lower ('u', 'l')
index_t _N, // >0 The order of matrix A
element_t _alpha, // Scalar parameter alpha
container_0_t _mA, // (_lda, _N) The input matrix
index_t _lda, // >max(1, _N) The first dimension of _mA
container_1_t _vx, // (1 + (_N-1)*abs(_incx)), input vector X
increment_t _incx, // !=0 The increment for the elements of X
element_t _beta, // Scalar parameter beta
container_2_t _vy, // (1 + (_N-1)*abs(_incy)), output vector Y
increment_t _incy // !=0 The increment for the elements of Y
);
/*!
@brief Generalised vector product followed by a sum with a rectangular
non-symmetric matrix.
Generalised vector product followed by a sum with a rectangular non-symmetric
matrix, i.e. computing the mathematical operation:
A = alpha*x*yT + A
See the netlib blas interface documentation for more details of the high level
interface: http://www.netlib.org/lapack/explore-html/db/d5c/sger_8f.html
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename increment_t, typename container_1_t,
typename container_2_t>
typename sb_handle_t::event_t _ger(
sb_handle_t& sb_handle, // sb_handle_t (sycl, parallel, serial, etc)
index_t _M, // The rows in matrix A
index_t _N, // The cols of matrix A
element_t _alpha, // Scalar alpha
container_0_t _vx, // >(1 + (_M-1)*abs(_incx)), input vector X
increment_t _incx, // Increment for vector X
container_1_t _vy, // >(1 + (_N-1)*abs(_incy)), input vector Y
increment_t _incy, // Increment for vector Y
container_2_t _mA, // (_lda, n) array containing A, the output
index_t _lda // >max(1, m), Leading dimension of A
);
/*!
@brief Generalised vector squaring followed by a sum with a symmetric matrix.
Generalised vector squaring followed by a sum with a symmetric matrix,
i.e. computing the mathematical operation:
A = alpha*x*xT + A
See the netlib blas interface documentation for more details of the high level
interface: http://www.netlib.org/lapack/explore-html/db/d99/ssyr2_8f.html
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename increment_t, typename container_1_t>
typename sb_handle_t::event_t _syr(
sb_handle_t& sb_handle, // sb_handle_t (sycl, parallel, serial, etc)
char _Uplo, // Whether the matrix is upper/lower ('u', 'l')
index_t _N, // >0 The order of matrix A
element_t _alpha, // Scalar alpha
container_0_t _vx, // (1 + (_N-1)*abs(_incx)), input vector X
increment_t _incx, // !=0 The increment for the elements of X
container_1_t _mA, // (_lda, _N) The output matrix
index_t _lda // >max(1, _N) The first dimension of _mA
);
/**
* @brief Generalised vector squaring followed by a sum with a packed symmetric
* matrix.
*
* Generalised vector squaring followed by a sum with a packed symmetric matrix,
* i.e. computing the mathematical operation:
* A = alpha*x*xT + A
* See the netlib blas interface documentation for more details of the high
* level interface:
* https://netlib.org/lapack/explore-html/d2/d9b/sspr_8f.html
*
* @param sb_handle sb_handle_t (sycl, parallel, serial, etc)
* @param _Uplo Whether the matrix is upper/lower ('u', 'l')
* @param _N >0 The order of matrix A
* @param _alpha Scalar multiplier
* @param _vx (1 + (_N-1)*abs(_incx)), input vector X
* @param _incx !=0 The increment for the elements of X
* @param _mPA (_lda, _N) The output matrix in packed format
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename increment_t, typename container_1_t>
typename sb_handle_t::event_t _spr(sb_handle_t& sb_handle, char _Uplo,
index_t _N, element_t _alpha,
container_0_t _vx, increment_t _incx,
container_1_t _mPA);
/**
* @brief Generalised two vectors squaring followed by a sum with a packed
* symmetric matrix.
*
* Generalised two vector squaring followed by a sum with a packed symmetric
* matrix, i.e. computing the mathematical operation:
* A = alpha*x*yT + alpha*y*xT + A
* See the netlib blas interface documentation for more details of the high
* level interface:
* https://netlib.org/lapack/explore-html/db/d3e/sspr2_8f.html
*
* @param sb_handle sb_handle_t (sycl, parallel, serial, etc)
* @param _Uplo Whether the matrix is upper/lower ('u', 'l')
* @param _N >0 The order of matrix A
* @param _alpha Scalar multiplier
* @param _vx (1 + (_N-1)*abs(_incx)), input vector X
* @param _incx !=0 The increment for the elements of X
* @param _vy (1 + (_N-1)*abs(_incy)), input vector Y
* @param _incy !=0 The increment for the elements of Y
* @param _mPA (_lda, _N) The output matrix in packed format
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_t0, typename increment_t, typename container_t1,
typename container_t2>
typename sb_handle_t::event_t _spr2(sb_handle_t& sb_handle, char _Uplo,
index_t _N, element_t _alpha,
container_t0 _vx, increment_t _incx,
container_t1 _vy, increment_t _incy,
container_t2 _mPA);
/*!
@brief Generalised vector products followed by a sum with a symmetric matrix.
Generalised vector products followed by a sum with a symmetric matrix,
i.e. computing the mathematical operation:
A = alpha*x*yT + alpha*y*xT + A
See the netlib blas interface documentation for more details of the high level
interface: http://www.netlib.org/lapack/explore-html/d6/dac/ssyr_8f.html
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename increment_t, typename container_1_t,
typename container_2_t>
typename sb_handle_t::event_t _syr2(
sb_handle_t& sb_handle, // sb_handle_t (sycl, parallel, serial, etc)
char _Uplo, // Whether the matrix is upper/lower ('u', 'l')
index_t _N, // >0 The order of matrix A
element_t _alpha, // Scalar alpha
container_0_t _vx, // (1 + (_N-1)*abs(_incx)), input vector X
increment_t _incx, // !=0 The increment for the elements of X
container_1_t _vy, // (1 + (_N-1)*abs(_incx)), input vector Y
increment_t _incy, // !=0 The increment for the elements of Y
container_2_t _mA, // (_lda, _N) The output matrix
index_t _lda // >max(1, _N) The first dimension of _mA
);
/**
* @brief Generalised matrix vector product with band matrices.
*
* Generalised matrix vector product with a band matrix, i.e. computing the
* mathematical operation:
*
* y = alpha*op(A)*x + beta*y
*
* See the netlib blas interface documentation for more details of the
* interface: https://netlib.org/lapack/explore-html/d6/d46/sgbmv_8f.html
*
* @param sb_handle SB_handle
* @param _trans Transposition operation applied to A ('n', 't', 'c')
* @param _M Number of rows of A
* @param _N Number of columns of A
* @param _KL Number of A sub-diagonals
* @param _KU Number of A super-diagonals
* @param _alpha Scalar parameter alpha
* @param _mA Buffer (_LDA,_N) containing the coefficient of A in the Band
* Matrix format
* @param _lda Leading dimension _mA at least (_KL + _KU + 1)
* @param _vx Buffer containing x of at least (1+(_N-1)*abs(_incx)) elements
* when trans = 'n' and (1+(_M-1)*abs(_incx) otherwise
* @param _incx Increment for _vx (nonzero)
* @param _beta Scalar parameter beta
* @param _vy Buffer containing y of at least (1+(_M-1)*abs(_incy)) elements
* when trans = 'n' and (1+(_N-1)*abs(_incy) otherwise
* @param _incy Increment for _vy
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename container_1_t, typename increment_t,
typename container_2_t>
typename sb_handle_t::event_t _gbmv(sb_handle_t& sb_handle, char _trans,
index_t _M, index_t _N, index_t _KL,
index_t _KU, element_t _alpha,
container_0_t _mA, index_t _lda,
container_1_t _vx, increment_t _incx,
element_t _beta, container_2_t _vy,
increment_t _incy);
template <uint32_t local_range, transpose_type trn, typename sb_handle_t,
typename index_t, typename element_t, typename container_t0,
typename container_t1, typename increment_t, typename container_t2>
typename sb_handle_t::event_t _gbmv_impl(sb_handle_t& sb_handle, index_t _M,
index_t _N, index_t _KL, index_t _KU,
element_t _alpha, container_t0 _mA,
index_t _lda, container_t1 _vx,
increment_t _incx, element_t _beta,
container_t2 _vy, increment_t _incy);
/**
* @brief Matrix vector product with symmetric band matrices.
*
* Matrix vector product with a symmetric band matrix, i.e. computing the
* mathematical operation:
*
* y = alpha*A*x + beta*y
*
* See the netlib blas interface documentation for more details of the
* interface: https://netlib.org/lapack/explore-html/d3/da1/ssbmv_8f.html
*
* @param sb_handle SB_handle
* @param _Uplo Specifies if A is upper or lower triangular
* @param _N Number of rows and columns of A
* @param _K Number of A super-diagonals
* @param _alpha Scalar parameter alpha
* @param _mA Buffer (_LDA,_N) containing the coefficient of A in the Band
* Matrix format
* @param _lda Leading dimension _mA at least (_K + 1)
* @param _vx Buffer containing x of at least (1+(_N-1)*abs(_incx)) elements
* @param _incx Increment for _vx (nonzero)
* @param _beta Scalar parameter beta
* @param _vy Buffer containing y of at least (1+(_N-1)*abs(_incy)) elements
* @param _incy Increment for _vy
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename container_1_t, typename increment_t,
typename container_2_t>
typename sb_handle_t::event_t _sbmv(sb_handle_t& sb_handle, char _Uplo,
index_t _N, index_t _K, element_t _alpha,
container_0_t _mA, index_t _lda,
container_1_t _vx, increment_t _incx,
element_t _beta, container_2_t _vy,
increment_t _incy);
template <uint32_t local_range, uplo_type uplo, typename sb_handle_t,
typename index_t, typename element_t, typename container_t0,
typename container_t1, typename increment_t, typename container_t2>
typename sb_handle_t::event_t _sbmv_impl(sb_handle_t& sb_handle, index_t _N,
index_t _K, element_t _alpha,
container_t0 _mA, index_t _lda,
container_t1 _vx, increment_t _incx,
element_t _beta, container_t2 _vy,
increment_t _incy);
/**
* @brief Matrix vector product with symmetric packed matrices.
*
* Matrix vector product with a symmetric packed matrix, i.e. computing the
* mathematical operation:
*
* y = alpha*A*x + beta*y
*
* See the netlib blas interface documentation for more details of the
* interface: https://netlib.org/lapack/explore-html/d8/d68/sspmv_8f.html
*
* @param sb_handle SB_handle
* @param _Uplo Specifies if A is upper or lower triangular
* @param _N Number of rows and columns of A
* @param _alpha Scalar parameter alpha
* @param _mA Buffer containing the coefficient of A in the Packed Triangular
* Matrix format
* @param _vx Buffer containing x of at least (1+(_N-1)*abs(_incx)) elements
* @param _incx Increment for _vx (nonzero)
* @param _beta Scalar parameter beta
* @param _vy Buffer containing y of at least (1+(_N-1)*abs(_incy)) elements
* @param _incy Increment for _vy
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename container_1_t, typename increment_t,
typename container_2_t>
typename sb_handle_t::event_t _spmv(sb_handle_t& sb_handle, char _Uplo,
index_t _N, element_t _alpha,
container_0_t _mA, container_1_t _vx,
increment_t _incx, element_t _beta,
container_2_t _vy, increment_t _incy);
template <uint32_t local_range_x, uint32_t local_range_y, uplo_type uplo,
typename sb_handle_t, typename index_t, typename element_t,
typename container_t0, typename container_t1, typename increment_t,
typename container_t2>
typename sb_handle_t::event_t _spmv_impl(sb_handle_t& sb_handle, index_t _N,
element_t _alpha, container_t0 _mA,
container_t1 _vx, increment_t _incx,
element_t _beta, container_t2 _vy,
increment_t _incy);
/**
* @brief Matrix vector product with triangular band matrices.
*
* Matrix vector product with a triangular band matrix, i.e. computing the
* mathematical operation:
*
* x = op(A)*x
*
* See the netlib blas interface documentation for more details of the
* interface: https://netlib.org/lapack/explore-html/d6/d7d/stbmv_8f.html
*
* @param sb_handle SB_handle
* @param _Uplo Specifies if A is upper or lower triangular
* @param _trans Transposition operation applied to A ('n', 't', 'c')
* @param _Diag Specifies if A unit triangular or not
* @param _N Number of rows and columns of A
* @param _K Number of A super-diagonals
* @param _mA Buffer (_LDA,_N) containing the coefficient of A in the Band
* Matrix format
* @param _lda Leading dimension _mA at least (_K + 1)
* @param _vx Buffer containing x of at least (1+(_N-1)*abs(_incx)) elements
* @param _incx Increment for _vx (nonzero)
*/
template <typename sb_handle_t, typename index_t, typename container_0_t,
typename container_1_t, typename increment_t>
typename sb_handle_t::event_t _tbmv(sb_handle_t& sb_handle, char _Uplo,
char _trans, char _Diag, index_t _N,
index_t _K, container_0_t _mA, index_t _lda,
container_1_t _vx, increment_t _incx);
template <uint32_t local_range, uplo_type uplo, transpose_type trn,
diag_type diag, typename sb_handle_t, typename index_t,
typename container_t0, typename container_t1, typename increment_t>
typename sb_handle_t::event_t _tbmv_impl(sb_handle_t& sb_handle, index_t _N,
index_t _K, container_t0 _mA,
index_t _lda, container_t1 _vx,
increment_t _incx);
/**
* @brief Linear system solver for triangular band matrices.
*
* Linear system solver for triangular band matrices, i.e., computing x s.t.
*
* op(A)*x = b
*
* See the netlib blas interface documentation for more details of the
* interface: https://netlib.org/lapack/explore-html/d0/d1f/stbsv_8f.html
*
* @param sb_handle SB_handle
* @param _Uplo Specifies if A is upper or lower triangular
* @param _trans Transposition operation applied to A ('n', 't', 'c')
* @param _Diag Specifies if A unit triangular or not
* @param _N Number of rows and columns of A
* @param _K Number of A super-diagonals
* @param _mA Buffer (_LDA,_N) containing the coefficient of A in the Band
* Matrix format
* @param _lda Leading dimension _mA at least (_K + 1)
* @param _vx Buffer containing x of at least (1+(_N-1)*abs(_incx)) elements
* @param _incx Increment for _vx (nonzero)
*/
template <typename sb_handle_t, typename index_t, typename container_0_t,
typename container_1_t, typename increment_t>
typename sb_handle_t::event_t _tbsv(sb_handle_t& sb_handle, char _Uplo,
char _trans, char _Diag, index_t _N,
index_t _K, container_0_t _mA, index_t _lda,
container_1_t _vx, increment_t _incx);
template <uint32_t subgroup_size, uint32_t subgroups, uplo_type uplo,
transpose_type trn, diag_type diag, typename sb_handle_t,
typename index_t, typename container_t0, typename container_t1,
typename increment_t>
typename sb_handle_t::event_t _tbsv_impl(sb_handle_t& sb_handle, index_t _N,
index_t _K, container_t0 _mA,
index_t _lda, container_t1 _vx,
increment_t _incx);
} // namespace internal
/*!
@brief Generalised matrix vector product with a rectangular non-symmetric
matrix.
Generalised matrix vector product with a rectangular non-symmetric matrix, i.e.
computing the mathematical operation:
y = alpha*A*x + beta*y
See the netlib blas interface documentation for more details of the high level
interface: http://www.netlib.org/lapack/explore-html/db/d58/sgemv_8f.html
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename container_1_t, typename increment_t,
typename container_2_t>
typename sb_handle_t::event_t inline _gemv(
sb_handle_t& sb_handle, // sb_handle_t (sycl, parallel, serial, etc)
char _trans, // The transposition of the matrix ('n', 't', 'c')
index_t _M, // The size of dimension M of the matrix (rows)
index_t _N, // The size of dimension N of the matrix (columns)
element_t _alpha, // Scalar parameter Alpha
container_0_t _mA, // An array (LDA,N), with the first m*n elements
index_t _lda, // Specifies the first dimension of a, max(1, m)
container_1_t _vx, // An array of dimension at least: (1+(n-1)*abs(incx))
// when trans = 'n' and (1+(m-1)*abs(incx) otherwise,
// containing the vector "x"
increment_t _incx, // The increment for elements in x (nonzero).
element_t _beta, // Scalar parameter Beta
container_2_t _vy, // An array of dimension at least: (1+(m-1)*abs(incy))
// when trans = "n" and (1+(n-1)*abs(incy) otherwise,
// containing the vector "y" (if beta is nonzero). When
// finished, y is overwritten with the updated vector.
increment_t _incy // The increment for elements in y (nonzero).
) {
return internal::_gemv(sb_handle, _trans, _M, _N, _alpha, _mA, _lda, _vx,
_incx, _beta, _vy, _incy);
}
/*!
@brief Generalised matrix vector product with a triangular symmetric matrix.
Generalised matrix vector product with a triangular symmetric matrix, i.e.
computing the mathematical operation:
x = A*x
See the netlib blas interface documentation for more details of the high level
interface: http://www.netlib.org/lapack/explore-html/de/d45/strmv_8f.html
*/
template <typename sb_handle_t, typename index_t, typename container_0_t,
typename container_1_t, typename increment_t>
typename sb_handle_t::event_t inline _trmv(
sb_handle_t& sb_handle, // sb_handle_t (sycl, parallel, serial, etc)
char _Uplo, // Whether the matrix is upper/lower ('u', 'l')
char _trans, // Whether the matrix is transposed ('n', 't', 'c')
char _Diag, // Whether the matrix is unit triangular ('u', 'n')
index_t _N, // >0 The order of matrix A
container_0_t _mA, // (_lda, _N) The input matrix
index_t _lda, // >max(1, _N) The first dimension of _mA
container_1_t _vx, // (1 + (_N-1)*abs(_incx)), output vector X
increment_t _incx // !=0 The increment for the elements of X
) {
return internal::_trmv(sb_handle, _Uplo, _trans, _Diag, _N, _mA, _lda, _vx,
_incx);
}
/**
* @brief Linear system solver for triangular matrices.
*
* Linear system solver for triangular matrices, i.e., computing x s.t.
*
* op(A)*x = x
*
* See the netlib blas interface documentation for more details of the
* interface: https://netlib.org/lapack/explore-html/d0/d2a/strsv_8f.html
*
* @param sb_handle SB_handle
* @param _Uplo Specifies if A is upper or lower triangular
* @param _trans Transposition operation applied to A ('n', 't', 'c')
* @param _Diag Specifies if A unit triangular or not
* @param _N Number of rows and columns of A
* @param _mA A buffer (_LDA,_N) containing the coefficient of A
* @param _lda Leading dimension _mA at least _N
* @param _vx Buffer containing x of at least (1+(_N-1)*abs(_incx)) elements
* @param _incx Increment for _vx (nonzero)
*/
template <typename sb_handle_t, typename index_t, typename container_0_t,
typename container_1_t, typename increment_t>
typename sb_handle_t::event_t inline _trsv(sb_handle_t& sb_handle, char _Uplo,
char _trans, char _Diag, index_t _N,
container_0_t _mA, index_t _lda,
container_1_t _vx,
increment_t _incx) {
return internal::_trsv(sb_handle, _Uplo, _trans, _Diag, _N, _mA, _lda, _vx,
_incx);
}
/*!
@brief Generalised matrix vector product with a rectangular symmetric
matrix, followed by a vector sum.
Generalised matrix vector product with a rectangular symmetric
matrix, followed by a vector sum, i.e.
computing the mathematical operation:
x = alpha*A*x + beta*y
See the netlib blas interface documentation for more details of the high level
interface: http://www.netlib.org/lapack/explore-html/d2/d94/ssymv_8f.html
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename container_1_t, typename increment_t,
typename container_2_t>
typename sb_handle_t::event_t inline _symv(
sb_handle_t& sb_handle, // sb_handle_t (sycl, parallel, serial, etc)
char _Uplo, // Whether the matrix is upper/lower ('u', 'l')
index_t _N, // >0 The order of matrix A
element_t _alpha, // Scalar parameter alpha
container_0_t _mA, // (_lda, _N) The input matrix
index_t _lda, // >max(1, _N) The first dimension of _mA
container_1_t _vx, // (1 + (_N-1)*abs(_incx)), input vector X
increment_t _incx, // !=0 The increment for the elements of X
element_t _beta, // Scalar parameter beta
container_2_t _vy, // (1 + (_N-1)*abs(_incy)), output vector Y
increment_t _incy // !=0 The increment for the elements of Y
) {
return internal::_symv(sb_handle, _Uplo, _N, _alpha, _mA, _lda, _vx, _incx,
_beta, _vy, _incy);
}
/*!
@brief Generalised vector product followed by a sum with a rectangular
non-symmetric matrix.
Generalised vector product followed by a sum with a rectangular non-symmetric
matrix, i.e.
computing the mathematical operation:
A = alpha*x*yT + A
See the netlib blas interface documentation for more details of the high level
interface: http://www.netlib.org/lapack/explore-html/db/d5c/sger_8f.html
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename increment_t, typename container_1_t,
typename container_2_t>
typename sb_handle_t::event_t inline _ger(
sb_handle_t& sb_handle, // sb_handle_t (sycl, parallel, serial, etc)
index_t _M, // The rows in matrix M
index_t _N, // The rows of matrix N
element_t _alpha, // Scalar alpha
container_0_t _vx, // >(1 + (_M-1)*abs(_incx)), input vector X
increment_t _incx, // Increment for vector X
container_1_t _vy, // >(1 + (_N-1)*abs(_incy)), input vector Y
increment_t _incy, // Increment for vector Y
container_2_t _mA, // (_lda, n) array containing A, the output
index_t _lda // >max(1, m), Leading dimension of A
) {
return internal::_ger(sb_handle, _M, _N, _alpha, _vx, _incx, _vy, _incy, _mA,
_lda);
}
/*!
@brief Generalised vector product sum.
Generalised vector squaring followed by a sum with a rectangular symmetric
matrix, i.e.
computing the mathematical operation:
A = alpha*x*xT + A
See the netlib blas interface documentation for more details of the high level
interface: http://www.netlib.org/lapack/explore-html/db/d99/ssyr2_8f.html
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename increment_t, typename container_1_t>
typename sb_handle_t::event_t inline _syr(
sb_handle_t& sb_handle, // sb_handle_t (sycl, parallel, serial, etc)
char _Uplo, // Whether the matrix is upper/lower ('u', 'l')
index_t _N, // >0 The order of matrix A
element_t _alpha, // Scalar alpha
container_0_t _vx, // (1 + (_N-1)*abs(_incx)), input vector X
increment_t _incx, // !=0 The increment for the elements of X
container_1_t _mA, // (_lda, _N) The output matrix
index_t _lda // >max(1, _N) The first dimension of _mA
) {
return internal::_syr(sb_handle, _Uplo, _N, _alpha, _vx, _incx, _mA, _lda);
}
/**
* @brief Generalised vector squaring followed by a sum with a packed symmetric
* matrix.
*
* Generalised vector squaring followed by a sum with a packed symmetric matrix,
* i.e. computing the mathematical operation:
* A = alpha*x*xT + A
* See the netlib blas interface documentation for more details of the high
* level interface:
* https://netlib.org/lapack/explore-html/d2/d9b/sspr_8f.html
*
* @param sb_handle sb_handle_t (sycl, parallel, serial, etc)
* @param _Uplo Whether the matrix is upper/lower ('u', 'l')
* @param _N >0 The order of matrix A
* @param _alpha Scalar multiplier
* @param _vx (1 + (_N-1)*abs(_incx)), input vector X
* @param _incx !=0 The increment for the elements of X
* @param _mPA (_lda, _N) The output matrix in packed format
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename increment_t, typename container_1_t>
typename sb_handle_t::event_t inline _spr(sb_handle_t& sb_handle, char _Uplo,
index_t _N, element_t _alpha,
container_0_t _vx, increment_t _incx,
container_1_t _mPA) {
return internal::_spr<sb_handle_t, index_t, element_t, container_0_t,
increment_t, container_1_t>(sb_handle, _Uplo, _N,
_alpha, _vx, _incx, _mPA);
}
/**
* @brief Generalised two vectors squaring followed by a sum with a packed
* symmetric matrix.
*
* Generalised two vector squaring followed by a sum with a packed symmetric
* matrix, i.e. computing the mathematical operation:
* A = alpha*x*yT + alpha*y*xT + A
* See the netlib blas interface documentation for more details of the high
* level interface:
* https://netlib.org/lapack/explore-html/db/d3e/sspr2_8f.html
*
* @param sb_handle sb_handle_t (sycl, parallel, serial, etc)
* @param _Uplo Whether the matrix is upper/lower ('u', 'l')
* @param _N >0 The order of matrix A
* @param _alpha Scalar multiplier
* @param _vx (1 + (_N-1)*abs(_incx)), input vector X
* @param _incx !=0 The increment for the elements of X
* @param _vy (1 + (_N-1)*abs(_incy)), input vector Y
* @param _incy !=0 The increment for the elements of Y
* @param _mPA (_lda, _N) The output matrix in packed format
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_t0, typename increment_t, typename container_t1,
typename container_t2>
typename sb_handle_t::event_t inline _spr2(sb_handle_t& sb_handle, char _Uplo,
index_t _N, element_t _alpha,
container_t0 _vx, increment_t _incx,
container_t1 _vy, increment_t _incy,
container_t2 _mPA) {
return internal::_spr2(sb_handle, _Uplo, _N, _alpha, _vx, _incx, _vy, _incy,
_mPA);
}
/*!
@brief Generalised vector product followed by a sum with a rectangular
symmetric matrix.
Generalised vector product followed by a sum with a rectangular symmetric
matrix, i.e.
computing the mathematical operation:
A = alpha*x*yT + alpha*y*xT + A
See the netlib blas interface documentation for more details of the high level
interface: http://www.netlib.org/lapack/explore-html/d6/dac/ssyr_8f.html
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename increment_t, typename container_1_t,
typename container_2_t>
typename sb_handle_t::event_t inline _syr2(
sb_handle_t& sb_handle, // sb_handle_t (sycl, parallel, serial, etc)
char _Uplo, // Whether the matrix is upper/lower ('u', 'l')
index_t _N, // >0 The order of matrix A
element_t _alpha, // Scalar alpha
container_0_t _vx, // (1 + (_N-1)*abs(_incx)), input vector X
increment_t _incx, // !=0 The increment for the elements of X
container_1_t _vy, // (1 + (_N-1)*abs(_incx)), input vector Y
increment_t _incy, // !=0 The increment for the elements of Y
container_2_t _mA, // (_lda, _N) The output matrix
index_t _lda // >max(1, _N) The first dimension of _mA
) {
return internal::_syr2(sb_handle, _Uplo, _N, _alpha, _vx, _incx, _vy, _incy,
_mA, _lda);
}
/**
* @brief Generalised matrix vector product with band matrices.
*
* Generalised matrix vector product with a band matrix, i.e. computing the
* mathematical operation:
*
* y = alpha*op(A)*x + beta*y
*
* See the netlib blas interface documentation for more details of the
* interface: https://netlib.org/lapack/explore-html/d6/d46/sgbmv_8f.html
*
* @param sb_handle SB_handle
* @param _trans Transposition operation applied to A ('n', 't', 'c')
* @param _M Number of rows of A
* @param _N Number of columns of A
* @param _KL Number of A sub-diagonals
* @param _KU Number of A super-diagonals
* @param _alpha Scalar parameter alpha
* @param _mA Buffer (_LDA,_N) containing the coefficient of A in the Band
* Matrix format
* @param _lda Leading dimension _mA at least (_KL + _KU + 1)
* @param _vx Buffer containing x of at least (1+(_N-1)*abs(_incx)) elements
* when trans = 'n' and (1+(_M-1)*abs(_incx) otherwise
* @param _incx Increment for _vx (nonzero)
* @param _beta Scalar parameter beta
* @param _vy Buffer containing y of at least (1+(_M-1)*abs(_incy)) elements
* when trans = 'n' and (1+(_N-1)*abs(_incy) otherwise
* @param _incy Increment for _vy
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename container_1_t, typename increment_t,
typename container_2_t>
typename sb_handle_t::event_t inline _gbmv(sb_handle_t& sb_handle, char _trans,
index_t _M, index_t _N, index_t _KL,
index_t _KU, element_t _alpha,
container_0_t _mA, index_t _lda,
container_1_t _vx, increment_t _incx,
element_t _beta, container_2_t _vy,
increment_t _incy) {
return internal::_gbmv(sb_handle, _trans, _M, _N, _KL, _KU, _alpha, _mA, _lda,
_vx, _incx, _beta, _vy, _incy);
}
/**
* @brief Matrix vector product with symmetric band matrices.
*
* Matrix vector product with a symmetric band matrix, i.e. computing the
* mathematical operation:
*
* y = alpha*A*x + beta*y
*
* See the netlib blas interface documentation for more details of the
* interface: https://netlib.org/lapack/explore-html/d3/da1/ssbmv_8f.html
*
* @param sb_handle SB_handle
* @param _Uplo Specifies if A is upper or lower triangular
* @param _N Number of rows and columns of A
* @param _K Number of A super-diagonals
* @param _alpha Scalar parameter alpha
* @param _mA Buffer (_LDA,_N) containing the coefficient of A in the Band
* Matrix format
* @param _lda Leading dimension _mA at least (_K + 1)
* @param _vx Buffer containing x of at least (1+(_N-1)*abs(_incx)) elements
* @param _incx Increment for _vx (nonzero)
* @param _beta Scalar parameter beta
* @param _vy Buffer containing y of at least (1+(_N-1)*abs(_incy)) elements
* @param _incy Increment for _vy
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename container_1_t, typename increment_t,
typename container_2_t>
typename sb_handle_t::event_t _sbmv(sb_handle_t& sb_handle, char _Uplo,
index_t _N, index_t _K, element_t _alpha,
container_0_t _mA, index_t _lda,
container_1_t _vx, increment_t _incx,
element_t _beta, container_2_t _vy,
increment_t _incy) {
return internal::_sbmv(sb_handle, _Uplo, _N, _K, _alpha, _mA, _lda, _vx,
_incx, _beta, _vy, _incy);
}
/**
* @brief Matrix vector product with symmetric packed matrices.
*
* Matrix vector product with a symmetric packed matrix, i.e. computing the
* mathematical operation:
*
* y = alpha*A*x + beta*y
*
* See the netlib blas interface documentation for more details of the
* interface: https://netlib.org/lapack/explore-html/d8/d68/sspmv_8f.html
*
* @param sb_handle SB_handle
* @param _Uplo Specifies if A is upper or lower triangular
* @param _N Number of rows and columns of A
* @param _alpha Scalar parameter alpha
* @param _mA Buffer containing the coefficient of A in the Packed Triangular
* Matrix format
* @param _lda Leading dimension _mA at least (_K + 1)
* @param _vx Buffer containing x of at least (1+(_N-1)*abs(_incx)) elements
* @param _incx Increment for _vx (nonzero)
* @param _beta Scalar parameter beta
* @param _vy Buffer containing y of at least (1+(_N-1)*abs(_incy)) elements
* @param _incy Increment for _vy
*/
template <typename sb_handle_t, typename index_t, typename element_t,
typename container_0_t, typename container_1_t, typename increment_t,
typename container_2_t>
typename sb_handle_t::event_t _spmv(sb_handle_t& sb_handle, char _Uplo,
index_t _N, element_t _alpha,
container_0_t _mA, container_1_t _vx,
increment_t _incx, element_t _beta,
container_2_t _vy, increment_t _incy) {
return internal::_spmv(sb_handle, _Uplo, _N, _alpha, _mA, _vx, _incx, _beta,
_vy, _incy);
}
/**
* @brief Matrix vector product with triangular band matrices.
*
* Matrix vector product with a triangular band matrix, i.e. computing the
* mathematical operation:
*
* x = op(A)*x
*
* See the netlib blas interface documentation for more details of the
* interface: https://netlib.org/lapack/explore-html/d6/d7d/stbmv_8f.html
*
* @param sb_handle SB_handle
* @param _Uplo Specifies if A is upper or lower triangular
* @param _trans Transposition operation applied to A ('n', 't', 'c')
* @param _Diag Specifies if A unit triangular or not
* @param _N Number of rows and columns of A
* @param _K Number of A super-diagonals
* @param _mA Buffer (_LDA,_N) containing the coefficient of A in the Band
* Matrix format
* @param _lda Leading dimension _mA at least (_K + 1)
* @param _vx Buffer containing x of at least (1+(_N-1)*abs(_incx)) elements
* @param _incx Increment for _vx (nonzero)
*/
template <typename sb_handle_t, typename index_t, typename container_0_t,
typename container_1_t, typename increment_t>
typename sb_handle_t::event_t _tbmv(sb_handle_t& sb_handle, char _Uplo,
char _trans, char _Diag, index_t _N,
index_t _K, container_0_t _mA, index_t _lda,
container_1_t _vx, increment_t _incx) {
return internal::_tbmv(sb_handle, _Uplo, _trans, _Diag, _N, _K, _mA, _lda,
_vx, _incx);
}
/**
* @brief Linear system solver for triangular band matrices.
*
* Linear system solver for triangular band matrices, i.e., computing x s.t.
*
* op(A)*x = b
*
* See the netlib blas interface documentation for more details of the
* interface: https://netlib.org/lapack/explore-html/d0/d1f/stbsv_8f.html
*
* @param sb_handle SB_handle
* @param _Uplo Specifies if A is upper or lower triangular
* @param _trans Transposition operation applied to A ('n', 't', 'c')
* @param _Diag Specifies if A unit triangular or not
* @param _N Number of rows and columns of A
* @param _K Number of A super-diagonals
* @param _mA Buffer (_LDA,_N) containing the coefficient of A in the Band
* Matrix format
* @param _lda Leading dimension _mA at least (_K + 1)
* @param _vx Buffer containing x of at least (1+(_N-1)*abs(_incx)) elements
* @param _incx Increment for _vx (nonzero)
*/
template <typename sb_handle_t, typename index_t, typename container_0_t,
typename container_1_t, typename increment_t>
typename sb_handle_t::event_t _tbsv(sb_handle_t& sb_handle, char _Uplo,