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Visible to Intel only — GUID: GUID-29DD150A-DEAA-4DC8-B372-78C4C837EC3C
oneapi::mkl::sparse::trsm
Solves a system of linear equations with multiple right-hand sides (RHS) for a triangular sparse matrix.
Description
The oneapi::mkl::sparse::trsm routine solves the sparse triangular system
where 
is a sparse triangular matrix of size 
rows by columns and 
is a matrix modifier:
The dense matrices 
and 
are stored with row-major or column-major layout and have an appropriate number of rows and columns number of columns for computing sparse::trsm() operation, that is, 
and are of dimensions rows by 
columns. The matrix is input right hand side data and is the resulting output matrix.
For a given matrix decomposition into lower, diagonal, and upper parts 
, the triangular solve with one of oneapi::mkl::uplo::lower or oneapi::mkl::uplo::upper selected will perform the appropriate forward or backward substitution using respectively 
or 
for oneapi::mkl::diag::nonunit or, for oneapi::mkl::diag::unit, will perform the appropriate forward or backward substitution for 
or 
where 
is the identity matrix.
- Refer to Sparse BLAS Supported Data and Integer Types for a list of supported <DATA_TYPE> and <INT_TYPE> data and integer types, and refer to Error Handling for a detailed description of the possible exceptions thrown.
While it can make sense to pass in the same array for both RHS (
) and solution () in order to update the RHS in-place, we currently do not support in-place sparse::trsm() operation.
API
Syntax
Using SYCL buffers:
namespace oneapi::mkl::sparse { void trsm ( sycl::queue &queue, oneapi::mkl::layout layout_val, oneapi::mkl::transpose opA, oneapi::mkl::transpose opX, oneapi::mkl::uplo uplo_val, oneapi::mkl::diag diag_val, const DATA_TYPE alpha, oneapi::mkl::sparse::matrix_handle_t A, sycl::buffer<DATA_TYPE, 1> &X, const std::int64_t columns, const std::int64_t ldx, sycl::buffer<DATA_TYPE, 1> &Y, const std::int64_t ldy); }
Using USM pointers:
namespace oneapi::mkl::sparse { sycl::event trsm( sycl::queue &queue, oneapi::mkl::layout layout_val, oneapi::mkl::transpose opA, oneapi::mkl::transpose opX, oneapi::mkl::uplo uplo_val, oneapi::mkl::diag diag_val, const DATA_TYPE alpha, oneapi::mkl::sparse::matrix_handle_t A, const DATA_TYPE *X, const std::int64_t columns, const std::int64_t ldx, DATA_TYPE *Y, const std::int64_t ldy, const std::vector<sycl::event> &dependencies = {}); }
Include Files
oneapi/mkl/spblas.hpp
Input Parameters
- queue
-
Specifies the SYCL command queue that will be used for SYCL kernels execution.
- layout_val
-
Specifies the storage scheme in memory for the dense matrices. Note that this layout applies to both X and Y dense matrices.
- opA
-
Specifies operation op() on the sparse input matrix,
.oneapi::mkl::transpose::nontrans
Non-transpose,
.oneapi::mkl::transpose::trans
Transpose,
.oneapi::mkl::transpose::conjtrans
Conjugate transpose,
.NOTE:Currently, the only supported case for operation is oneapi::mkl::transpose::nontrans. - opX
-
Specifies operation op() on the dense input matrix,
.oneapi::mkl::transpose::nontrans
Non-transpose,
.oneapi::mkl::transpose::trans
Transpose,
.oneapi::mkl::transpose::conjtrans
Conjugate transpose,
.NOTE:Currently, the only supported case for operation is oneapi::mkl::transpose::nontrans. - uplo_val
-
Specifies which part of the matrix is to be processed.
oneapi::mkl::uplo::lower
The lower triangular matrix part is processed.
oneapi::mkl::uplo::upper
The upper triangular matrix part is processed.
- diag_val
-
Specifies whether the diagonal used for computations is unit or based on provided matrix data.
oneapi::mkl::diag::nonunit
Diagonal elements are used as provided in the sparse matrix.
oneapi::mkl::diag::unit
The value of one is substituted for the diagonal elements in the triangular solve algorithm.
NOTE:If oneapi::mkl::diag::nonunit is selected, all diagonal values must be present in the sparse matrix sparsity profile and must not be zero valued. This is not necessary for the oneapi::mkl::diag::unit case. An exception of type onemkl::invalid_value() will be thrown in case this is violated. - alpha
-
Specifies the scalar,
. - A
-
Handle to object containing sparse matrix (
) and other internal data. Created using one of the oneapi::mkl::sparse::set_<sparse_matrix_type>_data routines.NOTE:The supported cases for <sparse_matrix_type> are csr on CPU and GPU devices, and coo only on CPU device. - X
-
SYCL buffer or device-accessible USM pointer for the right hand side dense matrix.
is of dimension by columns with a leading dimension stride of ldx based on the provided layout of X.For example, if
, i.e opX == oneapi::mkl::transpose::nontrans, we would havelayout=oneapi::mkl::layout::col-major
layout=oneapi::mkl::layout::row-major
nrows of
ldx
m
ncols of
columns
ldx
- columns
-
Number of columns of
and matrices. - ldx
-
Specifies the leading dimension of matrix X. Must be positive, and larger than or equal to the actual usable row (for layout_val=oneapi::mkl::layout::row_major) or column (for layout_val=oneapi::mkl::layout::col_major) dimension of X.
- ldy
-
Specifies the leading dimension of matrix Y. Must be positive, and at least columns if layout_val=oneapi::mkl::layout::row-major or at least number of rows in
if layout_val=oneapi::mkl::layout::col-major. - dependencies
-
A vector of type std::vector<sycl::event> containing the list of events that the oneapi::mkl::sparse::trsm routine depends on.
Output Parameters
- Y
-
SYCL buffer or device-accessible USM pointer for the dense matrix solution of the triangular solve.
is of dimension by columns with a leading dimension stride of ldy based on the provided layout of Y.layout=oneapi::mkl::layout::col-major
layout=oneapi::mkl::layout::row-major
nrows of
ldy
m (number of rows in
and )ncols of
columns
ldy
Return Values (USM Only)
- sycl::event
-
SYCL event that can be waited upon or added as a dependency for the completion of the trsm routine.
Examples
An example of how to use oneapi::mkl::sparse::trsm with SYCL buffers or USM can be found in the oneMKL installation directory, under:
share/doc/mkl/examples/sycl/sparse_blas/source/csr_trsm.cpp
share/doc/mkl/examples/sycl/sparse_blas/source/csr_trsm_usm.cpp