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oneapi::mkl::sparse::trsv
Solves a system of linear equations for a triangular sparse matrix.
Description
The oneapi::mkl::sparse::trsv routine solves the sparse triangular system
where 
is a sparse triangular matrix of size 
rows by columns and 
is a matrix modifier:
The dense vectors 
and 
must be at least of length . The vector is input right hand side data and math:y is the resulting output vector.
, and solution,
, to update the rhs in place, we currentlydo not guarantee that this will always work.
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 if using oneapi::mkl::diag::unit, will perform the appropriate forward or backward substitution for 
or 
where 
is the identity matrix.
API
Syntax
Using SYCL buffers:
namespace oneapi::mkl::sparse {
void trsv (
sycl::queue &queue,
oneapi::mkl::uplo uplo_flag,
oneapi::mkl::transpose transpose_flag,
oneapi::mkl::diag diag_flag,
oneapi::mkl::sparse::matrix_handle_t handle,
sycl::buffer<DATA_TYPE, 1> &x,
sycl::buffer<DATA_TYPE, 1> &y)
}
Using USM pointers:
namespace oneapi::mkl::sparse {
sycl::event trsv(
sycl::queue &queue,
oneapi::mkl::uplo uplo_flag,
oneapi::mkl::transpose transpose_flag,
oneapi::mkl::diag diag_flag,
oneapi::mkl::sparse::matrix_handle_t handle,
DATA_TYPE *x,
DATA_TYPE *y,
const std::vector<sycl::event> &dependencies = {})
}
Include Files
oneapi/mkl/spblas.hpp
Input Parameters
- queue
-
Specifies the SYCL command queue which will be used for SYCL kernels execution.
- uplo_flag
-
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.
- transpose_flag
-
Specifies operation op() on 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. - diag_flag
-
Specifies if 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. - handle
-
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:Currently, the only supported case for <sparse_matrix_type> is csr. - x
-
SYCL buffer or device-accessible USM pointer of size at least equal to the number of columns of input matrix if transpose_flag = oneapi::mkl::transpose::nontrans and at least the number of rows of input matrix otherwise. It is the input vector x
- dependencies
-
A vector of type std::vector<sycl::event> containing the list of events that the oneapi::mkl::sparse::trsv routine depends on.
Output Parameters
- y
-
SYCL buffer or device-accessible USM pointer of size at least equal to the number of rows of the input matrix if transpose_flag = oneapi::mkl::transpose::nontrans and at least the number of columns of the input matrix otherwise. The solution of the triangular solve is filled into this array.
Return Values (USM Only)
- sycl::event
-
SYCL event which can be waited upon or added as a dependency for the completion of the trsv routine.
Examples
An example of how to use oneapi::mkl::sparse::trsv with SYCL buffers or USM can be found in the oneMKL installation directory, under:
examples/dpcpp/sparse_blas/source/sparse_trsv.cpp
examples/dpcpp/sparse_blas/source/sparse_trsv_usm.cpp