oneapi::mkl::sparse::trsv¶
Solves a system of linear equations for a triangular sparse matrix.
Description¶
Note
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.
The oneapi::mkl::sparse::trsv
routine solves the sparse triangular system
where \(A\) is a sparse triangular matrix of size \(m\) rows by \(m\) columns and \(\text{op()}\) is a matrix modifier:
The dense vectors \(x\) and \(y\) must be at least of length \(m\). The vector \(x\) is input right hand side data and math:y is the resulting output vector.
Note
While it can make sense to pass the same array in for both rhs, \(x\), and solution, \(y\), 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 \(A = L + D + U\),
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
\(\text{op}(L+D)\) or \(\text{op}(D+U)\) for oneapi::mkl::diag::nonunit
or if
using oneapi::mkl::diag::unit
, will perform the appropriate forward or backward substitution for
\(\text{op}(L+I)\) or \(\text{op}(I+U)\) where \(I\) is the identity matrix.
API¶
Syntax¶
Note
Currently, complex types are not supported.
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, \(\text{op}(A) = A\).
oneapi::mkl::transpose::trans
Transpose, \(\text{op}(A) = A^{T}\).
oneapi::mkl::transpose::conjtrans
Conjugate transpose, \(\text{op}(A) = A^{H}\).
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 theoneapi::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 vectorx
- dependencies
A vector of type
std::vector<sycl::event>
containing the list of events that theoneapi::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.