oneapi::mkl::sparse::trmv
Computes a sparse matrix-dense vector product over upper or lower triangular parts of the matrix.
Description
The oneapi::mkl::sparse::trmv routine computes a sparse matrix-dense vector product over a triangular part defined as
\[y \leftarrow \alpha \cdot\text{op}(A)\cdot x + \beta\cdot y\]
where \(\alpha\) and \(\beta\) are scalars, \(A\) is a sparse triangular matrix of size m rows by m columns and \(x\) and \(y\) are dense vectors of size m. The operation \(\text{op}()\) is a matrix modifier:
\[\begin{split}\text{op}(A) = \begin{cases} A,& \text{ oneapi::mkl::transpose::nontrans}\\ A^{T},& \text{ oneapi::mkl::transpose::trans}\\A^{H},& \text{ oneapi::mkl::transpose::conjtrans} \end{cases}\end{split}\]
For a given matrix decomposition into lower, diagonal and upper parts \(A = L + D + U\), the triangular matrix vector product with one of oneapi::mkl::uplo::lower or oneapi::mkl::uplo::upper selected will perform the appropriate matrix product 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 matrix product for \(\text{op}(L+I)\) or \(\text{op}(I+U)\) where \(I\) is the identity matrix.
API
Syntax
Using SYCL buffers:
namespace oneapi::mkl::sparse {
void trmv (
sycl::queue &queue,
oneapi::mkl::uplo uplo_val,
oneapi::mkl::transpose opA,
oneapi::mkl::diag diag_val,
const DATA_TYPE alpha,
oneapi::mkl::sparse::matrix_handle_t A,
sycl::buffer<DATA_TYPE, 1> &x,
const DATA_TYPE beta,
sycl::buffer<DATA_TYPE, 1> &y)
}Using USM pointers:
namespace oneapi::mkl::sparse {
sycl::event trmv(
sycl::queue &queue,
oneapi::mkl::uplo uplo_val,
oneapi::mkl::transpose opA,
oneapi::mkl::diag
diag_val,
const DATA_TYPE alpha,
oneapi::mkl::sparse::matrix_handle_t A,
const DATA_TYPE *x,
const DATA_TYPE beta,
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_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.
- opA
-
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_val
-
Specifies if the diagonal used for computations is unit or not.
oneapi::mkl::diag::nonunit
Diagonal elements might not be equal to one.
oneapi::mkl::diag::unit
Diagonal elements are equal to one.
- alpha
-
Specifies the scalar, \(\alpha\).
- 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.
Formats Supported in sparse::trmv() for A
Compressed Sparse Row (CSR) format on CPU/GPU
Coordinate (COO) format on CPU
- x
-
SYCL buffer or device-accessible USM pointer of size at least equal to the number of columns of input matrix if opA = oneapi::mkl::transpose::nontrans and at least the number of rows of input matrix otherwise.
- beta
-
Specifies the scalar, \(\beta\).
- y
-
SYCL buffer or device-accessible USM pointer of size at least equal to the number of rows of the input matrix if opA = oneapi::mkl::transpose::nontrans and at least the number of columns of the input matrix otherwise.
- dependencies
-
A vector of type std::vector<sycl::event> containing the list of events that the oneapi::mkl::sparse::trmv routine depends on.
Output Parameters
- y
-
Overwritten by the updated vector, \(y\).
Return Values (USM Only)
- sycl::event
-
SYCL event which can be waited upon or added as a dependency for the completion of the trmv routine.
Examples
An example of how to use oneapi::mkl::sparse::trmv with SYCL buffers can be found in the oneMKL installation directory, under:
share/doc/mkl/examples/sycl/sparse_blas/source/csr_trmv.cpp