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 \(A\) 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 \(y\) is the resulting output vector.
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, for 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.
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.While it can make sense to pass in the same array for both RHS (\(x\)) and solution (\(y\)) in order to update the RHS in-place, we currently do not support in-place
sparse::trsv()
operation.
API#
Syntax#
Using SYCL buffers:
namespace oneapi::mkl::sparse {
void trsv (
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,
sycl::buffer<DATA_TYPE, 1> &y);
[[deprecated("Use oneapi::mkl::sparse::trsv(queue, uplo_val, opA, diag_val, /* alpha */ 1.0, ...) instead.")]]
void trsv (
sycl::queue &queue,
oneapi::mkl::uplo uplo_val,
oneapi::mkl::transpose opA,
oneapi::mkl::diag diag_val,
oneapi::mkl::sparse::matrix_handle_t A,
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_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,
DATA_TYPE *y,
const std::vector<sycl::event> &dependencies = {});
[[deprecated("Use oneapi::mkl::sparse::trsv(queue, uplo_val, opA, diag_val, /* alpha */ 1.0, ...) instead.")]]
sycl::event trsv(
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,
DATA_TYPE *y,
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.
- 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 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 theoneapi::mkl::diag::unit
case. An exception of type onemkl::invalid_value() will be thrown in case this is violated.- alpha
Specifies the scalar, \(\alpha\).
- A
Handle to object containing sparse matrix (A) 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>
arecsr
on CPU and GPU devices, andcoo
only on CPU device.- 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. 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
opA
=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 that 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:
share/doc/mkl/examples/sycl/sparse_blas/source/csr_trsv.cpp
share/doc/mkl/examples/sycl/sparse_blas/source/csr_trsv_usm.cpp