Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
mkl_sparse_?_trsm
Solves a system of linear equations with multiple right hand sides for a triangular sparse matrix.
Syntax
stat = mkl_sparse_s_trsm ( operation, alpha, A, descr, layout, x, columns, ldx, y, ldy )
stat = mkl_sparse_d_trsm ( operation, alpha, A, descr, layout, x, columns, ldx, y, ldy )
stat = mkl_sparse_c_trsm ( operation, alpha, A, descr, layout, x, columns, ldx, y, ldy )
stat = mkl_sparse_z_trsm ( operation, alpha, A, descr, layout, x, columns, ldx, y, ldy )Include Files
mkl_spblas.f90
Description
The mkl_sparse_?_trsm routine solves a system of linear equations with multiple right hand sides for a triangular sparse matrix:
\[Y \leftarrow \alpha \cdot \text{inv}(op(A)) \cdot X\]
where:
\(\alpha\) is a scalar, \(X\) and \(Y\) are dense matrices, \(A\) is a sparse matrix, and \(op()\) is a matrix modifier for matrix \(A\).
The mkl_sparse_?_mm and mkl_sparse_?_trsm routines support these configurations:
Column-major dense matrix: layout = SPARSE_LAYOUT_COLUMN_MAJOR |
Row-major dense matrix: layout = SPARSE_LAYOUT_ROW_MAJOR |
|
|---|---|---|
0-based sparse matrix: SPARSE_INDEX_BASE_ZERO |
CSR BSR: general non-transposed matrix multiplication only |
All formats |
1-based sparse matrix: SPARSE_INDEX_BASE_ONE |
All formats |
CSR BSR: general non-transposed matrix multiplication only |
( SPARSE_INDEX_BASE_ZERO, SPARSE_LAYOUT_ROW_MAJOR)
( SPARSE_INDEX_BASE_ONE, SPARSE_LAYOUT_COLUMN_MAJOR)
Input Parameters
operation
C_INT .
Specifies operation op() on input matrix:
operation |
Description |
|---|---|
SPARSE_OPERATION_NON_TRANSPOSE |
\(op(A) = A\) |
SPARSE_OPERATION_TRANSPOSE |
\(op(A) = A^{T}\) |
SPARSE_OPERATION_CONJUGATE_TRANSPOSE |
\(op(A) = A^{H}\) |
alpha
C_FLOAT |
for mkl_sparse_s_trsm |
C_DOUBLE |
for mkl_sparse_d_trsm |
C_FLOAT_COMPLEX |
for mkl_sparse_c_trsm |
C_DOUBLE_COMPLEX |
for mkl_sparse_z_trsm |
Specifies the scalar, \(\alpha\) .
A
SPARSE_MATRIX_T.
Handle which contains the sparse matrix A .
descr
MATRIX_DESCR .
Descriptor specifying sparse matrix properties.
sparse_matrix_type_t type |
Specifies the type of a sparse matrix:
|
sparse_fill_mode_t mode |
Specifies the triangular matrix part for symmetric, Hermitian, triangular, and block-triangular matrices:
|
sparse_diag_type_t diag |
Specifies diagonal type for non-general matrices:
|
layout
C_INT .
Describes the storage scheme for the dense matrix:
SPARSE_LAYOUT_COLUMN_MAJOR |
Storage of elements uses column major layout. |
SPARSE_LAYOUT_ROW_MAJOR |
Storage of elements uses row major layout. |
x
C_FLOAT |
for mkl_sparse_s_trsm |
C_DOUBLE |
for mkl_sparse_d_trsm |
C_FLOAT_COMPLEX |
for mkl_sparse_c_trsm |
C_DOUBLE_COMPLEX |
for mkl_sparse_z_trsm |
Array of size at least rows * cols .
layout = SPARSE_LAYOUT_COLUMN_MAJOR |
layout = SPARSE_LAYOUT_ROW_MAJOR |
|
|---|---|---|
rows (X_nrows) |
ldx |
number of rows in \(A\) |
cols (X_ncols) |
columns |
ldx |
On entry, the array x must contain the matrix, X .
columns
C_INT.
Number of columns of matrix \(Y\) .
ldx
C_INT.
Specifies the leading dimension of matrix \(X\) .
y
C_FLOAT |
for mkl_sparse_s_trsm |
C_DOUBLE |
for mkl_sparse_d_trsm |
C_FLOAT_COMPLEX |
for mkl_sparse_c_trsm |
C_DOUBLE_COMPLEX |
for mkl_sparse_z_trsm |
Array of size at least rows * cols , where
layout = SPARSE_LAYOUT_COLUMN_MAJOR |
layout = SPARSE_LAYOUT_ROW_MAJOR |
|
|---|---|---|
rows (Y_nrows) |
ldy |
number of rows in \(A\) |
cols (Y_ncols) |
columns |
ldy |
Output Parameters
y
C_FLOAT |
for mkl_sparse_s_trsm |
C_DOUBLE |
for mkl_sparse_d_trsm |
C_FLOAT_COMPLEX |
for mkl_sparse_c_trsm |
C_DOUBLE_COMPLEX |
for mkl_sparse_z_trsm |
Overwritten by the updated matrix \(Y\) .
stat
INTEGER
Value indicating whether the operation was successful, and if not, why:
SPARSE_STATUS_SUCCESS |
The operation was successful. |
SPARSE_STATUS_NOT_INITIALIZED |
The routine encountered an empty handle or matrix array. |
SPARSE_STATUS_ALLOC_FAILED |
Internal memory allocation failed. |
SPARSE_STATUS_INVALID_VALUE |
The input parameters contain an invalid value. |
SPARSE_STATUS_EXECUTION_FAILED |
Execution failed. |
SPARSE_STATUS_INTERNAL_ERROR |
An error in algorithm implementation occurred. |
SPARSE_STATUS_NOT_SUPPORTED |
The requested operation is not supported. |
Return Values
See Output Parameter, stat.