mkl_sparse_?

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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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 := alpha*inv(op(A))*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

NOTE:

For sparse matrices in the BSR format, the supported combinations of (indexing,block_layout) are:

(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.

`SPARSE_OPERATION_NON_TRANSPOSE`	Non-transpose, `op(A) = A`.
`SPARSE_OPERATION_TRANSPOSE`	Transpose, `op(A) = A^T`.
`SPARSE_OPERATION_CONJUGATE_TRANSPOSE`	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.

type - Specifies the type of a sparse matrix:

`SPARSE_MATRIX_TYPE_GENERAL`	The matrix is processed as is.
`SPARSE_MATRIX_TYPE_SYMMETRIC`	The matrix is symmetric (only the requested triangle is processed).
`SPARSE_MATRIX_TYPE_HERMITIAN`	The matrix is Hermitian (only the requested triangle is processed).
`SPARSE_MATRIX_TYPE_TRIANGULAR`	The matrix is triangular (only the requested triangle is processed).
`SPARSE_MATRIX_TYPE_DIAGONAL`	The matrix is diagonal (only diagonal elements are processed).
`SPARSE_MATRIX_TYPE_BLOCK_TRIANGULAR`	The matrix is block-triangular (only requested triangle is processed). Applies to BSR format only.
`SPARSE_MATRIX_TYPE_BLOCK_DIAGONAL`	The matrix is block-diagonal (only diagonal blocks are processed). Applies to BSR format only.

mode - Specifies the triangular matrix part for symmetric, Hermitian, triangular, and block-triangular matrices:

`SPARSE_FILL_MODE_LOWER`	The lower triangular matrix part is processed.
`SPARSE_FILL_MODE_UPPER`	The upper triangular matrix part is processed.

diag - Specifies diagonal type for non-general matrices:

`SPARSE_DIAG_NON_UNIT`	Diagonal elements might not be equal to one.
`SPARSE_DIAG_UNIT`	Diagonal elements are equal to one.

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` (number of rows in `x`)	ldx	number of rows in A
`cols` (number of columns in `x`)	columns	ldx

On entry, the array x must contain the matrix X.

columns

C_INT.

Number of columns in 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` (number of rows in `y`)	ldy	number of rows in A
`cols` (number of columns in `y`)	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 or not, and 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.

Parent topic: Inspector-Executor Sparse BLAS Execution Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

mkl_sparse_?_trsm