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, and A is a sparse matrix.

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) = AT.

SPARSE_OPERATION_CONJUGATE_TRANSPOSE

Conjugate transpose, op(A) = AH.

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 containing sparse matrix in internal data structure.

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.

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