mkl_?bsrsm

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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mkl_?bsrsm

Solves a system of linear matrix equations for a sparse matrix in the BSR format (deprecated).

Syntax

call mkl_scsrsm(transa, m, n, lb, alpha, matdescra, val, indx, pntrb, pntre, b, ldb, c, ldc)

call mkl_dcsrsm(transa, m, n, lb, alpha, matdescra, val, indx, pntrb, pntre, b, ldb, c, ldc)

call mkl_ccsrsm(transa, m, n, lb, alpha, matdescra, val, indx, pntrb, pntre, b, ldb, c, ldc)

call mkl_zcsrsm(transa, m, n, lb, alpha, matdescra, val, indx, pntrb, pntre, b, ldb, c, ldc)

Include Files

mkl.fi

Description

This routine is deprecated. Use mkl_sparse_?_trsmfrom the Intel® oneAPI Math Kernel Library Inspector-executor Sparse BLAS interface instead.

The mkl_?bsrsm routine solves a system of linear equations with matrix-matrix operations for a sparse matrix in the BSR format:

C := alpha*inv(A)*B

C := alpha*inv(A^T)*B,

where:

alpha is scalar, B and C are dense matrices, A is a sparse upper or lower triangular matrix with unit or non-unit main diagonal, A^T is the transpose of A.

NOTE:

This routine supports a BSR format both with one-based indexing and zero-based indexing.

Input Parameters

Parameter descriptions are common for all implemented interfaces with the exception of data types that refer here to the FORTRAN 77 standard types. Data types specific to the different interfaces are described in the section "Interfaces" below.

transa

CHARACTER*1. Specifies the operation.

If transa = 'N' or 'n', then the matrix-matrix product is computed as C := alpha*inv(A)*B.

If transa = 'T' or 't' or 'C' or 'c', then the matrix-vector product is computed as C := alpha*inv(A^T)*B.

m

INTEGER. Number of block columns of the matrix A.

n

INTEGER. Number of columns of the matrix C.

lb

INTEGER. Size of the block in the matrix A.

alpha

REAL for mkl_sbsrsm.

DOUBLE PRECISION for mkl_dbsrsm.

COMPLEX for mkl_cbsrsm.

DOUBLE COMPLEX for mkl_zbsrsm.

Specifies the scalar alpha.

matdescra

CHARACTER. Array of six elements, specifies properties of the matrix used for operation. Only first four array elements are used, their possible values are given in Table “Possible Values of the Parameter matdescra (descra)”. Possible combinations of element values of this parameter are given in Table “Possible Combinations of Element Values of the Parameter matdescra”.

val

REAL for mkl_sbsrsm.

DOUBLE PRECISION for mkl_dbsrsm.

COMPLEX for mkl_cbsrsm.

DOUBLE COMPLEX for mkl_zbsrsm.

Array containing elements of non-zero blocks of the matrix A. Its length is equal to the number of non-zero blocks in the matrix A multiplied by lb*lb. Refer to the values array description in BSR Format for more details.

NOTE:

The non-zero elements of the given row of the matrix must be stored in the same order as they appear in the row (from left to right).

No diagonal element can be omitted from a sparse storage if the solver is called with the non-unit indicator.

indx

INTEGER. Array containing the column indices for each non-zero element of the matrix A.

Its length is equal to the number of non-zero blocks in the matrix A.

Refer to the columns array description in BSR Format for more details.

pntrb

INTEGER. Array of length m.

For one-based indexing: this array contains row indices, such that pntrb(i) - pntrb(1) + 1 is the first index of block row i in the array indx.

For zero-based indexing: this array contains row indices, such that pntrb(i) - pntrb(0) is the first index of block row i in the array indx.

Refer to pointerB array description in BSR Format for more details.

pntre

INTEGER. Array of length m.

For one-based indexing this array contains row indices, such that pntre(i) - pntrb(1) is the last index of block row i in the array indx.

For zero-based indexing this array contains row indices, such that pntre(i) - pntrb(0) - 1 is the last index of block row i in the array indx.

Refer to pointerE array description in BSR Format for more details.

b

REAL for mkl_sbsrsm.

DOUBLE PRECISION for mkl_dbsrsm.

COMPLEX for mkl_cbsrsm.

DOUBLE COMPLEX for mkl_zbsrsm.

Array, size (ldb, n) for one-based indexing, size (m, ldb) for zero-based indexing.

On entry the leading m-by-n part of the array b must contain the matrix B.

ldb

INTEGER. Specifies the leading dimension (in blocks) of b as declared in the calling (sub)program.

ldc

INTEGER. Specifies the leading dimension (in blocks) of c as declared in the calling (sub)program.

Output Parameters

c

REAL for mkl_sbsrsm.

DOUBLE PRECISION for mkl_dbsrsm.

COMPLEX for mkl_cbsrsm.

DOUBLE COMPLEX for mkl_zbsrsm.

Array, size (ldc, n) for one-based indexing, size (m, ldc) for zero-based indexing.

The leading m-by-n part of the array c contains the output matrix C.

Interfaces

FORTRAN 77:

SUBROUTINE mkl_sbsrsm(transa, m, n, lb, alpha, matdescra, val, indx, pntrb, pntre, b, ldb, c, ldc)

  CHARACTER*1     transa

  CHARACTER     matdescra(*)

  INTEGER       m, n, lb, ldb, ldc

  INTEGER       indx(*), pntrb(m), pntre(m)

  REAL          alpha

  REAL          val(*), b(ldb,*), c(ldc,*)

SUBROUTINE mkl_dbsrsm(transa, m, n, lb, alpha, matdescra, val, indx, pntrb, pntre, b, ldb, c, ldc)

  CHARACTER*1     transa

  CHARACTER     matdescra(*)

  INTEGER       m, n, lb, ldb, ldc

  INTEGER       indx(*), pntrb(m), pntre(m)

  DOUBLE PRECISION        alpha

  DOUBLE PRECISION        val(*), b(ldb,*), c(ldc,*)

SUBROUTINE mkl_cbsrsm(transa, m, n, lb, alpha, matdescra, val, indx, pntrb, pntre, b, ldb, c, ldc)

  CHARACTER*1     transa

  CHARACTER     matdescra(*)

  INTEGER       m, n, lb, ldb, ldc

  INTEGER       indx(*), pntrb(m), pntre(m)

  COMPLEX        alpha

  COMPLEX        val(*), b(ldb,*), c(ldc,*)

SUBROUTINE mkl_zbsrsm(transa, m, n, lb, alpha, matdescra, val, indx, pntrb, pntre, b, ldb, c, ldc)

  CHARACTER*1     transa

  CHARACTER     matdescra(*)

  INTEGER       m, n, lb, ldb, ldc

  INTEGER       indx(*), pntrb(m), pntre(m)

  DOUBLE COMPLEX        alpha

  DOUBLE COMPLEX        val(*), b(ldb,*), c(ldc,*)

Parent topic: Sparse BLAS Level 2 and Level 3 Routines.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

mkl_?bsrsm

FORTRAN 77: