# mkl_dbsrsm

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

## Syntax

Fortran:

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

C:

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

## Description

The mkl_dbsrsm routine solves a system of linear equations with matrix-matrix operations for a sparse matrix in the BSR format:
`C := alpha*inv(A)*B`

or
`C := alpha*inv(A')*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' is the transpose of A.

### Note

This routine supports 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')*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*8. 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 the “Possible Values of the Parameter matdescra (descra)”.

val

  REAL*8. Array containing elements of non-zero blocks of the matrix A. Its length is equal to the ABAB number ABAB of non-zero blocks in the matrix A multiplied by `lb*lb`. Refer to the values array description in BSR Format for more details.

indx

  INTEGER. Array containing the column indices for each non-zero block in 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 intexing 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 intexing 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*8.

  Array, DIMENSION `(ldb, n)` for one-based indexing, DIMENSION `(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 first dimension (in blocks) of b as declared in the calling (sub)program.

ldc

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

## Output Parameters

c

  REAL*8.

  Array, DIMENSION `(ldc, n)` for one-based indexing, DIMENSION `(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_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)

REAL*8 alpha

REAL*8 val(*), b(ldb,*), c(ldc,*)

## C:

`void mkl_dbsrsm(char *transa, int *m, int *n, int *lb, double *alpha, char *matdescra,`
`double *val, int *indx, int *pntrb, int *pntre, double *b, int *ldb, double *c, int *ldc);`

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