# mkl_dcscsm

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

## Syntax

Fortran:

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

C:

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

## Description

The mkl_dcscsm routine solves a system of linear equations with matrix-matrix operations for a sparse matrix in the CSC 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 CSC 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 system of equations.

  If `transa = 'N'` or 'n', then `C := alpha*inv(A)*B`

  If `transa = 'T'` or 't' or 'C' or 'c', then `C := alpha*inv(A')*B`,

m

  INTEGER. Number of columns of the matrix A.

n

  INTEGER. Number of columns of the matrix C.

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 non-zero elements of the matrix A.

  For one-based indexing its length is `pntre(k) - pntrb(1)`.

  For zero-based indexing its length is `pntre(m-1) - pntrb(0)`.

  Refer to values array description in CSC Format for more details.

indx

  INTEGER. Array containing the row indices for each non-zero element of the matrix A. Its length is equal to length of the val array.

  Refer to rows array description in CSC Format for more details.

  ### Note

  Row indices must be sorted in increasing order for each column.

pntrb

  INTEGER. Array of length m.

  For one-based indexing this array contains column indices, such that `pntrb(i) - pntrb(1)+1` is the first index of column i in the arrays val and indx.

  For zero-based indexing this array contains column indices, such that `pntrb(i) - pntrb(0)` is the first index of column i in the arrays val and indx.

  Refer to pointerb array description in CSC Format for more details.

pntre

  INTEGER. Array of length m.

  For one-based indexing this array contains column indices, such that `pntre(i) - pntrb(1)` is the last index of column i in the arrays val and indx.

  For zero-based indexing this array contains column indices, such that `pntre(i) - pntrb(1)-1` is the last index of column i in the arrays val and indx.

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

b

  REAL*8.

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

ldc

  INTEGER. Specifies the first dimension of c for one-based indexing, and the second dimension of c for zero-based indexing, as declared in the calling (sub)program.

## Output Parameters

c

  REAL*8.

  Array, DIMENSION (ldc, n) for one-based indexing, and `(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_dcscsm(transa, m, n, alpha, matdescra, val, indx,

pntrb, pntre, b, ldb, c, ldc)

CHARACTER*1 transa

CHARACTER matdescra(*)

INTEGER m, n, ldb, ldc

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

REAL*8 alpha

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

## C:

`void mkl_dcscsm(char *transa, int *m, int *n, 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.