mkl_?csrsm

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

Syntax

Fortran:

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

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

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

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

C:

void mkl_scsrsm (char *transa, MKL_INT *m, MKL_INT *n, float *alpha, char *matdescra, float *val, MKL_INT *indx, MKL_INT *pntrb, MKL_INT *pntre, float *b, MKL_INT *ldb, float *c, MKL_INT *ldc);

void mkl_dcsrsm (char *transa, MKL_INT *m, MKL_INT *n, double *alpha, char *matdescra, double *val, MKL_INT *indx, MKL_INT *pntrb, MKL_INT *pntre, double *b, MKL_INT *ldb, double *c, MKL_INT *ldc);

void mkl_ccsrsm (char *transa, MKL_INT *m, MKL_INT *n, MKL_Complex8 *alpha, char *matdescra, MKL_Complex8 *val, MKL_INT *indx, MKL_INT *pntrb, MKL_INT *pntre, MKL_Complex8 *b, MKL_INT *ldb, MKL_Complex8 *c, MKL_INT *ldc);

void mkl_zcsrsm (char *transa, MKL_INT *m, MKL_INT *n, MKL_Complex16 *alpha, char *matdescra, MKL_Complex16 *val, MKL_INT *indx, MKL_INT *pntrb, MKL_INT *pntre, MKL_Complex16 *b, MKL_INT *ldb, MKL_Complex16 *c, MKL_INT *ldc);

Include Files

  • Fortran: mkl.fi
  • C: mkl.h

Description

The mkl_?csrsm routine solves a system of linear equations with matrix-matrix operations for a sparse matrix in the CSR 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 a CSR 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 linear 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 for mkl_scsrsm.

DOUBLE PRECISION for mkl_dcsrsm.

COMPLEX for mkl_ccsrsm.

DOUBLE COMPLEX for mkl_zcsrsm.

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_scsrsm.

DOUBLE PRECISION for mkl_dcsrsm.

COMPLEX for mkl_ccsrsm.

DOUBLE COMPLEX for mkl_zcsrsm.

Array containing non-zero elements of the matrix A.

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

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

Refer to values array description in CSR 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 length of the val array.

Refer to columns array description in CSR Format for more details.

Note

Column indices must be sorted in increasing order for each row.

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 row i in the arrays val and indx.

For zero-based indexing this array contains row indices, such that pntrb(i) - pntrb(0) is the first index of row i in the arrays val and indx. Refer to pointerb array description in CSR 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 row i in the arrays val and indx.

For zero-based indexing this array contains row indices, such that pntre(i) - pntrb(0) - 1 is the last index of row i in the arrays val and indx.Refer to pointerE array description in CSR Format for more details.

b

REAL for mkl_scsrsm.

DOUBLE PRECISION for mkl_dcsrsm.

COMPLEX for mkl_ccsrsm.

DOUBLE COMPLEX for mkl_zcsrsm.

Array, size (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 leading 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 leading 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, size ldc by 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_scsrsm(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          alpha
  REAL          val(*), b(ldb,*), c(ldc,*)

SUBROUTINE mkl_dcsrsm(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)
  DOUBLE PRECISION        alpha
  DOUBLE PRECISION        val(*), b(ldb,*), c(ldc,*)

SUBROUTINE mkl_ccsrsm(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)
  COMPLEX        alpha
  COMPLEX        val(*), b(ldb,*), c(ldc,*)

SUBROUTINE mkl_zcsrsm(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)
  DOUBLE COMPLEX        alpha
  DOUBLE COMPLEX        val(*), b(ldb,*), c(ldc,*)

C:

void mkl_scsrsm(char *transa, int *m, int *n, float *alpha,
char *matdescra, float  *val, int *indx, int *pntrb,
int *pntre, float *b, int *ldb, float *c, int *ldc);

void mkl_dcsrsm(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);

void mkl_ccsrsm(char *transa, int *m, int *n, MKL_Complex8 *alpha,
char *matdescra, MKL_Complex8  *val, int *indx, int *pntrb,
int *pntre, MKL_Complex8 *b, int *ldb, MKL_Complex8 *c, int *ldc);

void mkl_zcsrsm(char *transa, int *m, int *n, MKL_Complex16 *alpha,
char *matdescra, MKL_Complex16  *val, int *indx, int *pntrb,
int *pntre, MKL_Complex16 *b, int *ldb, MKL_Complex16 *c, int *ldc);

For more complete information about compiler optimizations, see our Optimization Notice.