mkl_?skysm

Syntax

Fortran:

call mkl_sskysm(transa, m, n, alpha, matdescra, val, pntr, b, ldb, c, ldc)

call mkl_dskysm(transa, m, n, alpha, matdescra, val, pntr, b, ldb, c, ldc)

call mkl_cskysm(transa, m, n, alpha, matdescra, val, pntr, b, ldb, c, ldc)

call mkl_zskysm(transa, m, n, alpha, matdescra, val, pntr, b, ldb, c, ldc)

C:

mkl_sskysm(&transa, &m, &n, &alpha, matdescra, val, pntr, b, &ldb, c, &ldc);

mkl_dskysm(&transa, &m, &n, &alpha, matdescra, val, pntr, b, &ldb, c, &ldc);

mkl_cskysm(&transa, &m, &n, &alpha, matdescra, val, pntr, b, &ldb, c, &ldc);

mkl_zskysm(&transa, &m, &n, &alpha, matdescra, val, pntr, b, &ldb, c, &ldc);

Include Files

The FORTRAN 77 interfaces are specified in the mkl_spblas.fi include file and the C interfaces are specified in the mkl_spblas.h include file.

Description

The mkl_?skysm routine solves a system of linear equations with matrix-matrix operations for a sparse matrix in the skyline storage 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 only one-based indexing of the input arrays.

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 rows of the matrix A.

n

INTEGER. Number of columns of the matrix C.

alpha

REAL for mkl_sskysm.

DOUBLE PRECISION for mkl_dskysm.

COMPLEX for mkl_cskysm.

DOUBLE COMPLEX for mkl_zskysm.

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”.

Note

General matrices (matdescra (1)='G') is not supported.

val

REAL for mkl_sskysm.

DOUBLE PRECISION for mkl_dskysm.

COMPLEX for mkl_cskysm.

DOUBLE COMPLEX for mkl_zskysm.

Array containing the set of elements of the matrix A in the skyline profile form.

If matdescrsa(2)= 'L', then val contains elements from the low triangle of the matrix A.

If matdescrsa(2)= 'U', then val contains elements from the upper triangle of the matrix A.

Refer to values array description in Skyline Storage Scheme for more details.

pntr

INTEGER. Array of length (m+m). It contains the indices specifying in the val the positions of the first non-zero element of each i-row (column) of the matrix A such that pointers(i)- pointers(1)+1. Refer to pointers array description in Skyline Storage Scheme for more details.

b

REAL for mkl_sskysm.

DOUBLE PRECISION for mkl_dskysm.

COMPLEX for mkl_cskysm.

DOUBLE COMPLEX for mkl_zskysm.

Array, DIMENSION (ldb, n).

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 as declared in the calling (sub)program.

ldc

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

Output Parameters

c

REAL for mkl_sskysm.

DOUBLE PRECISION for mkl_dskysm.

COMPLEX for mkl_cskysm.

DOUBLE COMPLEX for mkl_zskysm.

Array, DIMENSION (ldc, n).

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

Interfaces

SUBROUTINE mkl_sskysm(transa, m, n, alpha, matdescra, val, pntr, b, ldb, c, ldc)

  CHARACTER*1   transa

  CHARACTER     matdescra(*)

  INTEGER       m, n, ldb, ldc

  INTEGER       pntr(*)

  REAL          alpha

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

SUBROUTINE mkl_dskysm(transa, m, n, alpha, matdescra, val, pntr, b, ldb, c, ldc)

  CHARACTER*1   transa

  CHARACTER     matdescra(*)

  INTEGER       m, n, ldb, ldc

  INTEGER       pntr(*)

  DOUBLE PRECISION        alpha

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

SUBROUTINE mkl_cskysm(transa, m, n, alpha, matdescra, val, pntr, b, ldb, c, ldc)

  CHARACTER*1   transa

  CHARACTER     matdescra(*)

  INTEGER       m, n, ldb, ldc

  INTEGER       pntr(*)

  COMPLEX        alpha

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

SUBROUTINE mkl_zskysm(transa, m, n, alpha, matdescra, val, pntr, b, ldb, c, ldc)

  CHARACTER*1   transa

  CHARACTER     matdescra(*)

  INTEGER       m, n, ldb, ldc

  INTEGER       pntr(*)

  DOUBLE COMPLEX        alpha

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

void mkl_sskysm(char *transa, int *m, int *n, float *alpha, char *matdescra,

float *val, int *pntr, float *b, int *ldb, float *c, int *ldc);

void mkl_dskysm(char *transa, int *m, int *n, double *alpha, char *matdescra,

double *val, int *pntr, double *b, int *ldb, double *c, int *ldc);

void mkl_cskysm(char *transa, int *m, int *n, MKL_Complex8 *alpha, char *matdescra,

MKL_Complex8 *val, int *pntr, MKL_Complex8 *b, int *ldb, MKL_Complex8 *c, int *ldc);

void mkl_zskysm(char *transa, int *m, int *n, MKL_Complex16 *alpha, char *matdescra,

MKL_Complex16 *val, int *pntr, MKL_Complex16 *b, int *ldb, MKL_Complex16 *c, int *ldc);