mkl_?cscsm

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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mkl_?cscsm

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

Syntax

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

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

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

call mkl_zcscsm(transa, m, n, 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_?cscsm routine solves a system of linear equations with matrix-matrix operations for a sparse matrix in the CSC 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 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^T)*B,

m

INTEGER. Number of columns of the matrix A.

n

INTEGER. Number of columns of the matrix C.

alpha

REAL for mkl_scscsm.

DOUBLE PRECISION for mkl_dcscsm.

COMPLEX for mkl_ccscsm.

DOUBLE COMPLEX for mkl_zcscsm.

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_scscsm.

DOUBLE PRECISION for mkl_dcscsm.

COMPLEX for mkl_ccscsm.

DOUBLE COMPLEX for mkl_zcscsm.

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.

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 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 for mkl_scscsm.

DOUBLE PRECISION for mkl_dcscsm.

COMPLEX for mkl_ccscsm.

DOUBLE COMPLEX for mkl_zcscsm.

Array, size ldb by 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 for mkl_scscsm.

DOUBLE PRECISION for mkl_dcscsm.

COMPLEX for mkl_ccscsm.

DOUBLE COMPLEX for mkl_zcscsm.

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_scscsm(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_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)

  DOUBLE PRECISION        alpha

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

SUBROUTINE mkl_ccscsm(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_zcscsm(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,*)

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_?cscsm

FORTRAN 77: