?symm

Syntax

FORTRAN 77:

call ssymm(side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)

call dsymm(side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)

call csymm(side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)

call zsymm(side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)

Fortran 95:

call symm(a, b, c [,side][,uplo] [,alpha][,beta])

Include Files

The FORTRAN 77 interfaces are specified in the mkl_blas.fi include file, the Fortran 95 interfaces are specified in the blas.f90 include file, and the C interfaces are specified in the mkl_blas.h include file.

Description

The ?symm routines perform a matrix-matrix operation using symmetric matrices. The operation is defined as C := alpha*A*B + beta*C,

or C := alpha*B*A + beta*C,

where:

alpha and beta are scalars,

A is a symmetric matrix,

B and C are m-by-n matrices.

Input Parameters

side

CHARACTER*1. Specifies whether the symmetric matrix A appears on the left or right in the operation:

if side = 'L' or 'l', then C := alpha*A*B + beta*C;

if side = 'R' or 'r', then C := alpha*B*A + beta*C.

uplo

CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is used:

if uplo = 'U' or 'u', then the upper triangular part is used;

if uplo = 'L' or 'l', then the lower triangular part is used.

m

INTEGER. Specifies the number of rows of the matrix C.

The value of m must be at least zero.

n

INTEGER. Specifies the number of columns of the matrix C.

The value of n must be at least zero.

alpha

REAL for ssymm

DOUBLE PRECISION for dsymm

COMPLEX for csymm

DOUBLE COMPLEX for zsymm

Specifies the scalar alpha.

a

REAL for ssymm

DOUBLE PRECISION for dsymm

COMPLEX for csymm

DOUBLE COMPLEX for zsymm

Array, DIMENSION (lda, ka), where ka is m when side = 'L' or 'l' and is n otherwise.

Before entry with side = 'L' or 'l', the m-by-m part of the array a must contain the symmetric matrix, such that when uplo = 'U' or 'u', the leading m-by-m upper triangular part of the array a must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of a is not referenced, and when uplo = 'L' or 'l', the leading m-by-m lower triangular part of the array a must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of a is not referenced.

Before entry with side = 'R' or 'r', the n-by-n part of the array a must contain the symmetric matrix, such that when uplo = 'U' or 'u', the leading n-by-n upper triangular part of the array a must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of a is not referenced, and when uplo = 'L' or 'l', the leading n-by-n lower triangular part of the array a must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of a is not referenced.

lda

INTEGER. Specifies the leading dimension of a as declared in the calling (sub)program. When side = 'L' or 'l' then lda must be at least max(1, m), otherwise lda must be at least max(1, n).

b

REAL for ssymm

DOUBLE PRECISION for dsymm

COMPLEX for csymm

DOUBLE COMPLEX for zsymm

Array, DIMENSION (ldb,n). Before 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. The value of ldb must be at least max(1, m).

beta

REAL for ssymm

DOUBLE PRECISION for dsymm

COMPLEX for csymm

DOUBLE COMPLEX for zsymm

Specifies the scalar beta.

When beta is set to zero, then c need not be set on input.

c

REAL for ssymm

DOUBLE PRECISION for dsymm

COMPLEX for csymm

DOUBLE COMPLEX for zsymm

Array, DIMENSION (ldc,n). Before entry, the leading m-by-n part of the array c must contain the matrix C, except when beta is zero, in which case c need not be set on entry.

ldc

INTEGER. Specifies the leading dimension of c as declared in the calling (sub)program. The value of ldc must be at least max(1, m).

Output Parameters

c

Overwritten by the m-by-n updated matrix.

Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions.

Specific details for the routine symm interface are the following:

a

Holds the matrix A of size (k,k) where

k = m if side = 'L',

k = n otherwise.

b

Holds the matrix B of size (m,n).

c

Holds the matrix C of size (m,n).

side

Must be 'L' or 'R'. The default value is 'L'.

uplo

Must be 'U' or 'L'. The default value is 'U'.

alpha

The default value is 1.

beta

The default value is 0.