# ?symm

Performs a scalar-matrix-matrix product(one matrix operand is symmetric) and adds the result to a scalar-matrix product.

## 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])

## 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 first 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 first 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 first 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 1.

Parent topic: BLAS Level 3 Routines