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AIX Version 4.3 Base Operating System and Extensions Technical Reference, Volume 2

## SSYMM, DSYMM, CSYMM, or ZSYMM Subroutine

### Purpose

Performs matrix-matrix matrix operations on symmetric matrices.

### Library

BLAS Library (libblas.a)

### FORTRAN Syntax

```SUBROUTINE SSYMM(SIDE, UPLO, M, N, ALPHA,
A, LDA, B, LDB, BETA, C, LDC)
CHARACTER*1 SIDE,UPLO
INTEGER M,N,LDA,LDB,LDC
REAL ALPHA,BETA
REAL A(LDA,*), B(LDB,*), C(LDC,*)```
```SUBROUTINE DSYMM(SIDE, UPLO, M, N, ALPHA,
A, LDA, B, LDB, BETA, C, LDC)
CHARACTER*1 SIDE,UPLO
INTEGER M,N,LDA,LDB,LDC
DOUBLE PRECISION ALPHA,BETA
DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*)```
```SUBROUTINE CSYMM(SIDE, UPLO, M, N, ALPHA,
A, LDA, B, LDB, BETA, C, LDC)
CHARACTER*1 SIDE,UPLO
INTEGER M,N,LDA,LDB,LDC
COMPLEX ALPHA,BETA
COMPLEX A(LDA,*), B(LDB,*), C(LDC,*)```
```SUBROUTINE ZSYMM(SIDE, UPLO, M, N, ALPHA,
A, LDA, B, LDB, BETA, C, LDC)
CHARACTER*1 SIDE,UPLO
INTEGER M,N,LDA,LDB,LDC
COMPLEX*16 ALPHA,BETA
COMPLEX*16 A(LDA,*), B(LDB,*), C(LDC,*)```

### Description

The SSYMM, DSYMM, CSYMM, or ZSYMM subroutine performs one of the matrix-matrix operations:

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

OR

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

where alpha and beta are scalars, A is a symmetric matrix and B and C are M by N matrices.

### Parameters

SIDE On entry, SIDE specifies whether the symmetric matrix A appears on the left or right in the operation as follows:
 SIDE = 'L' or 'l' C := alpha * A * B + beta * C SIDE = 'R' or 'r' C := alpha * B * A + beta * C

Unchanged on exit.

UPLO On entry, UPLO specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced as follows:
 UPLO = 'U' or 'u' Only the upper triangular part of the symmetric matrix is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of the symmetric matrix is to be referenced.

Unchanged on exit.

M On entry, M specifies the number of rows of the matrix C; M must be at least 0; unchanged on exit.
N On entry, N specifies the number of columns of the matrix C; N must be at least 0; unchanged on exit.
ALPHA On entry, ALPHA specifies the scalar alpha; unchanged on exit.
A An array of dimension ( LDA, KA ), where KA is M when SIDE = 'L' or 'l' and is N otherwise; on 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. On 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; unchanged on exit.
LDA On entry, LDA 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 ); unchanged on exit.
B An array of dimension ( LDB, N ); on entry, the leading M by N part of the array B must contain the matrix B; unchanged on exit.
LDB On entry, LDB specifies the first dimension of B as declared in the calling (sub) program; LDB must be at least max( 1, M ); unchanged on exit.
BETA On entry, BETA specifies the scalar beta; when BETA is supplied as 0 then C need not be set on input; unchanged on exit.
C An array of dimension ( LDC, N ); on entry, the leading M by N part of the array C must contain the matrix C, except when beta is 0, in which case C need not be set on entry; on exit, the array C is overwritten by the M by N updated matrix.
LDC On entry, LDC specifies the first dimension of C as declared in the calling (sub) program; LDC must be at least max( 1, M ); unchanged on exit.

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