SSYRK(3)

SYNOPSIS
SUBROUTINE SSYRK (UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)

NAME
ssyrk - Perform symmetric rank k update of a real symmetric matrix.

LIBRARY
SLATEC (BLAS)

CATEGORY
D1B6

TYPE
SINGLE PRECISION (SSYRK-S, DSYRK-D, CSYRK-C)

KEYWORDS
LEVEL 3 BLAS, LINEAR ALGEBRA

AUTHOR
Dongarra, J., (ANL) Duff, I., (AERE) Du Croz, J., (NAG) Hammarling, S. (NAG)

DESCRIPTION
SSYRK performs one of the symmetric rank k operations C := alpha*A*A' + beta*C, or C := alpha*A'*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case. Parameters ========== UPLO - CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced. Unchanged on exit. TRANS - CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*A' + beta*C. TRANS = 'T' or 't' C := alpha*A'*A + beta*C. TRANS = 'C' or 'c' C := alpha*A'*A + beta*C. Unchanged on exit. N - INTEGER. On entry, N specifies the order of the matrix C. N must be at least zero. Unchanged on exit. K - INTEGER. On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrix A, and on entry with TRANS = 'T' or 't' or 'C' or 'c', K specifies the number of rows of the matrix A. K must be at least zero. Unchanged on exit. ALPHA - REAL . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - REAL array of DIMENSION ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k ). Unchanged on exit. BETA - REAL . On entry, BETA specifies the scalar beta. Unchanged on exit. C - REAL array of DIMENSION ( LDC, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. LDC - INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, n ). Unchanged on exit.

REFERENCES
Dongarra, J., Du Croz, J., Duff, I., and Hammarling, S. A set of level 3 basic linear algebra subprograms. ACM TOMS, Vol. 16, No. 1, pp. 1-17, March 1990.

ROUTINES CALLED
LSAME, XERBLA

REVISION HISTORY (YYMMDD)
890208 DATE WRITTEN
910605 Modified to meet SLATEC prologue standards. Only comment lines were modified. (BKS)