NAME

ssyrk - perform one of the symmetric rank k operations   C := alpha∗A∗A’ + beta∗C or C := alpha∗A’∗A + beta∗C

SYNOPSIS

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

CHARACTER∗1 UPLO, TRANS

INTEGER N, K, LDA, LDC

REAL ALPHA, BETA

REAL A( LDA, ∗ ), C( LDC, ∗ )

PURPOSE

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.

SunSoft, Inc.  —  Last change: 27 Jun 1995