NAME

csyr2k - perform one of the symmetric rank 2k operations   C := alpha∗A∗B’ + alpha∗B∗A’ + beta∗C or C := alpha∗A’∗B + alpha∗B’∗A + beta∗C

SYNOPSIS

SUBROUTINE CSYR2K(
UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC )

CHARACTER∗1 UPLO, TRANS

INTEGER N, K, LDA, LDB, LDC

COMPLEX ALPHA, BETA

COMPLEX A( LDA, ∗ ), B( LDB, ∗ ), C( LDC, ∗ )

PURPOSE

CSYR2K  performs one of the symmetric rank 2k operations C := alpha∗A∗B’ + alpha∗B∗A’ + beta∗C or C := alpha∗A’∗B + alpha∗B’∗A + beta∗C where  alpha and beta  are scalars,  C is an  n by n symmetric matrix and  A and B  are  n by k  matrices  in the  first  case  and  k by n matrices 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∗B’ + alpha∗B∗A’ + beta∗C.
 
TRANS = ’T’ or ’t’    C := alpha∗A’∗B + alpha∗B’∗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  matrices  A and B,  and on  entry  with TRANS = ’T’ or ’t’,  K  specifies  the number of rows of the matrices  A and B.  K must be at least zero. Unchanged on exit.

ALPHA  - COMPLEX         . 
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

A      - COMPLEX          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.

B      - COMPLEX          array of DIMENSION ( LDB, kb ), where kb 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  B  must contain the matrix  B,  otherwise the leading  k by n  part of the array  B  must contain  the matrix B. Unchanged on exit.

LDB    - INTEGER. 
On entry, LDB specifies the first dimension of B as declared in  the  calling  (sub)  program.   When  TRANS = ’N’ or ’n’ then  LDB must be at least  max( 1, n ), otherwise  LDB must be at least  max( 1, k ). Unchanged on exit.

BETA   - COMPLEX         . 
On entry, BETA specifies the scalar beta. Unchanged on exit.

C      - COMPLEX          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