SYNOPSIS
 SUBROUTINE CSYRK
 ( UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC )
 CHARACTER*1 UPLO, TRANS
 INTEGER N, K, LDA, LDC
 COMPLEX ALPHA, BETA
 COMPLEX A( LDA, * ), C( LDC, * )
PURPOSE
CSYRK performs one of the symmetric rank k operations
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.
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', K specifies the number of rows of the matrix A. 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.
 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.
Level 3 Blas routine.
 Written on 8February1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd.