Note: this is a BLAS routine and is not in libslatec.a
*DECK CSYR2K
SUBROUTINE CSYR2K (UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA,
$ C, LDC)
C***BEGIN PROLOGUE CSYR2K
C***PURPOSE Perform symmetric rank 2k update of a complex symmetric
C matrix.
C***LIBRARY SLATEC (BLAS)
C***CATEGORY D1B6
C***TYPE COMPLEX (SSYR2-S, DSYR2-D, CSYR2-C, CSYR2K-C)
C***KEYWORDS LEVEL 3 BLAS, LINEAR ALGEBRA
C***AUTHOR Dongarra, J., (ANL)
C Duff, I., (AERE)
C Du Croz, J., (NAG)
C Hammarling, S. (NAG)
C***DESCRIPTION
C
C CSYR2K performs one of the symmetric rank 2k operations
C
C C := alpha*A*B' + alpha*B*A' + beta*C,
C
C or
C
C C := alpha*A'*B + alpha*B'*A + beta*C,
C
C where alpha and beta are scalars, C is an n by n symmetric matrix
C and A and B are n by k matrices in the first case and k by n
C matrices in the second case.
C
C Parameters
C ==========
C
C UPLO - CHARACTER*1.
C On entry, UPLO specifies whether the upper or lower
C triangular part of the array C is to be referenced as
C follows:
C
C UPLO = 'U' or 'u' Only the upper triangular part of C
C is to be referenced.
C
C UPLO = 'L' or 'l' Only the lower triangular part of C
C is to be referenced.
C
C Unchanged on exit.
C
C TRANS - CHARACTER*1.
C On entry, TRANS specifies the operation to be performed as
C follows:
C
C TRANS = 'N' or 'n' C := alpha*A*B' + alpha*B*A' +
C beta*C.
C
C TRANS = 'T' or 't' C := alpha*A'*B + alpha*B'*A +
C beta*C.
C
C Unchanged on exit.
C
C N - INTEGER.
C On entry, N specifies the order of the matrix C. N must be
C at least zero.
C Unchanged on exit.
C
C K - INTEGER.
C On entry with TRANS = 'N' or 'n', K specifies the number
C of columns of the matrices A and B, and on entry with
C TRANS = 'T' or 't', K specifies the number of rows of the
C matrices A and B. K must be at least zero.
C Unchanged on exit.
C
C ALPHA - COMPLEX .
C On entry, ALPHA specifies the scalar alpha.
C Unchanged on exit.
C
C A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is
C k when TRANS = 'N' or 'n', and is n otherwise.
C Before entry with TRANS = 'N' or 'n', the leading n by k
C part of the array A must contain the matrix A, otherwise
C the leading k by n part of the array A must contain the
C matrix A.
C Unchanged on exit.
C
C LDA - INTEGER.
C On entry, LDA specifies the first dimension of A as declared
C in the calling (sub) program. When TRANS = 'N' or 'n'
C then LDA must be at least max( 1, n ), otherwise LDA must
C be at least max( 1, k ).
C Unchanged on exit.
C
C B - COMPLEX array of DIMENSION ( LDB, kb ), where kb is
C k when TRANS = 'N' or 'n', and is n otherwise.
C Before entry with TRANS = 'N' or 'n', the leading n by k
C part of the array B must contain the matrix B, otherwise
C the leading k by n part of the array B must contain the
C matrix B.
C Unchanged on exit.
C
C LDB - INTEGER.
C On entry, LDB specifies the first dimension of B as declared
C in the calling (sub) program. When TRANS = 'N' or 'n'
C then LDB must be at least max( 1, n ), otherwise LDB must
C be at least max( 1, k ).
C Unchanged on exit.
C
C BETA - COMPLEX .
C On entry, BETA specifies the scalar beta.
C Unchanged on exit.
C
C C - COMPLEX array of DIMENSION ( LDC, n ).
C Before entry with UPLO = 'U' or 'u', the leading n by n
C upper triangular part of the array C must contain the upper
C triangular part of the symmetric matrix and the strictly
C lower triangular part of C is not referenced. On exit, the
C upper triangular part of the array C is overwritten by the
C upper triangular part of the updated matrix.
C Before entry with UPLO = 'L' or 'l', the leading n by n
C lower triangular part of the array C must contain the lower
C triangular part of the symmetric matrix and the strictly
C upper triangular part of C is not referenced. On exit, the
C lower triangular part of the array C is overwritten by the
C lower triangular part of the updated matrix.
C
C LDC - INTEGER.
C On entry, LDC specifies the first dimension of C as declared
C in the calling (sub) program. LDC must be at least
C max( 1, n ).
C Unchanged on exit.
C
C***REFERENCES Dongarra, J., Du Croz, J., Duff, I., and Hammarling, S.
C A set of level 3 basic linear algebra subprograms.
C ACM TOMS, Vol. 16, No. 1, pp. 1-17, March 1990.
C***ROUTINES CALLED LSAME, XERBLA
C***REVISION HISTORY (YYMMDD)
C 890208 DATE WRITTEN
C 910605 Modified to meet SLATEC prologue standards. Only comment
C lines were modified. (BKS)
C***END PROLOGUE CSYR2K