ZSYR2K(1)

NAME
LAPACK-3 - performs one of the symmetric rank 2k operations C := alpha*A*B**T + alpha*B*A**T + beta*C,

SYNOPSIS

SUBROUTINE ZSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)

DOUBLE
    COMPLEX ALPHA,BETA

INTEGER
    K,LDA,LDB,LDC,N

CHARACTER
    TRANS,UPLO

DOUBLE
    COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)

PURPOSE
ZSYR2K performs one of the symmetric rank 2k operations
 or
    C := alpha*A**T*B + alpha*B**T*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.

ARGUMENTS

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**T + alpha*B*A**T +
     beta*C.
     TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*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*16      .
     On entry, ALPHA specifies the scalar alpha.
     Unchanged on exit.

A      - COMPLEX*16       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*16       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*16      .
     On entry, BETA specifies the scalar beta.
     Unchanged on exit.

C      - COMPLEX*16       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.

FURTHER DETAILS
 Level 3 Blas routine.
 -- Written on 8-February-1989.
    Jack Dongarra, Argonne National Laboratory.
    Iain Duff, AERE Harwell.
    Jeremy Du Croz, Numerical Algorithms Group Ltd.
    Sven Hammarling, Numerical Algorithms Group Ltd.