zsyr2k (l)  Linux Manuals
zsyr2k: performs one of the symmetric rank 2k operations C := alpha*A*Baq + alpha*B*Aaq + beta*C,
NAME
ZSYR2K  performs one of the symmetric rank 2k operations C := alpha*A*Baq + alpha*B*Aaq + 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 :=
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 = aqUaq or aquaq Only the upper triangular part of C is to be referenced.
UPLO = aqLaq or aqlaq 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 = aqNaq or aqnaq C := alpha*A*Baq + alpha*B*Aaq + beta*C.
TRANS = aqTaq or aqtaq C := alpha*Aaq*B + alpha*Baq*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 = aqNaq or aqnaq, K specifies the number of columns of the matrices A and B, and on entry with TRANS = aqTaq or aqtaq, 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 = aqNaq or aqnaq, and is n otherwise. Before entry with TRANS = aqNaq or aqnaq, 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 = aqNaq or aqnaq 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 = aqNaq or aqnaq, and is n otherwise. Before entry with TRANS = aqNaq or aqnaq, 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 = aqNaq or aqnaq 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 = aqUaq or aquaq, 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 = aqLaq or aqlaq, 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 8February1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.