zher2k (l)  Linux Man Pages
zher2k: performs one of the hermitian rank 2k operations C := alpha*A*conjg( Baq ) + conjg( alpha )*B*conjg( Aaq ) + beta*C,
NAME
ZHER2K  performs one of the hermitian rank 2k operations C := alpha*A*conjg( Baq ) + conjg( alpha )*B*conjg( Aaq ) + beta*C,SYNOPSIS
 SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
 DOUBLE COMPLEX ALPHA
 DOUBLE PRECISION BETA
 INTEGER K,LDA,LDB,LDC,N
 CHARACTER TRANS,UPLO
 DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
PURPOSE
ZHER2K performs one of the hermitian rank 2k operations
or
C :=
where alpha and beta are scalars with beta real, C is an n by n
hermitian 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*conjg( Baq ) + conjg( alpha )*B*conjg( Aaq ) + beta*C.
TRANS = aqCaq or aqcaq C := alpha*conjg( Aaq )*B + conjg( alpha )*conjg( 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 = aqCaq or aqcaq, 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  DOUBLE PRECISION .
 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 hermitian 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 hermitian 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. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero.
 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.
 Modified 8Nov93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
Ed Anderson, Cray Research Inc.