cher2k (l) - Linux Man Pages

cher2k: performs one of the hermitian rank 2k operations C := alpha*A*conjg( Baq ) + conjg( alpha )*B*conjg( Aaq ) + beta*C,

NAME

CHER2K - performs one of the hermitian rank 2k operations C := alpha*A*conjg( Baq ) + conjg( alpha )*B*conjg( Aaq ) + beta*C,

SYNOPSIS

SUBROUTINE CHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)

    
COMPLEX ALPHA

    
REAL BETA

    
INTEGER K,LDA,LDB,LDC,N

    
CHARACTER TRANS,UPLO

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

PURPOSE

CHER2K performs one of the hermitian rank 2k operations

or


C := alpha*conjg( Aaq )*B conjg( alpha )*conjg( Baq )*A beta*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 .
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
A - COMPLEX 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 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 - REAL .
On entry, BETA specifies the scalar beta. Unchanged on exit.
C - COMPLEX 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 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.

-- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1.
Ed Anderson, Cray Research Inc.