zsyr2k (l) - Linux Man Pages

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 := alpha*Aaq*B alpha*Baq*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 = 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 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.