.TH ZSYRK 1 "November 2006" "BLAS routine" "BLAS routine" .SH NAME ZSYRK - one of the symmetric rank k operations C := alpha*A*A\(aq + beta*C, .SH SYNOPSIS .TP 56 SUBROUTINE ZSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) .TP 56 .ti +4 DOUBLE COMPLEX ALPHA,BETA .TP 56 .ti +4 INTEGER K,LDA,LDC,N .TP 56 .ti +4 CHARACTER TRANS,UPLO .TP 56 .ti +4 DOUBLE COMPLEX A(LDA,*),C(LDC,*) .SH PURPOSE ZSYRK performs one of the symmetric rank k operations or .br C := alpha*A\(aq*A + beta*C, .br where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case. .br .SH ARGUMENTS .TP 7 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 = \(aqU\(aq or \(aqu\(aq Only the upper triangular part of C is to be referenced. UPLO = \(aqL\(aq or \(aql\(aq Only the lower triangular part of C is to be referenced. Unchanged on exit. .TP 7 TRANS - CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows: TRANS = \(aqN\(aq or \(aqn\(aq C := alpha*A*A\(aq + beta*C. TRANS = \(aqT\(aq or \(aqt\(aq C := alpha*A\(aq*A + beta*C. Unchanged on exit. .TP 7 N - INTEGER. On entry, N specifies the order of the matrix C. N must be at least zero. Unchanged on exit. .TP 7 K - INTEGER. On entry with TRANS = \(aqN\(aq or \(aqn\(aq, K specifies the number of columns of the matrix A, and on entry with TRANS = \(aqT\(aq or \(aqt\(aq, K specifies the number of rows of the matrix A. K must be at least zero. Unchanged on exit. .TP 7 ALPHA - COMPLEX*16 . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. .TP 7 A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is k when TRANS = \(aqN\(aq or \(aqn\(aq, and is n otherwise. Before entry with TRANS = \(aqN\(aq or \(aqn\(aq, 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. .TP 7 LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = \(aqN\(aq or \(aqn\(aq then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k ). Unchanged on exit. .TP 7 BETA - COMPLEX*16 . On entry, BETA specifies the scalar beta. Unchanged on exit. .TP 7 C - COMPLEX*16 array of DIMENSION ( LDC, n ). Before entry with UPLO = \(aqU\(aq or \(aqu\(aq, 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 = \(aqL\(aq or \(aql\(aq, 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. .TP 7 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. 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. .. External Functions .. .. .. External Subroutines .. ..