.TH "BLAS/SRC/zsyrk.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
BLAS/SRC/zsyrk.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzsyrk\fP (uplo, trans, n, k, alpha, a, lda, beta, c, ldc)"
.br
.RI "\fBZSYRK\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zsyrk (character uplo, character trans, integer n, integer k, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16 beta, complex*16, dimension(ldc,*) c, integer ldc)"

.PP
\fBZSYRK\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZSYRK  performs one of the symmetric rank k operations

    C := alpha*A*A**T + beta*C,

 or

    C := alpha*A**T*A + beta*C,

 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
           On  entry,   UPLO  specifies  whether  the  upper  or  lower
           triangular  part  of the  array  C  is to be  referenced  as
           follows:

              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                  is to be referenced\&.

              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                  is to be referenced\&.
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
           On entry,  TRANS  specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   C := alpha*A*A**T + beta*C\&.

              TRANS = 'T' or 't'   C := alpha*A**T*A + beta*C\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
           On entry,  N specifies the order of the matrix C\&.  N must be
           at least zero\&.
.fi
.PP
.br
\fIK\fP 
.PP
.nf
          K is INTEGER
           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
           of  columns   of  the   matrix   A,   and  on   entry   with
           TRANS = 'T' or 't',  K  specifies  the number of rows of the
           matrix A\&.  K must be at least zero\&.
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
          ALPHA is COMPLEX*16
           On entry, ALPHA specifies the scalar alpha\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is
           k  when  TRANS = 'N' or 'n',  and is  n  otherwise\&.
           Before entry with  TRANS = 'N' or 'n',  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\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
           On entry, LDA specifies the first dimension of A as declared
           in  the  calling  (sub)  program\&.   When  TRANS = 'N' or 'n'
           then  LDA must be at least  max( 1, n ), otherwise  LDA must
           be at least  max( 1, k )\&.
.fi
.PP
.br
\fIBETA\fP 
.PP
.nf
          BETA is COMPLEX*16
           On entry, BETA specifies the scalar beta\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is COMPLEX*16 array, dimension ( LDC, N )
           Before entry  with  UPLO = 'U' or 'u',  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 = 'L' or 'l',  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\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is 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 )\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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\&.
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB166\fP of file \fBzsyrk\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.