CSYR(3)                    MathKeisan LAPACK routine                   CSYR(3)



NAME
       CSYR - the symmetric rank 1 operation   A := alpha*x*( x' ) + A,

SYNOPSIS
       SUBROUTINE CSYR( UPLO, N, ALPHA, X, INCX, A, LDA )

           CHARACTER    UPLO

           INTEGER      INCX, LDA, N

           COMPLEX      ALPHA

           COMPLEX      A( LDA, * ), X( * )

PURPOSE
       CSYR   performs the symmetric rank 1 operation

       where alpha is a complex scalar, x is an n element vector and A is an n
       by n symmetric matrix.


ARGUMENTS
       UPLO     (input) CHARACTER*1
                On entry, UPLO specifies whether the upper or lower triangular
                part of the array A is to be referenced as follows:

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

                UPLO = 'L' or 'l'   Only the lower triangular part of A is  to
                be referenced.

                Unchanged on exit.

       N        (input) INTEGER
                On entry, N specifies the order of the matrix A.  N must be at
                least zero.  Unchanged on exit.

       ALPHA    (input) COMPLEX
                On entry, ALPHA specifies  the  scalar  alpha.   Unchanged  on
                exit.

       X        (input) COMPLEX array, dimension at least
                (  1 + ( N - 1 )*abs( INCX ) ).  Before entry, the incremented
                array X must contain the N- element vector  x.   Unchanged  on
                exit.

       INCX     (input) INTEGER
                On  entry, INCX specifies the increment for the elements of X.
                INCX must not be zero.  Unchanged on exit.

       A        (input/output) COMPLEX array, dimension ( LDA, N )
                Before entry, with  UPLO = 'U' or 'u',  the  leading  n  by  n
                upper  triangular  part  of the array A must contain the upper
                triangular part of the symmetric matrix and the strictly lower
                triangular  part  of  A  is not referenced. On exit, the upper
                triangular part of the array A 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 A must contain the lower triangular part of the sym-
                metric matrix and the strictly upper triangular part of  A  is
                not  referenced.  On  exit,  the  lower triangular part of the
                array A is overwritten by the lower  triangular  part  of  the
                updated matrix.

       LDA      (input) INTEGER
                On  entry,  LDA specifies the first dimension of A as declared
                in the calling (sub) program. LDA must be at least max(  1,  N
                ).  Unchanged on exit.



 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                         CSYR(3)