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NAME

       DSYR - perform the symmetric rank 1 operation   A := alpha*x*x’ + A,

SYNOPSIS

       SUBROUTINE DSYR ( UPLO, N, ALPHA, X, INCX, A, LDA )

           DOUBLE      PRECISION ALPHA

           INTEGER     INCX, LDA, N

           CHARACTER*1 UPLO

           DOUBLE      PRECISION A( LDA, * ), X( * )

PURPOSE

       DSYR   performs the symmetric rank 1 operation

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

PARAMETERS

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

       ALPHA  - DOUBLE PRECISION.
              On entry, ALPHA specifies the scalar alpha.  Unchanged on  exit.

       X      - DOUBLE PRECISION array of 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   - INTEGER.
              On  entry,  INCX  specifies the increment for the elements of X.
              INCX must not be zero.  Unchanged on exit.

       A      - DOUBLE PRECISION array of 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  symmetric  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    - 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.

              Level 2 Blas routine.

              -- Written on 22-October-1986.  Jack Dongarra, Argonne  National
              Lab.   Jeremy Du Croz, Nag Central Office.  Sven Hammarling, Nag
              Central Office.  Richard Hanson, Sandia National Labs.