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dsyr2

 NAME
      DSYR2 - perform the symmetric rank 2 operation   A :=
      alpha*x*y' + alpha*y*x' + A,

 SYNOPSIS
      SUBROUTINE DSYR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA
                       )

          DOUBLE       PRECISION ALPHA

          INTEGER      INCX, INCY, LDA, N

          CHARACTER*1  UPLO

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

 PURPOSE
      DSYR2  performs the symmetric rank 2 operation

      where alpha is a scalar, x and y are n element vectors 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.

      Y      - DOUBLE PRECISION array of dimension at least
             ( 1 + ( n - 1 )*abs( INCY ) ).  Before entry, the
             incremented array Y must contain the n element vector
             y.  Unchanged on exit.

      INCY   - INTEGER.
             On entry, INCY specifies the increment for the ele-
             ments of Y. INCY 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 con-
             tain 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 tri-
             angular 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.