DSYR2(1)

NAME
LAPACK-3 - performs the symmetric rank 2 operation A := alpha*x*y**T + alpha*y*x**T + A,

SYNOPSIS

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

DOUBLE
    PRECISION ALPHA

INTEGER
    INCX,INCY,LDA,N

CHARACTER
    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.

ARGUMENTS

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 elements 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 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.

FURTHER DETAILS
 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.