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NAME
     dlapll - two column vectors X and Y, let   A = ( X Y )

SYNOPSIS
     SUBROUTINE DLAPLL( N, X, INCX, Y, INCY, SSMIN )

     INTEGER INCX, INCY, N

     DOUBLE PRECISION SSMIN

     DOUBLE PRECISION X( * ), Y( * )



     #include <sunperf.h>

     void dlapll(int n, double *dx, int  incx,  double  *dy,  int
               incy, double *ssmin) ;

PURPOSE
     Given two column vectors X and Y, let

     The subroutine first computes the QR factorization  of  A  =
     Q*R,  and then computes the SVD of the 2-by-2 upper triangu-
     lar matrix R.  The smaller singular value of R  is  returned
     in  SSMIN,  which  is  used as the measurement of the linear
     dependency of the vectors X and Y.


ARGUMENTS
     N         (input) INTEGER
               The length of the vectors X and Y.

     X         (input/output) DOUBLE PRECISION array,
               dimension (1+(N-1)*INCX) On entry, X contains  the
               N-vector X.  On exit, X is overwritten.

     INCX      (input) INTEGER
               The increment between successive  elements  of  X.
               INCX > 0.

     Y         (input/output) DOUBLE PRECISION array,
               dimension (1+(N-1)*INCY) On entry, Y contains  the
               N-vector Y.  On exit, Y is overwritten.

     INCY      (input) INTEGER
               The increment between successive  elements  of  Y.
               INCY > 0.

     SSMIN     (output) DOUBLE PRECISION
               The smallest singular value of the N-by-2 matrix A
               = ( X Y ).

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