dlapll(3F)

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( * )

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 triangular 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 ).