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


SYNOPSIS

       SUBROUTINE SLAPLL( N, X, INCX, Y, INCY, SSMIN )

           INTEGER        INCX, INCY, N

           REAL           SSMIN

           REAL           X( * ), Y( * )


PURPOSE

       Given  two  column  vectors X and Y, let A = ( X Y ).  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) REAL 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) REAL 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) REAL
               The smallest singular value of the N-by-2 matrix A
               = ( X Y ).


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