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.

N

          N is INTEGER


          The length of the vectors X and Y.

X

          X is REAL array,


                         dimension (1+(N-1)*INCX)


          On entry, X contains the N-vector X.


          On exit, X is overwritten.

INCX

          INCX is INTEGER


          The increment between successive elements of X. INCX > 0.

Y

          Y is REAL array,


                         dimension (1+(N-1)*INCY)


          On entry, Y contains the N-vector Y.


          On exit, Y is overwritten.

INCY

          INCY is INTEGER


          The increment between successive elements of Y. INCY > 0.

SSMIN

          SSMIN is REAL


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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

September 2012