CLAPLL (3lapack)

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

SYNOPSIS

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

      INTEGER        INCX, INCY, N

      REAL           SSMIN

      COMPLEX        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) COMPLEX 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) COMPLEX 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 ).