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clapll

 NAME
      CLAPLL - 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 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) 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 ).