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LAPACK version 3.0
slapll(3)

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

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

      INTEGER	     INCX, INCY, N

      REAL	     SSMIN

      REAL	     X( * ), Y( * )

DESCRIPTION
  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 ).