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DLAPLL(3F)							    DLAPLL(3F)

NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

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

	 INTEGER	INCX, INCY, N

	 DOUBLE		PRECISION SSMIN

	 DOUBLE		PRECISION X( * ), Y( * )

PURPOSE    [Toc]    [Back]

     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    [Toc]    [Back]

     N	     (input) INTEGER
	     The length	of the vectors X and Y.

     X	     (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION
	     The smallest singular value of the	N-by-2 matrix A	= ( X Y	).
DLAPLL(3F)							    DLAPLL(3F)

NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

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

	 INTEGER	INCX, INCY, N

	 DOUBLE		PRECISION SSMIN

	 DOUBLE		PRECISION X( * ), Y( * )

PURPOSE    [Toc]    [Back]

     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    [Toc]    [Back]

     N	     (input) INTEGER
	     The length	of the vectors X and Y.

     X	     (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION
	     The smallest singular value of the	N-by-2 matrix A	= ( X Y	).


									PPPPaaaaggggeeee 1111
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