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SUBROUTINE DLAPLL( N, X, INCX, Y, INCY, SSMIN )
*
* -- LAPACK auxiliary routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
INTEGER INCX, INCY, N
DOUBLE PRECISION SSMIN
* ..
* .. Array Arguments ..
DOUBLE PRECISION X( * ), Y( * )
* ..
*
* Purpose
* =======
*
* 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) 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 ).
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
DOUBLE PRECISION A11, A12, A22, C, SSMAX, TAU
* ..
* .. External Functions ..
DOUBLE PRECISION DDOT
EXTERNAL DDOT
* ..
* .. External Subroutines ..
EXTERNAL DAXPY, DLARFG, DLAS2
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( N.LE.1 ) THEN
SSMIN = ZERO
RETURN
END IF
*
* Compute the QR factorization of the N-by-2 matrix ( X Y )
*
CALL DLARFG( N, X( 1 ), X( 1+INCX ), INCX, TAU )
A11 = X( 1 )
X( 1 ) = ONE
*
C = -TAU*DDOT( N, X, INCX, Y, INCY )
CALL DAXPY( N, C, X, INCX, Y, INCY )
*
CALL DLARFG( N-1, Y( 1+INCY ), Y( 1+2*INCY ), INCY, TAU )
*
A12 = Y( 1 )
A22 = Y( 1+INCY )
*
* Compute the SVD of 2-by-2 Upper triangular matrix.
*
CALL DLAS2( A11, A12, A22, SSMIN, SSMAX )
*
RETURN
*
* End of DLAPLL
*
END
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