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SUBROUTINE ZLAPLL( N, X, INCX, Y, INCY, SSMIN )
*
* -- LAPACK auxiliary routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER INCX, INCY, N
DOUBLE PRECISION SSMIN
* ..
* .. Array Arguments ..
COMPLEX*16 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) COMPLEX*16 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*16 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
PARAMETER ( ZERO = 0.0D+0 )
COMPLEX*16 CONE
PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
DOUBLE PRECISION SSMAX
COMPLEX*16 A11, A12, A22, C, TAU
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DCONJG
* ..
* .. External Functions ..
COMPLEX*16 ZDOTC
EXTERNAL ZDOTC
* ..
* .. External Subroutines ..
EXTERNAL DLAS2, ZAXPY, ZLARFG
* ..
* .. 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 ZLARFG( N, X( 1 ), X( 1+INCX ), INCX, TAU )
A11 = X( 1 )
X( 1 ) = CONE
*
C = -DCONJG( TAU )*ZDOTC( N, X, INCX, Y, INCY )
CALL ZAXPY( N, C, X, INCX, Y, INCY )
*
CALL ZLARFG( 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( ABS( A11 ), ABS( A12 ), ABS( A22 ), SSMIN, SSMAX )
*
RETURN
*
* End of ZLAPLL
*
END
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