text:       SUBROUTINE ZLAPLL( N, X, INCX, Y, INCY, SSMIN )
  *
  *  -- LAPACK auxiliary routine (version 3.0) --
  *     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
  