clapll.f

          SUBROUTINE CLAPLL( 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
          REAL               SSMIN
    *     ..
    *     .. Array Arguments ..
          COMPLEX            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 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 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 ).
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ZERO
          PARAMETER          ( ZERO = 0.0E+0 )
          COMPLEX            CONE
          PARAMETER          ( CONE = ( 1.0E+0, 0.0E+0 ) )
    *     ..
    *     .. Local Scalars ..
          REAL               SSMAX
          COMPLEX            A11, A12, A22, C, TAU
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, CONJG
    *     ..
    *     .. External Functions ..
          COMPLEX            CDOTC
          EXTERNAL           CDOTC
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CAXPY, CLARFG, SLAS2
    *     ..
    *     .. 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 CLARFG( N, X( 1 ), X( 1+INCX ), INCX, TAU )
          A11 = X( 1 )
          X( 1 ) = CONE
    *
          C = -CONJG( TAU )*CDOTC( N, X, INCX, Y, INCY )
          CALL CAXPY( N, C, X, INCX, Y, INCY )
    *
          CALL CLARFG( 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 SLAS2( ABS( A11 ), ABS( A12 ), ABS( A22 ), SSMIN, SSMAX )
    *
          RETURN
    *
    *     End of CLAPLL
    *
          END