subroutine kfit_back_to_back(ktrk1, ktrk2, update_track, chisq,
     *                             error)
*
* begin_doc
*
*  Fit two tracks so that they are back to back, i.e., part of a single
*  helix
*
*  Note: If the track is not updated here, you can update it later by
*  calling kfit_update_tracks.
*
*  Input Parameters:
*  ktrk1         integer variable
*                Track 1 to fit
*
*  ktrk2         integer variable
*                Track 2 to fit
*
*  update_track  integer variable
*                 0 ==> Calculate chisquare only (do not update track)
*                 1 ==> Calculate chisquare, update track
*                 2 ==> Calculate chisquare, update track & cov matrix
*
*  Output Parameters:
*  chisq         double precision variable
*                Chisquare of fit
*
*  error         integer variable
*                 0 ==> All OK
*                >0 ==> Error
*
*  Other routines:
*
*  Notes:
*
*  >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
*   The back to back constraint is imposed by the method of Lagrange
*   multipliers. There are 5 constraints, of which three are best
*   expressed in terms of the track parameters at the point of
*   closest approach to the origin:
*
*      1. pt1    =  pt2
*      3. d0_1   = -d0_2
*      4. pz1    = -pz2
*      5. z0_1   =  z0_2
*
*   chisq = (alpha-alpha0)(t) * Valpha0(inv) * (alpha-alpha0)
*             + 2*lambda(t)*(D*dalpha + d)
*
*   where
*    alpha0 are the unconstrained parameters, (2*7 of them)
*    alpha are the final parameters (2*7) and
*    D*dalpha + d = 0 represents the linearized constraint equations (5).
*
*  The solution is
*
*       alpha = alpha0 - Valpha0*D(t)*lambda
*      lambda = VD * (D*dalpha0 + d)
*          VD = [D * Valpha0 * D(t)](inv)
*      Valpha = Valpha0 - Valpha0*D(t)*VD*D*Valpha0
*
*   The covariance matrix of the resulting tracks can be computed as
*
*       Valpha = Valpha0 - Valpha0*D(t)*VD*D*Valpha0
*
*   The constraints are somehat complicated to show here in differential
*   form.
*  >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
*
*  Author:   Paul Avery      Created:  Fri Dec  4 22:12:52 EDT 1997
*
*  Major revisions:
*
*
* end_doc