c Copyright (C) 2008, 2009  VZLU Prague, a.s., Czech Republic
c
c Author: Jaroslav Hajek <highegg@gmail.com>
c
c This file is part of qrupdate.
c
c qrupdate is free software; you can redistribute it and/or modify
c it under the terms of the GNU General Public License as published by
c the Free Software Foundation; either version 3 of the License, or
c (at your option) any later version.
c
c This program is distributed in the hope that it will be useful,
c but WITHOUT ANY WARRANTY; without even the implied warranty of
c MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
c GNU General Public License for more details.
c
c You should have received a copy of the GNU General Public License
c along with this software; see the file COPYING.  If not, see
c <http://www.gnu.org/licenses/>.
c
      subroutine zch1dn(n,R,ldr,u,rw,info)
c purpose:      given an upper triangular matrix R that is a Cholesky
c               factor of a hermitian positive definite matrix A, i.e.
c               A = R'*R, this subroutine downdates R -> R1 so that
c               R1'*R1 = A - u*u'
c               (complex version)
c arguments:
c n (in)        the order of matrix R
c R (io)        on entry, the upper triangular matrix R
c               on exit, the updated matrix R1
c ldr (in)      leading dimension of R. ldr >= n.
c u (io)        the vector determining the rank-1 update
c               on exit, u contains the reflector sines
c               used to transform R to R1.
c rw (out)      cosine parts of reflectors.
c
c info (out)    on exit, error code:
c                info = 0: success.
c                info = 1: update violates positive-definiteness.
c                info = 2: R is singular.
c
      integer n,ldr
      double complex R(ldr,*),u(*)
      double precision rw(*)
      integer info
      external ztrsv,zlartg,dznrm2
      double complex crho,rr,ui,t
      double precision dznrm2,rho
      integer i,j

c quick return if possible.
      if (n == 0) return
c check arguments.
      info = 0
      if (n < 0) then
        info = -1
      else if (ldr < n) then
        info = -3
      end if
      if (info /= 0) then
        call xerbla('ZCH1DN',-info)
        return
      end if

c check for singularity of R.
      do i = 1,n
        if (R(i,i) == 0d0) goto 20
      end do
c form R' \ u
      call ztrsv('U','C','N',n,R,ldr,u,1)
      rho = dznrm2(n,u,1)
c check positive definiteness
      rho = 1 - rho**2
      if (rho <= 0d0) goto 10
      crho = sqrt(rho)
c eliminate R' \ u
      do i = n,1,-1
        ui = u(i)
c generate next rotation
        call zlartg(crho,ui,rw(i),u(i),rr)
        crho = rr
      end do
c apply rotations
      do i = n,1,-1
        ui = 0d0
        do j = i,1,-1
          t = rw(j)*ui + u(j)*R(j,i)
          R(j,i) = rw(j)*R(j,i) - conjg(u(j))*ui
          ui = t
        end do
      end do

c normal return
      return
c error returns
 10   info = 1
      return
 20   info = 2
      return
      end subroutine
