## Copyright (C) 1996,1998 Auburn University.  All Rights Reserved
##
## This file is part of Octave. 
##
## Octave is free software; you can redistribute it and/or modify it 
## under the terms of the GNU General Public License as published by the 
## Free Software Foundation; either version 2, or (at your option) any 
## later version. 
## 
## Octave is distributed in the hope that it will be useful, but WITHOUT 
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 
## FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License 
## for more details.
## 
## You should have received a copy of the GNU General Public License 
## along with Octave; see the file COPYING.  If not, write to the Free 
## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA. 

## -*- texinfo -*-
## @deftypefn {Function File } @var{y} = zgfmul(@var{a},@var{b},@var{c},@var{d},@var{x})
## 
## Compute product of zgep incidence matrix @var{F} with vector @var{x}.
## Used by zgepbal (in zgscal) as part of generalized conjugate gradient
## iteration.
## @end deftypefn
   
## References:
## ZGEP: Hodel, "Computation of Zeros with Balancing," 1992, submitted to  LAA
## Generalized CG: Golub and Van Loan, "Matrix Computations, 2nd ed" 1989

function y = zgfmul(a,b,c,d,x)

  ## A. S. Hodel July 24 1992
  ## Conversion to Octave July 3, 1994
  
  [n,m] = size(b);
  [p,m1] = size(c);
  nm = n+m;
  y = zeros(nm+p,1);

  ## construct F column by column
  for jj=1:n
    Fj = zeros(nm+p,1);

    ## rows 1:n: F1
    aridx = complement(jj,find(a(jj,:) != 0)); 
    acidx = complement(jj,find(a(:,jj) != 0));
    bidx = find(b(jj,:) != 0);
    cidx = find(c(:,jj) != 0);

    Fj(aridx) = Fj(aridx) - 1;      # off diagonal entries of F1
    Fj(acidx) = Fj(acidx) - 1;
    # diagonal entry of F1
    Fj(jj) = length(aridx)+length(acidx) + length(bidx) + length(cidx);
    
    if(!isempty(bidx)) Fj(n+bidx) = 1;     endif # B' incidence
    if(!isempty(cidx)) Fj(n+m+cidx) = -1;  endif # -C incidence
    y = y + x(jj)*Fj;   # multiply by corresponding entry of x
  endfor

  for jj=1:m
    Fj = zeros(nm+p,1);
    bidx = find(b(:,jj) != 0);   
    if(!isempty(bidx)) Fj(bidx) = 1; endif     # B incidence
    didx = find(d(:,jj) != 0);   
    if(!isempty(didx)) Fj(n+m+didx) = 1; endif # D incidence
    Fj(n+jj) = length(bidx) + length(didx);         # F2 is diagonal
    y = y + x(n+jj)*Fj;   # multiply by corresponding entry of x
  endfor

  for jj=1:p
    Fj = zeros(nm+p,1);
    cidx = find(c(jj,:) != 0);   
    if(!isempty(cidx)) Fj(cidx) = -1; endif  # -C' incidence
    didx = find(d(jj,:) != 0);   
    if(!isempty(didx)) Fj(n+didx) = 1;  endif # D' incidence
    Fj(n+m+jj) = length(cidx) + length(didx);     # F2 is diagonal
    y = y + x(n+m+jj)*Fj;   # multiply by corresponding entry of x
  endfor

endfunction