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function y = zgfmul(a,b,c,d,x)
  # y = zgfmul(a,b,c,d,x)
  # 
  # Compute product of zgep incidence matrix F with vector x.
  # Used by zgepbal (in zgscal) as part of generalized conjugate gradient
  # iteration.
  #
  # References:
  # ZGEP: Hodel, "Computation of Zeros with Balancing," Linear algebra and
  #    its Applications, 1993
  # Generalized CG: Golub and Van Loan, "Matrix Computations, 2nd ed" 1989
  
  # 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
