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## -*- texinfo -*-
## @deftypefn {Function File } {zz =} zginit(@var{a},@var{b},@var{c},@var{d})
## construct right hand side vector zz
## for the zero-computation generalized eigenvalue problem
## balancing procedure
## called by zgepbal
## 
## @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 zz = zginit(a,b,c,d)

  ## A. S. Hodel July 24 1992
  ## Conversion to Octave by R. Bruce Tenison, July 3, 1994

  [nn,mm] = size(b);
  [pp,mm] = size(d);

  nmp = nn+mm+pp;

  ## set up log vector zz
  zz = zeros(nmp,1);

  ## zz part 1:
  for i=1:nn
    ## nonzero off diagonal entries of a
    if(nn > 1)
      nidx = complement(i,1:nn);
      a_row_i = a(i,nidx);                 a_col_i = a(nidx,i);
      arnz = a_row_i(find(a_row_i != 0));  acnz = a_col_i(find(a_col_i != 0));
    else
      arnz = acnz = [];
    endif

    ## row of b
    bidx = find(b(i,:) != 0);
    b_row_i = b(i,bidx);

    ## column of c
    cidx = find(c(:,i) != 0);
    c_col_i = c(cidx,i);
   
    ## sum the entries
    zz(i) = sum(log(abs(acnz))) - sum(log(abs(arnz))) ...
            - sum(log(abs(b_row_i))) + sum(log(abs(c_col_i)));
  endfor

  ## zz part 2:
  bd = [b;d];
  for i=1:mm
    i1 = i+nn;

    ## column of [b;d]
    bdidx = find(bd(:,i) != 0);
    bd_col_i = bd(bdidx,i);
    zz(i1) = sum(log(abs(bd_col_i)));
  endfor

  ## zz part 3:
  cd = [c, d];
  for i=1:pp
    i1 = i+nn+mm;
    cdidx = find(cd(i,:) != 0);
    cd_row_i = cd(i,cdidx);
    zz(i1) = -sum(log(abs(cd_row_i)));
  endfor

  ## now set zz as log base 2
  zz = zz*(1/log(2));
endfunction