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## Copyright (C) 1996, 1998, 2000, 2004, 2005, 2007
## Auburn University. All rights reserved.
##
##
## This program 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 3 of the License, or (at
## your option) any later version.
##
## This program 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 this program; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{zz} =} zginit (@var{a}, @var{b}, @var{c}, @var{d})
## Construct right hand side vector @var{zz}
## for the zero-computation generalized eigenvalue problem
## balancing procedure. Called by @command{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
## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>
## Created: July 24, 1992
## Conversion to Octave by R. Bruce Tenison, July 3, 1994
function zz = zginit (a, b, c, d)
if (nargin != 4)
print_usage ();
endif
[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 *= (1 / log (2));
endfunction
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