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zginit.m
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1999-04-29
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# Copyright (C) 1996,1998 A. Scottedward Hodel
#
# 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, 675 Mass Ave, Cambridge, MA 02139, USA.
function zz = zginit(a,b,c,d)
# zz = zginit(a,b,c,d)
# construct right hand side vector zz
# for the zero-computation generalized eigenvalue problem
# balancing procedure
# called by zgepbal
# 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 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 = complmnt(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