# 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 
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# FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License 
# for more details.
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# 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. 
 
function x = zgfslv(n,m,p,b)
  # x = zgfslv(n,m,p,b)
  # solve system of equations for dense zgep problem
  
  # Written by A. Scotte Hodel
  # Converted to Octave by R Bruce Tenison, July 3, 1994

  nmp = n+m+p;
  gam1 = (2*n)+m+p;    gam2 = n+p;     gam3 = n+m;

  G1 = givens(sqrt(m),-sqrt(p))';
  G2 = givens(m+p,sqrt(n*(m+p)))';

  x = b;

  # 1) U1 e^n = sqrt(n)e_1^n
  # 2) U2 e^m = sqrt(m)e_1^m
  # 3) U3 e^p = sqrt(p)e_1^p
  xdx1 = 1:n; xdx2 = n+(1:m); xdx3 = n+m+(1:p);
  x(xdx1,1) = zgshsr(x(xdx1,1));
  x(xdx2,1) = zgshsr(x(xdx2,1));
  x(xdx3,1) = zgshsr(x(xdx3,1));

  # 4) Givens rotations to reduce stray non-zero elements
  idx1 = [n+1,n+m+1];     idx2 = [1,n+1];
  x(idx1) = G1'*x(idx1);
  x(idx2) = G2'*x(idx2);

  # 6) Scale x, then back-transform to get x
  en = ones(n,1);  em = ones(m,1);   ep = ones(p,1);
  lam = [gam1*en;gam2*em;gam3*ep]; 
  lam(1) = n+m+p; 
  lam(n+1) = 1;       # dummy value to avoid divide by zero
  lam(n+m+1)=n+m+p;

  x = x ./ lam;       x(n+1) = 0;  # minimum norm solution

  # back transform now.
  x(idx2) = G2*x(idx2);
  x(idx1) = G1*x(idx1);
  x(xdx3,1) = zgshsr(x(xdx3,1));
  x(xdx2,1) = zgshsr(x(xdx2,1));
  x(xdx1,1) = zgshsr(x(xdx1,1));

endfunction

