Commit 1ae1b5ff authored by Sébastien Villemot's avatar Sébastien Villemot
Browse files

Backporting bicgstab function from Octave 3.2 to Octave 3.0 (closes #81)

parent 99e0d248
......@@ -88,6 +88,25 @@ License: GPL-3+
You should have received a copy of the GNU General Public License
along with Dynare. If not, see <http://www.gnu.org/licenses/>.
Files: matlab/missing/bicgstab/bicgstab.m
Copyright: 2008, Radek Salac
License: GPL-3+
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 3 of the License, 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, see
<http://www.gnu.org/licenses/>.
Files: doc/manual.xml, doc/*.tex, doc/*.svg, doc/*.dia
Copyright: 1996-2010, Dynare Team
License: GFDL-1.3+
......
......@@ -61,9 +61,10 @@ if exist('OCTAVE_VERSION') || matlab_ver_less_than('7.0.1')
addpath([dynareroot '/missing/ordeig'])
end
% rcond() was introduced in Octave 3.2.0
% rcond() and bicgstable() were introduced in Octave 3.2.0
if exist('OCTAVE_VERSION') && octave_ver_less_than('3.2.0')
addpath([dynareroot '/missing/rcond'])
addpath([dynareroot '/missing/bicgstab'])
end
% orschur() is missing in Octave; we don't have a real replacement;
......
## Copyright (C) 2008 Radek Salac
##
## 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 3 of the License, 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, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} bicgstab (@var{A}, @var{b})
## @deftypefnx {Function File} {} bicgstab (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0})
## This procedure attempts to solve a system of linear equations A*x = b for x.
## The @var{A} must be square, symmetric and positive definite real matrix N*N.
## The @var{b} must be a one column vector with a length of N.
## The @var{tol} specifies the tolerance of the method, the default value is 1e-6.
## The @var{maxit} specifies the maximum number of iterations, the default value is min(20,N).
## The @var{M1} specifies a preconditioner, can also be a function handler which returns M\X.
## The @var{M2} combined with @var{M1} defines preconditioner as preconditioner=M1*M2.
## The @var{x0} is the initial guess, the default value is zeros(N,1).
##
## The value @var{x} is a computed result of this procedure.
## The value @var{flag} can be 0 when we reach tolerance in @var{maxit} iterations, 1 when
## we don't reach tolerance in @var{maxit} iterations and 3 when the procedure stagnates.
## The value @var{relres} is a relative residual - norm(b-A*x)/norm(b).
## The value @var{iter} is an iteration number in which x was computed.
## The value @var{resvec} is a vector of @var{relres} for each iteration.
##
## @end deftypefn
function [x, flag, relres, iter, resvec] = bicgstab (A, b, tol, maxit, M1, M2, x0)
if (nargin < 2 || nargin > 7 || nargout > 5)
print_usage ();
elseif (!isnumeric (A) || rows (A) != columns (A))
error ("bicgstab: the first argument must be a n-by-n matrix");
elseif (!isvector (b))
error ("bicgstab: b must be a vector");
elseif (!any (b))
error ("bicgstab: b shuldn't be a vector of zeros");
elseif (rows (A) != rows (b))
error ("bicgstab: the first and second argument must have the same number of rows");
elseif (nargin > 2 && !isscalar (tol))
error ("bicgstab: tol must be a scalar");
elseif (nargin > 3 && !isscalar (maxit))
error ("bicgstab: maxit must be a scalar");
elseif (nargin > 4 && ismatrix (M1) && (rows (M1) != rows (A) || columns (M1) != columns (A)))
error ("bicgstab: M1 must have the same number of rows and columns as A");
elseif (nargin > 5 && (!ismatrix (M2) || rows (M2) != rows (A) || columns (M2) != columns (A)))
error ("bicgstab: M2 must have the same number of rows and columns as A");
elseif (nargin > 6 && !isvector (x0))
error ("bicgstab: x0 must be a vector");
elseif (nargin > 6 && rows (x0) != rows (b))
error ("bicgstab: x0 must have the same number of rows as b");
endif
## Default tolerance.
if (nargin < 3)
tol = 1e-6;
endif
## Default maximum number of iteration.
if (nargin < 4)
maxit = min (rows (b), 20);
endif
## Left preconditioner.
if (nargin == 5)
if (isnumeric (M1))
precon = @(x) M1 \ x;
endif
elseif (nargin > 5)
if (issparse (M1) && issparse (M2))
precon = @(x) M2 \ (M1 \ x);
else
M = M1*M2;
precon = @(x) M \ x;
endif
else
precon = @(x) x;
endif
## specifies initial estimate x0
if (nargin < 7)
x = zeros (rows (b), 1);
else
x = x0;
endif
norm_b = norm (b);
res = b - A*x;
rr = res;
## Vector of the residual norms for each iteration.
resvec = [norm(res)/norm_b];
## Default behaviour we don't reach tolerance tol within maxit iterations.
flag = 1;
for iter = 1:maxit
rho_1 = res' * rr;
if (iter == 1)
p = res;
else
beta = (rho_1 / rho_2) * (alpha / omega);
p = res + beta * (p - omega * v);
endif
phat = precon (p);
v = A * phat;
alpha = rho_1 / (rr' * v);
s = res - alpha * v;
shat = precon (s);
t = A * shat;
omega = (t' * s) / (t' * t);
x = x + alpha * phat + omega * shat;
res = s - omega * t;
rho_2 = rho_1;
relres = norm (res) / norm_b;
resvec = [resvec; relres];
if (relres <= tol)
## We reach tolerance tol within maxit iterations.
flag = 0;
break;
elseif (resvec (end) == resvec (end - 1))
## The method stagnates.
flag = 3;
break;
endif
endfor
if (nargout < 2)
if (flag == 0)
printf (["bicgstab converged at iteration %i ",
"to a solution with relative residual %e\n"],iter,relres);
elseif (flag == 3)
printf (["bicgstab stopped at iteration %i ",
"without converging to the desired tolerance %e\n",
"because the method stagnated.\n",
"The iterate returned (number %i) has relative residual %e\n"],iter,tol,iter,relres);
else
printf (["bicgstab stopped at iteration %i ",
"without converging to the desired toleranc %e\n",
"because the maximum number of iterations was reached.\n",
"The iterate returned (number %i) has relative residual %e\n"],iter,tol,iter,relres);
endif
endif
endfunction
%!demo
%! % Solve system of A*x=b
%! A = [5 -1 3;-1 2 -2;3 -2 3]
%! b = [7;-1;4]
%! [x, flag, relres, iter, resvec] = bicgstab(A, b)
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