Backporting bicgstab function from Octave 3.2 to Octave 3.0 (closes #81)
Sébastien Villemot
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99e0d248c7
commit
1ae1b5ff20
19
license.txt
19
license.txt
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@ -88,6 +88,25 @@ License: GPL-3+
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You should have received a copy of the GNU General Public License
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along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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Files: matlab/missing/bicgstab/bicgstab.m
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Copyright: 2008, Radek Salac
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License: GPL-3+
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This file is part of Octave.
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.
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Octave is free software; you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 3 of the License, or (at
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your option) any later version.
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.
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Octave is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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General Public License for more details.
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.
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You should have received a copy of the GNU General Public License
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along with Octave; see the file COPYING. If not, see
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<http://www.gnu.org/licenses/>.
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Files: doc/manual.xml, doc/*.tex, doc/*.svg, doc/*.dia
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Copyright: 1996-2010, Dynare Team
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License: GFDL-1.3+
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@ -61,9 +61,10 @@ if exist('OCTAVE_VERSION') || matlab_ver_less_than('7.0.1')
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addpath([dynareroot '/missing/ordeig'])
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end
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% rcond() was introduced in Octave 3.2.0
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% rcond() and bicgstable() were introduced in Octave 3.2.0
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if exist('OCTAVE_VERSION') && octave_ver_less_than('3.2.0')
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addpath([dynareroot '/missing/rcond'])
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addpath([dynareroot '/missing/bicgstab'])
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end
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% orschur() is missing in Octave; we don't have a real replacement;
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@ -0,0 +1,172 @@
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## Copyright (C) 2008 Radek Salac
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##
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## This file is part of Octave.
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##
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## Octave is free software; you can redistribute it and/or modify it
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## under the terms of the GNU General Public License as published by
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## the Free Software Foundation; either version 3 of the License, or (at
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## your option) any later version.
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##
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## Octave is distributed in the hope that it will be useful, but
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## WITHOUT ANY WARRANTY; without even the implied warranty of
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## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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## General Public License for more details.
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##
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## You should have received a copy of the GNU General Public License
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## along with Octave; see the file COPYING. If not, see
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## <http://www.gnu.org/licenses/>.
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## -*- texinfo -*-
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## @deftypefn {Function File} {} bicgstab (@var{A}, @var{b})
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## @deftypefnx {Function File} {} bicgstab (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0})
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## This procedure attempts to solve a system of linear equations A*x = b for x.
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## The @var{A} must be square, symmetric and positive definite real matrix N*N.
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## The @var{b} must be a one column vector with a length of N.
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## The @var{tol} specifies the tolerance of the method, the default value is 1e-6.
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## The @var{maxit} specifies the maximum number of iterations, the default value is min(20,N).
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## The @var{M1} specifies a preconditioner, can also be a function handler which returns M\X.
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## The @var{M2} combined with @var{M1} defines preconditioner as preconditioner=M1*M2.
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## The @var{x0} is the initial guess, the default value is zeros(N,1).
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##
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## The value @var{x} is a computed result of this procedure.
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## The value @var{flag} can be 0 when we reach tolerance in @var{maxit} iterations, 1 when
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## we don't reach tolerance in @var{maxit} iterations and 3 when the procedure stagnates.
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## The value @var{relres} is a relative residual - norm(b-A*x)/norm(b).
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## The value @var{iter} is an iteration number in which x was computed.
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## The value @var{resvec} is a vector of @var{relres} for each iteration.
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##
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## @end deftypefn
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function [x, flag, relres, iter, resvec] = bicgstab (A, b, tol, maxit, M1, M2, x0)
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if (nargin < 2 || nargin > 7 || nargout > 5)
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print_usage ();
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elseif (!isnumeric (A) || rows (A) != columns (A))
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error ("bicgstab: the first argument must be a n-by-n matrix");
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elseif (!isvector (b))
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error ("bicgstab: b must be a vector");
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elseif (!any (b))
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error ("bicgstab: b shuldn't be a vector of zeros");
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elseif (rows (A) != rows (b))
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error ("bicgstab: the first and second argument must have the same number of rows");
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elseif (nargin > 2 && !isscalar (tol))
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error ("bicgstab: tol must be a scalar");
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elseif (nargin > 3 && !isscalar (maxit))
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error ("bicgstab: maxit must be a scalar");
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elseif (nargin > 4 && ismatrix (M1) && (rows (M1) != rows (A) || columns (M1) != columns (A)))
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error ("bicgstab: M1 must have the same number of rows and columns as A");
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elseif (nargin > 5 && (!ismatrix (M2) || rows (M2) != rows (A) || columns (M2) != columns (A)))
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error ("bicgstab: M2 must have the same number of rows and columns as A");
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elseif (nargin > 6 && !isvector (x0))
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error ("bicgstab: x0 must be a vector");
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elseif (nargin > 6 && rows (x0) != rows (b))
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error ("bicgstab: x0 must have the same number of rows as b");
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endif
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## Default tolerance.
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if (nargin < 3)
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tol = 1e-6;
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endif
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## Default maximum number of iteration.
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if (nargin < 4)
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maxit = min (rows (b), 20);
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endif
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## Left preconditioner.
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if (nargin == 5)
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if (isnumeric (M1))
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precon = @(x) M1 \ x;
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endif
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elseif (nargin > 5)
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if (issparse (M1) && issparse (M2))
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precon = @(x) M2 \ (M1 \ x);
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else
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M = M1*M2;
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precon = @(x) M \ x;
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endif
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else
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precon = @(x) x;
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endif
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## specifies initial estimate x0
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if (nargin < 7)
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x = zeros (rows (b), 1);
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else
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x = x0;
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endif
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norm_b = norm (b);
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res = b - A*x;
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rr = res;
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## Vector of the residual norms for each iteration.
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resvec = [norm(res)/norm_b];
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## Default behaviour we don't reach tolerance tol within maxit iterations.
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flag = 1;
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for iter = 1:maxit
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rho_1 = res' * rr;
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if (iter == 1)
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p = res;
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else
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beta = (rho_1 / rho_2) * (alpha / omega);
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p = res + beta * (p - omega * v);
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endif
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phat = precon (p);
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v = A * phat;
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alpha = rho_1 / (rr' * v);
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s = res - alpha * v;
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shat = precon (s);
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t = A * shat;
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omega = (t' * s) / (t' * t);
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x = x + alpha * phat + omega * shat;
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res = s - omega * t;
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rho_2 = rho_1;
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relres = norm (res) / norm_b;
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resvec = [resvec; relres];
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if (relres <= tol)
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## We reach tolerance tol within maxit iterations.
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flag = 0;
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break;
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elseif (resvec (end) == resvec (end - 1))
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## The method stagnates.
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flag = 3;
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break;
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endif
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endfor
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if (nargout < 2)
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if (flag == 0)
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printf (["bicgstab converged at iteration %i ",
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"to a solution with relative residual %e\n"],iter,relres);
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elseif (flag == 3)
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printf (["bicgstab stopped at iteration %i ",
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"without converging to the desired tolerance %e\n",
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"because the method stagnated.\n",
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"The iterate returned (number %i) has relative residual %e\n"],iter,tol,iter,relres);
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else
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printf (["bicgstab stopped at iteration %i ",
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"without converging to the desired toleranc %e\n",
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"because the maximum number of iterations was reached.\n",
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"The iterate returned (number %i) has relative residual %e\n"],iter,tol,iter,relres);
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endif
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endif
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endfunction
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%!demo
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%! % Solve system of A*x=b
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%! A = [5 -1 3;-1 2 -2;3 -2 3]
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%! b = [7;-1;4]
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%! [x, flag, relres, iter, resvec] = bicgstab(A, b)
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