diff --git a/license.txt b/license.txt index 10f10415c..94e618186 100644 --- a/license.txt +++ b/license.txt @@ -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 . +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 + . + Files: doc/manual.xml, doc/*.tex, doc/*.svg, doc/*.dia Copyright: 1996-2010, Dynare Team License: GFDL-1.3+ diff --git a/matlab/dynare_config.m b/matlab/dynare_config.m index 0027f7db0..8fc38b9f6 100644 --- a/matlab/dynare_config.m +++ b/matlab/dynare_config.m @@ -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; diff --git a/matlab/missing/bicgstab/bicgstab.m b/matlab/missing/bicgstab/bicgstab.m new file mode 100644 index 000000000..07083a1e4 --- /dev/null +++ b/matlab/missing/bicgstab/bicgstab.m @@ -0,0 +1,172 @@ +## 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 +## . + +## -*- 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) +