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

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 <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+

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;

matlab/missing/bicgstab/bicgstab.m

+## 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)
+