--- a/scripts/linear-algebra/gmres.m	Fri May 06 18:45:05 2011 -0400
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,214 +0,0 @@
-## Copyright (C) 2009-2011 Carlo de Falco
-##  
-## 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} {@var{x} =} gmres (@var{A}, @var{b}, @var{m}, @var{rtol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0})
-## @deftypefnx {Function File} {@var{x} =} gmres (@var{A}, @var{b}, @var{m}, @var{rtol}, @var{maxit}, @var{P})
-## @deftypefnx {Function File} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}] =} gmres (@dots{})
-## Solve @code{A x = b} using the Preconditioned GMRES iterative method
-## with restart, a.k.a. PGMRES(m).
-##
-## @itemize @minus
-## @item @var{rtol} is the relative tolerance,
-## if not given or set to [] the default value 1e-6 is used.
-##
-## @item @var{maxit} is the maximum number of outer iterations,
-## if not given or set to [] the default value
-## @code{min (10, numel (b) / restart)} is used.
-##
-## @item @var{x0} is the initial guess,
-## if not given or set to [] the default value @code{zeros(size (b))} is used.
-##
-## @item @var{m} is the restart parameter,
-## if not given or set to [] the default value @code{numel (b)} is used.
-## @end itemize
-##
-## Argument @var{A} can be passed as a matrix, function handle, or
-## inline function @code{f} such that @code{f(x) = A*x}.
-##
-## The preconditioner @var{P} is given as @code{P = M1 * M2}.
-## Both @var{M1} and @var{M2} can be passed as a matrix, function handle, or
-## inline function @code{g} such that @code{g(x) = M1\x} or @code{g(x) = M2\x}.
-##
-## Besides the vector @var{x}, additional outputs are:
-##
-## @itemize @minus
-## @item @var{flag} indicates the exit status:
-##
-## @table @asis
-##   @item 0 : iteration converged to within the specified tolerance
-##
-##   @item 1 : maximum number of iterations exceeded
-##
-##   @item 2 : unused, but skipped for compatibility
-##
-##   @item 3 : algorithm reached stagnation
-## @end table
-##
-## @item @var{relres} is the final value of the relative residual.
-##
-## @item @var{iter} is a vector containing the number of outer iterations and
-## total iterations performed.
-##
-## @item @var{resvec} is a vector containing the relative residual at each
-## iteration.
-## @end itemize
-##
-## @seealso{pcg, cgs, bigcstab}
-## @end deftypefn
-
-function [x, flag, prec_res_norm, itcnt] = gmres (A, b, restart, rtol, maxit, M1, M2, x0)
-
-  if (nargin < 2 || nargin > 8)
-    print_usage ();    
-  end
-      
-  if (ischar (A))
-    Ax = str2func (A);
-  elseif (ismatrix (A))
-    Ax = @(x) A*x;
-  elseif (isa (A, "function_handle"))
-    Ax = A;
-  else
-    error ("gmres: A must be a function or matrix");
-  endif
-
-  if (nargin < 3 || isempty (restart))
-    restart = rows (b);
-  endif
-
-  if (nargin < 4 || isempty (rtol))
-    rtol = 1e-6;
-  endif
-
-  if (nargin < 5 || isempty (maxit))
-    maxit = min (rows (b)/restart, 10);
-  endif
-
-  if (nargin < 6 || isempty (M1))
-    M1m1x = @(x) x;
-  elseif (ischar (M1))
-    M1m1x = str2func (M1);
-  elseif (ismatrix (M1))
-    M1m1x = @(x) M1 \ x;
-  elseif (isa (M1, "function_handle"))
-    M1m1x = M1;
-  else
-    error ("gmres: preconditioner M1 must be a function or matrix");
-  endif
-  
-  if (nargin < 7 || isempty (M2))
-    M2m1x = @(x) x;
-  elseif (ischar (M2))
-    M2m1x = str2func (M2);
-  elseif (ismatrix (M2))
-    M2m1x = @(x) M2 \ x;
-  elseif (isa (M2, "function_handle"))
-    M2m1x = M2;
-  else
-    error ("gmres: preconditioner M2 must be a function or matrix");
-  endif
-
-  Pm1x = @(x) M2m1x (M1m1x (x));
-
-  if (nargin < 8 || isempty (x0))
-    x0 = zeros (size (b));
-  endif
-
-  x_old = x0; 
-  x = x_old;
-  prec_res = Pm1x (b - Ax (x_old));
-  prec_res_norm = norm (prec_res, 2);
-  
-  B = zeros (restart + 1, 1);
-  V = zeros (rows (x), restart);
-  H = zeros (restart + 1, restart);
-
-  ## begin loop
-  iter = 1;
-  restart_it  = restart + 1; 
-  resids      = zeros (maxit, 1);
-  resids(1)   = prec_res_norm;
-  prec_b_norm = norm (Pm1x (b), 2);
-  flag        = 1;
-
-  while ((iter <= maxit * restart) && (prec_res_norm > rtol * prec_b_norm))
-  
-    ## restart
-    if (restart_it > restart)
-      restart_it = 1;
-      x_old = x;	      
-      prec_res = Pm1x (b - Ax (x_old));
-      prec_res_norm = norm (prec_res, 2);
-      B(1) = prec_res_norm;
-      H(:) = 0;
-      V(:, 1) = prec_res / prec_res_norm;
-    endif  
-    
-    ## basic iteration
-    tmp = Pm1x (Ax (V(:, restart_it)));
-    [V(:,restart_it+1), H(1:restart_it+1, restart_it)] = mgorth (tmp, V(:,1:restart_it));
-    
-    Y = (H(1:restart_it+1, 1:restart_it) \ B (1:restart_it+1));
-	      
-    little_res = B(1:restart_it+1) - H(1:restart_it+1, 1:restart_it) * Y(1:restart_it);
-    prec_res_norm = norm (little_res, 2);
-	      
-    x = x_old + V(:, 1:restart_it) * Y(1:restart_it);
-    
-    resids(iter) = prec_res_norm ;
-    if (norm (x - x_old, inf) <= eps)
-      flag = 3;
-      break
-    endif
-
-    restart_it++ ; iter++;
-  endwhile
-
-  if (prec_res_norm > rtol * prec_b_norm)
-    flag = 0;
-  endif
-
-  resids = resids(1:iter-1);
-  itcnt = [floor(maxit/restart), rem(maxit, restart)];
-endfunction
-
-
-%!shared A, b, dim
-%! dim = 100;
-%!test
-%! A = spdiags ([-ones(dim,1) 2*ones(dim,1) ones(dim,1)], [-1:1], dim, dim);
-%! b = ones(dim, 1); 
-%! x = gmres (A, b, 10, 1e-10, dim, @(x) x./diag(A), [],  b);
-%! assert(x, A\b, 1e-9*norm(x,inf));
-%!
-%!test
-%! x = gmres (A, b, dim, 1e-10, 1e4, @(x) diag(diag(A))\x, [],  b);  
-%! assert(x, A\b, 1e-7*norm(x,inf));
-%!
-%!test
-%! A = spdiags ([[1./(2:2:2*(dim-1)) 0]; 1./(1:2:2*dim-1); [0 1./(2:2:2*(dim-1))]]', -1:1, dim, dim);
-%! A = A'*A;
-%! b = rand (dim, 1);
-%! [x, resids] = gmres (@(x) A*x, b, dim, 1e-10, dim, @(x) x./diag(A), [],  []);
-%! assert(x, A\b, 1e-9*norm(x,inf))
-%! x = gmres (@(x) A*x, b, dim, 1e-10, 1e6, @(x) diag(diag(A))\x, [],  []);
-%! assert(x, A\b, 1e-9*norm(x,inf));
-%!test
-%! x =  gmres (@(x) A*x, b, dim, 1e-10, 1e6, @(x) x./diag(A), [],  []);
-%! assert(x, A\b, 1e-7*norm(x,inf));