Mercurial > octave-nkf

annotate scripts/sparse/gmres.m @ 17744:d63878346099

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
maint: Update copyright notices for release.
author John W. Eaton <jwe@octave.org>
date Wed, 23 Oct 2013 22:09:27 -0400
parents 1c89599167a6
children 4197fc428c7d
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
17744
d63878346099 maint: Update copyright notices for release.
John W. Eaton <jwe@octave.org>
parents: 17338
diff changeset
1 ## Copyright (C) 2009-2013 Carlo de Falco
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
2 ##
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
3 ## This file is part of Octave.
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
4 ##
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
5 ## Octave is free software; you can redistribute it and/or modify it
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
6 ## under the terms of the GNU General Public License as published by the
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
7 ## Free Software Foundation; either version 3 of the License, or (at your
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
8 ## option) any later version.
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
9 ##
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
10 ## Octave is distributed in the hope that it will be useful, but WITHOUT
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
11 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
12 ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
13 ## for more details.
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
14 ##
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
15 ## You should have received a copy of the GNU General Public License
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
16 ## along with Octave; see the file COPYING. If not, see
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
17 ## <http://www.gnu.org/licenses/>.
12761
13bcd62824a7 doc: Add documentation for gmres, rectangle to manual
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
18
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
19 ## -*- texinfo -*-
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
20 ## @deftypefn {Function File} {@var{x} =} gmres (@var{A}, @var{b}, @var{m}, @var{rtol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0})
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
21 ## @deftypefnx {Function File} {@var{x} =} gmres (@var{A}, @var{b}, @var{m}, @var{rtol}, @var{maxit}, @var{P})
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
22 ## @deftypefnx {Function File} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}] =} gmres (@dots{})
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
23 ## Solve @code{A x = b} using the Preconditioned GMRES iterative method
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
24 ## with restart, a.k.a. PGMRES(m).
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
25 ##
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
26 ## @itemize @minus
12642
f96b9b9f141b doc: Periodic grammarcheck and spellcheck of documentation.
Rik <octave@nomad.inbox5.com>
parents: 12509
diff changeset
27 ## @item @var{rtol} is the relative tolerance,
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
28 ## if not given or set to [] the default value 1e-6 is used.
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
29 ##
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
30 ## @item @var{maxit} is the maximum number of outer iterations,
12642
f96b9b9f141b doc: Periodic grammarcheck and spellcheck of documentation.
Rik <octave@nomad.inbox5.com>
parents: 12509
diff changeset
31 ## if not given or set to [] the default value
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
32 ## @code{min (10, numel (b) / restart)} is used.
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
33 ##
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
34 ## @item @var{x0} is the initial guess,
14773
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
35 ## if not given or set to [] the default value @code{zeros (size (b))} is used.
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
36 ##
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
37 ## @item @var{m} is the restart parameter,
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
38 ## if not given or set to [] the default value @code{numel (b)} is used.
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
39 ## @end itemize
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
40 ##
12642
f96b9b9f141b doc: Periodic grammarcheck and spellcheck of documentation.
Rik <octave@nomad.inbox5.com>
parents: 12509
diff changeset
41 ## Argument @var{A} can be passed as a matrix, function handle, or
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
42 ## inline function @code{f} such that @code{f(x) = A*x}.
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
43 ##
12642
f96b9b9f141b doc: Periodic grammarcheck and spellcheck of documentation.
Rik <octave@nomad.inbox5.com>
parents: 12509
diff changeset
44 ## The preconditioner @var{P} is given as @code{P = M1 * M2}.
f96b9b9f141b doc: Periodic grammarcheck and spellcheck of documentation.
Rik <octave@nomad.inbox5.com>
parents: 12509
diff changeset
45 ## Both @var{M1} and @var{M2} can be passed as a matrix, function handle, or
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
46 ## inline function @code{g} such that @code{g(x) = M1\x} or @code{g(x) = M2\x}.
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
47 ##
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
48 ## Besides the vector @var{x}, additional outputs are:
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
49 ##
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
50 ## @itemize @minus
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
51 ## @item @var{flag} indicates the exit status:
14366
b76f0740940e doc: Periodic grammar check of documentation.
Rik <octave@nomad.inbox5.com>
parents: 14363
diff changeset
52 ##
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
53 ## @table @asis
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
54 ## @item 0 : iteration converged to within the specified tolerance
13929
9cae456085c2 Grammarcheck of documentation before 3.6.0 release.
Rik <octave@nomad.inbox5.com>
parents: 13861
diff changeset
55 ##
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
56 ## @item 1 : maximum number of iterations exceeded
13929
9cae456085c2 Grammarcheck of documentation before 3.6.0 release.
Rik <octave@nomad.inbox5.com>
parents: 13861
diff changeset
57 ##
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
58 ## @item 2 : unused, but skipped for compatibility
13929
9cae456085c2 Grammarcheck of documentation before 3.6.0 release.
Rik <octave@nomad.inbox5.com>
parents: 13861
diff changeset
59 ##
14773
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
60 ## @item 3 : algorithm reached stagnation (no change between iterations)
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
61 ## @end table
13929
9cae456085c2 Grammarcheck of documentation before 3.6.0 release.
Rik <octave@nomad.inbox5.com>
parents: 13861
diff changeset
62 ##
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
63 ## @item @var{relres} is the final value of the relative residual.
13929
9cae456085c2 Grammarcheck of documentation before 3.6.0 release.
Rik <octave@nomad.inbox5.com>
parents: 13861
diff changeset
64 ##
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
65 ## @item @var{iter} is a vector containing the number of outer iterations and
12642
f96b9b9f141b doc: Periodic grammarcheck and spellcheck of documentation.
Rik <octave@nomad.inbox5.com>
parents: 12509
diff changeset
66 ## total iterations performed.
13929
9cae456085c2 Grammarcheck of documentation before 3.6.0 release.
Rik <octave@nomad.inbox5.com>
parents: 13861
diff changeset
67 ##
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
68 ## @item @var{resvec} is a vector containing the relative residual at each
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
69 ## iteration.
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
70 ## @end itemize
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
71 ##
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
72 ## @seealso{bicg, bicgstab, cgs, pcg}
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
73 ## @end deftypefn
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
74
14773
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
75 function [x, flag, relres, it, resvec] = gmres (A, b, restart, rtol, maxit, M1, M2, x0)
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
76
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
77 if (nargin < 2 || nargin > 8)
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
78 print_usage ();
13174
bd2cd4fd3edf maint: use specific endif, endfor tokens instead of simple end
John W. Eaton <jwe@octave.org>
parents: 12761
diff changeset
79 endif
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
80
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
81 if (ischar (A))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
82 Ax = str2func (A);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
83 elseif (ismatrix (A))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
84 Ax = @(x) A*x;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
85 elseif (isa (A, "function_handle"))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
86 Ax = A;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
87 else
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
88 error ("gmres: A must be a function or matrix");
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
89 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
90
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
91 if (nargin < 3 || isempty (restart))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
92 restart = rows (b);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
93 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
94
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
95 if (nargin < 4 || isempty (rtol))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
96 rtol = 1e-6;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
97 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
98
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
99 if (nargin < 5 || isempty (maxit))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
100 maxit = min (rows (b)/restart, 10);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
101 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
102
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
103 if (nargin < 6 || isempty (M1))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
104 M1m1x = @(x) x;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
105 elseif (ischar (M1))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
106 M1m1x = str2func (M1);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
107 elseif (ismatrix (M1))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
108 M1m1x = @(x) M1 \ x;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
109 elseif (isa (M1, "function_handle"))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
110 M1m1x = M1;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
111 else
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
112 error ("gmres: preconditioner M1 must be a function or matrix");
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
113 endif
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
114
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
115 if (nargin < 7 || isempty (M2))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
116 M2m1x = @(x) x;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
117 elseif (ischar (M2))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
118 M2m1x = str2func (M2);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
119 elseif (ismatrix (M2))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
120 M2m1x = @(x) M2 \ x;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
121 elseif (isa (M2, "function_handle"))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
122 M2m1x = M2;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
123 else
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
124 error ("gmres: preconditioner M2 must be a function or matrix");
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
125 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
126
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
127 Pm1x = @(x) M2m1x (M1m1x (x));
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
128
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
129 if (nargin < 8 || isempty (x0))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
130 x0 = zeros (size (b));
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
131 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
132
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
133 x_old = x0;
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
134 x = x_old;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
135 prec_res = Pm1x (b - Ax (x_old));
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
136 presn = norm (prec_res, 2);
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
137
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
138 B = zeros (restart + 1, 1);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
139 V = zeros (rows (x), restart);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
140 H = zeros (restart + 1, restart);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
141
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
142 ## begin loop
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
143 iter = 1;
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
144 restart_it = restart + 1;
14773
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
145 resvec = zeros (maxit, 1);
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
146 resvec(1) = presn;
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
147 prec_b_norm = norm (Pm1x (b), 2);
14773
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
148 flag = 1; # Default flag is maximum # of iterations exceeded
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
149
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
150 while (iter <= maxit * restart && presn > rtol * prec_b_norm)
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
151
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
152 ## restart
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
153 if (restart_it > restart)
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
154 restart_it = 1;
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
155 x_old = x;
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
156 prec_res = Pm1x (b - Ax (x_old));
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
157 presn = norm (prec_res, 2);
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
158 B(1) = presn;
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
159 H(:) = 0;
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
160 V(:, 1) = prec_res / presn;
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
161 endif
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
162
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
163 ## basic iteration
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
164 tmp = Pm1x (Ax (V(:, restart_it)));
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
165 [V(:,restart_it+1), H(1:restart_it+1, restart_it)] = ...
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
166 mgorth (tmp, V(:,1:restart_it));
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
167
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
168 Y = (H(1:restart_it+1, 1:restart_it) \ B (1:restart_it+1));
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
169
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
170 little_res = B(1:restart_it+1) - ...
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
171 H(1:restart_it+1, 1:restart_it) * Y(1:restart_it);
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
172
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
173 presn = norm (little_res, 2);
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
174
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
175 x = x_old + V(:, 1:restart_it) * Y(1:restart_it);
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
176
14822
93e5ade3fda4 Improve matlab compatibility of gmres
Carlo de Falco <cdf@users.sourceforge.net>
parents: 14773
diff changeset
177 resvec(iter+1) = presn;
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
178 if (norm (x - x_old, inf) <= eps)
14773
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
179 flag = 3; # Stagnation: no change between iterations
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
180 break;
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
181 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
182
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
183 restart_it++ ;
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
184 iter++;
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
185 endwhile
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
186
14773
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
187 if (nargout > 1)
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
188 ## Calculate extra outputs as requested
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
189 relres = presn / prec_b_norm;
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
190 if (relres <= rtol)
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
191 flag = 0; # Converged to solution within tolerance
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
192 endif
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
193
14822
93e5ade3fda4 Improve matlab compatibility of gmres
Carlo de Falco <cdf@users.sourceforge.net>
parents: 14773
diff changeset
194 it = [floor(iter/restart), restart_it-1];
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
195 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
196
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
197 endfunction
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
198
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
199
14773
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
200 %!demo
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
201 %! dim = 20;
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
202 %! A = spdiags ([-ones(dim,1) 2*ones(dim,1) ones(dim,1)], [-1:1], dim, dim);
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
203 %! b = ones (dim, 1);
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
204 %! [x, flag, relres, iter, resvec] = gmres (A, b, 10, 1e-10, dim, @(x) x ./ diag (A), [], b)
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
205
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
206 %!shared A, b, dim
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
207 %! dim = 100;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
208 %!test
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
209 %! A = spdiags ([-ones(dim,1) 2*ones(dim,1) ones(dim,1)], [-1:1], dim, dim);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
210 %! b = ones (dim, 1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
211 %! x = gmres (A, b, 10, 1e-10, dim, @(x) x ./ diag (A), [], b);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
212 %! assert (x, A\b, 1e-9*norm (x, Inf));
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
213 %!
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
214 %!test
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
215 %! x = gmres (A, b, dim, 1e-10, 1e4, @(x) diag (diag (A)) \ x, [], b);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
216 %! assert(x, A\b, 1e-7*norm (x, Inf));
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
217 %!
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
218 %!test
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
219 %! 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);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
220 %! A = A'*A;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
221 %! b = rand (dim, 1);
14773
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
222 %! [x, resvec] = gmres (@(x) A*x, b, dim, 1e-10, dim, @(x) x./diag (A), [], []);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
223 %! assert (x, A\b, 1e-9*norm (x, Inf));
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
224 %! x = gmres (@(x) A*x, b, dim, 1e-10, 1e6, @(x) diag (diag (A)) \ x, [], []);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
225 %! assert (x, A\b, 1e-9*norm (x, Inf));
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
226 %!test
14868
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory
Rik <octave@nomad.inbox5.com>
parents: 14822
diff changeset
227 %! x = gmres (@(x) A*x, b, dim, 1e-10, 1e6, @(x) x ./ diag (A), [], []);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
228 %! assert (x, A\b, 1e-7*norm (x, Inf));
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
229
14773
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
230
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
231 %!error gmres (1)
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
232 %!error gmres (1,2,3,4,5,6,7,8,9)
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
233 %!error <A must be> gmres ({1},2)
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
234 %!error <A must be a function or matrix> gmres ({1},2)
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
235 %!error <M1 must be a function or matrix> gmres (1,2,3,4,5,{6})
5c269b73f467 gmres.m: Overhaul function. Fix bug #36568.
Rik <octave@nomad.inbox5.com>
parents: 14366
diff changeset
236 %!error <M2 must be a function or matrix> gmres (1,2,3,4,5,6,{7})
17338
1c89599167a6 maint: End m-files with 1 blank line.
Rik <rik@octave.org>
parents: 14868
diff changeset
237