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annotate scripts/sparse/gmres.m @ 13141:e81ddf9cacd5

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maint: untabify and remove trailing whitespace from source files * bicg.m, gmres.m, pkg.m: Untabify and remove trailing whitespace. * libcruft/Makefile.am, libcruft/blas-xtra/cdotc3.f, libcruft/blas-xtra/cmatm3.f, libcruft/blas-xtra/ddot3.f, libcruft/blas-xtra/dmatm3.f, libcruft/blas-xtra/sdot3.f, libcruft/blas-xtra/smatm3.f, libcruft/blas-xtra/zdotc3.f, libcruft/blas-xtra/zmatm3.f, libcruft/lapack-xtra/crsf2csf.f, libcruft/lapack-xtra/zrsf2csf.f, liboctave/Array.cc, liboctave/DASPK-opts.in, liboctave/DASRT-opts.in, liboctave/DASSL-opts.in, liboctave/LSODE-opts.in, liboctave/Makefile.a,mliboctave/Quad-opts.in, liboctave/Sparse-perm-op-defs.h, scripts/Makefile.a,mscripts/deprecated/glpkmex.m, scripts/general/blkdiag.m, scripts/general/interp1.m, scripts/general/profshow.m, scripts/general/quadl.m, scripts/general/triplequad.m, scripts/help/__makeinfo__.m, scripts/io/strread.m, scripts/io/textread.m, scripts/io/textscan.m, scripts/linear-algebra/rank.m, scripts/miscellaneous/gzip.m, scripts/miscellaneous/private/__xzip__.m, scripts/miscellaneous/tempdir.m, scripts/miscellaneous/unpack.m, scripts/pkg/pkg.m, scripts/plot/allchild.m, scripts/plot/ancestor.m, scripts/plot/cla.m, scripts/plot/clf.m, scripts/plot/findall.m, scripts/plot/findobj.m, scripts/plot/gca.m, scripts/plot/gcf.m, scripts/plot/hggroup.m, scripts/plot/isfigure.m, scripts/plot/ishghandle.m, scripts/plot/legend.m, scripts/plot/line.m, scripts/plot/loglog.m, scripts/plot/patch.m, scripts/plot/print.m, scripts/plot/private/__quiver__.m, scripts/plot/private/__scatter__.m, scripts/plot/rectangle.m, scripts/plot/semilogx.m, scripts/plot/semilogy.m, scripts/plot/surface.m, scripts/plot/text.m, scripts/plot/title.m, scripts/plot/trisurf.m, scripts/plot/view.m, scripts/plot/whitebg.m, scripts/plot/xlabel.m, scripts/plot/xlim.m, scripts/plot/ylabel.m, scripts/plot/ylim.m, scripts/plot/zlabel.m, scripts/plot/zlim.m, scripts/polynomial/mkpp.m, scripts/polynomial/polygcd.m, scripts/polynomial/ppint.m, scripts/polynomial/ppjumps.m, scripts/polynomial/ppval.m, scripts/set/setxor.m, scripts/sparse/bicgstab.m, scripts/sparse/cgs.m, scripts/sparse/spconvert.m, scripts/specfun/nthroot.m, scripts/strings/strmatch.m, scripts/strings/untabify.m, scripts/testfun/demo.m, scripts/testfun/example.m, src/DLD-FUNCTIONS/filter.cc, src/DLD-FUNCTIONS/mgorth.cc, src/DLD-FUNCTIONS/quadcc.cc, src/DLD-FUNCTIONS/str2double.cc, src/Makefile.a,msrc/gl-render.cc, src/gl2ps-renderer.cc, src/graphics.cc, src/octave-config.cc.in, src/octave-config.in, src/ov-class.h, src/ov-fcn.h, src/profiler.cc, src/profiler.h, src/pt-binop.cc, src/pt-unop.cc, src/symtab.cc, src/txt-eng-ft.cc: Remove trailing whitespace.
author John W. Eaton <jwe@octave.org>
date Thu, 15 Sep 2011 12:51:10 -0400
parents e5aaba072d2b
children 8aaaef4a69aa
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 ## Copyright (C) 2009-2011 Carlo de Falco
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by the
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7 ## Free Software Foundation; either version 3 of the License, or (at your
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8 ## option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but WITHOUT
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11 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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12 ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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13 ## for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {@var{x} =} gmres (@var{A}, @var{b}, @var{m}, @var{rtol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0})
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21 ## @deftypefnx {Function File} {@var{x} =} gmres (@var{A}, @var{b}, @var{m}, @var{rtol}, @var{maxit}, @var{P})
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22 ## @deftypefnx {Function File} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}] =} gmres (@dots{})
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23 ## Solve @code{A x = b} using the Preconditioned GMRES iterative method
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24 ## with restart, a.k.a. PGMRES(m).
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25 ##
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26 ## @itemize @minus
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27 ## @item @var{rtol} is the relative tolerance,
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28 ## if not given or set to [] the default value 1e-6 is used.
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29 ##
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30 ## @item @var{maxit} is the maximum number of outer iterations,
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31 ## if not given or set to [] the default value
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32 ## @code{min (10, numel (b) / restart)} is used.
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33 ##
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34 ## @item @var{x0} is the initial guess,
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35 ## if not given or set to [] the default value @code{zeros(size (b))} is used.
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36 ##
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37 ## @item @var{m} is the restart parameter,
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38 ## if not given or set to [] the default value @code{numel (b)} is used.
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39 ## @end itemize
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40 ##
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41 ## Argument @var{A} can be passed as a matrix, function handle, or
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42 ## inline function @code{f} such that @code{f(x) = A*x}.
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43 ##
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44 ## The preconditioner @var{P} is given as @code{P = M1 * M2}.
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45 ## Both @var{M1} and @var{M2} can be passed as a matrix, function handle, or
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46 ## inline function @code{g} such that @code{g(x) = M1\x} or @code{g(x) = M2\x}.
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47 ##
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48 ## Besides the vector @var{x}, additional outputs are:
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49 ##
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50 ## @itemize @minus
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51 ## @item @var{flag} indicates the exit status:
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52 ## @table @asis
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53 ## @item 0 : iteration converged to within the specified tolerance
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54 ## @item 1 : maximum number of iterations exceeded
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55 ## @item 2 : unused, but skipped for compatibility
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56 ## @item 3 : algorithm reached stagnation
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57 ## @end table
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58 ## @item @var{relres} is the final value of the relative residual.
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59 ## @item @var{iter} is a vector containing the number of outer iterations and
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60 ## total iterations performed.
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61 ## @item @var{resvec} is a vector containing the relative residual at each
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62 ## iteration.
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63 ## @end itemize
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64 ##
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65 ## @seealso{bicg, bicgstab, cgs, pcg}
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66 ## @end deftypefn
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67
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68 function [x, flag, presn, it] = gmres (A, b, restart, rtol, maxit, M1, M2, x0)
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69
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70 if (nargin < 2 || nargin > 8)
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71 print_usage ();
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72 end
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73
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74 if (ischar (A))
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75 Ax = str2func (A);
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76 elseif (ismatrix (A))
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77 Ax = @(x) A*x;
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78 elseif (isa (A, "function_handle"))
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79 Ax = A;
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80 else
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81 error ("gmres: A must be a function or matrix");
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82 endif
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83
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84 if (nargin < 3 || isempty (restart))
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85 restart = rows (b);
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86 endif
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87
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88 if (nargin < 4 || isempty (rtol))
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89 rtol = 1e-6;
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90 endif
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91
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92 if (nargin < 5 || isempty (maxit))
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93 maxit = min (rows (b)/restart, 10);
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94 endif
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95
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96 if (nargin < 6 || isempty (M1))
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97 M1m1x = @(x) x;
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98 elseif (ischar (M1))
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99 M1m1x = str2func (M1);
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100 elseif (ismatrix (M1))
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101 M1m1x = @(x) M1 \ x;
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102 elseif (isa (M1, "function_handle"))
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103 M1m1x = M1;
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104 else
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105 error ("gmres: preconditioner M1 must be a function or matrix");
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parents:
diff changeset
106 endif
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107
12509
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diff changeset
108 if (nargin < 7 || isempty (M2))
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parents:
diff changeset
109 M2m1x = @(x) x;
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parents:
diff changeset
110 elseif (ischar (M2))
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parents:
diff changeset
111 M2m1x = str2func (M2);
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diff changeset
112 elseif (ismatrix (M2))
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parents:
diff changeset
113 M2m1x = @(x) M2 \ x;
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diff changeset
114 elseif (isa (M2, "function_handle"))
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parents:
diff changeset
115 M2m1x = M2;
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parents:
diff changeset
116 else
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parents:
diff changeset
117 error ("gmres: preconditioner M2 must be a function or matrix");
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parents:
diff changeset
118 endif
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parents:
diff changeset
119
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diff changeset
120 Pm1x = @(x) M2m1x (M1m1x (x));
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parents:
diff changeset
121
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parents:
diff changeset
122 if (nargin < 8 || isempty (x0))
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diff changeset
123 x0 = zeros (size (b));
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parents:
diff changeset
124 endif
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parents:
diff changeset
125
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diff changeset
126 x_old = x0;
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127 x = x_old;
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diff changeset
128 prec_res = Pm1x (b - Ax (x_old));
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diff changeset
129 presn = norm (prec_res, 2);
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diff changeset
130
12509
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diff changeset
131 B = zeros (restart + 1, 1);
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diff changeset
132 V = zeros (rows (x), restart);
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diff changeset
133 H = zeros (restart + 1, restart);
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parents:
diff changeset
134
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parents:
diff changeset
135 ## begin loop
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diff changeset
136 iter = 1;
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diff changeset
137 restart_it = restart + 1;
12509
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diff changeset
138 resids = zeros (maxit, 1);
13091
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diff changeset
139 resids(1) = presn;
12509
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diff changeset
140 prec_b_norm = norm (Pm1x (b), 2);
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parents:
diff changeset
141 flag = 1;
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parents:
diff changeset
142
13091
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diff changeset
143 while (iter <= maxit * restart && presn > rtol * prec_b_norm)
13141
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diff changeset
144
12509
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diff changeset
145 ## restart
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parents:
diff changeset
146 if (restart_it > restart)
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diff changeset
147 restart_it = 1;
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diff changeset
148 x_old = x;
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diff changeset
149 prec_res = Pm1x (b - Ax (x_old));
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diff changeset
150 presn = norm (prec_res, 2);
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diff changeset
151 B(1) = presn;
12509
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diff changeset
152 H(:) = 0;
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diff changeset
153 V(:, 1) = prec_res / presn;
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154 endif
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diff changeset
155
12509
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diff changeset
156 ## basic iteration
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diff changeset
157 tmp = Pm1x (Ax (V(:, restart_it)));
13091
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diff changeset
158 [V(:,restart_it+1), H(1:restart_it+1, restart_it)] = ...
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parents: 12763
diff changeset
159 mgorth (tmp, V(:,1:restart_it));
13141
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diff changeset
160
12509
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diff changeset
161 Y = (H(1:restart_it+1, 1:restart_it) \ B (1:restart_it+1));
13141
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parents: 13091
diff changeset
162
13091
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diff changeset
163 little_res = B(1:restart_it+1) - ...
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diff changeset
164 H(1:restart_it+1, 1:restart_it) * Y(1:restart_it);
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diff changeset
165
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diff changeset
166 presn = norm (little_res, 2);
13141
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diff changeset
167
12509
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parents:
diff changeset
168 x = x_old + V(:, 1:restart_it) * Y(1:restart_it);
13141
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parents: 13091
diff changeset
169
13091
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diff changeset
170 resids(iter) = presn;
12509
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parents:
diff changeset
171 if (norm (x - x_old, inf) <= eps)
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parents:
diff changeset
172 flag = 3;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
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parents:
diff changeset
173 break
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
174 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
175
13141
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diff changeset
176 restart_it++ ;
13091
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diff changeset
177 iter++;
12509
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parents:
diff changeset
178 endwhile
e742720c5e71 Add mgorth and gmres functions from Octave Forge
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parents:
diff changeset
179
13091
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diff changeset
180 if (presn > rtol * prec_b_norm)
12509
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parents:
diff changeset
181 flag = 0;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
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parents:
diff changeset
182 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
183
e742720c5e71 Add mgorth and gmres functions from Octave Forge
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parents:
diff changeset
184 resids = resids(1:iter-1);
13091
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diff changeset
185 it = [floor(maxit/restart), rem(maxit, restart)];
e5aaba072d2b maint: style fixes in iterative linear solvers
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diff changeset
186
12509
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parents:
diff changeset
187 endfunction
e742720c5e71 Add mgorth and gmres functions from Octave Forge
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parents:
diff changeset
188
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
189
e742720c5e71 Add mgorth and gmres functions from Octave Forge
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parents:
diff changeset
190 %!shared A, b, dim
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parents:
diff changeset
191 %! dim = 100;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
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parents:
diff changeset
192 %!test
e742720c5e71 Add mgorth and gmres functions from Octave Forge
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parents:
diff changeset
193 %! A = spdiags ([-ones(dim,1) 2*ones(dim,1) ones(dim,1)], [-1:1], dim, dim);
13141
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diff changeset
194 %! b = ones(dim, 1);
12509
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parents:
diff changeset
195 %! x = gmres (A, b, 10, 1e-10, dim, @(x) x./diag(A), [], b);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
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parents:
diff changeset
196 %! assert(x, A\b, 1e-9*norm(x,inf));
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parents:
diff changeset
197 %!
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
198 %!test
13141
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diff changeset
199 %! x = gmres (A, b, dim, 1e-10, 1e4, @(x) diag(diag(A))\x, [], b);
12509
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parents:
diff changeset
200 %! assert(x, A\b, 1e-7*norm(x,inf));
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Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
201 %!
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
202 %!test
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
203 %! 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
204 %! A = A'*A;
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Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
205 %! b = rand (dim, 1);
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parents:
diff changeset
206 %! [x, resids] = gmres (@(x) A*x, b, dim, 1e-10, dim, @(x) x./diag(A), [], []);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
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parents:
diff changeset
207 %! assert(x, A\b, 1e-9*norm(x,inf))
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parents:
diff changeset
208 %! x = gmres (@(x) A*x, b, dim, 1e-10, 1e6, @(x) diag(diag(A))\x, [], []);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
209 %! assert(x, A\b, 1e-9*norm(x,inf));
e742720c5e71 Add mgorth and gmres functions from Octave Forge
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parents:
diff changeset
210 %!test
e742720c5e71 Add mgorth and gmres functions from Octave Forge
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parents:
diff changeset
211 %! x = gmres (@(x) A*x, b, dim, 1e-10, 1e6, @(x) x./diag(A), [], []);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
212 %! assert(x, A\b, 1e-7*norm(x,inf));