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annotate scripts/sparse/bicg.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 53674ceb9133
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rev   line source
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1 ## Copyright (C) 2006 Sylvain Pelissier <sylvain.pelissier@gmail.com>
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2 ## Copyright (C) 2011 Carlo de Falco
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3 ##
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4 ## This program is free software; you can redistribute it and/or modify
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5 ## it under the terms of the GNU General Public License as published by
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6 ## the Free Software Foundation; either version 2 of the License, or
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7 ## (at your option) any later version.
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8 ##
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9 ## This program is distributed in the hope that it will be useful,
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10 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
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11 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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12 ## GNU General Public License for more details.
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13 ##
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14 ## You should have received a copy of the GNU General Public License
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15 ## along with this program; If not, see <http://www.gnu.org/licenses/>.
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16
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17 ## -*- texinfo -*-
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18 ##
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19 ## @deftypefn {Function File} {@var{x} =} bicg (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0})
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20 ## @deftypefnx {Function File} {@var{x} =} bicg (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{P})
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21 ## @deftypefnx {Function File} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}] =} bicg (@var{A}, @var{b}, ...)
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22 ## Solve @code{A x = b} using the Bi-conjugate gradient iterative method.
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23 ##
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24 ## @itemize @minus
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25 ## @item @var{rtol} is the relative tolerance, if not given
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26 ## or set to [] the default value 1e-6 is used.
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27 ## @item @var{maxit} the maximum number of outer iterations,
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28 ## if not given or set to [] the default value
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29 ## @code{min (20, numel (b))} is used.
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30 ## @item @var{x0} the initial guess, if not given or set to []
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31 ## the default value @code{zeros (size (b))} is used.
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32 ## @end itemize
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33 ##
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34 ## @var{A} can be passed as a matrix or as a function handle or
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35 ## inline function @code{f} such that @code{f(x, "notransp") = A*x}
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36 ## and @code{f(x, "transp") = A'*x}.
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37 ##
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38 ## The preconditioner @var{P} is given as @code{P = M1 * M2}.
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39 ## Both @var{M1} and @var{M2} can be passed as a matrix or as
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40 ## a function handle or inline function @code{g} such that
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41 ## @code{g(x, 'notransp') = M1 \ x} or @code{g(x, 'notransp') = M2 \ x} and
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42 ## @code{g(x, 'transp') = M1' \ x} or @code{g(x, 'transp') = M2' \ x}.
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43 ##
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44 ## If colled with more than one output parameter
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45 ##
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46 ## @itemize @minus
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47 ## @item @var{flag} indicates the exit status:
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48 ## @itemize @minus
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49 ## @item 0: iteration converged to the within the chosen tolerance
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50 ## @item 1: the maximum number of iterations was reached before convergence
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51 ## @item 3: the algorithm reached stagnation
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52 ## @end itemize
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53 ## (the value 2 is unused but skipped for compatibility).
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54 ## @item @var{relres} is the final value of the relative residual.
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55 ## @item @var{iter} is the number of iterations performed.
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56 ## @item @var{resvec} is a vector containing the relative residual at each iteration.
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57 ## @end itemize
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58 ##
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59 ## @seealso{bicgstab,cgs,gmres,pcg}
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60 ##
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61 ## @end deftypefn
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62
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63
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64 function [x, flag, res1, k, resvec] = bicg (A, b, tol, maxit, M1, M2, x0)
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65
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66 if (nargin >= 2 && isvector (full (b)))
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67
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68 if (ischar (A))
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69 fun = str2func (A);
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70 Ax = @(x) feval (fun, x, "notransp");
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71 Atx = @(x) feval (fun, x, "transp");
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72 elseif (ismatrix (A))
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73 Ax = @(x) A * x;
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74 Atx = @(x) A' * x;
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75 elseif (isa (A, "function_handle"))
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76 Ax = @(x) feval (A, x, "notransp");
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77 Atx = @(x) feval (A, x, "transp");
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78 else
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79 error (["bicg: first argument is expected to " ...
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80 "be a function or a square matrix"]);
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81 endif
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82
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83 if (nargin < 3 || isempty (tol))
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84 tol = 1e-6;
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85 endif
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86
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87 if (nargin < 4 || isempty (maxit))
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88 maxit = min (rows (b), 20);
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89 endif
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90
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91 if (nargin < 5 || isempty (M1))
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92 M1m1x = @(x, ignore) x;
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93 M1tm1x = M1m1x;
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94 elseif (ischar (M1))
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95 fun = str2func (M1);
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96 M1m1x = @(x) feval (fun, x, "notransp");
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97 M1tm1x = @(x) feval (fun, x, "transp");
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98 elseif (ismatrix (M1))
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99 M1m1x = @(x) M1 \ x;
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100 M1tm1x = @(x) M1' \ x;
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101 elseif (isa (M1, "function_handle"))
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102 M1m1x = @(x) feval (M1, x, "notransp");
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103 M1tm1x = @(x) feval (M1, x, "transp");
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104 else
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
105 error (["bicg: preconditioner is expected to " ...
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
106 "be a function or matrix"]);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
107 endif
13141
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John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
108
13091
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Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
109 if (nargin < 6 || isempty (M2))
13021
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Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
110 M2m1x = @(x, ignore) x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
111 M2tm1x = M2m1x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
112 elseif (ischar (M2))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
113 fun = str2func (M2);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
114 M2m1x = @(x) feval (fun, x, "notransp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
115 M2tm1x = @(x) feval (fun, x, "transp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
116 elseif (ismatrix (M2))
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Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
117 M2m1x = @(x) M2 \ x;
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Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
118 M2tm1x = @(x) M2' \ x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
119 elseif (isa (M2, "function_handle"))
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Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
120 M2m1x = @(x) feval (M2, x, "notransp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
121 M2tm1x = @(x) feval (M2, x, "transp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
122 else
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
123 error (["bicg: preconditioner is expected to " ...
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
124 "be a function or matrix"]);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
125 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
126
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
127 Pm1x = @(x) M2m1x (M1m1x (x));
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
128 Ptm1x = @(x) M1tm1x (M2tm1x (x));
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
129
13091
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Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
130 if (nargin < 7 || isempty (x0))
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
131 x0 = zeros (size (b));
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Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
132 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
133
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
134 y = x = x0;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
135 c = b;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
136
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
137 r0 = b - Ax (x);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
138 s0 = c - Atx (y);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
139
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
140 d = Pm1x (r0);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
141 f = Ptm1x (s0);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
142
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
143 bnorm = norm (b);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
144 res0 = Inf;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
145
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
146 if (any (r0 != 0))
13141
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John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
147
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
148 for k = 1:maxit
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
149
13141
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John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
150 a = (s0' * Pm1x (r0)) ./ (f' * Ax (d));
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
151
13141
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parents: 13091
diff changeset
152 x += a * d;
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parents: 13091
diff changeset
153 y += conj (a) * f;
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
154
13141
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John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
155 r1 = r0 - a * Ax (d);
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
156 s1 = s0 - conj (a) * Atx (f);
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
157
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
158 beta = (s1' * Pm1x (r1)) ./ (s0' * Pm1x (r0));
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
159
13141
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parents: 13091
diff changeset
160 d = Pm1x (r1) + beta * d;
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parents: 13091
diff changeset
161 f = Ptm1x (s1) + conj (beta) * f;
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
162
13141
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diff changeset
163 r0 = r1;
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parents: 13091
diff changeset
164 s0 = s1;
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
165
13141
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diff changeset
166 res1 = norm (b - Ax (x)) / bnorm;
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parents: 13091
diff changeset
167 if (res1 < tol)
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
168 flag = 0;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
169 if (nargout < 2)
13141
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parents: 13091
diff changeset
170 printf ("bicg converged at iteration %i ", k);
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
171 printf ("to a solution with relative residual %e\n", res1);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
172 endif
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
173 break;
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
174 endif
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
175
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
176 if (res0 <= res1)
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
177 flag = 3;
13141
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John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
178 printf ("bicg stopped at iteration %i ", k);
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
179 printf ("without converging to the desired tolerance %e\n", tol);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
180 printf ("because the method stagnated.\n");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
181 printf ("The iterate returned (number %i) ", k-1);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
182 printf ("has relative residual %e\n", res0);
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
183 break
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
184 endif
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
185 res0 = res1;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
186 if (nargout > 4)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
187 resvec(k) = res0;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
188 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
189 endfor
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
190
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
191 if (k == maxit)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
192 flag = 1;
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
193 printf ("bicg stopped at iteration %i ", maxit);
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
194 printf ("without converging to the desired tolerance %e\n", tol);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
195 printf ("because the maximum number of iterations was reached. ");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
196 printf ("The iterate returned (number %i) has ", maxit);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
197 printf ("relative residual %e\n", res1);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
198 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
199
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
200 else
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
201 flag = 0;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
202 if (nargout < 2)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
203 printf ("bicg converged after 0 interations\n");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
204 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
205 endif
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
206
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
207 else
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
208 print_usage ();
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
209 endif
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
210
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
211 endfunction;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
212
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
213
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
214 %!test
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
215 %! n = 100;
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
216 %! A = spdiags ([-2*ones(n,1) 4*ones(n,1) -ones(n,1)], -1:1, n, n);
13141
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John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
217 %! b = sum (A, 2);
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John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
218 %! tol = 1e-8;
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
219 %! maxit = 15;
13141
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parents: 13091
diff changeset
220 %! M1 = spdiags ([ones(n,1)/(-2) ones(n,1)],-1:0, n, n);
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
221 %! M2 = spdiags ([4*ones(n,1) -ones(n,1)], 0:1, n, n);
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
222 %! [x, flag, relres, iter, resvec] = bicg (A, b, tol, maxit, M1, M2);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
223 %! assert (x, ones (size (b)), 1e-7);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
224 %!
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
225 %!test
13141
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John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
226 %! n = 100;
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
227 %! A = spdiags ([-2*ones(n,1) 4*ones(n,1) -ones(n,1)], -1:1, n, n);
13141
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parents: 13091
diff changeset
228 %! b = sum (A, 2);
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
229 %! tol = 1e-8;
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
230 %! maxit = 15;
13141
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John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
231 %! M1 = spdiags ([ones(n,1)/(-2) ones(n,1)],-1:0, n, n);
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
232 %! M2 = spdiags ([4*ones(n,1) -ones(n,1)], 0:1, n, n);
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233 %!
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234 %! function y = afun (x, t, a)
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235 %! switch t
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236 %! case "notransp"
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237 %! y = a * x;
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238 %! case "transp"
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239 %! y = a' * x;
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240 %! endswitch
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241 %! endfunction
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242 %!
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243 %! [x, flag, relres, iter, resvec] = bicg (@(x, t) afun (x, t, A),
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244 %! b, tol, maxit, M1, M2);
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245 %! assert (x, ones (size (b)), 1e-7);
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246
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247 %!test
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248 %! n = 100;
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249 %! tol = 1e-8;
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250 %! a = sprand (n, n, .1);
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251 %! A = a' * a + 100 * eye (n);
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252 %! b = sum (A, 2);
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253 %! [x, flag, relres, iter, resvec] = bicg (A, b, tol, [], diag (diag (A)));
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254 %! assert (x, ones (size (b)), 1e-7);