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annotate scripts/sparse/cgs.m @ 20164:df437a52bcaf stable

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doc: Update more docstrings to have one sentence summary as first line. Reviewed miscellaneous, sparse, strings in scripts directory. * scripts/miscellaneous/bzip2.m, scripts/miscellaneous/citation.m, scripts/miscellaneous/compare_versions.m, scripts/miscellaneous/computer.m, scripts/miscellaneous/debug.m, scripts/miscellaneous/dir.m, scripts/miscellaneous/edit.m, scripts/miscellaneous/error_ids.m, scripts/miscellaneous/fileattrib.m, scripts/miscellaneous/fullfile.m, scripts/miscellaneous/genvarname.m, scripts/miscellaneous/gzip.m, scripts/miscellaneous/mkoctfile.m, scripts/miscellaneous/news.m, scripts/miscellaneous/open.m, scripts/miscellaneous/parseparams.m, scripts/miscellaneous/recycle.m, scripts/miscellaneous/run.m, scripts/miscellaneous/swapbytes.m, scripts/miscellaneous/tar.m, scripts/miscellaneous/tmpnam.m, scripts/miscellaneous/unpack.m, scripts/miscellaneous/what.m, scripts/sparse/bicg.m, scripts/sparse/bicgstab.m, scripts/sparse/cgs.m, scripts/sparse/colperm.m, scripts/sparse/eigs.m, scripts/sparse/etreeplot.m, scripts/sparse/gmres.m, scripts/sparse/gplot.m, scripts/sparse/ichol.m, scripts/sparse/ilu.m, scripts/sparse/pcg.m, scripts/sparse/pcr.m, scripts/sparse/qmr.m, scripts/sparse/spaugment.m, scripts/sparse/spconvert.m, scripts/sparse/spdiags.m, scripts/sparse/spfun.m, scripts/sparse/spones.m, scripts/sparse/sprandsym.m, scripts/sparse/spstats.m, scripts/sparse/spy.m, scripts/sparse/svds.m, scripts/sparse/treelayout.m, scripts/sparse/treeplot.m, scripts/strings/base2dec.m, scripts/strings/bin2dec.m, scripts/strings/blanks.m, scripts/strings/cstrcat.m, scripts/strings/deblank.m, scripts/strings/dec2base.m, scripts/strings/dec2bin.m, scripts/strings/dec2hex.m, scripts/strings/findstr.m, scripts/strings/hex2dec.m, scripts/strings/index.m, scripts/strings/isletter.m, scripts/strings/isstrprop.m, scripts/strings/mat2str.m, scripts/strings/ostrsplit.m, scripts/strings/regexptranslate.m, scripts/strings/rindex.m, scripts/strings/str2num.m, scripts/strings/strcat.m, scripts/strings/strchr.m, scripts/strings/strjoin.m, scripts/strings/strjust.m, scripts/strings/strmatch.m, scripts/strings/strsplit.m, scripts/strings/strtok.m, scripts/strings/strtrim.m, scripts/strings/strtrunc.m, scripts/strings/substr.m, scripts/strings/untabify.m, scripts/time/datenum.m: Update more docstrings to have one sentence summary as first line.
author Rik <rik@octave.org>
date Mon, 04 May 2015 14:22:02 -0700
parents 0a3ca546d7fc
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 ## Copyright (C) 2008-2015 Radek Salac
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2 ## Copyright (C) 2012 Carlo de Falco
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {@var{x} =} cgs (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0})
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22 ## @deftypefnx {Function File} {@var{x} =} cgs (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{P})
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23 ## @deftypefnx {Function File} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}] =} cgs (@var{A}, @var{b}, @dots{})
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24 ## Solve @code{A x = b}, where @var{A} is a square matrix, using the
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25 ## Conjugate Gradients Squared method.
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26 ##
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27 ## @itemize @minus
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28 ## @item @var{rtol} is the relative tolerance, if not given or set to [] the
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29 ## default value 1e-6 is used.
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30 ##
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31 ## @item @var{maxit} the maximum number of outer iterations, if not given or
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32 ## set to [] the default value @code{min (20, numel (b))} is used.
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33 ##
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34 ## @item @var{x0} the initial guess, if not given or set to [] the default
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35 ## value @code{zeros (size (b))} is used.
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36 ## @end itemize
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37 ##
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38 ## @var{A} can be passed as a matrix or as a function handle or inline
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39 ## function @code{f} such that @code{f(x) = A*x}.
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40 ##
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41 ## The preconditioner @var{P} is given as @code{P = M1 * M2}. Both @var{M1}
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42 ## and @var{M2} can be passed as a matrix or as a function handle or inline
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43 ## function @code{g} such that @code{g(x) = M1 \ x} or @code{g(x) = M2 \ x}.
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44 ##
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45 ## If called with more than one output parameter
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46 ##
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47 ## @itemize @minus
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48 ## @item @var{flag} indicates the exit status:
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49 ##
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50 ## @itemize @minus
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51 ## @item 0: iteration converged to the within the chosen tolerance
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52 ##
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53 ## @item 1: the maximum number of iterations was reached before convergence
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54 ##
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55 ## @item 3: the algorithm reached stagnation
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56 ## @end itemize
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57 ##
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58 ## (the value 2 is unused but skipped for compatibility).
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59 ##
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60 ## @item @var{relres} is the final value of the relative residual.
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61 ##
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62 ## @item @var{iter} is the number of iterations performed.
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63 ##
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64 ## @item @var{resvec} is a vector containing the relative residual at
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65 ## each iteration.
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66 ## @end itemize
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67 ##
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68 ## @seealso{pcg, bicgstab, bicg, gmres, qmr}
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69 ## @end deftypefn
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70
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71 function [x, flag, relres, iter, resvec] = cgs (A, b, tol, maxit, M1, M2, x0)
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72
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73 if (nargin >= 2 && nargin <= 7 && isvector (full (b)))
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74
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75 if (ischar (A))
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76 A = str2func (A);
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77 elseif (isnumeric (A) && ismatrix (A))
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78 Ax = @(x) A * x;
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79 elseif (isa (A, "function_handle"))
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80 Ax = @(x) feval (A, x);
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81 else
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82 error (["cgs: first argument is expected to "...
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83 "be a function or a square matrix"]);
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84 endif
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85
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86 if (nargin < 3 || isempty (tol))
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87 tol = 1e-6;
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88 endif
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89
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90 if (nargin < 4 || isempty (maxit))
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91 maxit = min (rows (b), 20);
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92 endif
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93
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94 if (nargin < 5 || isempty (M1))
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95 M1m1x = @(x) x;
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96 elseif (ischar (M1))
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97 M1m1x = str2func (M1);
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98 elseif (isnumeric (M1) && ismatrix (M1))
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99 M1m1x = @(x) M1 \ x;
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100 elseif (isa (M1, "function_handle"))
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101 M1m1x = @(x) feval (M1, x);
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102 else
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103 error ("cgs: preconditioner is expected to be a function or matrix");
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104 endif
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105
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106 if (nargin < 6 || isempty (M2))
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107 M2m1x = @(x) x;
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108 elseif (ischar (M2))
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109 M2m1x = str2func (M2);
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110 elseif (isnumeric (M2) && ismatrix (M2))
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111 M2m1x = @(x) M2 \ x;
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112 elseif (isa (M2, "function_handle"))
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113 M2m1x = @(x) feval (M2, x);
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114 else
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115 error ("cgs: preconditioner is expected to be a function or matrix");
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116 endif
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117
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118 precon = @(x) M2m1x (M1m1x (x));
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diff changeset
119
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120 if (nargin < 7 || isempty (x0))
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121 x0 = zeros (size (b));
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122 endif
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123
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124
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125 x = x0;
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126
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127 res = b - Ax (x);
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128 norm_b = norm (b);
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129 ## Vector of the residual norms for each iteration.
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130 resvec = norm (res) / norm_b;
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131 ro = 0;
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132 ## Default behavior we don't reach tolerance tol within maxit iterations.
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133 flag = 1;
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134 for iter = 1:maxit
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135
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136 z = precon (res);
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137
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138 ## Cache.
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139 ro_old = ro;
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140 ro = res' * z;
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141 if (iter == 1)
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142 p = z;
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143 else
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144 beta = ro / ro_old;
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145 p = z + beta * p;
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diff changeset
146 endif
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147 ## Cache.
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148 q = Ax (p);
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149 alpha = ro / (p' * q);
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150 x = x + alpha * p;
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151
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152 res = res - alpha * q;
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153 relres = norm (res) / norm_b;
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154 resvec = [resvec; relres];
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155
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156 if (relres <= tol)
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157 ## We reach tolerance tol within maxit iterations.
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diff changeset
158 flag = 0;
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diff changeset
159 break
19833
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160 elseif (resvec(end) == resvec(end - 1))
13063
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161 ## The method stagnates.
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diff changeset
162 flag = 3;
13077
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diff changeset
163 break
13063
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164 endif
13077
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165 endfor
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166
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167 if (nargout < 1)
13077
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diff changeset
168 if (flag == 0)
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169 printf ("cgs converged at iteration %i to a solution with relative residual %e\n",
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170 iter, relres);
13063
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171 elseif (flag == 3)
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172 printf (["cgs stopped at iteration %i without converging to the desired tolerance %e\n",
13063
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173 "because the method stagnated.\n",
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174 "The iterate returned (number %i) has relative residual %e\n"],
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diff changeset
175 iter, tol, iter, relres);
13063
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diff changeset
176 else
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177 printf (["cgs stopped at iteration %i without converging to the desired tolerance %e\n",
13063
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178 "because the maximum number of iterations was reached.\n",
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diff changeset
179 "The iterate returned (number %i) has relative residual %e\n"],
13077
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diff changeset
180 iter, tol, iter, relres);
13063
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diff changeset
181 endif
9278
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diff changeset
182 endif
13063
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183
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diff changeset
184 else
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185 print_usage ();
9278
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186 endif
2b35cb600d50 improve bicgstab and cgs
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diff changeset
187
8338
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188 endfunction
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189
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190
a35bf360b919 Add the cgs and treelayout functions
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diff changeset
191 %!demo
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192 %! % Solve system of A*x=b
14237
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193 %! A = [5 -1 3;-1 2 -2;3 -2 3];
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194 %! b = [7;-1;4];
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195 %! [a,b,c,d,e] = cgs (A,b)
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196
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197 %!shared A, b, n, M
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diff changeset
198 %!
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199 %!test
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200 %! n = 100;
13063
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diff changeset
201 %! A = spdiags ([-ones(n,1) 4*ones(n,1) -ones(n,1)], -1:1, n, n);
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202 %! b = sum (A, 2);
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
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203 %! tol = 1e-8;
13063
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diff changeset
204 %! maxit = 1000;
13141
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205 %! M = 4*eye (n);
13063
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diff changeset
206 %! [x, flag, relres, iter, resvec] = cgs (A, b, tol, maxit, M);
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diff changeset
207 %! assert (x, ones (size (b)), 1e-7);
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Carlo de Falco <kingcrimson@tiscali.it>
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diff changeset
208 %!
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diff changeset
209 %!test
13141
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210 %! tol = 1e-8;
13063
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diff changeset
211 %! maxit = 15;
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diff changeset
212 %!
13076
59def8890992 codesprint: avoid crash after running tests
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diff changeset
213 %! [x, flag, relres, iter, resvec] = cgs (@(x) A * x, b, tol, maxit, M);
13063
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diff changeset
214 %! assert (x, ones (size (b)), 1e-7);
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diff changeset
215
4b110dd204b9 codesprint: Allow passing a function handle for the coefficient matrix in cgs
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diff changeset
216 %!test
13141
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217 %! n = 100;
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218 %! tol = 1e-8;
13063
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diff changeset
219 %! a = sprand (n, n, .1);
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diff changeset
220 %! A = a'*a + 100 * eye (n);
13141
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diff changeset
221 %! b = sum (A, 2);
13063
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diff changeset
222 %! [x, flag, relres, iter, resvec] = cgs (A, b, tol, [], diag (diag (A)));
4b110dd204b9 codesprint: Allow passing a function handle for the coefficient matrix in cgs
Carlo de Falco <kingcrimson@tiscali.it>
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223 %! assert (x, ones (size (b)), 1e-7);
14237
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Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
224