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annotate scripts/sparse/bicg.m @ 13073:51bc892d5cf8

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Move bicg.m to scripts/sparse for uniformity * bicg.m : Move to scripts/sparse where the other iterative solvers are.
author Carlo de Falco <kingcrimson@tiscali.it>
date Sat, 03 Sep 2011 21:51:26 +0200
parents scripts/linear-algebra/bicg.m@a0d854f079d2
children e5aaba072d2b
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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13021
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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 ##
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23 ## Solve @code{A x = b} using the Bi-conjugate gradient iterative method.
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24 ##
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25 ## @itemize @minus
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26 ## @item @var{rtol} is the relative tolerance, if not given or set to [] the default value 1e-6 is used.
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27 ## @item @var{maxit} the maximum number of outer iterations, if not given or set to [] the default value @code{min (20, numel (b))} is used.
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28 ## @item @var{x0} the initial guess, if not given or set to [] the default value @code{zeros (size (b))} is used.
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29 ## @end itemize
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30 ##
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31 ## @var{A} can be passed as a matrix or as a function handle or
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32 ## inline function @code{f} such that @code{f(x, "notransp") = A*x} and @code{f(x, "transp") = A'*x}.
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33 ##
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34 ## The preconditioner @var{P} is given as @code{P = M1 * M2}.
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35 ## Both @var{M1} and @var{M2} can be passed as a matrix or as a function handle or
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36 ## inline function @code{g} such that @code{g(x, 'notransp') = M1 \ x} or @code{g(x, 'notransp') = M2 \ x} and
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37 ## @code{g(x, 'transp') = M1' \ x} or @code{g(x, 'transp') = M2' \ x}.
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38 ##
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39 ## If colled with more than one output parameter
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40 ##
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41 ## @itemize @minus
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42 ## @item @var{flag} indicates the exit status:
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43 ## @itemize @minus
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44 ## @item 0: iteration converged to the within the chosen tolerance
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45 ## @item 1: the maximum number of iterations was reached before convergence
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46 ## @item 3: the algorithm reached stagnation
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47 ## @end itemize
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48 ## (the value 2 is unused but skipped for compatibility).
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49 ## @item @var{relres} is the final value of the relative residual.
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50 ## @item @var{iter} is the number of iterations performed.
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51 ## @item @var{resvec} is a vector containing the relative residual at each iteration.
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52 ## @end itemize
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53 ##
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54 ## @seealso{pcg,cgs,bicgstab,gmres}
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55 ##
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56 ## @end deftypefn
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57
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58
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59 function [x, flag, res1, k, resvec] = bicg (A, b, tol, maxit, M1, M2, x0)
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60
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61 if ((nargin >= 2) && isvector (full (b)))
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62
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63 if (ischar (A))
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64 fun = str2func (A);
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65 Ax = @(x) feval (fun, x, "notransp");
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66 Atx = @(x) feval (fun, x, "transp");
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67 elseif (ismatrix (A))
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68 Ax = @(x) A * x;
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69 Atx = @(x) A' * x;
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70 elseif (isa (A, "function_handle"))
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71 Ax = @(x) feval (A, x, "notransp");
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72 Atx = @(x) feval (A, x, "transp");
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73 else
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74 error (["bicg: first argument is expected to " ...
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75 "be a function or a square matrix"]);
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76 endif
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77
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78 if ((nargin < 3) || (isempty (tol)))
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79 tol = 1e-6;
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80 endif
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81
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82 if ((nargin < 4) || (isempty (maxit)))
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83 maxit = min (rows (b), 20);
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84 endif
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85
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86 if ((nargin < 5) || isempty (M1))
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87 M1m1x = @(x, ignore) x;
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88 M1tm1x = M1m1x;
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89 elseif (ischar (M1))
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90 fun = str2func (M1);
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91 M1m1x = @(x) feval (fun, x, "notransp");
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92 M1tm1x = @(x) feval (fun, x, "transp");
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93 elseif (ismatrix (M1))
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94 M1m1x = @(x) M1 \ x;
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95 M1tm1x = @(x) M1' \ x;
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96 elseif (isa (M1, "function_handle"))
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97 M1m1x = @(x) feval (M1, x, "notransp");
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98 M1tm1x = @(x) feval (M1, x, "transp");
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99 else
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100 error (["bicg: preconditioner is expected to " ...
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101 "be a function or matrix"]);
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102 endif
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103
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104 if ((nargin < 6) || isempty (M2))
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105 M2m1x = @(x, ignore) x;
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106 M2tm1x = M2m1x;
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107 elseif (ischar (M2))
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108 fun = str2func (M2);
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109 M2m1x = @(x) feval (fun, x, "notransp");
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110 M2tm1x = @(x) feval (fun, x, "transp");
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111 elseif (ismatrix (M2))
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112 M2m1x = @(x) M2 \ x;
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113 M2tm1x = @(x) M2' \ x;
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114 elseif (isa (M2, "function_handle"))
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115 M2m1x = @(x) feval (M2, x, "notransp");
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116 M2tm1x = @(x) feval (M2, x, "transp");
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117 else
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118 error (["bicg: preconditioner is expected to " ...
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119 "be a function or matrix"]);
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120 endif
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121
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
122 Pm1x = @(x) M2m1x (M1m1x (x));
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
123 Ptm1x = @(x) M1tm1x (M2tm1x (x));
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
124
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
125 if ((nargin < 7) || (isempty (x0)))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
126 x0 = zeros (size (b));
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
127 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
128
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
129 y = x = x0;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
130 c = b;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
131
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
132 r0 = b - Ax (x);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
133 s0 = c - Atx (y);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
134
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
135 d = Pm1x (r0);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
136 f = Ptm1x (s0);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
137
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
138 bnorm = norm (b);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
139 res0 = Inf;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
140
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
141 if (any (r0 != 0))
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 for k = 1:maxit
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
144
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
145 a = (s0' * Pm1x (r0)) ./ (f' * Ax (d));
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
146
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
147 x += a * d;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
148 y += conj (a) * f;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
149
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
150 r1 = r0 - a * Ax (d);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
151 s1 = s0 - conj (a) * Atx (f);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
152
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
153 beta = (s1' * Pm1x (r1)) ./ (s0' * Pm1x (r0));
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
154
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
155 d = Pm1x (r1) + beta * d;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
156 f = Ptm1x (s1) + conj (beta) * f;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
157
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
158 r0 = r1;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
159 s0 = s1;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
160
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
161 res1 = norm (b - Ax (x)) / bnorm;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
162 if (res1 < tol)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
163 flag = 0;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
164 if (nargout < 2)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
165 printf ("bicg converged at iteration %i ", k);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
166 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
167 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
168 break;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
169 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
170
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
171 if (res0 <= res1)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
172 flag = 3;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
173 printf ("bicg stopped at iteration %i ", k);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
174 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
175 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
176 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
177 printf ("has relative residual %e\n", res0);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
178 break
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
179 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
180 res0 = res1;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
181 if (nargout > 4)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
182 resvec(k) = res0;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
183 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
184 endfor
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
185
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
186 if (k == maxit)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
187 flag = 1;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
188 printf ("bicg stopped at iteration %i ", maxit);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
189 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
190 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
191 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
192 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
193 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
194
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
195 else
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
196 flag = 0;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
197 if (nargout < 2)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
198 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
199 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
200 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
201
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
202 else
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
203 print_usage ();
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
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
206 endfunction;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
207
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
208
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
209 %!test
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
210 %! n = 100;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
211 %! A = spdiags ([-2*ones(n,1) 4*ones(n,1) -ones(n,1)], -1:1, n, n);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
212 %! b = sum (A, 2);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
213 %! tol = 1e-8;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
214 %! maxit = 15;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
215 %! M1 = spdiags ([ones(n,1)/(-2) ones(n,1)],-1:0, n, n);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
216 %! M2 = spdiags ([4*ones(n,1) -ones(n,1)], 0:1, n, n);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
217 %! [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
218 %! 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
219 %!
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
220 %!test
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
221 %! n = 100;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
222 %! A = spdiags ([-2*ones(n,1) 4*ones(n,1) -ones(n,1)], -1:1, n, n);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
223 %! b = sum (A, 2);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
224 %! tol = 1e-8;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
225 %! maxit = 15;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
226 %! M1 = spdiags ([ones(n,1)/(-2) ones(n,1)],-1:0, n, n);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
227 %! M2 = spdiags ([4*ones(n,1) -ones(n,1)], 0:1, n, n);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
228 %!
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
229 %! function y = afun (x, t, a)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
230 %! switch t
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
231 %! case "notransp"
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
232 %! y = a * x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
233 %! case "transp"
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
234 %! y = a' * x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
235 %! endswitch
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
236 %! endfunction
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
237 %!
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
238 %! [x, flag, relres, iter, resvec] = bicg (@(x, t) afun (x, t, A),
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
239 %! b, tol, maxit, M1, M2);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
240 %! 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
241
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
242 %!test
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
243 %! n = 100;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
244 %! tol = 1e-8;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
245 %! a = sprand (n, n, .1);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
246 %! A = a' * a + 100 * eye (n);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
247 %! b = sum (A, 2);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
248 %! [x, flag, relres, iter, resvec] = bicg (A, b, tol, [], diag (diag (A)));
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
249 %! assert (x, ones (size (b)), 1e-7);