Mercurial > hg > octave-lyh

annotate scripts/sparse/bicg.m @ 13091:e5aaba072d2b

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
maint: style fixes in iterative linear solvers * bicg.m, bicgstab.m, cgs.m, gmres.m: Style fixes.
author Carlo de Falco <kingcrimson@tiscali.it>
date Sun, 04 Sep 2011 01:21:43 +0200
parents 51bc892d5cf8
children e81ddf9cacd5
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
1 ## Copyright (C) 2006 Sylvain Pelissier <sylvain.pelissier@gmail.com>
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
2 ## Copyright (C) 2011 Carlo de Falco
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
3 ##
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
4 ## This program is free software; you can redistribute it and/or modify
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
5 ## it under the terms of the GNU General Public License as published by
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
6 ## the Free Software Foundation; either version 2 of the License, or
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
7 ## (at your option) any later version.
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
8 ##
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
9 ## This program is distributed in the hope that it will be useful,
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
10 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
11 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
12 ## GNU General Public License for more details.
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
13 ##
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
14 ## You should have received a copy of the GNU General Public License
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
15 ## along with this program; If not, see <http://www.gnu.org/licenses/>.
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
16
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
17 ## -*- texinfo -*-
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
18 ##
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
19 ## @deftypefn {Function File} {@var{x} =} bicg (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0})
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
20 ## @deftypefnx {Function File} {@var{x} =} bicg (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{P})
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
21 ## @deftypefnx {Function File} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}] =} bicg (@var{A}, @var{b}, ...)
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
22 ## Solve @code{A x = b} using the Bi-conjugate gradient iterative method.
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
23 ##
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
24 ## @itemize @minus
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
25 ## @item @var{rtol} is the relative tolerance, if not given
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
26 ## or set to [] the default value 1e-6 is used.
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
27 ## @item @var{maxit} the maximum number of outer iterations,
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
28 ## if not given or set to [] the default value
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
29 ## @code{min (20, numel (b))} is used.
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
30 ## @item @var{x0} the initial guess, if not given or set to []
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
31 ## the default value @code{zeros (size (b))} is used.
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
32 ## @end itemize
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
33 ##
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
34 ## @var{A} can be passed as a matrix or as a function handle or
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
35 ## inline function @code{f} such that @code{f(x, "notransp") = A*x}
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
36 ## and @code{f(x, "transp") = A'*x}.
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
37 ##
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
38 ## The preconditioner @var{P} is given as @code{P = M1 * M2}.
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
39 ## Both @var{M1} and @var{M2} can be passed as a matrix or as
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
40 ## a function handle or inline function @code{g} such that
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
41 ## @code{g(x, 'notransp') = M1 \ x} or @code{g(x, 'notransp') = M2 \ x} and
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
42 ## @code{g(x, 'transp') = M1' \ x} or @code{g(x, 'transp') = M2' \ x}.
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
43 ##
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
44 ## If colled with more than one output parameter
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
45 ##
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
46 ## @itemize @minus
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
47 ## @item @var{flag} indicates the exit status:
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
48 ## @itemize @minus
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
49 ## @item 0: iteration converged to the within the chosen tolerance
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
50 ## @item 1: the maximum number of iterations was reached before convergence
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
51 ## @item 3: the algorithm reached stagnation
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
52 ## @end itemize
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
53 ## (the value 2 is unused but skipped for compatibility).
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
54 ## @item @var{relres} is the final value of the relative residual.
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
55 ## @item @var{iter} is the number of iterations performed.
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
56 ## @item @var{resvec} is a vector containing the relative residual at each iteration.
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
57 ## @end itemize
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
58 ##
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
59 ## @seealso{bicgstab,cgs,gmres,pcg}
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
60 ##
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
61 ## @end deftypefn
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
62
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
63
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
64 function [x, flag, res1, k, resvec] = bicg (A, b, tol, maxit, M1, M2, x0)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
65
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
66 if (nargin >= 2 && isvector (full (b)))
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
67
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
68 if (ischar (A))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
69 fun = str2func (A);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
70 Ax = @(x) feval (fun, x, "notransp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
71 Atx = @(x) feval (fun, x, "transp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
72 elseif (ismatrix (A))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
73 Ax = @(x) A * x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
74 Atx = @(x) A' * x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
75 elseif (isa (A, "function_handle"))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
76 Ax = @(x) feval (A, x, "notransp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
77 Atx = @(x) feval (A, x, "transp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
78 else
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
79 error (["bicg: first argument is expected to " ...
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
80 "be a function or a square matrix"]);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
81 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
82
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
83 if (nargin < 3 || isempty (tol))
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
84 tol = 1e-6;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
85 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
86
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
87 if (nargin < 4 || isempty (maxit))
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
88 maxit = min (rows (b), 20);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
89 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
90
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
91 if (nargin < 5 || isempty (M1))
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
92 M1m1x = @(x, ignore) x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
93 M1tm1x = M1m1x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
94 elseif (ischar (M1))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
95 fun = str2func (M1);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
96 M1m1x = @(x) feval (fun, x, "notransp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
97 M1tm1x = @(x) feval (fun, x, "transp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
98 elseif (ismatrix (M1))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
99 M1m1x = @(x) M1 \ x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
100 M1tm1x = @(x) M1' \ x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
101 elseif (isa (M1, "function_handle"))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
102 M1m1x = @(x) feval (M1, x, "notransp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
103 M1tm1x = @(x) feval (M1, x, "transp");
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
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
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
108
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13073
diff changeset
109 if (nargin < 6 || isempty (M2))
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
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))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
117 M2m1x = @(x) M2 \ x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
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"))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
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
e5aaba072d2b maint: style fixes in iterative linear solvers
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));
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
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))
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
147
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
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
150 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
151
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
152 x += a * d;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
153 y += conj (a) * f;
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 r1 = r0 - a * Ax (d);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
156 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
157
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
158 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
159
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
160 d = Pm1x (r1) + beta * d;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
161 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
162
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
163 r0 = r1;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
164 s0 = s1;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
165
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
166 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
167 if (res1 < tol)
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)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
170 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
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
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
173 break;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
174 endif
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
175
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
176 if (res0 <= res1)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
177 flag = 3;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
178 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
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);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
183 break
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
184 endif
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;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
193 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
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
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
206
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
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
210
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
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
215 %! n = 100;
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);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
217 %! b = sum (A, 2);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
218 %! tol = 1e-8;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
219 %! maxit = 15;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
220 %! 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
221 %! 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
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
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
226 %! n = 100;
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);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
228 %! b = sum (A, 2);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
229 %! tol = 1e-8;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
230 %! maxit = 15;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
231 %! 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
232 %! 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
233 %!
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
234 %! 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
235 %! switch t
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
236 %! case "notransp"
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
237 %! y = a * x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
238 %! case "transp"
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
239 %! y = a' * x;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
240 %! endswitch
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
241 %! endfunction
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
242 %!
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
243 %! [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
244 %! b, tol, maxit, M1, M2);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
245 %! 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
246
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
247 %!test
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
248 %! n = 100;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
249 %! tol = 1e-8;
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
250 %! a = sprand (n, n, .1);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
251 %! 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
252 %! b = sum (A, 2);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
253 %! [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
254 %! assert (x, ones (size (b)), 1e-7);