Mercurial > hg > octave-lyh

annotate scripts/sparse/cgs.m @ 11100:cdf940db26a0

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
provide mxIsFunctionHandle MEX interface function
author John W. Eaton <jwe@octave.org>
date Sat, 16 Oct 2010 13:27:18 -0400
parents be55736a0783
children 1740012184f9
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
9278
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
1 ## Copyright (C) 2008 Radek Salac
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
2 ##
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
3 ## This file is part of Octave.
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
4 ##
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
5 ## Octave is free software; you can redistribute it and/or modify it
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
6 ## under the terms of the GNU General Public License as published by
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
7 ## the Free Software Foundation; either version 3 of the License, or (at
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
8 ## your option) any later version.
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
9 ##
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
10 ## Octave is distributed in the hope that it will be useful, but
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
13 ## General Public License for more details.
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
14 ##
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
15 ## You should have received a copy of the GNU General Public License
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
16 ## along with Octave; see the file COPYING. If not, see
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
17 ## <http://www.gnu.org/licenses/>.
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
18
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
19 ## -*- texinfo -*-
10793
be55736a0783 Grammarcheck the documentation from m-files.
Rik <octave@nomad.inbox5.com>
parents: 9279
diff changeset
20 ## @deftypefn {Function File} {} cgs (@var{A}, @var{b})
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
21 ## @deftypefnx {Function File} {} cgs (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0})
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
22 ## This procedure attempts to solve a system of linear equations A*x = b for x.
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
23 ## The @var{A} must be square, symmetric and positive definite real matrix N*N.
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
24 ## The @var{b} must be a one column vector with a length of N.
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
25 ## The @var{tol} specifies the tolerance of the method, default value is 1e-6.
10793
be55736a0783 Grammarcheck the documentation from m-files.
Rik <octave@nomad.inbox5.com>
parents: 9279
diff changeset
26 ## The @var{maxit} specifies the maximum number of iteration, default value is
be55736a0783 Grammarcheck the documentation from m-files.
Rik <octave@nomad.inbox5.com>
parents: 9279
diff changeset
27 ## MIN(20,N).
be55736a0783 Grammarcheck the documentation from m-files.
Rik <octave@nomad.inbox5.com>
parents: 9279
diff changeset
28 ## The @var{M1} specifies a preconditioner, can also be a function handler which
be55736a0783 Grammarcheck the documentation from m-files.
Rik <octave@nomad.inbox5.com>
parents: 9279
diff changeset
29 ## returns M\X.
be55736a0783 Grammarcheck the documentation from m-files.
Rik <octave@nomad.inbox5.com>
parents: 9279
diff changeset
30 ## The @var{M2} combined with @var{M1} defines preconditioner as
be55736a0783 Grammarcheck the documentation from m-files.
Rik <octave@nomad.inbox5.com>
parents: 9279
diff changeset
31 ## preconditioner=M1*M2.
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
32 ## The @var{x0} is initial guess, default value is zeros(N,1).
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
33 ##
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
34 ## @end deftypefn
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
35
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
36 function [x, flag, relres, iter, resvec] = cgs (A, b, tol, maxit, M1, M2, x0)
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
37
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
38 if (nargin < 2 || nargin > 7 || nargout > 5)
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
39 print_usage ();
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
40 elseif (!isnumeric (A) || rows (A) != columns (A))
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
41 error ("cgs: first argument must be a n-by-n matrix");
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
42 elseif (!isvector (b))
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
43 error ("cgs: b must be a vector");
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
44 elseif (rows (A) != rows (b))
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
45 error ("cgs: first and second argument must have the same number of rows");
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
46 elseif (nargin > 2 && !isscalar (tol))
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
47 error ("cgs: tol must be a scalar");
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
48 elseif (nargin > 3 && !isscalar (maxit))
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
49 error ("cgs: maxit must be a scalar");
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
50 elseif (nargin > 4 && ismatrix (M1) && (rows (M1) != rows (A) || columns (M1) != columns (A)))
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
51 error ("cgs: M1 must have the same number of rows and columns as A");
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
52 elseif (nargin > 5 && (!ismatrix (M2) || rows (M2) != rows (A) || columns (M2) != columns (A)))
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
53 error ("cgs: M2 must have the same number of rows and columns as A");
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
54 elseif (nargin > 6 && !isvector (x0))
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
55 error ("cgs: x0 must be a vector");
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
56 elseif (nargin > 6 && rows (x0) != rows (b))
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8338
diff changeset
57 error ("cgs: x0 must have the same number of rows as b");
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
58 endif
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
59
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8338
diff changeset
60 ## Default tolerance.
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
61 if (nargin < 3)
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
62 tol = 1e-6;
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
63 endif
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
64
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8338
diff changeset
65 ## Default maximum number of iteration.
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
66 if (nargin < 4)
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
67 maxit = min (rows (b),20);
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
68 endif
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
69
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8338
diff changeset
70 ## Left preconditioner.
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
71 if (nargin == 5)
9279
1673a0dc019f fix & improve preconditioning strategy in cgs & bicgstab
Jaroslav Hajek <highegg@gmail.com>
parents: 9278
diff changeset
72 if (isnumeric (M1))
1673a0dc019f fix & improve preconditioning strategy in cgs & bicgstab
Jaroslav Hajek <highegg@gmail.com>
parents: 9278
diff changeset
73 precon = @(x) M1 \ x;
1673a0dc019f fix & improve preconditioning strategy in cgs & bicgstab
Jaroslav Hajek <highegg@gmail.com>
parents: 9278
diff changeset
74 endif
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
75 elseif (nargin > 5)
9279
1673a0dc019f fix & improve preconditioning strategy in cgs & bicgstab
Jaroslav Hajek <highegg@gmail.com>
parents: 9278
diff changeset
76 if (issparse (M1) && issparse (M2))
1673a0dc019f fix & improve preconditioning strategy in cgs & bicgstab
Jaroslav Hajek <highegg@gmail.com>
parents: 9278
diff changeset
77 precon = @(x) M2 \ (M1 \ x);
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
78 else
9279
1673a0dc019f fix & improve preconditioning strategy in cgs & bicgstab
Jaroslav Hajek <highegg@gmail.com>
parents: 9278
diff changeset
79 M = M1*M2;
1673a0dc019f fix & improve preconditioning strategy in cgs & bicgstab
Jaroslav Hajek <highegg@gmail.com>
parents: 9278
diff changeset
80 precon = @(x) M \ x;
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
81 endif
9279
1673a0dc019f fix & improve preconditioning strategy in cgs & bicgstab
Jaroslav Hajek <highegg@gmail.com>
parents: 9278
diff changeset
82 else
1673a0dc019f fix & improve preconditioning strategy in cgs & bicgstab
Jaroslav Hajek <highegg@gmail.com>
parents: 9278
diff changeset
83 precon = @(x) x;
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
84 endif
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
85
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8338
diff changeset
86 ## Specifies initial estimate x0.
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
87 if (nargin < 7)
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
88 x = zeros (rows (b), 1);
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
89 else
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
90 x = x0;
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
91 endif
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
92
9278
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
93 res = b - A * x;
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
94 norm_b = norm (b);
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8338
diff changeset
95 ## Vector of the residual norms for each iteration.
9278
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
96 resvec = [ norm(res)/norm_b ];
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
97 ro = 0;
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8338
diff changeset
98 ## Default behavior we don't reach tolerance tol within maxit iterations.
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
99 flag = 1;
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
100 for iter = 1 : maxit
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
101
9279
1673a0dc019f fix & improve preconditioning strategy in cgs & bicgstab
Jaroslav Hajek <highegg@gmail.com>
parents: 9278
diff changeset
102 z = precon (res);
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
103
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8338
diff changeset
104 ## Cache.
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
105 ro_old = ro;
9278
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
106 ro = res' * z;
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
107 if (iter == 1)
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
108 p = z;
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
109 else
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
110 beta = ro / ro_old;
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
111 p = z + beta * p;
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
112 endif
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8338
diff changeset
113 ## Cache.
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8338
diff changeset
114 q = A * p;
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
115 alpha = ro / (p' * q);
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
116 x = x + alpha * p;
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
117
9278
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
118 res = res - alpha * q;
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
119 relres = norm(res) / norm_b;
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
120 resvec = [resvec;relres];
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
121
9278
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
122 if (relres <= tol)
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8338
diff changeset
123 ## We reach tolerance tol within maxit iterations.
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
124 flag = 0;
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
125 break;
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8338
diff changeset
126 elseif (resvec (end) == resvec (end - 1))
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8338
diff changeset
127 ## The method stagnates.
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
128 flag = 3;
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
129 break;
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
130 endif
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
131 endfor;
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
132
9278
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
133 if (nargout < 1)
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
134 if ( flag == 0 )
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
135 printf (["cgs converged at iteration %i ",
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
136 "to a solution with relative residual %e\n"],iter,relres);
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
137 elseif (flag == 3)
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
138 printf (["cgs stopped at iteration %i ",
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
139 "without converging to the desired tolerance %e\n",
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
140 "because the method stagnated.\n",
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
141 "The iterate returned (number %i) has relative residual %e\n"],iter,tol,iter,relres);
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
142 else
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
143 printf (["cgs stopped at iteration %i ",
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
144 "without converging to the desired tolerance %e\n",
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
145 "because the maximum number of iterations was reached.\n",
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
146 "The iterate returned (number %i) has relative residual %e\n"],iter,tol,iter,relres);
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
147 endif
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
148 endif
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
149
8338
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
150 endfunction
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
151
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
152
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
153
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
154 %!demo
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
155 %! % Solve system of A*x=b
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
156 %! A=[5 -1 3;-1 2 -2;3 -2 3]
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
157 %! b=[7;-1;4]
a35bf360b919 Add the cgs and treelayout functions
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
158 %! [a,b,c,d,e]=cgs(A,b)