octave: scripts/sparse/bicgstab.m annotate

annotate scripts/sparse/bicgstab.m @ 33658:b1d6e40ac737 stable tip

NEWS.9.md: Fix typo and minor formatting changes. * etc/NEWS.9.md: Fix typo. Adjust whitespace. Use markdown syntax for code snippets.

author	Markus Mützel <markus.muetzel@gmx.de>
date	Wed, 05 Jun 2024 11:27:35 +0200
parents	2e484f9f1f18
children

rev	line source
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	1 ########################################################################
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	2 ##
32632 2e484f9f1f18 maint: update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 31706 diff changeset	3 ## Copyright (C) 2008-2024 The Octave Project Developers
27918 b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 27356 diff changeset	4 ##
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	5 ## See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	6 ## distribution or <https://octave.org/copyright/>.
8416 0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	7 ##
0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	8 ## This file is part of Octave.
0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	9 ##
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 24003 diff changeset	10 ## Octave is free software: you can redistribute it and/or modify it
8416 0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	11 ## under the terms of the GNU General Public License as published by
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 24003 diff changeset	12 ## the Free Software Foundation, either version 3 of the License, or
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	13 ## (at your option) any later version.
8416 0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	14 ##
0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	15 ## Octave is distributed in the hope that it will be useful, but
0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	18 ## GNU General Public License for more details.
8416 0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	19 ##
0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	20 ## You should have received a copy of the GNU General Public License
0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	21 ## along with Octave; see the file COPYING. If not, see
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 24003 diff changeset	22 ## <https://www.gnu.org/licenses/>.
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	23 ##
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	24 ########################################################################
8416 0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	25
0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	26 ## -- texinfo --
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	27 ## @deftypefn {} {@var{x} =} bicgstab (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0}, @dots{})
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	28 ## @deftypefnx {} {@var{x} =} bicgstab (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M}, [], @var{x0}, @dots{})
20852 516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20711 diff changeset	29 ## @deftypefnx {} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}] =} bicgstab (@var{A}, @var{b}, @dots{})
27356 4e632e942e84 doc: Improve documentation of sparse functions. Kai T. Ohlhus <k.ohlhus@gmail.com> parents: 27355 diff changeset	30 ## Solve @code{A x = b} using the stabilized Bi-conjugate gradient iterative
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13837 diff changeset	31 ## method.
13070 a0d854f079d2 codesprint: Fix building of docs for new bicg functions Jordi Gutiérrez Hermoso <jordigh@gmail.com> parents: 13061 diff changeset	32 ##
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	33 ## The input parameters are:
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	34 ##
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13070 diff changeset	35 ## @itemize @minus
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	36 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	37 ## @item @var{A} is the matrix of the linear system and it must be square.
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	38 ## @var{A} can be passed as a matrix, function handle, or inline
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	39 ## function @code{Afcn} such that @code{Afcn(x) = A * x}. Additional
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	40 ## parameters to @code{Afcn} are passed after @var{x0}.
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	41 ##
24985 d85b2485af9e doc: grammarcheck m-files ahead of 4.4 release. Rik <rik@octave.org> parents: 24860 diff changeset	42 ## @item @var{b} is the right hand side vector. It must be a column vector
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	43 ## with the same number of rows as @var{A}.
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	44 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	45 ## @item
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	46 ## @var{tol} is the required relative tolerance for the residual error,
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	47 ## @w{@code{@var{b} - @var{A} * @var{x}}}. The iteration stops if
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	48 ## @w{@code{norm (@var{b} - @var{A} * @var{x})} @leq{}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	49 ## @w{@code{@var{tol} * norm (@var{b})}}}.
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	50 ## If @var{tol} is omitted or empty, then a tolerance of 1e-6 is used.
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13837 diff changeset	51 ##
20164 df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19854 diff changeset	52 ## @item @var{maxit} the maximum number of outer iterations, if not given or
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19854 diff changeset	53 ## set to [] the default value @code{min (20, numel (b))} is used.
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13837 diff changeset	54 ##
24985 d85b2485af9e doc: grammarcheck m-files ahead of 4.4 release. Rik <rik@octave.org> parents: 24860 diff changeset	55 ## @item @var{M1}, @var{M2} are the preconditioners. The preconditioner
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	56 ## @var{M} is given as @code{@var{M} = @var{M1} * @var{M2}}.
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	57 ## Both @var{M1} and @var{M2} can be passed as a matrix or as a function
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	58 ## handle or inline function @code{g} such that
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	59 ## @code{g(@var{x}) = @var{M1} \ @var{x}} or
24992 3d5a39077708 avoid some warnings from old versions of makeinfo (bug #53479) Guillaume Flandin parents: 24985 diff changeset	60 ## @code{g(@var{x}) = @var{M2} \ @var{x}}.
25003 2365c2661b3c doc: Spellcheck documentation ahead of 4.4 release. Rik <rik@octave.org> parents: 24992 diff changeset	61 ## The technique used is the right preconditioning, i.e., it is
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	62 ## solved @code{@var{A} * inv (@var{M}) * @var{y} = @var{b}} and then
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	63 ## @code{@var{x} = inv (@var{M}) * @var{y}}.
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	64 ##
20164 df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19854 diff changeset	65 ## @item @var{x0} the initial guess, if not given or set to [] the default
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	66 ## value @code{zeros (size (@var{b}))} is used.
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	67 ##
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13070 diff changeset	68 ## @end itemize
13070 a0d854f079d2 codesprint: Fix building of docs for new bicg functions Jordi Gutiérrez Hermoso <jordigh@gmail.com> parents: 13061 diff changeset	69 ##
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	70 ## The arguments which follow @var{x0} are treated as parameters, and passed in
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	71 ## a proper way to any of the functions (@var{A} or @var{M}) which are passed
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	72 ## to @code{bicstab}.
8416 0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	73 ##
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	74 ## The output parameters are:
13061 addfc0ae69c0 Make bicgstab interface more compatible Carlo de Falco <kingcrimson@tiscali.it> parents: 11587 diff changeset	75 ##
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13070 diff changeset	76 ## @itemize @minus
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	77 ##
24985 d85b2485af9e doc: grammarcheck m-files ahead of 4.4 release. Rik <rik@octave.org> parents: 24860 diff changeset	78 ## @item @var{x} is the approximation computed. If the method doesn't
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	79 ## converge then it is the iterated with the minimum residual.
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	80 ##
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13070 diff changeset	81 ## @item @var{flag} indicates the exit status:
14853 72b8b39e12be doc: Periodic grammarcheck of documentation. Rik <octave@nomad.inbox5.com> parents: 14609 diff changeset	82 ##
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13070 diff changeset	83 ## @itemize @minus
e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13070 diff changeset	84 ## @item 0: iteration converged to the within the chosen tolerance
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13837 diff changeset	85 ##
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13070 diff changeset	86 ## @item 1: the maximum number of iterations was reached before convergence
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13837 diff changeset	87 ##
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	88 ## @item 2: the preconditioner matrix is singular
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	89 ##
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13070 diff changeset	90 ## @item 3: the algorithm reached stagnation
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	91 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	92 ## @item 4: the algorithm can't continue due to a division by zero
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	93 ## @end itemize
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	94 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	95 ## @item @var{relres} is the relative residual obtained with as
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	96 ## @code{(@var{A}*@var{x}-@var{b}) / @code{norm(@var{b})}}.
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	97 ##
27356 4e632e942e84 doc: Improve documentation of sparse functions. Kai T. Ohlhus <k.ohlhus@gmail.com> parents: 27355 diff changeset	98 ## @item @var{iter} is the (possibly half) iteration which @var{x} is
24985 d85b2485af9e doc: grammarcheck m-files ahead of 4.4 release. Rik <rik@octave.org> parents: 24860 diff changeset	99 ## computed. If it is an half iteration then it is @code{@var{iter} + 0.5}
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	100 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	101 ## @item @var{resvec} is a vector containing the residual of each half and
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	102 ## total iteration (There are also the half iterations since @var{x} is
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	103 ## computed in two steps at each iteration).
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	104 ## Doing @code{(length(@var{resvec}) - 1) / 2} is possible to see the
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	105 ## total number of (total) iterations performed.
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	106 ##
13091 e5aaba072d2b maint: style fixes in iterative linear solvers Carlo de Falco <kingcrimson@tiscali.it> parents: 13070 diff changeset	107 ## @end itemize
16816 12005245b645 doc: Periodic grammarcheck of documentation. Rik <rik@octave.org> parents: 14868 diff changeset	108 ##
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	109 ## Let us consider a trivial problem with a tridiagonal matrix
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	110 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	111 ## @example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	112 ## @group
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	113 ## n = 20;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	114 ## A = toeplitz (sparse ([1, 1], [1, 2], [2, 1] * n ^ 2, 1, n)) + ...
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	115 ## toeplitz (sparse (1, 2, -1, 1, n) * n / 2, ...
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	116 ## sparse (1, 2, 1, 1, n) * n / 2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	117 ## b = A * ones (n, 1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	118 ## restart = 5;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	119 ## [M1, M2] = ilu (A); # in this tridiag case, it corresponds to lu (A)
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	120 ## M = M1 * M2;
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	121 ## Afcn = @@(x) A * x;
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	122 ## Mfcn = @@(x) M \ x;
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	123 ## M1fcn = @@(x) M1 \ x;
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	124 ## M2fcn = @@(x) M2 \ x;
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	125 ## @end group
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	126 ## @end example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	127 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	128 ## @sc{Example 1:} simplest usage of @code{bicgstab}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	129 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	130 ## @example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	131 ## x = bicgstab (A, b, [], n)
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	132 ## @end example
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13837 diff changeset	133 ##
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	134 ## @sc{Example 2:} @code{bicgstab} with a function which computes
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	135 ## @code{@var{A} * @var{x}}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	136 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	137 ## @example
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	138 ## x = bicgstab (Afcn, b, [], n)
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	139 ## @end example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	140 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	141 ## @sc{Example 3:} @code{bicgstab} with a preconditioner matrix @var{M}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	142 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	143 ## @example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	144 ## x = bicgstab (A, b, [], 1e-06, n, M)
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	145 ## @end example
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13837 diff changeset	146 ##
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	147 ## @sc{Example 4:} @code{bicgstab} with a function as preconditioner
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	148 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	149 ## @example
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	150 ## x = bicgstab (Afcn, b, 1e-6, n, Mfcn)
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	151 ## @end example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	152 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	153 ## @sc{Example 5:} @code{bicgstab} with preconditioner matrices @var{M1}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	154 ## and @var{M2}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	155 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	156 ## @example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	157 ## x = bicgstab (A, b, [], 1e-6, n, M1, M2)
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	158 ## @end example
13929 9cae456085c2 Grammarcheck of documentation before 3.6.0 release. Rik <octave@nomad.inbox5.com> parents: 13837 diff changeset	159 ##
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	160 ## @sc{Example 6:} @code{bicgstab} with functions as preconditioners
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	161 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	162 ## @example
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	163 ## x = bicgstab (Afcn, b, 1e-6, n, M1fcn, M2fcn)
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	164 ## @end example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	165 ##
24992 3d5a39077708 avoid some warnings from old versions of makeinfo (bug #53479) Guillaume Flandin parents: 24985 diff changeset	166 ## @sc{Example 7:} @code{bicgstab} with as input a function requiring
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	167 ## an argument
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	168 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	169 ## @example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	170 ## @group
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	171 ## function y = Ap (A, x, z) # compute A^z * x
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	172 ## y = x;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	173 ## for i = 1:z
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	174 ## y = A * y;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	175 ## endfor
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	176 ## endfunction
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	177 ## Apfcn = @@(x, string, p) Ap (A, x, string, p);
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	178 ## x = bicgstab (Apfcn, b, [], [], [], [], [], 2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	179 ## @end group
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	180 ## @end example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	181 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	182 ## @sc{Example 8:} explicit example to show that @code{bicgstab} uses a
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	183 ## right preconditioner
13061 addfc0ae69c0 Make bicgstab interface more compatible Carlo de Falco <kingcrimson@tiscali.it> parents: 11587 diff changeset	184 ##
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	185 ## @example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	186 ## @group
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	187 ## [M1, M2] = ilu (A + 0.1 * eye (n)); # factorization of A perturbed
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	188 ## M = M1 * M2;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	189 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	190 ## ## reference solution computed by bicgstab after one iteration
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	191 ## [x_ref, fl] = bicgstab (A, b, [], 1, M)
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	192 ##
25003 2365c2661b3c doc: Spellcheck documentation ahead of 4.4 release. Rik <rik@octave.org> parents: 24992 diff changeset	193 ## ## right preconditioning
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	194 ## [y, fl] = bicgstab (A / M, b, [], 1)
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	195 ## x = M \ y # compare x and x_ref
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	196 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	197 ## @end group
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	198 ## @end example
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	199 ##
27984 b09432b20a84 maint: Remove special cases of old version control keywords in code base. Rik <rik@octave.org> parents: 27923 diff changeset	200 ## Reference:
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	201 ##
27984 b09432b20a84 maint: Remove special cases of old version control keywords in code base. Rik <rik@octave.org> parents: 27923 diff changeset	202 ## @nospell{Y. Saad}, @cite{Iterative Methods for Sparse Linear
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	203 ## Systems}, Second edition, 2003, SIAM
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	204 ##
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	205 ## @seealso{bicg, cgs, gmres, pcg, qmr, tfqmr}
8416 0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	206 ##
0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	207 ## @end deftypefn
0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	208
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	209 function [x_min, flag, relres, iter_min, resvec] = ...
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	210 bicgstab (A, b, tol = [], maxit = [], M1 = [], M2 = [], ...
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	211 x0 = [], varargin)
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 21634 diff changeset	212
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	213 ## Check consistency and type of A, M1, M2
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	214 [Afcn, M1fcn, M2fcn] = __alltohandles__ (A, b, M1, M2, "bicgstab");
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	215
28942 fc4bb4bd1d5e maint: Use '##' as lead-in for full-line comments. Rik <rik@octave.org> parents: 28917 diff changeset	216 ## Check if input tol are empty (set them to default if necessary)
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	217 [tol, maxit, x0] = __default__input__ ({1e-06, min(rows(b), 20), ...
28912 0de38a6ef693 maint: Use Octave convention of space after function name in scripts dir. Rik <rik@octave.org> parents: 27984 diff changeset	218 zeros(rows (b), 1)}, tol, maxit, x0);
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	219
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	220 norm_b = norm (b, 2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	221 if (norm_b == 0)
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	222 if (nargout < 2)
28912 0de38a6ef693 maint: Use Octave convention of space after function name in scripts dir. Rik <rik@octave.org> parents: 27984 diff changeset	223 printf ("The right hand side vector is all zero so bicgstab \n")
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	224 printf ("returned an all zero solution without iterating.\n")
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	225 endif
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	226 x_min = zeros (numel (b), 1);
29373 23a5daf1e809 bicgstab.m, cgs.m: Fix typo in "iter_min" variable name (bug #60071). Rik <rik@octave.org> parents: 29358 diff changeset	227 iter_min = 0;
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	228 flag = 0;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	229 resvec = 0;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	230 relres = 0;
28917 72d57dbcc305 maint: Add semicolon after break and return keywords. Rik <rik@octave.org> parents: 28912 diff changeset	231 return;
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 21634 diff changeset	232 endif
ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 21634 diff changeset	233
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	234 ## Double maxit to mind also the "half iterations"
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	235 d_maxit = 2 * maxit;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	236 iter = iter_min = 0;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	237 resvec = zeros (d_maxit,1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	238 x = x_min = x_pr = x0;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	239 iter = iter_min = 0;
27355 f724ef9124fc doc: Improve spelling of bicgstab (bug #56812). Tomi Pannila <tpannila@gmail.com> parents: 26376 diff changeset	240 ## default setting of flag is 1 (i.e. max number of iterations reached)
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 21634 diff changeset	241 flag = 1;
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	242
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	243 res = b - feval (Afcn, x, varargin{:});
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	244 rr = p = res; # rr is r_star
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	245 rho_1 = rr' * res;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	246 resvec (1) = norm (res,2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	247 real_tol = norm_b * tol;
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 21634 diff changeset	248
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	249 ## To check if the preconditioners are singular or they have some NaN
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	250 try
28912 0de38a6ef693 maint: Use Octave convention of space after function name in scripts dir. Rik <rik@octave.org> parents: 27984 diff changeset	251 warning ("error", "Octave:singular-matrix", "local");
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	252 p_hat = feval (M1fcn, p, varargin{:});
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	253 p_hat = feval (M2fcn, p_hat, varargin{:});
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	254 catch
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	255 flag = 2;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	256 end_try_catch
8416 0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	257
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	258 while (flag !=2) && (iter < d_maxit) && (resvec (iter + 1) >= real_tol)
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	259 v = feval (Afcn, p_hat, varargin{:});
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	260 prod_tmp = (rr' * v);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	261 if (prod_tmp == 0)
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	262 flag = 4;
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 21634 diff changeset	263 break;
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	264 endif
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	265 alpha = rho_1 / (prod_tmp);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	266 x += alpha * p_hat;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	267 s = res - alpha * v;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	268 iter += 1;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	269 resvec (iter+1) = norm (s,2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	270 if (resvec (iter + 1) <= real_tol) # reached the tol
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	271 x_min = x;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	272 iter_min = iter;
28917 72d57dbcc305 maint: Add semicolon after break and return keywords. Rik <rik@octave.org> parents: 28912 diff changeset	273 break;
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	274 elseif (resvec (iter + 1) <= resvec (iter_min + 1)) # Found min residual
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	275 x_min = x;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	276 iter_min = iter;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	277 endif
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	278 s_hat = feval (M1fcn, s, varargin{:});
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	279 s_hat = feval (M2fcn, s_hat, varargin{:});
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	280 t = feval (Afcn, s_hat, varargin{:});
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	281 omega = (t' * s) / (t' * t);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	282 if (omega == 0) # x and residual don't change and the next it will be NaN
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	283 flag = 4;
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 21634 diff changeset	284 break;
ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 21634 diff changeset	285 endif
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	286 x += omega * s_hat;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	287 res = s - omega * t;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	288 iter += 1;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	289 resvec (iter + 1) = norm (res);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	290 if (resvec (iter + 1) <= resvec (iter_min + 1))
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	291 x_min = x;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	292 iter_min = iter;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	293 endif
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	294 if (norm (x - x_pr) <= norm (x) * eps)
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	295 flag = 3;
28917 72d57dbcc305 maint: Add semicolon after break and return keywords. Rik <rik@octave.org> parents: 28912 diff changeset	296 break;
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	297 endif
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	298 x_pr = x;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	299 rho_2 = rho_1;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	300 rho_1 = rr' * res;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	301 if (rho_1 == 0) # x and residual don't change and the next it will be NaN
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	302 flag = 4;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	303 break;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	304 endif
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	305 beta = (rho_1 / rho_2) * (alpha / omega);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	306 p = res + beta * (p - omega* v);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	307 p_hat = feval (M1fcn, p, varargin{:});
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	308 p_hat = feval (M2fcn, p_hat, varargin{:});
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	309 endwhile
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	310 resvec = resvec (1:iter+1,1);
8416 0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	311
28943 e3a337a57588 maint: Use only one '#' character for comments that trail code. Rik <rik@octave.org> parents: 28942 diff changeset	312 relres = resvec (iter_min + 1) / norm_b; # I set the relative residual
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	313 iter /= 2;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	314 iter_min /= 2;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	315
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	316 if (flag == 1) && (relres <= tol)
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	317 flag = 0;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	318 endif
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	319
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	320 ## output strings to print when the outputs requested are less than 2
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 21634 diff changeset	321 if (nargout < 2)
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	322 switch (flag)
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	323 case {0}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	324 printf ("bicgstab converged at iteration %i ", iter_min);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	325 printf ("to a solution with relative residual %e\n", relres);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	326 case {1}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	327 printf ("bicgstab stopped at iteration %i ", iter);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	328 printf ("without converging to the desired tolerance %e\n", tol);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	329 printf ("because the maximum number of iterations was reached.\n");
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	330 printf ("The iterate returned (number %i) ", iter_min);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	331 printf ("has relative residual %e\n", relres);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	332 case {2}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	333 printf ("bicgstab stopped at iteration %i ", iter);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	334 printf ("without converging to the desired tolerance %e\n", tol);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	335 printf ("because the preconditioner matrix is singular.\n");
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	336 printf ("The iterate returned (number %i) ", iter_min);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	337 printf ("has relative residual %e\n", relres);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	338 case {3}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	339 printf ("bicgstab stopped at iteration %i ", iter);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	340 printf ("without converging to the desired tolerance %e\n", tol);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	341 printf ("because the method stagnated.\n");
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	342 printf ("The iterate returned (number %i) ", iter_min);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	343 printf ("has relative residual %e\n", relres);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	344 case {4}
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	345 printf ("bicgstab stopped at iteration %i ", iter);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	346 printf ("without converging to the desired tolerance %e\n", tol);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	347 printf ("because the method can't continue.\n");
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	348 printf ("The iterate returned (number %i) ", iter_min);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	349 printf ("has relative residual %e\n", relres);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	350 endswitch
9278 2b35cb600d50 improve bicgstab and cgs Radek Salac <salac.r@gmail.com> parents: 8920 diff changeset	351 endif
2b35cb600d50 improve bicgstab and cgs Radek Salac <salac.r@gmail.com> parents: 8920 diff changeset	352
8416 0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	353 endfunction
0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	354
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	355
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	356 %!demo # simplest use
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	357 %! n = 20;
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	358 %! A = toeplitz (sparse ([1, 1], [1, 2], [2, 1] * n ^ 2, 1, n)) + ...
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	359 %! toeplitz (sparse (1, 2, -1, 1, n) * n / 2, ...
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	360 %! sparse (1, 2, 1, 1, n) * n / 2);
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	361 %! b = A * ones (n, 1);
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	362 %! [M1, M2] = ilu (A + 0.1 * eye (n));
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	363 %! M = M1 * M2;
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	364 %! x = bicgstab (A, b, [], n);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	365 %! Afcn = @(x) A * x;
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	366 %! x = bicgstab (Afcn, b, [], n);
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	367 %! x = bicgstab (A, b, 1e-6, n, M);
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	368 %! x = bicgstab (A, b, 1e-6, n, M1, M2);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	369 %! Mfcn = @(z) M \ z;
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	370 %! x = bicgstab (Afcn, b, 1e-6, n, Mfcn);
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	371 %! M1fcn = @(z) M1 \ z;
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	372 %! M2fcn = @(z) M2 \ z;
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	373 %! x = bicgstab (Afcn, b, 1e-6, n, M1fcn, M2fcn);
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	374 %! function y = Ap (A, x, z)
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	375 %! ## compute A^z * x or (A^z)' * x
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	376 %! y = x;
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	377 %! for i = 1:z
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	378 %! y = A * y;
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	379 %! endfor
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	380 %! endfunction
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	381 %! Afcn = @(x, p) Ap (A, x, p);
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	382 %! x = bicgstab (Afcn, b, [], 2 * n, [], [], [], 2); # solution of A^2 * x = b
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	383
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	384 %!demo
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	385 %! n = 10;
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	386 %! A = toeplitz (sparse ([1, 1], [1, 2], [2, 1] * n ^ 2, 1, n)) + ...
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	387 %! toeplitz (sparse (1, 2, -1, 1, n) * n / 2, ...
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	388 %! sparse (1, 2, 1, 1, n) * n / 2);
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	389 %! b = A * ones (n, 1);
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	390 %! [M1, M2] = ilu (A + 0.3 * eye (n)); # factorization of A perturbed
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	391 %! M = M1 * M2;
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	392 %!
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	393 %! ## Reference solution computed by bicgstab after one iteration
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	394 %! [x_ref, fl] = bicgstab (A, b, [], 1, M);
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	395 %! x_ref
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	396 %!
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	397 %! ## right preconditioning
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	398 %! [y, fl] = bicgstab (A / M, b, [], 1);
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	399 %! ## Compare x and x_ref
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	400 %! x = M \ y
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	401
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	402 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	403 %! ## Check that all type of inputs work
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	404 %! A = toeplitz (sparse ([2, 1, 0, 0, 0]), sparse ([2, -1, 0, 0, 0]));
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	405 %! b = sum (A, 2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	406 %! M1 = diag (sqrt (diag (A)));
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	407 %! M2 = M1;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	408 %! maxit = 20;
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	409 %! Afcn = @(z) A*z;
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	410 %! M1_fcn = @(z) M1 \ z;
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	411 %! M2_fcn = @(z) M2 \ z;
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	412 %! [x, flag] = bicgstab (A,b );
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	413 %! assert (flag, 0);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	414 %! [x, flag] = bicgstab (A, b, [], maxit, M1, M2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	415 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	416 %! [x, flag] = bicgstab (A, b, [], maxit, M1_fcn, M2_fcn);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	417 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	418 %! [x, flag] = bicgstab (A, b, [], maxit, M1_fcn, M2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	419 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	420 %! [x, flag] = bicgstab (A, b, [], maxit, M1, M2_fcn);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	421 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	422 %! [x, flag] = bicgstab (Afcn, b);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	423 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	424 %! [x, flag] = bicgstab (Afcn, b, [], maxit, M1, M2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	425 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	426 %! [x, flag] = bicgstab (Afcn, b, [], maxit, M1_fcn, M2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	427 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	428 %! [x, flag] = bicgstab (Afcn, b, [], maxit, M1, M2_fcn);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	429 %! assert (flag, 0);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	430 %! [x, flag] = bicgstab (Afcn, b, [], maxit, M1_fcn, M2_fcn);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	431 %! assert (flag, 0);
8416 0a56e5c21c29 Add the bicgstab function Radek Salac <salac.r@gmail.com> parents: diff changeset	432
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	433 %!shared n, A, b, tol, maxit, M1, M2
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	434 %! n = 100;
13061 addfc0ae69c0 Make bicgstab interface more compatible Carlo de Falco <kingcrimson@tiscali.it> parents: 11587 diff changeset	435 %! A = spdiags ([-2ones(n,1) 4ones(n,1) -ones(n,1)], -1:1, n, n);
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	436 %! b = sum (A, 2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	437 %! tol = 1e-8;
13061 addfc0ae69c0 Make bicgstab interface more compatible Carlo de Falco <kingcrimson@tiscali.it> parents: 11587 diff changeset	438 %! maxit = 15;
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	439 %! M1 = spdiags ([ones(n,1)/(-2) ones(n,1)],-1:0, n, n);
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	440 %! M2 = spdiags ([4*ones(n,1) -ones(n,1)], 0:1, n, n);
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	441
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	442 %!test
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	443 %! [x, flag, relres, iter, resvec] = bicgstab (A, b, tol, maxit, M1, M2);
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	444 %! assert (norm (b - A*x) / norm (b), 0, tol);
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	445
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	446 %!function y = afcn (x, a)
13837 2c80bbd87f5d don't define functions in test and demo blocks John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	447 %! y = a * x;
2c80bbd87f5d don't define functions in test and demo blocks John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	448 %!endfunction
2c80bbd87f5d don't define functions in test and demo blocks John W. Eaton <jwe@octave.org> parents: 13141 diff changeset	449 %!
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	450 %!test
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	451 %! [x, flag, relres, iter, resvec] = bicgstab (@(x) afcn (x, A), b,
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	452 %! tol, maxit, M1, M2);
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	453 %! assert (norm (b - A*x) / norm (b), 0, tol);
13061 addfc0ae69c0 Make bicgstab interface more compatible Carlo de Falco <kingcrimson@tiscali.it> parents: 11587 diff changeset	454
addfc0ae69c0 Make bicgstab interface more compatible Carlo de Falco <kingcrimson@tiscali.it> parents: 11587 diff changeset	455 %!test
addfc0ae69c0 Make bicgstab interface more compatible Carlo de Falco <kingcrimson@tiscali.it> parents: 11587 diff changeset	456 %! a = sprand (n, n, .1);
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	457 %! A = a'a + 100 speye (n);
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13091 diff changeset	458 %! b = sum (A, 2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	459 %! [x, flag, relres, iter, resvec] = bicgstab (A, b, tol, [], diag (diag (A)));
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	460 %! assert (norm (b - A*x) / norm (b), 0, tol);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14237 diff changeset	461
17422 7ad3b9ca66f5 fix behaviour of bicgstab for complex matrices (bug #40017) Marco Caliari <marco.caliari@univr.it> parents: 16816 diff changeset	462 %!test
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	463 %! ## bicgstab solves complex linear systems
17422 7ad3b9ca66f5 fix behaviour of bicgstab for complex matrices (bug #40017) Marco Caliari <marco.caliari@univr.it> parents: 16816 diff changeset	464 %! A = [1 + 1i, 1 + 1i; 2 - 1i, 2 + 1i];
7ad3b9ca66f5 fix behaviour of bicgstab for complex matrices (bug #40017) Marco Caliari <marco.caliari@univr.it> parents: 16816 diff changeset	465 %! b = A * [1; 1];
7ad3b9ca66f5 fix behaviour of bicgstab for complex matrices (bug #40017) Marco Caliari <marco.caliari@univr.it> parents: 16816 diff changeset	466 %! [x, flag, relres, iter, resvec] = bicgstab (A, b);
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	467 %! assert (norm (b - A*x) / norm (b), 0, 1e-6);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	468
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	469 %!test
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	470 %! ## test with a non-symmetric matrix
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	471 %! A = diag (1:50);
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	472 %! A(1,50) = 10000;
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	473 %! b = ones (50,1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	474 %! [x, flag, relres, iter, resvec] = bicgstab (A, b, [], 100);
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	475 %! assert (flag, 0);
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	476 %! assert (norm (b - A*x) / norm (b), 0, 1e-6);
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	477
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	478 %!test
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	479 %! ## test that bicgstab detects a singular preconditioner
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	480 %! M = ones (50);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	481 %! M(1,1) = 0;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	482 %! [x, flag] = bicgstab (A, b, [], 100, M);
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	483 %! assert (flag, 2);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	484
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	485 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	486 %! A = single (1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	487 %! b = 1;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	488 %! [x, flag] = bicgstab (A, b);
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	489 %! assert (class (x), "single");
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	490
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	491 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	492 %! A = 1;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	493 %! b = single (1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	494 %! [x, flag] = bicgstab (A, b);
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	495 %! assert (class (x), "single");
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	496
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	497 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	498 %! A = single (1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	499 %! b = single (1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	500 %! [x, flag] = bicgstab (A, b);
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	501 %! assert (class (x), "single");
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	502
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	503 %!test
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	504 %!function y = Afcn (x)
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	505 %! A = sparse (toeplitz ([2, 1, 0, 0], [2, -1, 0, 0]));
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	506 %! y = A * x;
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	507 %!endfunction
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	508 %!
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	509 %! b = [1; 2; 2; 3];
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	510 %! [x, flag] = bicgstab ("Afcn", b);
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	511 %! assert (norm (b - A*x) / norm (b), 0, 1e-6);
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	512
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	513 %!test
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	514 %! ## unpreconditioned residual
ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	515 %! A = sparse (toeplitz ([2, 1, 0, 0, 0], [2, -1, 0, 0, 0]));
24860 6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	516 %! b = sum (A, 2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	517 %! M = magic (5);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com) Cristiano Dorigo <cristiano.dorigo@hotmail.it> parents: 24534 diff changeset	518 %! [x, flag, relres] = bicgstab (A, b, [], 2, M);
25153 ccc468973fc8 bicgstab.m: Overhaul BIST tests. Rik <rik@octave.org> parents: 25054 diff changeset	519 %! assert (norm (b - A * x) / norm (b), relres, 8*eps);