Mercurial > hg > octave-lyh
annotate scripts/optimization/fzero.m @ 17346:1c89599167a6
maint: End m-files with 1 blank line.
Simplifies automated grammarchecking script.
* scripts/@ftp/ascii.m, scripts/@ftp/binary.m, scripts/@ftp/cd.m,
scripts/@ftp/close.m, scripts/@ftp/delete.m, scripts/@ftp/dir.m,
scripts/@ftp/display.m, scripts/@ftp/ftp.m, scripts/@ftp/loadobj.m,
scripts/@ftp/mget.m, scripts/@ftp/mkdir.m, scripts/@ftp/mput.m,
scripts/@ftp/rename.m, scripts/@ftp/rmdir.m, scripts/@ftp/saveobj.m,
scripts/audio/lin2mu.m, scripts/audio/loadaudio.m, scripts/audio/mu2lin.m,
scripts/audio/record.m, scripts/audio/saveaudio.m, scripts/audio/setaudio.m,
scripts/deprecated/__error_text__.m, scripts/deprecated/cut.m,
scripts/deprecated/error_text.m, scripts/deprecated/isstr.m,
scripts/deprecated/polyderiv.m, scripts/deprecated/studentize.m,
scripts/deprecated/sylvester_matrix.m, scripts/general/bicubic.m,
scripts/general/celldisp.m, scripts/general/colon.m,
scripts/general/cplxpair.m, scripts/general/del2.m, scripts/general/display.m,
scripts/general/isdir.m, scripts/general/isequaln.m, scripts/general/loadobj.m,
scripts/general/private/__isequal__.m, scripts/general/private/__splinen__.m,
scripts/general/profexplore.m, scripts/general/quadgk.m,
scripts/general/randi.m, scripts/general/repmat.m, scripts/general/saveobj.m,
scripts/geometry/delaunay.m, scripts/help/__unimplemented__.m,
scripts/help/doc_cache_create.m, scripts/help/get_first_help_sentence.m,
scripts/help/help.m, scripts/help/print_usage.m,
scripts/help/private/__additional_help_message__.m,
scripts/help/private/__strip_html_tags__.m, scripts/help/type.m,
scripts/image/imfinfo.m, scripts/image/imformats.m, scripts/image/imread.m,
scripts/image/imwrite.m, scripts/image/private/__imfinfo__.m,
scripts/image/private/__imread__.m, scripts/image/private/__imwrite__.m,
scripts/image/private/imageIO.m, scripts/image/private/imwrite_filename.m,
scripts/image/private/ind2x.m, scripts/io/beep.m, scripts/io/strread.m,
scripts/io/textread.m, scripts/io/textscan.m, scripts/linear-algebra/krylov.m,
scripts/linear-algebra/subspace.m, scripts/miscellaneous/bug_report.m,
scripts/miscellaneous/bunzip2.m, scripts/miscellaneous/cast.m,
scripts/miscellaneous/copyfile.m, scripts/miscellaneous/debug.m,
scripts/miscellaneous/dir.m, scripts/miscellaneous/dump_prefs.m,
scripts/miscellaneous/error_ids.m, scripts/miscellaneous/fileattrib.m,
scripts/miscellaneous/gunzip.m, scripts/miscellaneous/isdeployed.m,
scripts/miscellaneous/ismac.m, scripts/miscellaneous/mex.m,
scripts/miscellaneous/mexext.m, scripts/miscellaneous/mkoctfile.m,
scripts/miscellaneous/movefile.m, scripts/miscellaneous/namelengthmax.m,
scripts/miscellaneous/news.m, scripts/miscellaneous/pack.m,
scripts/miscellaneous/perl.m,
scripts/miscellaneous/private/display_info_file.m,
scripts/miscellaneous/python.m, scripts/miscellaneous/rmappdata.m,
scripts/miscellaneous/run.m, scripts/miscellaneous/tar.m,
scripts/miscellaneous/tempname.m, scripts/miscellaneous/untar.m,
scripts/miscellaneous/unzip.m, scripts/miscellaneous/what.m,
scripts/miscellaneous/zip.m, scripts/optimization/fminunc.m,
scripts/optimization/fsolve.m, scripts/optimization/fzero.m,
scripts/optimization/glpk.m, scripts/optimization/optimget.m,
scripts/optimization/optimset.m, scripts/optimization/qp.m,
scripts/optimization/sqp.m, scripts/path/pathdef.m, scripts/pkg/pkg.m,
scripts/pkg/private/build.m, scripts/pkg/private/describe.m,
scripts/pkg/private/dirempty.m, scripts/pkg/private/get_forge_download.m,
scripts/pkg/private/get_forge_pkg.m,
scripts/pkg/private/get_unsatisfied_deps.m, scripts/pkg/private/install.m,
scripts/pkg/private/is_architecture_dependent.m,
scripts/pkg/private/list_forge_packages.m, scripts/pkg/private/rebuild.m,
scripts/pkg/private/shell.m, scripts/pkg/private/uninstall.m,
scripts/plot/axes.m, scripts/plot/box.m, scripts/plot/closereq.m,
scripts/plot/diffuse.m, scripts/plot/ezpolar.m, scripts/plot/findfigs.m,
scripts/plot/gco.m, scripts/plot/guidata.m, scripts/plot/guihandles.m,
scripts/plot/hdl2struct.m, scripts/plot/linkprop.m, scripts/plot/peaks.m,
scripts/plot/print.m, scripts/plot/private/__add_datasource__.m,
scripts/plot/private/__axis_label__.m, scripts/plot/private/__clabel__.m,
scripts/plot/private/__color_str_rgb__.m, scripts/plot/private/__contour__.m,
scripts/plot/private/__default_plot_options__.m,
scripts/plot/private/__errcomm__.m, scripts/plot/private/__file_filter__.m,
scripts/plot/private/__fltk_file_filter__.m,
scripts/plot/private/__getlegenddata__.m,
scripts/plot/private/__gnuplot_open_stream__.m,
scripts/plot/private/__gnuplot_print__.m,
scripts/plot/private/__go_draw_axes__.m,
scripts/plot/private/__interp_cube__.m, scripts/plot/private/__is_function__.m,
scripts/plot/private/__line__.m, scripts/plot/private/__marching_cube__.m,
scripts/plot/private/__next_line_style__.m, scripts/plot/private/__patch__.m,
scripts/plot/private/__pie__.m, scripts/plot/private/__pltopt__.m,
scripts/plot/private/__quiver__.m, scripts/plot/private/__scatter__.m,
scripts/plot/private/__stem__.m, scripts/plot/private/__uigetdir_fltk__.m,
scripts/plot/private/__uigetfile_fltk__.m,
scripts/plot/private/__uiobject_split_args__.m,
scripts/plot/private/__uiputfile_fltk__.m, scripts/plot/refresh.m,
scripts/plot/saveas.m, scripts/plot/shg.m, scripts/plot/specular.m,
scripts/plot/sphere.m, scripts/plot/struct2hdl.m, scripts/plot/subplot.m,
scripts/plot/uicontextmenu.m, scripts/plot/uicontrol.m, scripts/plot/uipanel.m,
scripts/plot/uipushtool.m, scripts/plot/uiresume.m,
scripts/plot/uitoggletool.m, scripts/plot/uitoolbar.m, scripts/plot/uiwait.m,
scripts/plot/waitforbuttonpress.m, scripts/polynomial/pchip.m,
scripts/polynomial/polyeig.m, scripts/polynomial/ppval.m,
scripts/prefs/addpref.m, scripts/prefs/getpref.m, scripts/prefs/ispref.m,
scripts/prefs/private/loadprefs.m, scripts/prefs/private/prefsfile.m,
scripts/prefs/private/saveprefs.m, scripts/prefs/setpref.m,
scripts/set/private/validargs.m, scripts/set/unique.m,
scripts/signal/arch_fit.m, scripts/signal/arch_rnd.m,
scripts/signal/arch_test.m, scripts/signal/arma_rnd.m,
scripts/signal/durbinlevinson.m, scripts/signal/fractdiff.m,
scripts/signal/freqz.m, scripts/signal/freqz_plot.m, scripts/signal/hurst.m,
scripts/signal/periodogram.m, scripts/signal/private/rectangle_lw.m,
scripts/signal/private/rectangle_sw.m, scripts/signal/private/triangle_sw.m,
scripts/signal/spectral_adf.m, scripts/signal/spectral_xdf.m,
scripts/signal/stft.m, scripts/signal/synthesis.m, scripts/signal/yulewalker.m,
scripts/sparse/colperm.m, scripts/sparse/eigs.m, scripts/sparse/etreeplot.m,
scripts/sparse/gmres.m, scripts/sparse/private/__sprand_impl__.m,
scripts/sparse/spdiags.m, scripts/sparse/sprandn.m, scripts/specfun/bessel.m,
scripts/specfun/betaln.m, scripts/specfun/expint.m,
scripts/special-matrix/gallery.m, scripts/startup/__finish__.m,
scripts/statistics/base/qqplot.m, scripts/statistics/distributions/tcdf.m,
scripts/statistics/distributions/wienrnd.m,
scripts/statistics/models/logistic_regression.m,
scripts/statistics/models/private/logistic_regression_derivatives.m,
scripts/statistics/models/private/logistic_regression_likelihood.m,
scripts/statistics/tests/anova.m, scripts/statistics/tests/bartlett_test.m,
scripts/statistics/tests/chisquare_test_homogeneity.m,
scripts/statistics/tests/chisquare_test_independence.m,
scripts/statistics/tests/cor_test.m,
scripts/statistics/tests/f_test_regression.m,
scripts/statistics/tests/hotelling_test.m,
scripts/statistics/tests/hotelling_test_2.m,
scripts/statistics/tests/kolmogorov_smirnov_test_2.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/manova.m, scripts/statistics/tests/mcnemar_test.m,
scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/run_test.m,
scripts/statistics/tests/sign_test.m, scripts/statistics/tests/t_test.m,
scripts/statistics/tests/t_test_2.m,
scripts/statistics/tests/t_test_regression.m,
scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m,
scripts/statistics/tests/welch_test.m,
scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m,
scripts/statistics/tests/z_test_2.m, scripts/strings/strcat.m,
scripts/strings/strjoin.m, scripts/strings/strsplit.m,
scripts/testfun/__have_feature__.m, scripts/testfun/__printf_assert__.m,
scripts/testfun/__prog_output_assert__.m, scripts/testfun/__run_test_suite__.m,
scripts/time/clock.m, scripts/time/datenum.m, scripts/ui/errordlg.m,
scripts/ui/private/message_dialog.m: End m-files with 1 blank line.
| author | Rik <rik@octave.org> |
|---|---|
| date | Wed, 28 Aug 2013 08:33:02 -0700 |
| parents | bc924baa2c4e |
| children |
| rev | line source |
|---|---|
|
14138
72c96de7a403
maint: update copyright notices for 2012
John W. Eaton <jwe@octave.org>
parents:
13027
diff
changeset
|
1 ## Copyright (C) 2008-2012 VZLU Prague, a.s. |
| 8305 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7 ## the Free Software Foundation; either version 3 of the License, or (at | |
| 8 ## your option) any later version. | |
| 9 ## | |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 16 ## along with Octave; see the file COPYING. If not, see | |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 18 ## | |
| 19 ## Author: Jaroslav Hajek <highegg@gmail.com> | |
| 20 | |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
21 ## -*- texinfo -*- |
|
10687
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
22 ## @deftypefn {Function File} {} fzero (@var{fun}, @var{x0}) |
|
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
23 ## @deftypefnx {Function File} {} fzero (@var{fun}, @var{x0}, @var{options}) |
|
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
24 ## @deftypefnx {Function File} {[@var{x}, @var{fval}, @var{info}, @var{output}] =} fzero (@dots{}) |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
25 ## Find a zero of a univariate function. |
|
10687
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
26 ## |
|
12632
2dbac27e0e40
doc: miscellaneous touch-ups to documentation strings
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
27 ## @var{fun} is a function handle, inline function, or string |
|
2dbac27e0e40
doc: miscellaneous touch-ups to documentation strings
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
28 ## containing the name of the function to evaluate. |
|
2dbac27e0e40
doc: miscellaneous touch-ups to documentation strings
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
29 ## @var{x0} should be a two-element vector specifying two points which |
|
2dbac27e0e40
doc: miscellaneous touch-ups to documentation strings
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
30 ## bracket a zero. In other words, there must be a change in sign of the |
|
2dbac27e0e40
doc: miscellaneous touch-ups to documentation strings
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
31 ## function between @var{x0}(1) and @var{x0}(2). More mathematically, the |
|
2dbac27e0e40
doc: miscellaneous touch-ups to documentation strings
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
32 ## following must hold |
|
10821
693e22af08ae
Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents:
10687
diff
changeset
|
33 ## |
| 10470 | 34 ## @example |
| 35 ## sign (@var{fun}(@var{x0}(1))) * sign (@var{fun}(@var{x0}(2))) <= 0 | |
| 36 ## @end example | |
|
10821
693e22af08ae
Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents:
10687
diff
changeset
|
37 ## |
|
10687
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
38 ## If @var{x0} is a single scalar then several nearby and distant |
|
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
39 ## values are probed in an attempt to obtain a valid bracketing. If this |
| 10470 | 40 ## is not successful, the function fails. |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
41 ## @var{options} is a structure specifying additional options. |
| 10470 | 42 ## Currently, @code{fzero} |
|
17289
bc924baa2c4e
doc: Add new @qcode macro for code samples which are quoted.
Rik <rik@octave.org>
parents:
17182
diff
changeset
|
43 ## recognizes these options: @qcode{"FunValCheck"}, @qcode{"OutputFcn"}, |
|
bc924baa2c4e
doc: Add new @qcode macro for code samples which are quoted.
Rik <rik@octave.org>
parents:
17182
diff
changeset
|
44 ## @qcode{"TolX"}, @qcode{"MaxIter"}, @qcode{"MaxFunEvals"}. |
|
17101
e7a059a9a644
doc: Use XREF as anchor prefix in documentation for clearer results in Info viewer.
Rik <rik@octave.org>
parents:
16772
diff
changeset
|
45 ## For a description of these options, see @ref{XREFoptimset,,optimset}. |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
46 ## |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
47 ## On exit, the function returns @var{x}, the approximate zero point |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
48 ## and @var{fval}, the function value thereof. |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
49 ## @var{info} is an exit flag that can have these values: |
|
10297
ed88ea036716
improve docs of fzero/fminbnd
Jaroslav Hajek <highegg@gmail.com>
parents:
10296
diff
changeset
|
50 ## |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
51 ## @itemize |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
52 ## @item 1 |
|
10687
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
53 ## The algorithm converged to a solution. |
|
10821
693e22af08ae
Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents:
10687
diff
changeset
|
54 ## |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
55 ## @item 0 |
|
10687
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
56 ## Maximum number of iterations or function evaluations has been reached. |
|
10821
693e22af08ae
Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents:
10687
diff
changeset
|
57 ## |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
58 ## @item -1 |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
59 ## The algorithm has been terminated from user output function. |
|
10821
693e22af08ae
Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents:
10687
diff
changeset
|
60 ## |
|
10337
7c97da90fc8f
check for discontinuities in fzero
Rik <rdrider0-list@yahoo.com>
parents:
10297
diff
changeset
|
61 ## @item -5 |
|
7c97da90fc8f
check for discontinuities in fzero
Rik <rdrider0-list@yahoo.com>
parents:
10297
diff
changeset
|
62 ## The algorithm may have converged to a singular point. |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
63 ## @end itemize |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
64 ## |
|
10687
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
65 ## @var{output} is a structure containing runtime information about the |
|
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
66 ## @code{fzero} algorithm. Fields in the structure are: |
|
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
67 ## |
|
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
68 ## @itemize |
|
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
69 ## @item iterations |
|
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
70 ## Number of iterations through loop. |
|
10821
693e22af08ae
Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents:
10687
diff
changeset
|
71 ## |
|
10687
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
72 ## @item nfev |
|
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
73 ## Number of function evaluations. |
|
10821
693e22af08ae
Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents:
10687
diff
changeset
|
74 ## |
|
10687
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
75 ## @item bracketx |
|
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
76 ## A two-element vector with the final bracketing of the zero along the x-axis. |
|
10821
693e22af08ae
Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents:
10687
diff
changeset
|
77 ## |
|
10687
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
78 ## @item brackety |
|
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
79 ## A two-element vector with the final bracketing of the zero along the y-axis. |
|
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
80 ## @end itemize |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
81 ## @seealso{optimset, fsolve} |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
82 ## @end deftypefn |
| 8305 | 83 |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
84 ## This is essentially the ACM algorithm 748: Enclosing Zeros of |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
85 ## Continuous Functions due to Alefeld, Potra and Shi, ACM Transactions |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
86 ## on Mathematical Software, Vol. 21, No. 3, September 1995. Although |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
87 ## the workflow should be the same, the structure of the algorithm has |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
88 ## been transformed non-trivially; instead of the authors' approach of |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
89 ## sequentially calling building blocks subprograms we implement here a |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
90 ## FSM version using one interior point determination and one bracketing |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
91 ## per iteration, thus reducing the number of temporary variables and |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
92 ## simplifying the algorithm structure. Further, this approach reduces |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
93 ## the need for external functions and error handling. The algorithm has |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
94 ## also been slightly modified. |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
95 |
|
13027
b9a89ca0fb75
prevent optimization functions from setting ans in workspace at startup
John W. Eaton <jwe@octave.org>
parents:
12632
diff
changeset
|
96 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. |
|
b9a89ca0fb75
prevent optimization functions from setting ans in workspace at startup
John W. Eaton <jwe@octave.org>
parents:
12632
diff
changeset
|
97 ## PKG_ADD: [~] = __all_opts__ ("fzero"); |
|
8648
ff61b53eb294
optimization: use PKG_ADD: comments instead of PKG_ADD file
John W. Eaton <jwe@octave.org>
parents:
8596
diff
changeset
|
98 |
| 8305 | 99 function [x, fval, info, output] = fzero (fun, x0, options = struct ()) |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
100 |
|
8596
8833c0b18eb2
enable default settings queries in optim funcs
Jaroslav Hajek <highegg@gmail.com>
parents:
8515
diff
changeset
|
101 ## Get default options if requested. |
|
8833c0b18eb2
enable default settings queries in optim funcs
Jaroslav Hajek <highegg@gmail.com>
parents:
8515
diff
changeset
|
102 if (nargin == 1 && ischar (fun) && strcmp (fun, 'defaults')) |
|
14552
86854d032a37
maint: miscellaneous style fixes for .m files
John W. Eaton <jwe@octave.org>
parents:
14363
diff
changeset
|
103 x = optimset ("MaxIter", Inf, "MaxFunEvals", Inf, "TolX", 1e-8, |
|
86854d032a37
maint: miscellaneous style fixes for .m files
John W. Eaton <jwe@octave.org>
parents:
14363
diff
changeset
|
104 "OutputFcn", [], "FunValCheck", "off"); |
|
8596
8833c0b18eb2
enable default settings queries in optim funcs
Jaroslav Hajek <highegg@gmail.com>
parents:
8515
diff
changeset
|
105 return; |
|
8833c0b18eb2
enable default settings queries in optim funcs
Jaroslav Hajek <highegg@gmail.com>
parents:
8515
diff
changeset
|
106 endif |
|
8833c0b18eb2
enable default settings queries in optim funcs
Jaroslav Hajek <highegg@gmail.com>
parents:
8515
diff
changeset
|
107 |
| 8305 | 108 if (nargin < 2 || nargin > 3) |
| 109 print_usage (); | |
| 110 endif | |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
111 |
| 8305 | 112 if (ischar (fun)) |
|
9464
e598248a060d
safer str2func use in optim functions
Jaroslav Hajek <highegg@gmail.com>
parents:
9143
diff
changeset
|
113 fun = str2func (fun, "global"); |
| 8305 | 114 endif |
| 115 | |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
116 ## TODO |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
117 ## displev = optimget (options, "Display", "notify"); |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
118 funvalchk = strcmpi (optimget (options, "FunValCheck", "off"), "on"); |
| 8305 | 119 outfcn = optimget (options, "OutputFcn"); |
| 10296 | 120 tolx = optimget (options, "TolX", 1e-8); |
| 8305 | 121 maxiter = optimget (options, "MaxIter", Inf); |
| 122 maxfev = optimget (options, "MaxFunEvals", Inf); | |
| 123 | |
| 124 persistent mu = 0.5; | |
| 125 | |
| 126 if (funvalchk) | |
| 8507 | 127 ## Replace fun with a guarded version. |
| 8305 | 128 fun = @(x) guarded_eval (fun, x); |
| 129 endif | |
| 130 | |
| 8507 | 131 ## The default exit flag if exceeded number of iterations. |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
132 info = 0; |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
133 niter = 0; |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
134 nfev = 0; |
| 8305 | 135 |
| 136 x = fval = a = fa = b = fb = NaN; | |
| 10296 | 137 eps = eps (class (x0)); |
| 8305 | 138 |
| 8507 | 139 ## Prepare... |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
140 a = x0(1); |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
141 fa = fun (a); |
| 8305 | 142 nfev = 1; |
| 143 if (length (x0) > 1) | |
| 144 b = x0(2); | |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
145 fb = fun (b); |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
146 nfev += 1; |
| 8305 | 147 else |
| 8507 | 148 ## Try to get b. |
| 8305 | 149 if (a == 0) |
| 150 aa = 1; | |
| 151 else | |
| 152 aa = a; | |
| 153 endif | |
| 154 for b = [0.9*aa, 1.1*aa, aa-1, aa+1, 0.5*aa 1.5*aa, -aa, 2*aa, -10*aa, 10*aa] | |
| 155 fb = fun (b); nfev += 1; | |
| 156 if (sign (fa) * sign (fb) <= 0) | |
| 157 break; | |
| 158 endif | |
| 159 endfor | |
| 160 endif | |
| 161 | |
| 162 if (b < a) | |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
163 u = a; |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
164 a = b; |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
165 b = u; |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
166 |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
167 fu = fa; |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
168 fa = fb; |
|
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
169 fb = fu; |
| 8305 | 170 endif |
| 171 | |
| 172 if (! (sign (fa) * sign (fb) <= 0)) | |
|
8468
866492035ecf
fsolve.m, fzero.m: undo part of previous change
John W. Eaton <jwe@octave.org>
parents:
8467
diff
changeset
|
173 error ("fzero:bracket", "fzero: not a valid initial bracketing"); |
| 8305 | 174 endif |
| 175 | |
|
10337
7c97da90fc8f
check for discontinuities in fzero
Rik <rdrider0-list@yahoo.com>
parents:
10297
diff
changeset
|
176 slope0 = (fb - fa) / (b - a); |
|
7c97da90fc8f
check for discontinuities in fzero
Rik <rdrider0-list@yahoo.com>
parents:
10297
diff
changeset
|
177 |
| 10470 | 178 if (fa == 0) |
| 179 b = a; | |
| 180 fb = fa; | |
| 181 elseif (fb == 0) | |
| 182 a = b; | |
| 183 fa = fb; | |
| 184 endif | |
| 185 | |
| 8305 | 186 itype = 1; |
| 187 | |
| 188 if (abs (fa) < abs (fb)) | |
| 189 u = a; fu = fa; | |
| 190 else | |
| 191 u = b; fu = fb; | |
| 192 endif | |
| 193 | |
| 194 d = e = u; | |
| 195 fd = fe = fu; | |
| 196 mba = mu*(b - a); | |
| 197 while (niter < maxiter && nfev < maxfev) | |
| 198 switch (itype) | |
|
17182
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
199 case 1 |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
200 ## The initial test. |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
201 if (b - a <= 2*(2 * abs (u) * eps + tolx)) |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
202 x = u; fval = fu; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
203 info = 1; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
204 break; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
205 endif |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
206 if (abs (fa) <= 1e3*abs (fb) && abs (fb) <= 1e3*abs (fa)) |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
207 ## Secant step. |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
208 c = u - (a - b) / (fa - fb) * fu; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
209 else |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
210 ## Bisection step. |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
211 c = 0.5*(a + b); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
212 endif |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
213 d = u; fd = fu; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
214 itype = 5; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
215 case {2, 3} |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
216 l = length (unique ([fa, fb, fd, fe])); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
217 if (l == 4) |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
218 ## Inverse cubic interpolation. |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
219 q11 = (d - e) * fd / (fe - fd); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
220 q21 = (b - d) * fb / (fd - fb); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
221 q31 = (a - b) * fa / (fb - fa); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
222 d21 = (b - d) * fd / (fd - fb); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
223 d31 = (a - b) * fb / (fb - fa); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
224 q22 = (d21 - q11) * fb / (fe - fb); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
225 q32 = (d31 - q21) * fa / (fd - fa); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
226 d32 = (d31 - q21) * fd / (fd - fa); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
227 q33 = (d32 - q22) * fa / (fe - fa); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
228 c = a + q31 + q32 + q33; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
229 endif |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
230 if (l < 4 || sign (c - a) * sign (c - b) > 0) |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
231 ## Quadratic interpolation + newton. |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
232 a0 = fa; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
233 a1 = (fb - fa)/(b - a); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
234 a2 = ((fd - fb)/(d - b) - a1) / (d - a); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
235 ## Modification 1: this is simpler and does not seem to be worse. |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
236 c = a - a0/a1; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
237 if (a2 != 0) |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
238 c = a - a0/a1; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
239 for i = 1:itype |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
240 pc = a0 + (a1 + a2*(c - b))*(c - a); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
241 pdc = a1 + a2*(2*c - a - b); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
242 if (pdc == 0) |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
243 c = a - a0/a1; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
244 break; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
245 endif |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
246 c -= pc/pdc; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
247 endfor |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
248 endif |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
249 endif |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
250 itype += 1; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
251 case 4 |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
252 ## Double secant step. |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
253 c = u - 2*(b - a)/(fb - fa)*fu; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
254 ## Bisect if too far. |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
255 if (abs (c - u) > 0.5*(b - a)) |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
256 c = 0.5 * (b + a); |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
257 endif |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
258 itype = 5; |
|
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
259 case 5 |
| 8507 | 260 ## Bisection step. |
| 8305 | 261 c = 0.5 * (b + a); |
|
17182
c3c1ebfaa7dc
maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents:
17101
diff
changeset
|
262 itype = 2; |
| 8305 | 263 endswitch |
| 264 | |
| 8507 | 265 ## Don't let c come too close to a or b. |
| 8305 | 266 delta = 2*0.7*(2 * abs (u) * eps + tolx); |
| 267 if ((b - a) <= 2*delta) | |
| 268 c = (a + b)/2; | |
| 269 else | |
| 270 c = max (a + delta, min (b - delta, c)); | |
| 271 endif | |
| 272 | |
| 8507 | 273 ## Calculate new point. |
| 8305 | 274 x = c; |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
275 fval = fc = fun (c); |
| 8305 | 276 niter ++; nfev ++; |
| 277 | |
| 8507 | 278 ## Modification 2: skip inverse cubic interpolation if |
| 279 ## nonmonotonicity is detected. | |
| 8305 | 280 if (sign (fc - fa) * sign (fc - fb) >= 0) |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
281 ## The new point broke monotonicity. |
| 8507 | 282 ## Disable inverse cubic. |
| 8305 | 283 fe = fc; |
| 284 else | |
| 285 e = d; fe = fd; | |
| 286 endif | |
| 287 | |
| 8507 | 288 ## Bracketing. |
| 8305 | 289 if (sign (fa) * sign (fc) < 0) |
| 290 d = b; fd = fb; | |
| 291 b = c; fb = fc; | |
| 292 elseif (sign (fb) * sign (fc) < 0) | |
| 293 d = a; fd = fa; | |
| 294 a = c; fa = fc; | |
| 295 elseif (fc == 0) | |
| 296 a = b = c; fa = fb = fc; | |
| 297 info = 1; | |
| 298 break; | |
| 299 else | |
| 8507 | 300 ## This should never happen. |
|
8468
866492035ecf
fsolve.m, fzero.m: undo part of previous change
John W. Eaton <jwe@octave.org>
parents:
8467
diff
changeset
|
301 error ("fzero:bracket", "fzero: zero point is not bracketed"); |
| 8305 | 302 endif |
| 303 | |
| 8507 | 304 ## If there's an output function, use it now. |
| 8305 | 305 if (outfcn) |
| 10296 | 306 optv.funccount = nfev; |
| 8305 | 307 optv.fval = fval; |
| 308 optv.iteration = niter; | |
| 309 if (outfcn (x, optv, "iter")) | |
| 310 info = -1; | |
| 311 break; | |
| 312 endif | |
| 313 endif | |
| 314 | |
| 315 if (abs (fa) < abs (fb)) | |
| 316 u = a; fu = fa; | |
| 317 else | |
| 318 u = b; fu = fb; | |
| 319 endif | |
| 320 if (b - a <= 2*(2 * abs (u) * eps + tolx)) | |
| 321 info = 1; | |
| 322 break; | |
| 323 endif | |
| 324 | |
| 8507 | 325 ## Skip bisection step if successful reduction. |
| 8305 | 326 if (itype == 5 && (b - a) <= mba) |
| 327 itype = 2; | |
| 328 endif | |
| 329 if (itype == 2) | |
| 330 mba = mu * (b - a); | |
| 331 endif | |
| 332 endwhile | |
| 333 | |
|
10337
7c97da90fc8f
check for discontinuities in fzero
Rik <rdrider0-list@yahoo.com>
parents:
10297
diff
changeset
|
334 ## Check solution for a singularity by examining slope |
|
7c97da90fc8f
check for discontinuities in fzero
Rik <rdrider0-list@yahoo.com>
parents:
10297
diff
changeset
|
335 if (info == 1) |
|
10394
bc475cd49147
avoid div by zero in fzero
Jaroslav Hajek <highegg@gmail.com>
parents:
10337
diff
changeset
|
336 if ((b - a) != 0 && abs ((fb - fa)/(b - a) / slope0) > max (1e6, 0.5/(eps+tolx))) |
|
10337
7c97da90fc8f
check for discontinuities in fzero
Rik <rdrider0-list@yahoo.com>
parents:
10297
diff
changeset
|
337 info = -5; |
|
7c97da90fc8f
check for discontinuities in fzero
Rik <rdrider0-list@yahoo.com>
parents:
10297
diff
changeset
|
338 endif |
|
7c97da90fc8f
check for discontinuities in fzero
Rik <rdrider0-list@yahoo.com>
parents:
10297
diff
changeset
|
339 endif |
|
7c97da90fc8f
check for discontinuities in fzero
Rik <rdrider0-list@yahoo.com>
parents:
10297
diff
changeset
|
340 |
| 8305 | 341 output.iterations = niter; |
| 10296 | 342 output.funcCount = nfev; |
|
10687
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
343 output.bracketx = [a, b]; |
|
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10470
diff
changeset
|
344 output.brackety = [fa, fb]; |
| 8305 | 345 |
| 346 endfunction | |
| 347 | |
| 8507 | 348 ## An assistant function that evaluates a function handle and checks for |
|
8467
77b8d4aa2743
fsolve.m, fzero.m: style fixes; use strcmpi to compare options
John W. Eaton <jwe@octave.org>
parents:
8305
diff
changeset
|
349 ## bad results. |
| 8305 | 350 function fx = guarded_eval (fun, x) |
| 351 fx = fun (x); | |
| 352 fx = fx(1); | |
| 353 if (! isreal (fx)) | |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
354 error ("fzero:notreal", "fzero: non-real value encountered"); |
| 8305 | 355 elseif (isnan (fx)) |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
356 error ("fzero:isnan", "fzero: NaN value encountered"); |
| 8305 | 357 endif |
| 358 endfunction | |
| 359 | |
|
17346
1c89599167a6
maint: End m-files with 1 blank line.
Rik <rik@octave.org>
parents:
17289
diff
changeset
|
360 |
| 10296 | 361 %!shared opt0 |
| 362 %! opt0 = optimset ("tolx", 0); | |
|
14363
f3d52523cde1
Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents:
14138
diff
changeset
|
363 %!assert (fzero (@cos, [0, 3], opt0), pi/2, 10*eps) |
|
f3d52523cde1
Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents:
14138
diff
changeset
|
364 %!assert (fzero (@(x) x^(1/3) - 1e-8, [0,1], opt0), 1e-24, 1e-22*eps) |
|
f3d52523cde1
Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents:
14138
diff
changeset
|
365 |