Mercurial > octave
changeset 23885:86a49caa5100
new function humps (bug #33935)
* scripts/optimization/humps.m: New file.
* scripts/optimization/module.mk: Update.
* nonlin.txi: Document.
* NEWS: Note addition.
| author | Nicholas R. Jankowski <jankowskin@asme.org> |
|---|---|
| date | Wed, 08 Feb 2017 09:01:27 -0500 |
| parents | bd9e719f04cc |
| children | 6d73cb87591a |
| files | NEWS doc/interpreter/nonlin.txi scripts/optimization/humps.m scripts/optimization/module.mk |
| diffstat | 4 files changed, 112 insertions(+), 1 deletions(-) [+] |
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--- a/NEWS Tue Aug 08 16:25:44 2017 -0700 +++ b/NEWS Wed Feb 08 09:01:27 2017 -0500 @@ -38,9 +38,10 @@ ** Other new functions added in 4.4: corrcoef + getframe gsvd hgtransform - getframe + humps ** Deprecated functions.
--- a/doc/interpreter/nonlin.txi Tue Aug 08 16:25:44 2017 -0700 +++ b/doc/interpreter/nonlin.txi Wed Feb 08 09:01:27 2017 -0500 @@ -192,3 +192,8 @@ @DOCSTRING(fminunc) @DOCSTRING(fminsearch) + +The function @code{humps} is a useful function for testing zero and +extrema finding functions. + +@DOCSTRING(humps)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/optimization/humps.m Wed Feb 08 09:01:27 2017 -0500 @@ -0,0 +1,104 @@ +## Copyright (C) 2017 Nicholas R. Jankowski +## +## This file is part of Octave. +## +## Octave is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or +## (at your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, +## see <http://www.gnu.org/licenses/>. + +## Author: Nicholas R. Jankowski <jankowskin@asme.org> + +## -*- texinfo -*- +## @deftypefn {} {} humps (@var{x}) +## @deftypefnx {} {[@var{x}, @var{y}] =} humps (@var{x}) +## Return the output of the rational function: +## +## @tex +## $$y = -{ {1200x^4 - 2880x^3 + 2036x^2 - 340x - 88} \over {200x^4 - 480x^3 + 406x^2 - 138x - 17} }$$ +## @end tex +## @ifnottex +## +## @example +## @group +## 1200*@var{x}^4 - 2880*@var{x}^3 + 2036*@var{x}^2 - 348*@var{x} - 88 +## @var{y} = - --------------------------------------------- +## 200*@var{x}^4 - 480*@var{x}^3 + 406*@var{x}^2 - 138*@var{x} + 17 +## @end group +## @end example +## +## @end ifnottex +## +## @var{x} may be a scalar, vector or array. @code{humps} is vectorized such +## that @var{yi} = humps (@var{xi}) +## +## If @var{x} is omitted, the range [0:0.05:1] is used instead. +## +## When called with two output arguments, [@var{x},@var{y}], @var{x} will +## contain the input value(s), and @var{y} will contain the output from +## @code{humps}. +## +## @code{humps} has two local maxima located near @var{x} = 0.300 and 0.893, +## a local minimum near @var{x} = 0.637, and zeros near @var{x} = -0.132 and +## 1.300. @code{humps} is a useful function for testing algorithms to find +## zeros or local minima and maxima. +## +## Try @code{demo humps} to see a plot of the @code{humps} function. +## @end deftypefn + +function varargout = humps (x = [0:0.05:1]) + + if (nargin > 1) + print_usage (); + endif + + y = - 4*( 300*x.^4 - 720*x.^3 + 509*x.^2 - 87*x - 22) ./ ... + ((10*x.^2 - 6*x + 1).*(20*x.^2 - 36*x + 17)); + + if (nargout > 1) + varargout = {x, y}; + else + varargout = {y}; + endif + +endfunction + +%!demo +%! clf; +%! fplot (@humps, [0, 2]); +%! title ("humps() function"); + +## tests +## value checks +%!assert (humps (0), 88/17, 10*eps) +%!assert (humps (1), 16, 10*eps) +%!assert (humps (-1), -6376/1241, 10*eps) +%!assert (humps (), [88/17, 16106/1769, 263/17, 82802/3133, 2432/53, ... +%! 2818/37, 193/2, 10538/137, 1376/29, 36434/1261, 19, 5258/377, ... +%! 152/13, 24562/2173, 421/34, 250/17, 232/13, 1762/85, 803/37, ... +%! 58354/2941, 16], 1000*eps) + +## vector checks +%!assert (humps ([0, 1]), [88/17, 16], 10*eps) +%!assert (humps ([0, 1]'), [88/17, 16]', 10*eps) +%!assert (humps ([0, 1; 1, 0]'), [88/17, 16; 16, 88/17]', 10*eps) + +## array checks +%!assert (humps (repmat (eye (2), 1, 1, 2)), +%! repmat ([16, 88/17; 88/17, 16], 1, 1, 2), 10*eps) + +## other checks +%!assert (humps (NaN), NaN) +%!assert (humps ([]), []) + +## errors +%!error humps (1,3)