annotate scripts/general/integral3.m @ 27918:b442ec6dda5c

use centralized file for copyright info for individual contributors * COPYRIGHT.md: New file. * In most other files, use "Copyright (C) YYYY-YYYY The Octave Project Developers" instead of tracking individual names in separate source files. The motivation is to reduce the effort required to update the notices each year. Until now, the Octave source files contained copyright notices that list individual contributors. I adopted these file-scope copyright notices because that is what everyone was doing 30 years ago in the days before distributed version control systems. But now, with many contributors and modern version control systems, having these file-scope copyright notices causes trouble when we update copyright years or refactor code. Over time, the file-scope copyright notices may become outdated as new contributions are made or code is moved from one file to another. Sometimes people contribute significant patches but do not add a line claiming copyright. Other times, people add a copyright notice for their contribution but then a later refactoring moves part or all of their contribution to another file and the notice is not moved with the code. As a practical matter, moving such notices is difficult -- determining what parts are due to a particular contributor requires a time-consuming search through the project history. Even managing the yearly update of copyright years is problematic. We have some contributors who are no longer living. Should we update the copyright dates for their contributions when we release new versions? Probably not, but we do still want to claim copyright for the project as a whole. To minimize the difficulty of maintaining the copyright notices, I would like to change Octave's sources to use what is described here: https://softwarefreedom.org/resources/2012/ManagingCopyrightInformation.html in the section "Maintaining centralized copyright notices": The centralized notice approach consolidates all copyright notices in a single location, usually a top-level file. This file should contain all of the copyright notices provided project contributors, unless the contribution was clearly insignificant. It may also credit -- without a copyright notice -- anyone who helped with the project but did not contribute code or other copyrighted material. This approach captures less information about contributions within individual files, recognizing that the DVCS is better equipped to record those details. As we mentioned before, it does have one disadvantage as compared to the file-scope approach: if a single file is separated from the distribution, the recipient won't see the contributors' copyright notices. But this can be easily remedied by including a single copyright notice in each file's header, pointing to the top-level file: Copyright YYYY-YYYY The Octave Project Developers See the COPYRIGHT file at the top-level directory of this distribution or at https://octave.org/COPYRIGHT.html. followed by the usual GPL copyright statement. For more background, see the discussion here: https://lists.gnu.org/archive/html/octave-maintainers/2020-01/msg00009.html Most files in the following directories have been skipped intentinally in this changeset: doc libgui/qterminal liboctave/external m4
author John W. Eaton <jwe@octave.org>
date Mon, 06 Jan 2020 15:38:17 -0500
parents 5a6a19a4e3da
children 1891570abac8
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1 ## Copyright (C) 2017-2019 The Octave Project Developers
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2 ##
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3 ## See the file COPYRIGHT.md in the top-level directory of this distribution
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4 ## or <https://octave.org/COPYRIGHT.html/>.
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5 ##
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6 ##
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7 ## This file is part of Octave.
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8 ##
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9 ## Octave is free software: you can redistribute it and/or modify it
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10 ## under the terms of the GNU General Public License as published by
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11 ## the Free Software Foundation, either version 3 of the License, or
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12 ## (at your option) any later version.
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13 ##
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14 ## Octave is distributed in the hope that it will be useful, but
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15 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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16 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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17 ## GNU General Public License for more details.
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18 ##
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19 ## You should have received a copy of the GNU General Public License
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20 ## along with Octave; see the file COPYING. If not, see
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21 ## <https://www.gnu.org/licenses/>.
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22
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23 ## -*- texinfo -*-
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24 ## @deftypefn {} {@var{q} =} integral3 (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb})
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25 ## @deftypefnx {} {@var{q} =} integral3 (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{prop}, @var{val}, @dots{})
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26 ##
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27 ## Numerically evaluate the three-dimensional integral of @var{f} using
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28 ## adaptive quadrature over the three-dimensional domain defined by
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29 ## @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb} (scalars may
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30 ## be finite or infinite). Additionally, @var{ya} and @var{yb} may be
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31 ## scalar functions of @var{x} and @var{za}, and @var{zb} maybe be scalar
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32 ## functions of @var{x} and @var{y}, allowing for integration over
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33 ## non-rectangular domains.
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34 ##
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35 ## @var{f} is a function handle, inline function, or string containing the name
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36 ## of the function to evaluate. The function @var{f} must be of the form
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37 ## @math{z = f(x,y)} where @var{x} is a vector and @var{y} is a scalar. It
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38 ## should return a vector of the same length and orientation as @var{x}.
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39 ##
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40 ## Additional optional parameters can be specified using
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41 ## @qcode{"@var{property}", @var{value}} pairs. Valid properties are:
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42 ##
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43 ## @table @code
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44 ## @item AbsTol
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45 ## Define the absolute error tolerance for the quadrature. The default
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46 ## value is 1e-10 (1e-5 for single).
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47 ##
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48 ## @item RelTol
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49 ## Define the relative error tolerance for the quadrature. The default
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50 ## value is 1e-6 (1e-4 for single).
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51 ##
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52 ## @item Method
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53 ## Specify the two-dimensional integration method to be used, with valid
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54 ## options being @qcode{"auto"} (default), @qcode{"tiled"}, or
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55 ## @qcode{"iterated"}. When using @qcode{"auto"}, Octave will choose the
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56 ## @qcode{"tiled"} method unless any of the integration limits are infinite.
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57 ##
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58 ## @item Vectorized
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59 ## Enable or disable vectorized integration. A value of @code{false} forces
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60 ## Octave to use only scalar inputs when calling the integrand, which enables
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61 ## integrands @math{f(x,y)} that have not been vectorized and only accept
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62 ## @var{x} and @var{y} as scalars to be used. The default value is
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63 ## @code{true}.
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64 ## @end table
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65 ##
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66 ## Adaptive quadrature is used to minimize the estimate of error until the
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67 ## following is satisfied:
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68 ## @tex
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69 ## $$error \leq \max \left( AbsTol, RelTol\cdot\vert q\vert \right)$$
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70 ## @end tex
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71 ## @ifnottex
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72 ##
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73 ## @example
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74 ## @group
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75 ## @var{error} <= max (@var{AbsTol}, @var{RelTol}*|@var{q}|)
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76 ## @end group
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77 ## @end example
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78 ##
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79 ## @end ifnottex
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80 ##
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81 ## @var{err} is an approximate bound on the error in the integral
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82 ## @code{abs (@var{q} - @var{I})}, where @var{I} is the exact value of the
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83 ## integral.
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84 ##
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85 ## Example 1 : integrate over a rectangular volume
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86 ##
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87 ## @example
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88 ## @group
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89 ## @var{f} = @@(@var{x},@var{y},@var{z}) ones (size (@var{x}));
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90 ## @var{q} = integral3 (@var{f}, 0, 1, 0, 1, 0, 1)
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91 ## @result{} @var{q} = 1.00000
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92 ## @end group
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93 ## @end example
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94 ##
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95 ## For this constant-value integrand, the result is a volume which is just
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96 ## @code{@var{Length} * @var{Width} * @var{Height}}.
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97 ##
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98 ## Example 2 : integrate over a spherical volume
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99 ##
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100 ## @example
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101 ## @group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
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diff changeset
102 ## @var{f} = @@(@var{x},@var{y}) ones (size (@var{x}));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
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diff changeset
103 ## @var{ymax} = @@(@var{x}) sqrt (1 - @var{x}.^2);
26600
f6730533820e doc: clean up doc example blocks for accuracy and consistent formatting
Mike Miller <mtmiller@octave.org>
parents: 26376
diff changeset
104 ## @var{zmax} = @@(@var{x},@var{y}) sqrt (1 - @var{x}.^2 - @var{y}.^2);
f6730533820e doc: clean up doc example blocks for accuracy and consistent formatting
Mike Miller <mtmiller@octave.org>
parents: 26376
diff changeset
105 ## @var{q} = integral3 (@var{f}, 0, 1, 0, @var{ymax}, 0, @var{zmax})
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
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diff changeset
106 ## @result{} @var{q} = 0.52360
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
107 ## @end group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
108 ## @end example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
109 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
110 ## For this constant-value integrand, the result is a volume which is 1/8th
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
111 ## of a unit sphere or @code{1/8 * 4/3 * pi}.
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
112 ##
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
113 ## Programming Notes: If there are singularities within the integration region
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
114 ## it is best to split the integral and place the singularities on the
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
115 ## boundary.
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
116 ##
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
117 ## Known @sc{matlab} incompatibility: If tolerances are left unspecified, and
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
118 ## any integration limits are of type @code{single}, then Octave's integral
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
119 ## functions automatically reduce the default absolute and relative error
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
120 ## tolerances as specified above. If tighter tolerances are desired they
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
121 ## must be specified. @sc{matlab} leaves the tighter tolerances appropriate
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
122 ## for @code{double} inputs in place regardless of the class of the
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
123 ## integration limits.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
124 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
125 ## Reference: @nospell{L.F. Shampine},
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
126 ## @cite{@sc{matlab} program for quadrature in 2D}, Applied Mathematics and
27800
5a6a19a4e3da doc: Use Texinfo non-sentence ending periods in citations.
Rik <rik@octave.org>
parents: 26600
diff changeset
127 ## Computation, pp.@: 266--274, Vol 1, 2008.
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
128 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
129 ## @seealso{triplequad, integral, quad, quadgk, quadv, quadl,
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
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diff changeset
130 ## quadcc, trapz, integral2, quad2d, dblquad}
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
131 ## @end deftypefn
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
132
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
133 function q = integral3 (f, xa, xb, ya, yb, za, zb, varargin)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
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diff changeset
134
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
135 if (nargin < 7 || mod (nargin, 2) == 0)
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
136 print_usage ();
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
137 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
138
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
139 if (! is_function_handle (f))
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
140 print_usage ();
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
141 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
142
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
143 if (! (isreal (xa) && isscalar (xa) && isreal (xb) && isscalar (xb)))
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
144 print_usage ();
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
145 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
146
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
147 ## Check for single or double limits to set appropriate default tolerance.
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
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diff changeset
148 issingle = (isa ([xa, xb], "single")
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
149 || (! is_function_handle (ya) && isa (ya, "single"))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
150 || (! is_function_handle (yb) && isa (yb, "single"))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
151 || (! is_function_handle (za) && isa (za, "single"))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
152 || (! is_function_handle (zb) && isa (zb, "single")));
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
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diff changeset
153
24158
f9549e90d620 integral3.m: Return single type output if an input is of single type (bug #52243).
Rik <rik@octave.org>
parents: 24149
diff changeset
154 ## Communicate to downstream quadrature routines that at least one limit of
f9549e90d620 integral3.m: Return single type output if an input is of single type (bug #52243).
Rik <rik@octave.org>
parents: 24149
diff changeset
155 ## integration was of single type by casting xa, xb to single.
f9549e90d620 integral3.m: Return single type output if an input is of single type (bug #52243).
Rik <rik@octave.org>
parents: 24149
diff changeset
156 if (issingle)
f9549e90d620 integral3.m: Return single type output if an input is of single type (bug #52243).
Rik <rik@octave.org>
parents: 24149
diff changeset
157 xa = single (xa);
f9549e90d620 integral3.m: Return single type output if an input is of single type (bug #52243).
Rik <rik@octave.org>
parents: 24149
diff changeset
158 xb = single (xb);
f9549e90d620 integral3.m: Return single type output if an input is of single type (bug #52243).
Rik <rik@octave.org>
parents: 24149
diff changeset
159 endif
f9549e90d620 integral3.m: Return single type output if an input is of single type (bug #52243).
Rik <rik@octave.org>
parents: 24149
diff changeset
160
f9549e90d620 integral3.m: Return single type output if an input is of single type (bug #52243).
Rik <rik@octave.org>
parents: 24149
diff changeset
161 ## Set default tolerances, and then update with any specified parameters.
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
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parents:
diff changeset
162 if (issingle)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
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diff changeset
163 abstol = 1e-5;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
164 reltol = 1e-4;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
165 else
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
166 abstol = 1e-10;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
167 reltol = 1e-6;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
168 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
169
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
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diff changeset
170 method = "auto";
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
171 vectorized = true;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
172 idx = 1;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
173 while (idx < nargin - 7)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
174 prop = varargin{idx++};
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
175 if (! ischar (prop))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
176 error ("integral3: property PROP must be a string");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
177 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
178
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
179 switch (tolower (prop))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
180 case "abstol"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
181 abstol = varargin{idx++};
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
182 if (! (isnumeric (abstol) && isscalar (abstol) && abstol >= 0))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
183 error ("integral3: AbsTol value must be a numeric scalar >= 0");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
184 endif
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
185
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
186 case "reltol"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
187 reltol = varargin{idx++};
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
188 if (! (isnumeric (reltol) && isscalar (reltol) && reltol >= 0))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
189 error ("integral3: RelTol value must be a numeric scalar >= 0");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
190 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
191
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
192 case "method"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
193 method = tolower (varargin{idx++});
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
194 if (! any (strcmp (method, {"auto", "iterated", "tiled"})))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
195 error ("integral3 : unrecognized method '%s'", method);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
196 endif
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
197
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
198 case "vectorized"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
199 vectorized = varargin{idx++};
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
200 if (! (isscalar (vectorized) && isreal (vectorized)))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
201 error ('integral3: Vectorized must be a logical value');
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
202 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
203
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
204 otherwise
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
205 error ("integral3: unknown property '%s'", prop);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
206
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
207 endswitch
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
208 endwhile
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
209
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
210 if (strcmp (method, "auto"))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
211 if (isinf (xa) || isinf (xb)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
212 || (! is_function_handle (ya) && isinf (ya))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
213 || (! is_function_handle (yb) && isinf (yb))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
214 || (! is_function_handle (za) && isinf (za))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
215 || (! is_function_handle (zb) && isinf (zb)))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
216 method = "iterated";
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
217 else
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
218 method = "tiled";
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
219 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
220 endif
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
221
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
222 ## check upper and lower bounds of y
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
223 if (! is_function_handle (ya))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
224 if (! (isreal (ya) && isscalar (ya)))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
225 error ("integral3: YA must be a real scalar or a function");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
226 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
227 ya = @(x) ya * ones (size (x));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
228 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
229 if (! is_function_handle (yb))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
230 if (! (isreal (yb) && isscalar (yb)))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
231 error ("integral3: YB must be a real scalar or a function");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
232 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
233 yb = @(x) yb * ones (size (x));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
234 endif
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
235
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
236 ## check upper and lower bounds of z
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
237 if (! is_function_handle (za))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
238 if (! (isreal (za) && isscalar (za)))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
239 error ("integral3: ZA must be a real scalar or a function");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
240 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
241 za = @(x, y) za * ones (size(y));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
242 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
243 if (! is_function_handle (zb))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
244 if (! (isreal (zb) && isscalar (zb)))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
245 error ("integral3: ZB must be a real scalar or a function")
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
246 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
247 zb = @(x, y) zb * ones (size (y));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
248 endif
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
249
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
250 finner = @(x) inner (x, f, ya, yb, za, zb, vectorized, method, abstol, reltol);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
251 q = quadcc (finner, xa, xb, [abstol, reltol]);
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
252
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
253 endfunction
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
254
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
255 function q = inner (x, f, ya, yb, za, zb, vectorized, method, abstol, reltol)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
256 q = zeros (size (x));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
257 for i = 1 : length (x)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
258 za2 = @(y) za(x(i), y);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
259 zb2 = @(y) zb(x(i), y);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
260 f2 = @(y, z) f(x(i), y, z);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
261 if (! vectorized)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
262 f2 = @(y, z) arrayfun (f2, y, z);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
263 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
264 if (strcmp (method, "iterated"))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
265 finner_iter = @(y) inner_iterated (y, f2, za2, zb2, abstol, reltol);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
266 q(i) = quadcc (finner_iter, ya(x(i)), yb(x(i)), [abstol, reltol]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
267 else
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
268 q(i) = quad2d (f2, ya(x(i)), yb(x(i)), za2, zb2,
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
269 "AbsTol", abstol, "RelTol", reltol);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
270 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
271 endfor
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
272 endfunction
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
273
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
274 function q = inner_iterated (y, f2, za2, zb2, abstol, reltol)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
275 q = zeros (size (y));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
276 for i = 1 : length (y)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
277 q(i) = quadcc (@(z) f2(y(i), z), za2(y(i)), zb2(y(i)), [abstol, reltol]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
278 endfor
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
279 endfunction
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
280
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
281
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
282 ## method tests
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
283 %!shared f
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
284 %! f = @(x, y, z) x .* y .* z;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
285
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
286 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1), 0.125, 1e-10);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
287 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1, "method", "tiled"), 0.125, 1e-10);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
288 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1, "method", "iterated"), 0.125, 1e-10);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
289 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1, "method", "auto"), 0.125, 1e-10);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
290
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
291 ## vectorized = false test
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
292 %!test
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
293 %! f = @(x, y, z) x * y * z;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
294 %! assert (integral3 (f, 0, 1, 0, 1, 0, 1, "vectorized", false), 0.125, 1e-10);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
295
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
296 ## tolerance tests
24149
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests.
Rik <rik@octave.org>
parents: 24148
diff changeset
297 %!test
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
298 %! f = @(x, y, z) 2 * x.^2 + 3 * y.^2 + 4 * z.^2;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
299 %!assert (integral3 (f, 0, 5, -5, 0, 0, 5, "AbsTol", 1e-9), 9375, 1e-9)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
300 %!assert (integral3 (f, 0, 5, -5, 0, 0, 5, "RelTol", 1e-5), 9375, -1e-5)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
301 %!assert (integral3 (f, 0, 5, -5, 0, 0, 5, "RelTol", 1e-6, "AbsTol", 1e-9),
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
302 %! 9375, 1e-9)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
303
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
304 ## non-rectangular region
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
305 ## This test is too slow with "iterated" method
24149
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests.
Rik <rik@octave.org>
parents: 24148
diff changeset
306 %!test
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests.
Rik <rik@octave.org>
parents: 24148
diff changeset
307 %! f = @(x,y,z) 1 ./ (x + y + z);
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests.
Rik <rik@octave.org>
parents: 24148
diff changeset
308 %! ymax = @(x) 1 - x;
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests.
Rik <rik@octave.org>
parents: 24148
diff changeset
309 %! zmax = @(x, y) 1 - x - y;
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests.
Rik <rik@octave.org>
parents: 24148
diff changeset
310 %! assert (integral3 (f, 0, 1, 0, ymax, 0, zmax, "method", "tiled"), 0.25, 1e-6);
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
311
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
312 ## Test input validation
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
313 %!error integral3
24102
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
314 %!error integral3 (@plus)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
315 %!error integral3 (@plus, 1)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
316 %!error integral3 (@plus, 1, 2)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
317 %!error integral3 (@plus, 1, 2, 3)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
318 %!error integral3 (@plus, 1, 2, 3, 4)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
319 %!error integral3 (@plus, 1, 2, 3, 4, 5)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff changeset
320 %!error integral3 (@plus, 1, 2, 3, 4, 5, 6, "foo")
24148
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
321 %!error integral3 (0, 1, 2, 3, 4, 5, 6) # f must be a function handle
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
322 %!error integral3 (@plus, 1i, 2, 3, 4, 5, 6) # real limits
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
323 %!error integral3 (@plus, 1, 2i, 3, 4, 5, 6) # real limits
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
324 %!error integral3 (@plus, [1 1], 2, 3, 4, 5, 6) # scalar limits
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
325 %!error integral3 (@plus, 1, [2 2], 3, 4, 5, 6) # scalar limits
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
326 %!error <property PROP must be a string>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
327 %! integral3 (@plus, 1, 2, 3, 4, 5, 6, 99, "bar");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
328 %!error <AbsTol value must be a numeric>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
329 %! integral3 (@plus, 1, 2, 3, 4, 5, 6, "AbsTol", "foo");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
330 %!error <AbsTol value must be a .* scalar>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
331 %! integral3 (@plus, 1, 2, 3, 4, 5, 6, "AbsTol", [1, 2]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
332 %!error <AbsTol value must be.* .= 0>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
333 %! integral3 (@plus, 1, 2, 3, 4, 5, 6, "AbsTol", -1);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
334 %!error <RelTol value must be a numeric>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
335 %! integral3 (@plus, 1, 2, 3, 4, 5, 6, "RelTol", "foo");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
336 %!error <RelTol value must be a .* scalar>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
337 %! integral3 (@plus, 1, 2, 3, 4, 5, 6, "RelTol", [1, 2]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
338 %!error <RelTol value must be.* .= 0>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
339 %! integral3 (@plus, 1, 2, 3, 4, 5, 6, "RelTol", -1);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
340 %!error <unrecognized method 'foo'>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
341 %! integral3 (@plus,1,2,3,4,5,6, "method", "foo");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
342 %!error <Vectorized must be a logical value>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
343 %! integral3 (@plus,1,2,3,4,5,6, "Vectorized", [0 1]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
344 %!error <Vectorized must be a logical value>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
345 %! integral3 (@plus,1,2,3,4,5,6, "Vectorized", {true});
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
346 %!error <unknown property 'foo'>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
347 %! integral3 (@plus, 1, 2, 3, 4, 6, 6, "foo", "bar");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
348 %!error <YA must be a real scalar> integral3 (@plus, 1, 2, 3i, 4, 5, 6)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
349 %!error <YA must be a real scalar> integral3 (@plus, 1, 2, [3 3], 4, 5, 6)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
350 %!error <YB must be a real scalar> integral3 (@plus, 1, 2, 3, 4i, 5, 6)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
351 %!error <YB must be a real scalar> integral3 (@plus, 1, 2, 3, [4 4], 5, 6)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
352 %!error <ZA must be a real scalar> integral3 (@plus, 1, 2, 3, 4, 5i, 6)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
353 %!error <ZA must be a real scalar> integral3 (@plus, 1, 2, 3, 4, [5 5], 6)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
354 %!error <ZB must be a real scalar> integral3 (@plus, 1, 2, 3, 4, 5, 6i)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 24102
diff changeset
355 %!error <ZB must be a real scalar> integral3 (@plus, 1, 2, 3, 4, 5, [6 6])