octave: scripts/general/quad2d.m annotate

annotate scripts/general/quad2d.m @ 30564:796f54d4ddbf stable

update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2021. In all .txi and .texi files except gpl.txi and gpl.texi in the doc/liboctave and doc/interpreter directories, change the copyright to "Octave Project Developers", the same as used for other source files. Update copyright notices for 2022 (not done since 2019). For gpl.txi and gpl.texi, change the copyright notice to be "Free Software Foundation, Inc." and leave the date at 2007 only because this file only contains the text of the GPL, not anything created by the Octave Project Developers. Add Paul Thomas to contributors.in.

author	John W. Eaton <jwe@octave.org>
date	Tue, 28 Dec 2021 18:22:40 -0500
parents	363fb10055df
children	b0e90ca8e679

rev	line source
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	1 ########################################################################
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	2 ##
30564 796f54d4ddbf update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 30379 diff changeset	3 ## Copyright (C) 2017-2022 The Octave Project Developers
27918 b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 27800 diff changeset	4 ##
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	5 ## See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	6 ## distribution or <https://octave.org/copyright/>.
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	7 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	8 ## This file is part of Octave.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	9 ##
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 24148 diff changeset	10 ## Octave is free software: you can redistribute it and/or modify it
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	11 ## under the terms of the GNU General Public License as published by
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 24148 diff changeset	12 ## the Free Software Foundation, either version 3 of the License, or
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	13 ## (at your option) any later version.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	14 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	15 ## Octave is distributed in the hope that it will be useful, but
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	18 ## GNU General Public License for more details.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	19 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	20 ## You should have received a copy of the GNU General Public License
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	21 ## along with Octave; see the file COPYING. If not, see
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 24148 diff changeset	22 ## <https://www.gnu.org/licenses/>.
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	23 ##
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	24 ########################################################################
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	25
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	26 ## -- texinfo --
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	27 ## @deftypefn {} {@var{q} =} quad2d (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb})
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	28 ## @deftypefnx {} {@var{q} =} quad2d (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{prop}, @var{val}, @dots{})
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	29 ## @deftypefnx {} {[@var{q}, @var{err}, @var{iter}] =} quad2d (@dots{})
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	30 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	31 ## Numerically evaluate the two-dimensional integral of @var{f} using adaptive
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	32 ## quadrature over the two-dimensional domain defined by @var{xa}, @var{xb},
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	33 ## @var{ya}, @var{yb} using tiled integration. Additionally, @var{ya} and
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	34 ## @var{yb} may be scalar functions of @var{x}, allowing for the integration
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	35 ## over non-rectangular domains.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	36 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	37 ## @var{f} is a function handle, inline function, or string containing the name
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	38 ## of the function to evaluate. The function @var{f} must be of the form
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	39 ## @math{z = f(x,y)} where @var{x} is a vector and @var{y} is a scalar. It
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	40 ## should return a vector of the same length and orientation as @var{x}.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	41 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	42 ## Additional optional parameters can be specified using
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	43 ## @qcode{"@var{property}", @var{value}} pairs. Valid properties are:
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	44 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	45 ## @table @code
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	46 ## @item AbsTol
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	47 ## Define the absolute error tolerance for the quadrature. The default
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	48 ## value is 1e-10 (1e-5 for single).
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	49 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	50 ## @item RelTol
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	51 ## Define the relative error tolerance for the quadrature. The default
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	52 ## value is 1e-6 (1e-4 for single).
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	53 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	54 ## @item MaxFunEvals
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	55 ## The maximum number of function calls to the vectorized function @var{f}.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	56 ## The default value is 5000.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	57 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	58 ## @item Singular
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	59 ## Enable/disable transforms to weaken singularities on the edge of the
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	60 ## integration domain. The default value is @var{true}.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	61 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	62 ## @item Vectorized
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	63 ## Option to disable vectorized integration, forcing Octave to use only scalar
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	64 ## inputs when calling the integrand. The default value is @var{false}.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	65 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	66 ## @item FailurePlot
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	67 ## If @code{quad2d} fails to converge to the desired error tolerance before
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	68 ## MaxFunEvals is reached, a plot of the areas that still need refinement
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	69 ## is created. The default value is @var{false}.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	70 ## @end table
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	71 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	72 ## Adaptive quadrature is used to minimize the estimate of error until the
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	73 ## following is satisfied:
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	74 ## @tex
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	75 ## $$error \leq \max \left( AbsTol, RelTol\cdot\vert q\vert \right)$$
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	76 ## @end tex
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	77 ## @ifnottex
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	78 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	79 ## @example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	80 ## @group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	81 ## @var{error} <= max (@var{AbsTol}, @var{RelTol}*\|@var{q}\|)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	82 ## @end group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	83 ## @end example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	84 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	85 ## @end ifnottex
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	86 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	87 ## The optional output @var{err} is an approximate bound on the error in the
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	88 ## integral @code{abs (@var{q} - @var{I})}, where @var{I} is the exact value
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	89 ## of the integral. The optional output @var{iter} is the number of vectorized
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	90 ## function calls to the function @var{f} that were used.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	91 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	92 ## Example 1 : integrate a rectangular region in x-y plane
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	93 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	94 ## @example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	95 ## @group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	96 ## @var{f} = @@(@var{x},@var{y}) 2*ones (size (@var{x}));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	97 ## @var{q} = quad2d (@var{f}, 0, 1, 0, 1)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	98 ## @result{} @var{q} = 2
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	99 ## @end group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	100 ## @end example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	101 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	102 ## The result is a volume, which for this constant-value integrand, is just
25579 07c2c42f457e doc: Miscellaneous documentation fixes all over the manual (bug #54288). Rik <rik@octave.org> parents: 25054 diff changeset	103 ## @code{@var{Length} * @var{Width} * @var{Height}}.
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	104 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	105 ## Example 2 : integrate a triangular region in x-y plane
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	106 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	107 ## @example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	108 ## @group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	109 ## @var{f} = @@(@var{x},@var{y}) 2*ones (size (@var{x}));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	110 ## @var{ymax} = @@(@var{x}) 1 - @var{x};
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	111 ## @var{q} = quad2d (@var{f}, 0, 1, 0, @var{ymax})
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	112 ## @result{} @var{q} = 1
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	113 ## @end group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	114 ## @end example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	115 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	116 ## The result is a volume, which for this constant-value integrand, is the
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	117 ## Triangle Area x Height or
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	118 ## @code{1/2 * @var{Base} * @var{Width} * @var{Height}}.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	119 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	120 ## 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: diff changeset	121 ## 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: diff changeset	122 ## boundary.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	123 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	124 ## 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: diff changeset	125 ## 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: diff changeset	126 ## 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: diff changeset	127 ## 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: diff changeset	128 ## 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: diff changeset	129 ## 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: diff changeset	130 ## integration limits.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	131 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	132 ## Reference: @nospell{L.F. Shampine},
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	133 ## @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: 26376 diff changeset	134 ## 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: diff changeset	135 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	136 ## @seealso{integral2, dblquad, integral, quad, quadgk, quadv, quadl, quadcc,
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	137 ## trapz, integral3, triplequad}
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	138 ## @end deftypefn
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	139
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	140 function [q, err, iter] = quad2d (f, xa, xb, ya, yb, varargin)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	141
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	142 if (nargin < 5 \|\| mod (nargin, 2) == 0)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	143 print_usage ();
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	144 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	145
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	146 if (ischar (f))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	147 ## Convert function given as a string to a function handle
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	148 f = @(x) feval (f, x);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	149 elseif (! is_function_handle (f))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	150 print_usage ();
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	151 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	152
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	153 if (! (isreal (xa) && isscalar (xa) && isreal (xb) && isscalar (xb)))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	154 print_usage ();
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	155 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	156
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	157 ## Check for single or double limits to set appropriate default tolerance.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	158 issingle = (isa ([xa, xb], "single")
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	159 \|\| (! 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: diff changeset	160 \|\| (! 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: diff changeset	161
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	162 ## Set defaults, update with any specified parameters.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	163 if (issingle)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	164 abstol = 1e-5;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	165 reltol = 1e-4;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	166 else
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	167 abstol = 1e-10;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	168 reltol = 1e-6;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	169 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	170
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	171 vectorized = true;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	172 singular = true;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	173 idx = 1;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	174 maxiter = 5000;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	175 failureplot = false;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	176
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	177 while (idx < nargin - 5)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	178 prop = varargin{idx++};
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	179 if (! ischar (prop))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	180 error ("quad2d: 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: diff changeset	181 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	182
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	183 switch (tolower (prop))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	184 case "abstol"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	185 abstol = varargin{idx++};
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	186 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: diff changeset	187 error ("quad2d: 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: diff changeset	188 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	189
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	190 case "reltol"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	191 reltol = varargin{idx++};
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	192 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: diff changeset	193 error ("quad2d: 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: diff changeset	194 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	195
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	196 case "maxfunevals"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	197 maxiter = varargin{idx++};
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	198 if (! (isnumeric (maxiter) && isscalar (maxiter)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	199 && fix (maxiter) == maxiter && maxiter >= 1))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	200 error ("quad2d: MaxFunEvals value must be a scalar integer >= 1");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	201 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	202
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	203 case "singular"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	204 singular = varargin{idx++};
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	205 if (! (isscalar (singular) && isreal (singular)))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	206 error ("quad2d: Singular must be a logical value");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	207 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	208
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	209 case "vectorized"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	210 vectorized = varargin{idx++};
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	211 if (! (isscalar (vectorized) && isreal (vectorized)))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	212 error ("quad2d: 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: diff changeset	213 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	214
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	215 case "failureplot"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	216 failureplot = varargin{idx++};
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	217 if (! (isscalar (failureplot) && isreal (failureplot)))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	218 error ("quad2d: FailurePlot must be a logical value");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	219 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	220
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	221 otherwise
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	222 error ("quad2d: unknown property '%s'", prop);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	223
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	224 endswitch
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	225 endwhile
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	226
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	227 if (! vectorized)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	228 f = @(x, y) arrayfun (f, x, y);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	229 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	230
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	231 ## 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: diff changeset	232 if (! is_function_handle (ya))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	233 if (! (isreal (ya) && isscalar (ya)))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	234 error ("quad2d: 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: diff changeset	235 endif
28912 0de38a6ef693 maint: Use Octave convention of space after function name in scripts dir. Rik <rik@octave.org> parents: 28896 diff changeset	236 ya = @(x) ya * ones (rows (x), columns (x));
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	237 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	238 if (! is_function_handle (yb))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	239 if (! (isreal (yb) && isscalar (yb)))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	240 error ("quad2d: 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: diff changeset	241 endif
28912 0de38a6ef693 maint: Use Octave convention of space after function name in scripts dir. Rik <rik@octave.org> parents: 28896 diff changeset	242 yb = @(x) yb * ones (rows (x), columns (x));
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	243 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	244
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	245 iter = 0;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	246 qaccept = 0;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	247 qerraccept = 0;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	248
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	249 if (singular)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	250 ## Shampine suggests using the singularity weakening transform
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	251 ## suggested by Havie.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	252 ## \int_a^b f(x) dx = \int_0^pi f (g(t)) (dx / dt) dt
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	253 ## where
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	254 ## g(t) = ((a - b) * cos(t) + (a + b)) / 2
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	255 ## dx = - (a - b) * sin(t) / 2 dt
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	256 ## Now our integral is
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	257 ## \int_a^b \int_0^1 f(x,y) dydx
27956 2310164737b3 fix many spelling errors (bug #57613) John W. Eaton <jwe@octave.org> parents: 26376 diff changeset	258 ## as we already substitute for "y", so
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	259 ## gx(tx) = ((a - b) * cos(tx) + (a + b)) / 2
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	260 ## gy(ty) = (1 - cos(ty)) / 2
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	261 ## dydx = (b - a) * sin(tx) * sin(ty) / 4 dtydtx
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	262
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	263 xtrans = @(tx) ((xa - xb) .* cos (tx) + (xa + xb)) ./ 2;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	264 ytrans = @(ty) (1 - cos (ty)) ./ 2;
28912 0de38a6ef693 maint: Use Octave convention of space after function name in scripts dir. Rik <rik@octave.org> parents: 28896 diff changeset	265 ztrans = @(tx, ty) (xb - xa) .* sin (tx) .* sin (ty) ./ 4;
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	266 area = pi ^ 2;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	267
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	268 ## Initialize tile list
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	269 tilelist(1) = struct ("xa", 0, "xb", pi, "ya", 0, "yb", pi, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	270 "q", 0, "qerr", Inf);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	271 else
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	272 xtrans = @(tx) tx;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	273 ytrans = @(ty) ty;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	274 ztrans = @(tx, ty) 1;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	275 area = (xb - xa);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	276
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	277 ## Initialize tile list
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	278 tilelist(1) = struct ("xa", xa, "xb", xb, "ya", 0, "yb", 1, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	279 "q", 0, "qerr", Inf);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	280 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	281
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	282 while (length (tilelist) > 0 && iter < maxiter)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	283 ## Get tile with the largest error
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	284 [~, idx] = max ([tilelist.qerr]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	285 tile = tilelist(idx);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	286 tilelist(idx) = [];
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	287
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	288 ## Subdivide the tile into 4 subtiles
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	289 iter += 4;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	290 tiles(4) = struct ("xa", tile.xa, "xb", tile.xa + (tile.xb - tile.xa) / 2,
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	291 "ya", tile.ya, "yb", tile.ya + (tile.yb - tile.ya) / 2,
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	292 "q", 0, "qerr", 0);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	293 tiles(3) = struct ("xa", tile.xa, "xb", tile.xa + (tile.xb - tile.xa) / 2,
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	294 "ya", tile.ya + (tile.yb - tile.ya) / 2, "yb", tile.yb,
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	295 "q", 0, "qerr", 0);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	296 tiles(2) = struct ("xa", tile.xa + (tile.xb - tile.xa) / 2, "xb", tile.xb,
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	297 "ya", tile.ya, "yb", tile.ya + (tile.yb - tile.ya) / 2,
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	298 "q", 0, "qerr", 0);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	299 tiles(1) = struct ("xa", tile.xa + (tile.xb - tile.xa) / 2, "xb", tile.xb,
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	300 "ya", tile.ya + (tile.yb - tile.ya) / 2, "yb", tile.yb,
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	301 "q", 0, "qerr", 0);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	302
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	303 ## Perform the quadrature of 4 subtiles
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	304 for i = 1:4
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	305 [tiles(i).q, tiles(i).qerr] = ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	306 tensorproduct (f, ya, yb, tiles(i), xtrans, ytrans, ztrans, singular);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	307 endfor
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	308
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	309 q = qaccept + sum ([[tilelist.q], tiles.q]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	310 err = qerraccept + sum ([[tilelist.qerr], tiles.qerr]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	311 tol = max (abstol, reltol .* abs (q));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	312
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	313 ## Shampine suggests taking a margin of a factor of 8 for
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	314 ## the local tolerance. That, and the fact that we are subdividing
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	315 ## into 4 tiles, means we divide by 32 at this point.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	316 localtol = tol * ([tile.xb] - [tile.xa]) * ([tile.yb] - [tile.ya]) ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	317 / area / 32;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	318
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	319 ## If global tolerance is met, return.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	320 if (err < tol)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	321 break;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	322 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	323
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	324 ## Accept the tiles meeting the tolerance, and add the others back to
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	325 ## the list of tiles to treat.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	326 idx = find ([tiles.qerr] < localtol);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	327 qaccept += sum ([tiles(idx).q]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	328 qerraccept += sum ([tiles(idx).qerr]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	329 tiles(idx) = [];
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	330 tilelist = [tilelist, tiles];
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	331 endwhile
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	332
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	333 ## Verify convergence
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	334 if (iter >= maxiter)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	335 if (err > max (abstol, reltol .* abs (q)))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	336 warning (["quad2d: " ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	337 "Maximum number of sub-tiles reached without convergence"]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	338 else
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	339 warning (["quad2d: " ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	340 "Maximum number of sub-tiles reached, accuracy may be low"]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	341 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	342 if (failureplot)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	343 newplot ();
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	344 title ("quad2d : Areas needing refinement");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	345 for tile = tilelist
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	346 xaa = xtrans(tile.xa);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	347 xbb = xtrans(tile.xb);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	348 y1 = ya(xaa) + ytrans(tile.ya) * (yb(xaa) - ya(xaa));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	349 y2 = ya(xaa) + ytrans(tile.yb) * (yb(xaa) - ya(xaa));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	350 y3 = ya(xbb) + ytrans(tile.yb) * (yb(xbb) - ya(xbb));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	351 y4 = ya(xbb) + ytrans(tile.ya) * (yb(xbb) - ya(xbb));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	352 patch ([xaa, xaa, xbb, xbb, xaa], [y1, y2, y3, y4, y1], "b");
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	353 endfor
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	354 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	355 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	356
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	357 endfunction
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	358
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	359 function [q, qerr] = tensorproduct (f, ya, yb, tile, xtrans, ytrans, ztrans, singular)
30379 363fb10055df maint: Style check m-files ahead of 7.1 release. Rik <rik@octave.org> parents: 29359 diff changeset	360
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	361 ## The Shampine TwoD paper proposes using a G3,K7 rule in a tensor product.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	362 ## I couldn't find a tabulated abscissas and weights of a G3,K7 rule publicly
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	363 ## available, so use a G7,K15 rule from Octave's implementation of quadgk.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	364
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	365 persistent abscissa = [-0.9914553711208126e+00, -0.9491079123427585e+00, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	366 -0.8648644233597691e+00, -0.7415311855993944e+00, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	367 -0.5860872354676911e+00, -0.4058451513773972e+00, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	368 -0.2077849550078985e+00, 0.0000000000000000e+00, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	369 0.2077849550078985e+00, 0.4058451513773972e+00, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	370 0.5860872354676911e+00, 0.7415311855993944e+00, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	371 0.8648644233597691e+00, 0.9491079123427585e+00, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	372 0.9914553711208126e+00];
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	373
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	374 persistent weights15 = [0.2293532201052922e-01, 0.6309209262997855e-01, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	375 0.1047900103222502e+00, 0.1406532597155259e+00, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	376 0.1690047266392679e+00, 0.1903505780647854e+00, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	377 0.2044329400752989e+00, 0.2094821410847278e+00, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	378 0.2044329400752989e+00, 0.1903505780647854e+00, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	379 0.1690047266392679e+00, 0.1406532597155259e+00, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	380 0.1047900103222502e+00, 0.6309209262997855e-01, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	381 0.2293532201052922e-01];
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	382
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	383 persistent weights7 = [0.0, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	384 0.1294849661688697e+00, 0.0, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	385 0.2797053914892767e+00, 0.0, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	386 0.3818300505051889e+00, 0.0, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	387 0.4179591836734694e+00, 0.0, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	388 0.3818300505051889e+00, 0.0, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	389 0.2797053914892767e+00, 0.0, ...
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	390 0.1294849661688697e+00, 0.0];
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	391
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	392 xaa = tile.xa;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	393 xbb = tile.xb;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	394 yaa = tile.ya;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	395 ybb = tile.yb;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	396
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	397 tx = ((xbb - xaa) * abscissa + xaa + xbb) / 2;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	398 x = xtrans(tx);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	399 ty = (abscissa' * (ybb - yaa) + yaa + ybb) / 2;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	400 y = ones (15, 1) * ya(x) + ytrans(ty) * (yb(x) - ya(x));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	401
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	402 xhalfwidth = (xbb - xaa ) / 2;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	403 yhalfwidth = ones (15, 1) * (yb(x) - ya(x)) .* (ybb - yaa) ./ 2;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	404
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	405 x = ones (15, 1) * x;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	406 tx = ones (15,1) * tx;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	407 ty = ty * ones (1, 15);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	408
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	409 z = yhalfwidth .* f (x, y) .* ztrans(tx, ty) .* xhalfwidth;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	410 q = weights15 * (weights15 * z)';
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	411 qerr = abs (weights7 * (weights7 * z)' - q);
28945 6e460773bdda maint: Use newlines after "function" and before "endfunction" for clarity. Rik <rik@octave.org> parents: 28912 diff changeset	412
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	413 endfunction
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	414
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	415
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	416 %!shared f
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	417 %! f = @(x, y) x .* y;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	418 %!assert (quad2d (f, 0, 1, 0, 1), 0.25, 1e-10)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	419
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	420 %!test
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	421 %! f = @(x, y) 9 * x.^2 + 15 * y.^2;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	422 %!assert (quad2d (f, 0, 5, -5, 0, "AbsTol", 1e-9), 5000, 1e-9)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	423 %!assert (quad2d (f, 0, 5, -5, 0, "RelTol", 1e-6), 5000, -1e-6)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	424 %!assert (quad2d (f, 0, 5, -5, 0, "RelTol", 1e-6, "AbsTol", 1e-9), 5000, 1e-9)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	425
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	426 ## tests from dblquad
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	427 %!test
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	428 %! f = @(x, y) 1 ./ (x+y);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	429 %!assert (quad2d (f, 0, 1, 0, 1, "AbsTol", 1e-7), 2*log (2), 1e-7)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	430 %!assert (quad2d (f, 0, 1, 0, 1, "RelTol", 1e-5), 2*log (2), -1e-5)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	431 %!assert (quad2d (f, 0, 1, 0, 1, "AbsTol", 1e-8, "RelTol", 1e-6),
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	432 %! 2*log (2), -1e-6)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	433 %!assert (quad2d (f, 0, 1, 0, @(x) 1 - x), 1, -1e-6)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	434 %!assert (quad2d (f, 0, 1, 0, @(x) 1 - x, "Singular", true), 1, -1e-6)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	435
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	436 %!assert (quad2d (@(x, y) exp (-x.^2 - y.^2) , -1, 1, -1, 1),
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	437 %! pi * erf (1).^2, 1e-10)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	438
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	439 %!assert (quad2d (@plus, 1, 2, 3, 4), 5, 1e-10)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	440
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	441 ## Test input validation
28896 90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 27957 diff changeset	442 %!error <Invalid call> quad2d ()
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 27957 diff changeset	443 %!error <Invalid call> quad2d (@plus)
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 27957 diff changeset	444 %!error <Invalid call> quad2d (@plus, 1)
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 27957 diff changeset	445 %!error <Invalid call> quad2d (@plus, 1, 2)
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 27957 diff changeset	446 %!error <Invalid call> quad2d (@plus, 1, 2, 3)
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 27957 diff changeset	447 %!error <Invalid call> quad2d (@plus, 1, 2, 3, 4, "foo")
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	448 %!error quad2d (0, 1, 2, 3, 4) # f must be function handle
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	449 %!error quad2d (@plus, 1i, 2, 3, 4) # real limits
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	450 %!error quad2d (@plus, 1, 2i, 3, 4) # real limits
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	451 %!error quad2d (@plus, [1 1], 2, 3, 4) # scalar limits
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	452 %!error quad2d (@plus, 1, [2 2], 3, 4) # scalar limits
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	453 %!error <property PROP must be a string> quad2d (@plus, 1, 2, 3, 4, 99, "bar")
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	454 %!error <AbsTol value must be a numeric> quad2d (@plus, 1, 2, 3, 4, "AbsTol", "foo")
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	455 %!error <AbsTol value must be a .* scalar> quad2d (@plus, 1, 2, 3, 4, "AbsTol", [1, 2])
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	456 %!error <AbsTol value must be.* .= 0> quad2d (@plus, 1, 2, 3, 4, "AbsTol", -1)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	457 %!error <RelTol value must be a numeric> quad2d (@plus, 1, 2, 3, 4, "RelTol", "foo")
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	458 %!error <RelTol value must be a .* scalar> quad2d (@plus, 1, 2, 3, 4, "RelTol", [1, 2])
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	459 %!error <RelTol value must be.* .= 0> quad2d (@plus, 1, 2, 3, 4, "RelTol", -1)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	460 %!error <MaxFunEvals value must be a scalar integer>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	461 %! quad2d (@plus,1,2,3,4, "MaxFunEvals", {1});
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	462 %!error <MaxFunEvals value must be a scalar integer>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	463 %! quad2d (@plus,1,2,3,4, "MaxFunEvals", [1 1]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	464 %!error <MaxFunEvals value must be a scalar integer>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	465 %! quad2d (@plus,1,2,3,4, "MaxFunEvals", 1.5);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	466 %!error <MaxFunEvals value must be a scalar integer .= 1>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	467 %! quad2d (@plus,1,2,3,4, "MaxFunEvals", -1);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	468 %!error <Singular must be a logical value>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	469 %! quad2d (@plus,1,2,3,4, "Singular", [0 1]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	470 %!error <Singular must be a logical value>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	471 %! quad2d (@plus,1,2,3,4, "Singular", {true});
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	472 %!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: diff changeset	473 %! quad2d (@plus,1,2,3,4, "Vectorized", [0 1]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	474 %!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: diff changeset	475 %! quad2d (@plus,1,2,3,4, "Vectorized", {true});
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	476 %!error <FailurePlot must be a logical value>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	477 %! quad2d (@plus,1,2,3,4, "FailurePlot", [0 1]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	478 %!error <FailurePlot must be a logical value>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	479 %! quad2d (@plus,1,2,3,4, "FailurePlot", {true});
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	480 %!error <unknown property 'foo'> quad2d (@plus, 1, 2, 3, 4, "foo", "bar")
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	481 %!error <YA must be a real scalar> quad2d (@plus, 1, 2, 3i, 4)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	482 %!error <YA must be a real scalar> quad2d (@plus, 1, 2, [3 3], 4)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	483 %!error <YB must be a real scalar> quad2d (@plus, 1, 2, 3, 4i)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	484 %!error <YB must be a real scalar> quad2d (@plus, 1, 2, 3, [4 4])
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	485 %!warning <Maximum number of> quad2d (@plus, 1, 2, 3, 4, "MaxFunEvals", 1);