octave: scripts/general/integral3.m annotate

annotate scripts/general/integral3.m @ 33623:4517f929c59d bytecode-interpreter tip

maint: Merge default to bytecode-interpreter

author	Arun Giridhar <arungiridhar@gmail.com>
date	Fri, 24 May 2024 16:22:41 -0400
parents	2da9214df7a4
children

rev	line source
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	1 ########################################################################
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	2 ##
32632 2e484f9f1f18 maint: update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 32002 diff changeset	3 ## Copyright (C) 2017-2024 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/>.
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	7 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	8 ## This file is part of Octave.
c723faa56ab4 Add missing functions integral2.m and integral3.m (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: 24158 diff changeset	10 ## Octave is free software: you can redistribute it and/or modify it
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (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: 24158 diff changeset	12 ## the Free Software Foundation, either version 3 of the License, or
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	13 ## (at your option) any later version.
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	14 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	15 ## Octave is distributed in the hope that it will be useful, but
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	18 ## GNU General Public License for more details.
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	19 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	20 ## You should have received a copy of the GNU General Public License
c723faa56ab4 Add missing functions integral2.m and integral3.m (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: 24158 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 ########################################################################
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	25
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	26 ## -- texinfo --
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	27 ## @deftypefn {} {@var{q} =} integral3 (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb})
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	28 ## @deftypefnx {} {@var{q} =} integral3 (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{prop}, @var{val}, @dots{})
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	29 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	30 ## Numerically evaluate the three-dimensional integral of @var{f} using
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	31 ## adaptive quadrature over the three-dimensional domain defined by
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	32 ## @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb} (scalars may
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	33 ## be finite or infinite). Additionally, @var{ya} and @var{yb} may be
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	34 ## scalar functions of @var{x} and @var{za}, and @var{zb} maybe be scalar
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	35 ## functions of @var{x} and @var{y}, allowing for integration over
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	36 ## non-rectangular domains.
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	37 ##
32886 2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	38 ## @var{f} is a function handle, inline function, or string containing the
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	39 ## name of the function to evaluate. The function @var{f} must be of the form
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	40 ## @math{z = f(x,y,z)}, and all operations must be vectorized such that
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	41 ## @var{x}, @var{y}, and @var{z} accept array inputs and return array outputs
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	42 ## of the same size. (It can be assumed that @var{x}, @var{y}, and @var{z}
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	43 ## will either be same-size arrays or scalars.) The underlying integrators
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	44 ## will input arrays of integration points into @var{f} and/or use internal
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	45 ## vector expansions to speed computation that can produce unpredictable
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	46 ## results if @var{f} is not restricted to elementwise operations. For
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	47 ## integrands where this is unavoidable, the @qcode("Vectorized") option
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	48 ## described below may produce more reliable results.
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	49 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	50 ## Additional optional parameters can be specified using
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	51 ## @qcode{"@var{property}", @var{value}} pairs. Valid properties are:
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	52 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	53 ## @table @code
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	54 ## @item AbsTol
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	55 ## Define the absolute error tolerance for the quadrature. The default
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	56 ## value is 1e-10 (1e-5 for single).
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	57 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	58 ## @item RelTol
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	59 ## Define the relative error tolerance for the quadrature. The default
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	60 ## value is 1e-6 (1e-4 for single).
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	61 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	62 ## @item Method
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	63 ## Specify the two-dimensional integration method to be used, with valid
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	64 ## options being @qcode{"auto"} (default), @qcode{"tiled"}, or
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	65 ## @qcode{"iterated"}. When using @qcode{"auto"}, Octave will choose the
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	66 ## @qcode{"tiled"} method unless any of the integration limits are infinite.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	67 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	68 ## @item Vectorized
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	69 ## Enable or disable vectorized integration. A value of @code{false} forces
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	70 ## Octave to use only scalar inputs when calling the integrand, which enables
32886 2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	71 ## integrands @math{f(x,y,z)} that have not been vectorized or only accept
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	72 ## scalar values of @var{x}, @var{y}, or @var{z}. The default value is
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	73 ## @code{true}. Note that this is achieved by wrapping @math{f(x,y,z)} with
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	74 ## the function @code{arrayfun}, which may significantly decrease computation
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	75 ## speed.
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	76 ## @end table
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	77 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	78 ## Adaptive quadrature is used to minimize the estimate of error until the
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	79 ## following is satisfied:
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	80 ## @tex
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	81 ## $$error \leq \max \left( AbsTol, RelTol\cdot\vert q\vert \right)$$
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	82 ## @end tex
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	83 ## @ifnottex
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	84 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	85 ## @example
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	86 ## @group
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	87 ## @var{error} <= max (@var{AbsTol}, @var{RelTol}*\|@var{q}\|)
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	88 ## @end group
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	89 ## @end example
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	90 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	91 ## @end ifnottex
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	92 ##
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	93 ## @var{err} is an approximate bound on the error in the integral
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	94 ## @code{abs (@var{q} - @var{I})}, where @var{I} is the exact value of the
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	95 ## integral.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	96 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	97 ## Example 1 : integrate over a rectangular volume
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	98 ##
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	99 ## @example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	100 ## @group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	101 ## @var{f} = @@(@var{x},@var{y},@var{z}) ones (size (@var{x}));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	102 ## @var{q} = integral3 (@var{f}, 0, 1, 0, 1, 0, 1)
26600 f6730533820e doc: clean up doc example blocks for accuracy and consistent formatting Mike Miller <mtmiller@octave.org> parents: 26376 diff changeset	103 ## @result{} @var{q} = 1.00000
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	104 ## @end group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	105 ## @end example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	106 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	107 ## For this constant-value integrand, the result is a volume which is just
25579 07c2c42f457e doc: Miscellaneous documentation fixes all over the manual (bug #54288). Rik <rik@octave.org> parents: 25054 diff changeset	108 ## @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: 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 ## Example 2 : integrate over a spherical volume
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	111 ##
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	112 ## @example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	113 ## @group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	114 ## @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> parents: 24102 diff changeset	115 ## @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	116 ## @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	117 ## @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> parents: 24102 diff changeset	118 ## @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	119 ## @end group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	120 ## @end example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	121 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	122 ## 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	123 ## 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	124 ##
32886 2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	125 ## Example 3 : integrate a non-vectorized function over a cubic volume
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	126 ##
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	127 ## @example
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	128 ## @group
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	129 ## @var{f} = @@(@var{x},@var{y}) sinc (@var{x}) * sinc (@var{y}), * sinc (@var{z});
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	130 ## @var{q} = integral3 (@var{f}, -1, 1, -1, 1, -1, 1)
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	131 ## @result{} @var{q} = 14.535 (incorrect)
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	132 ## @var{q} = integral3 (@var{f}, -1, 1, -1, 1, -1, 1, "Vectorized", false)
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	133 ## @result{} @var{q} = 1.6388 (correct)
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	134 ## @var{f} = @@(@var{x},@var{y},@var{z}) sinc (@var{x}) .* sinc (@var{y}), .* sinc (@var{z});
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	135 ## @var{q} = integral3 (@var{f}, -1, 1, -1, 1, -1, 1)
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	136 ## @result{} @var{q} = 1.6388 (correct)
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	137 ## @end group
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	138 ## @end example
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	139 ##
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	140 ## The first result is incorrect as the non-elementwise operator between the
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	141 ## sinc functions in @var{f} create unintended matrix multiplications between
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	142 ## the internal integration arrays used by @code{integral3}. In the second
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	143 ## result, setting @qcode{"Vectorized"} to false forces @code{integral3} to
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	144 ## perform scalar internal operations to compute the integral, resulting in
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	145 ## the correct numerical result at the cost of about a 30x increase in
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	146 ## computation time. In the third result, vectorizing the integrand @var{f}
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	147 ## using the elementwise multiplication operator gets the correct result
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	148 ## without increasing computation time.
2da9214df7a4 doc: Correct integrand restriction descriptions in integral funcs (bug #59403) Nicholas R. Jankowski <jankowski.nicholas@gmail.com> parents: 32632 diff changeset	149 ##
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	150 ## 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	151 ## 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	152 ## boundary.
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	153 ##
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	154 ## 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	155 ## 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	156 ## 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	157 ## 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	158 ## 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	159 ## 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	160 ## integration limits.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	161 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	162 ## 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	163 ## @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	164 ## 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	165 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	166 ## @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> parents: 24102 diff changeset	167 ## 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	168 ## @end deftypefn
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	169
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	170 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> parents: diff changeset	171
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	172 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	173 print_usage ();
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	174 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	175
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	176 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	177 print_usage ();
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	178 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	179
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	180 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	181 print_usage ();
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	182 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	183
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	184 ## 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> parents: 24102 diff changeset	185 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	186 \|\| (! 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	187 \|\| (! 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	188 \|\| (! 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	189 \|\| (! 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> parents: diff changeset	190
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	191 ## 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	192 ## 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	193 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	194 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	195 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	196 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	197
f9549e90d620 integral3.m: Return single type output if an input is of single type (bug #52243). Rik <rik@octave.org> parents: 24149 diff changeset	198 ## Set default tolerances, and then update with any specified parameters.
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	199 if (issingle)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	200 abstol = 1e-5;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	201 reltol = 1e-4;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	202 else
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	203 abstol = 1e-10;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	204 reltol = 1e-6;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	205 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	206
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	207 method = "auto";
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	208 vectorized = true;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	209 idx = 1;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	210 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	211 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	212 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	213 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	214 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	215
32002 939e5d952675 Use upper/lower in preference to toupper/tolower to match Matlab. Rik <rik@octave.org> parents: 31706 diff changeset	216 switch (lower (prop))
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	217 case "abstol"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	218 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	219 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	220 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	221 endif
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	222
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	223 case "reltol"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	224 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	225 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	226 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	227 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	228
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	229 case "method"
32002 939e5d952675 Use upper/lower in preference to toupper/tolower to match Matlab. Rik <rik@octave.org> parents: 31706 diff changeset	230 method = lower (varargin{idx++});
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	231 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	232 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	233 endif
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	234
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	235 case "vectorized"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	236 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	237 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	238 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	239 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	240
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	241 otherwise
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	242 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	243
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	244 endswitch
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	245 endwhile
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	246
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	247 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	248 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	249 \|\| (! 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	250 \|\| (! 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	251 \|\| (! 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	252 \|\| (! 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	253 method = "iterated";
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	254 else
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	255 method = "tiled";
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	256 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	257 endif
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	258
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	259 ## 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	260 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	261 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	262 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	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 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	265 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	266 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	267 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	268 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	269 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	270 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	271 endif
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	272
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	273 ## 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	274 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	275 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	276 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	277 endif
28912 0de38a6ef693 maint: Use Octave convention of space after function name in scripts dir. Rik <rik@octave.org> parents: 28907 diff changeset	278 za = @(x, y) za * ones (size (y));
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	279 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	280 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	281 if (! (isreal (zb) && isscalar (zb)))
28928 ae7ce8358953 maint: Add semicolon to end of all warning() and error() invocations. Rik <rik@octave.org> parents: 28912 diff changeset	282 error ("integral3: ZB must be a real scalar or a function");
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	283 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	284 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	285 endif
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	286
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	287 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	288 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	289
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	290 endfunction
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	291
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	292 function q = inner (x, f, ya, yb, za, zb, vectorized, method, abstol, reltol)
30379 363fb10055df maint: Style check m-files ahead of 7.1 release. Rik <rik@octave.org> parents: 30330 diff changeset	293
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	294 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	295 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	296 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	297 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	298 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	299 if (! vectorized)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	300 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	301 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	302 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	303 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	304 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	305 else
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	306 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	307 "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	308 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	309 endfor
30379 363fb10055df maint: Style check m-files ahead of 7.1 release. Rik <rik@octave.org> parents: 30330 diff changeset	310
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	311 endfunction
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	312
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	313 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	314 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	315 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	316 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	317 endfor
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	318 endfunction
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	319
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	320
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	321 ## method tests
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	322 %!shared f
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	323 %! 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	324
28907 11f1207111c5 maint: Don't use semicolon at end of single-line BIST tests. Rik <rik@octave.org> parents: 27923 diff changeset	325 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1), 0.125, 1e-10)
11f1207111c5 maint: Don't use semicolon at end of single-line BIST tests. Rik <rik@octave.org> parents: 27923 diff changeset	326 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1, "method", "tiled"), 0.125, 1e-10)
11f1207111c5 maint: Don't use semicolon at end of single-line BIST tests. Rik <rik@octave.org> parents: 27923 diff changeset	327 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1, "method", "iterated"), 0.125, 1e-10)
11f1207111c5 maint: Don't use semicolon at end of single-line BIST tests. Rik <rik@octave.org> parents: 27923 diff changeset	328 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1, "method", "auto"), 0.125, 1e-10)
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	329
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	330 ## vectorized = false test
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	331 %!test
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	332 %! 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	333 %! 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	334
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	335 ## tolerance tests
24149 1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	336 %!test
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	337 %! 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	338 %!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	339 %!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	340 %!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	341 %! 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	342
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	343 ## 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	344 ## 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	345 %!test
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	346 %! 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	347 %! ymax = @(x) 1 - x;
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	348 %! zmax = @(x, y) 1 - x - y;
30330 01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599) Rik <rik@octave.org> parents: 29359 diff changeset	349 %! assert (integral3 (f, 0, 1, 0, ymax, 0, zmax, "method", "tiled"),
01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599) Rik <rik@octave.org> parents: 29359 diff changeset	350 %! 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	351
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	352 ## 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	353 %!error integral3
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	354 %!error integral3 (@plus)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	355 %!error integral3 (@plus, 1)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	356 %!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	357 %!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	358 %!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	359 %!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	360 %!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	361 %!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	362 %!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	363 %!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	364 %!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	365 %!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	366 %!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	367 %! 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	368 %!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	369 %! 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	370 %!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	371 %! 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	372 %!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	373 %! 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	374 %!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	375 %! 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	376 %!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	377 %! 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	378 %!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	379 %! 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	380 %!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	381 %! 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	382 %!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	383 %! 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	384 %!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	385 %! 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	386 %!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	387 %! 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	388 %!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	389 %!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	390 %!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	391 %!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	392 %!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	393 %!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	394 %!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	395 %!error <ZB must be a real scalar> integral3 (@plus, 1, 2, 3, 4, 5, [6 6])