octave: scripts/general/integral2.m annotate

annotate scripts/general/integral2.m @ 31706:597f3ee61a48 stable

update Octave Project Developers copyright for the new year

author	John W. Eaton <jwe@octave.org>
date	Fri, 06 Jan 2023 13:11:27 -0500
parents	796f54d4ddbf
children	939e5d952675

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 ##
31706 597f3ee61a48 update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 30564 diff changeset	3 ## Copyright (C) 2017-2023 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: 24208 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: 24208 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: 24208 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} =} integral2 (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb})
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	28 ## @deftypefnx {} {@var{q} =} integral2 (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{prop}, @var{val}, @dots{})
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	29 ## @deftypefnx {} {[@var{q}, @var{err}] =} integral2 (@dots{})
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	30 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	31 ## Numerically evaluate the two-dimensional integral of @var{f} using adaptive
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	32 ## quadrature over the two-dimensional domain defined by @var{xa}, @var{xb},
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	33 ## @var{ya}, @var{yb} (scalars may be finite or infinite). Additionally,
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	34 ## @var{ya} and @var{yb} may be scalar functions of @var{x}, allowing for
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	35 ## integration over non-rectangular domains.
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	36 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (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
c723faa56ab4 Add missing functions integral2.m and integral3.m (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
c723faa56ab4 Add missing functions integral2.m and integral3.m (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
c723faa56ab4 Add missing functions integral2.m and integral3.m (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}.
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	41 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	42 ## 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	43 ## @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	44 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	45 ## @table @code
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	46 ## @item AbsTol
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	47 ## 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	48 ## 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	49 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	50 ## @item RelTol
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	51 ## 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	52 ## 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	53 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	54 ## @item Method
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	55 ## 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	56 ## 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	57 ## @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	58 ## @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	59 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	60 ## @item Vectorized
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	61 ## 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	62 ## Octave to use only scalar inputs when calling the integrand, which enables
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	63 ## integrands @math{f(x,y)} that have not been vectorized and only accept
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	64 ## @var{x} and @var{y} as scalars to be used. The default value is
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	65 ## @code{true}.
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	66 ## @end table
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	67 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	68 ## 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	69 ## following is satisfied:
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	70 ## @tex
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	71 ## $$error \leq \max \left( AbsTol, RelTol\cdot\vert q\vert \right)$$
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	72 ## @end tex
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	73 ## @ifnottex
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	74 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	75 ## @example
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	76 ## @group
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	77 ## @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	78 ## @end group
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	79 ## @end example
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	80 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	81 ## @end ifnottex
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	82 ##
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	83 ## @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	84 ## @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	85 ## integral.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	86 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	87 ## 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: 24102 diff changeset	88 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	89 ## @example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	90 ## @group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	91 ## @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: 24102 diff changeset	92 ## @var{q} = integral2 (@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: 24102 diff changeset	93 ## @result{} @var{q} = 2
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	94 ## @end group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	95 ## @end example
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 ## 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	98 ## @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	99 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	100 ## Example 2 : integrate a triangular region in x-y plane
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	101 ##
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	102 ## @example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	103 ## @group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	104 ## @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: 24102 diff changeset	105 ## @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: 24102 diff changeset	106 ## @var{q} = integral2 (@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: 24102 diff changeset	107 ## @result{} @var{q} = 1
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	108 ## @end group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	109 ## @end example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	110 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	111 ## 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: 24102 diff changeset	112 ## Triangle Area x Height or
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	113 ## @code{1/2 * @var{Base} * @var{Width} * @var{Height}}.
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	114 ##
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	115 ## 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	116 ## 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	117 ## boundary.
24208 eec262017c6a maint: Strip trailing whitespace from source files. John W. Eaton <jwe@octave.org> parents: 24149 diff changeset	118 ##
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	119 ## 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	120 ## 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	121 ## 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	122 ## 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	123 ## 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	124 ## 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	125 ## integration limits.
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	126 ##
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	127 ## 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	128 ## @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	129 ## 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	130 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	131 ## @seealso{quad2d, 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: 24102 diff changeset	132 ## trapz, integral3, triplequad}
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	133 ## @end deftypefn
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	134
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	135 function [q, err] = integral2 (f, xa, xb, ya, yb, varargin)
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	136
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	137 if (nargin < 5 \|\| 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	138 print_usage ();
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	139 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	140
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	141 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	142 print_usage ();
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	143 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	144
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	145 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	146 print_usage ();
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	147 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	148
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	149 ## 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	150 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	151 \|\| (! 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	152 \|\| (! is_function_handle (yb) && isa (yb, "single")));
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	153
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	154 ## Set defaults, update with any specified parameters.
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	155 if (issingle)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	156 abstol = 1e-5;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	157 reltol = 1e-4;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	158 else
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	159 abstol = 1e-10;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	160 reltol = 1e-6;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	161 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	162
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	163 method = "auto";
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	164 idx = 1;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	165 while (idx < nargin - 5)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	166 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	167 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	168 error ("integral2: 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	169 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	170
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	171 switch (tolower (prop))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	172 case "abstol"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	173 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	174 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	175 error ("integral2: 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	176 endif
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	177
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	178 case "reltol"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	179 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	180 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	181 error ("integral2: 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	182 endif
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	183
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	184 case "method"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	185 method = tolower (varargin{idx++});
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	186 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	187 error ("integral2 : 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	188 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	189
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	190 case "vectorized"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	191 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	192 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	193 error ('integral2: 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	194 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	195 if (! vectorized)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	196 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: 24102 diff changeset	197 endif
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	198
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	199 otherwise
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	200 error ("integral2: 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	201
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	202 endswitch
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	203 endwhile
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	204
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	205 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	206 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	207 \|\| (! 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	208 \|\| (! 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	209 method = "iterated";
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	210 else
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	211 method = "tiled";
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	212 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	213 endif
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	214
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	215 ## 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	216 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	217 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	218 error ("integral2: 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	219 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	220 ya = @(x) ya * ones (rows (x), columns (x));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	221 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	222 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	223 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	224 error ("integral2: 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	225 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	226 yb = @(x) yb * ones (rows (x), columns (x));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	227 endif
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	228
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	229 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	230 q = outer_iterated (f, xa, xb, ya, yb, abstol, reltol);
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	231
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	232 if (nargout == 2)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	233 warning ('integral2: "iterated" method can not return estimated error');
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	234 err = 0;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	235 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	236 else
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	237 [q, err] = quad2d (f, xa, xb, ya, yb, "AbsTol", abstol, "RelTol", reltol);
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	238 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	239
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	240 endfunction
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	241
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	242 function q = outer_iterated (f, xa, xb, ya, yb, abstol, reltol)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	243 finner_iter = @(x) inner_iterated (x, f, ya, yb, abstol, reltol);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	244 q = quadcc (finner_iter, xa, xb, [abstol, reltol]);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	245 endfunction
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 function q = inner_iterated (x, f, ya, yb, abstol, reltol)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	248 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	249 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	250 q(i) = quadcc (@(y) f(x(i), y), 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	251 endfor
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	252 endfunction
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	253
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	254
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	255 ## method tests
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	256 %!shared f
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	257 %! f = @(x, y) x .* y;
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 %!assert (integral2 (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: 24102 diff changeset	260 %!assert (integral2 (f, 0, 1, 0, 1, "method", "tiled"), 0.25, 1e-10)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	261 %!assert (integral2 (f, 0, 1, 0, 1, "method", "iterated"), 0.25, 1e-10)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	262 %!assert (integral2 (f, 0, 1, 0, 1, "method", "auto"), 0.25, 1e-10)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	263
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	264 ## vectorized = false test
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	265 %!test
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	266 %! f = @(x, y) x * y;
24149 1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	267 %!assert (integral2 (f, 0, 1, 0, 1, "vectorized", false), 0.25, 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	268
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	269 ## tolerance tests
24149 1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	270 %!test
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	271 %! f = @(x, y) 9 * x.^2 + 15 * y.^2;
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	272 %!assert (integral2 (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: 24102 diff changeset	273 %!assert (integral2 (f, 0, 5, -5, 0, "RelTol", 1e-5), 5000, -1e-5)
30330 01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599) Rik <rik@octave.org> parents: 29359 diff changeset	274 %!assert (integral2 (f, 0, 5, -5, 0, "RelTol", 1e-6, "AbsTol", 1e-9),
01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599) Rik <rik@octave.org> parents: 29359 diff changeset	275 %! 5000, 1e-9)
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	276
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	277 ## tests from dblquad
24149 1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	278 %!test
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	279 %! f = @(x, y) 1 ./ (x+y);
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	280 %!assert (integral2 (f, 0, 1, 0, 1, "AbsTol", 1e-7), 2*log (2), 1e-7)
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	281 %!assert (integral2 (f, 0, 1, 0, 1, "RelTol", 1e-5), 2*log (2), -1e-5)
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	282 %!assert (integral2 (f, 0, 1, 0, 1, "AbsTol", 1e-8, "RelTol", 1e-6),
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	283 %! 2*log (2), -1e-6)
24149 1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	284 %!assert (integral2 (f, 0, 1, 0, @(x) 1 - x), 1, -1e-6)
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	285
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	286 %!assert (integral2 (@(x, y) exp (-x.^2 - y.^2) , -1, 1, -1, 1),
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	287 %! pi * erf (1).^2, 1e-10)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	288
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	289 %!assert (integral2 (@plus, 1, 2, 3, 4), 5, 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	290
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	291 ## tests from dblquad w/method specified
24149 1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	292 %!assert (integral2 (f, 0, 1, 0, 1, "AbsTol", 1e-7, "method", "iterated"),
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	293 %! 2*log (2), 1e-7)
24149 1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	294 %!assert (integral2 (f, 0, 1, 0, 1, "RelTol", 1e-5, "method", "iterated"),
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	295 %! 2*log (2), -1e-5)
24149 1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	296 %!assert (integral2 (f, 0, 1, 0, 1, "AbsTol", 1e-8, "RelTol", 1e-6,
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	297 %! "Method", "iterated"),
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	298 %! 2*log (2), -1e-6)
24149 1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	299 %!assert (integral2 (f, 0, 1, 0, @(x) 1 - x, "Method", "iterated"), 1, -1e-6)
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	300 %!assert (integral2 (@(x, y) exp (-x.^2 - y.^2) , -1, 1, -1, 1,
24149 1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	301 %! "Method", "iterated"),
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	302 %! 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: 24102 diff changeset	303
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	304 %!assert (integral2 (@plus, 1, 2, 3, 4, "method", "iterated"), 5, 1e-10)
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	305
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	306 ## Test input validation
28896 90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 27923 diff changeset	307 %!error <Invalid call> integral2 ()
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 27923 diff changeset	308 %!error <Invalid call> integral2 (@plus)
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 27923 diff changeset	309 %!error <Invalid call> integral2 (@plus, 1)
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 27923 diff changeset	310 %!error <Invalid call> integral2 (@plus, 1, 2)
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 27923 diff changeset	311 %!error <Invalid call> integral2 (@plus, 1, 2, 3)
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 27923 diff changeset	312 %!error <Invalid call> integral2 (@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: 24102 diff changeset	313 %!error integral2 (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: 24102 diff changeset	314 %!error integral2 (@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: 24102 diff changeset	315 %!error integral2 (@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: 24102 diff changeset	316 %!error integral2 (@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: 24102 diff changeset	317 %!error integral2 (@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: 24102 diff changeset	318 %!error <property PROP must be a string> integral2 (@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: 24102 diff changeset	319 %!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	320 %! integral2 (@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: 24102 diff changeset	321 %!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	322 %! integral2 (@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: 24102 diff changeset	323 %!error <AbsTol value must be.* .= 0> integral2 (@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: 24102 diff changeset	324 %!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	325 %! integral2 (@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: 24102 diff changeset	326 %!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	327 %! integral2 (@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: 24102 diff changeset	328 %!error <RelTol value must be.* .= 0> integral2 (@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: 24102 diff changeset	329 %!error <unrecognized method 'foo'> integral2 (@plus,1,2,3,4, "method", "foo")
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	330 %!error <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	331 %! integral2 (@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: 24102 diff changeset	332 %!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	333 %! integral2 (@plus,1,2,3,4, "Vectorized", {true});
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	334 %!error <unknown property 'foo'> integral2 (@plus, 1, 2, 3, 4, "foo", "bar")
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	335 %!error <YA must be a real scalar> integral2 (@plus, 1, 2, 3i, 4)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	336 %!error <YA must be a real scalar> integral2 (@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: 24102 diff changeset	337 %!error <YB must be a real scalar> integral2 (@plus, 1, 2, 3, 4i)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	338 %!error <YB must be a real scalar> integral2 (@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: 24102 diff changeset	339 %!warning <"iterated" method can not return estimated error>
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	340 %! [q, err] = integral2 (@plus, 0, 0, 0, 0, "method", "iterated");