octave: scripts/general/integral3.m annotate

annotate scripts/general/integral3.m @ 25054:6652d3823428 stable

maint: Update copyright dates in all source files.

author	John W. Eaton <jwe@octave.org>
date	Fri, 30 Mar 2018 09:19:05 -0400
parents	194eb4bd202b
children	07c2c42f457e

rev	line source
25054 6652d3823428 maint: Update copyright dates in all source files. John W. Eaton <jwe@octave.org> parents: 24534 diff changeset	1 ## Copyright (C) 2017-2018 David Bateman
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	2 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	3 ## 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	4 ##
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 24158 diff changeset	5 ## 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	6 ## 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	7 ## 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	8 ## (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	9 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	10 ## 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	11 ## 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	12 ## 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	13 ## 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	14 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	15 ## 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	16 ## 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	17 ## <https://www.gnu.org/licenses/>.
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	18
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	19 ## -- texinfo --
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	20 ## @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	21 ## @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	22 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	23 ## 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	24 ## 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	25 ## @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	26 ## 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	27 ## 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	28 ## 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	29 ## non-rectangular domains.
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 ## @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	32 ## of the function to evaluate. The function @var{f} must be of the form
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	33 ## @math{z = f(x,y)} where @var{x} is a vector and @var{y} is a scalar. It
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	34 ## should return a vector of the same length and orientation as @var{x}.
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	35 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	36 ## 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	37 ## @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	38 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	39 ## @table @code
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	40 ## @item AbsTol
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	41 ## 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	42 ## 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	43 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	44 ## @item RelTol
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	45 ## 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	46 ## 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	47 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	48 ## @item Method
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	49 ## 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	50 ## 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	51 ## @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	52 ## @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	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 Vectorized
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	55 ## 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	56 ## 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	57 ## 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	58 ## @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	59 ## @code{true}.
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	60 ## @end table
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	61 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	62 ## 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	63 ## following is satisfied:
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	64 ## @tex
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	65 ## $$error \leq \max \left( AbsTol, RelTol\cdot\vert q\vert \right)$$
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	66 ## @end tex
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	67 ## @ifnottex
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	68 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	69 ## @example
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	70 ## @group
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	71 ## @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	72 ## @end group
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	73 ## @end example
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 ## @end ifnottex
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	76 ##
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{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	78 ## @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	79 ## integral.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	80 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	81 ## 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	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 ## @example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	84 ## @group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	85 ## @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	86 ## @var{q} = integral3 (@var{f}, 0, 1, 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	87 ## @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	88 ## @end group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	89 ## @end example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	90 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	91 ## For this constant-value integrand, the result is a volume which is just
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	92 ## @code{@var{Length} * @var{Width} x @var{Height}}.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	93 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	94 ## 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	95 ##
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	96 ## @example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	97 ## @group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	98 ## @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	99 ## @var{ymax} = @@(@var{x}) sqrt (1 - @var{x}.^2);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	100 ## @var{zmax} = @@(@var{x}) sqrt (1 - @var{x}.^2 - @var{y}.^2);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	101 ## @var{q} = integral3 (@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	102 ## @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	103 ## @end group
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	104 ## @end example
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	105 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	106 ## 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	107 ## 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	108 ##
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	109 ## 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	110 ## 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	111 ## boundary.
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	112 ##
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	113 ## 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	114 ## 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	115 ## 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	116 ## 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	117 ## 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	118 ## 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	119 ## integration limits.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	120 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	121 ## 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	122 ## @cite{@sc{matlab} program for quadrature in 2D}, Applied Mathematics and
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	123 ## Computation, pp. 266--274, Vol 1, 2008.
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	124 ##
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	125 ## @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	126 ## 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	127 ## @end deftypefn
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	128
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	129 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	130
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	131 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	132 print_usage ();
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	133 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	134
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	135 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	136 print_usage ();
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	137 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	138
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	139 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	140 print_usage ();
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	141 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	142
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	143 ## 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	144 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	145 \|\| (! 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	146 \|\| (! 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	147 \|\| (! 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	148 \|\| (! 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	149
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	150 ## 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	151 ## 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	152 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	153 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	154 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	155 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	156
f9549e90d620 integral3.m: Return single type output if an input is of single type (bug #52243). Rik <rik@octave.org> parents: 24149 diff changeset	157 ## 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	158 if (issingle)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	159 abstol = 1e-5;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	160 reltol = 1e-4;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	161 else
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	162 abstol = 1e-10;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	163 reltol = 1e-6;
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	164 endif
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	165
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	166 method = "auto";
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	167 vectorized = true;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	168 idx = 1;
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	169 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	170 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	171 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	172 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	173 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	174
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	175 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	176 case "abstol"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	177 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	178 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	179 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	180 endif
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	181
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	182 case "reltol"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	183 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	184 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	185 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	186 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	187
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	188 case "method"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	189 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	190 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	191 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	192 endif
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	193
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	194 case "vectorized"
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	195 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	196 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	197 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	198 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	199
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	200 otherwise
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	201 error ("integral3: 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	202
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	203 endswitch
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	204 endwhile
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	205
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	206 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	207 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	208 \|\| (! 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	209 \|\| (! 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	210 \|\| (! 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	211 \|\| (! 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	212 method = "iterated";
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	213 else
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	214 method = "tiled";
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	215 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	216 endif
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	217
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	218 ## 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	219 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	220 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	221 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	222 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	223 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	224 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	225 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	226 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	227 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	228 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	229 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	230 endif
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 ## 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	233 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	234 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	235 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	236 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	237 za = @(x, y) za * ones (size(y));
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	238 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	239 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	240 if (! (isreal (zb) && isscalar (zb)))
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	241 error ("integral3: ZB must be a real scalar or a function")
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	242 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	243 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	244 endif
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	245
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	246 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	247 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	248
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	249 endfunction
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	250
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	251 function q = inner (x, f, ya, yb, za, zb, vectorized, method, abstol, reltol)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	252 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	253 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	254 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	255 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	256 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	257 if (! vectorized)
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	258 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	259 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	260 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	261 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	262 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	263 else
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	264 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	265 "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	266 endif
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	267 endfor
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	268 endfunction
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	269
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	270 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	271 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	272 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	273 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	274 endfor
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	275 endfunction
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	276
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	277
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	278 ## method tests
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	279 %!shared f
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	280 %! 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	281
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	282 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1), 0.125, 1e-10);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	283 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1, "method", "tiled"), 0.125, 1e-10);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	284 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1, "method", "iterated"), 0.125, 1e-10);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	285 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1, "method", "auto"), 0.125, 1e-10);
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	286
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	287 ## vectorized = false test
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	288 %!test
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	289 %! 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	290 %! 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	291
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	292 ## tolerance tests
24149 1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	293 %!test
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	294 %! 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	295 %!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	296 %!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	297 %!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	298 %! 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	299
2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	300 ## 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	301 ## 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	302 %!test
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	303 %! 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	304 %! ymax = @(x) 1 - x;
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	305 %! zmax = @(x, y) 1 - x - y;
1a3229a2f1ab integral2.m, integral3.m: Clean up BIST tests. Rik <rik@octave.org> parents: 24148 diff changeset	306 %! assert (integral3 (f, 0, 1, 0, ymax, 0, zmax, "method", "tiled"), 0.25, 1e-6);
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	307
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	308 ## 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	309 %!error integral3
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	310 %!error integral3 (@plus)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	311 %!error integral3 (@plus, 1)
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	312 %!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	313 %!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	314 %!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	315 %!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	316 %!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	317 %!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	318 %!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	319 %!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	320 %!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	321 %!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	322 %!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	323 %! 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	324 %!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	325 %! 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	326 %!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	327 %! 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	328 %!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	329 %! 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	330 %!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	331 %! 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	332 %!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	333 %! 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	334 %!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	335 %! 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	336 %!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	337 %! 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	338 %!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	339 %! 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	340 %!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	341 %! 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	342 %!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	343 %! 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	344 %!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	345 %!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	346 %!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	347 %!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	348 %!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	349 %!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	350 %!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	351 %!error <ZB must be a real scalar> integral3 (@plus, 1, 2, 3, 4, 5, [6 6])