octave: scripts/general/integral3.m annotate

annotate scripts/general/integral3.m @ 24158:f9549e90d620

integral3.m: Return single type output if an input is of single type (bug #52243). * integral3.m: Check for any limit of integration (x, y, or z) being of type single. If found, cast xa, xb limits of integration to single. This will signal to downstream quadrature routines to use single variables.

author	Rik <rik@octave.org>
date	Wed, 18 Oct 2017 21:59:38 -0700
parents	1a3229a2f1ab
children	194eb4bd202b

rev	line source
24148 2e64bed0bb3a Updated integral2.m and integral3.m and added quad2d (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24102 diff changeset	1 ## Copyright (C) 2017 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 ##
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
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
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or
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
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: diff changeset	17 ## <http://www.gnu.org/licenses/>.
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])