scripts/general/dblquad.m

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author	John W. Eaton <jwe@octave.org>
date	Tue, 28 Dec 2021 18:22:40 -0500
parents	168da23530b4
children	5d3faba0342e
rev	line source
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	1 ########################################################################
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	2 ##
30564 796f54d4ddbf update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 30400 diff changeset	3 ## Copyright (C) 2008-2022 The Octave Project Developers
27918 b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 26376 diff changeset	4 ##
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	5 ## See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	6 ## distribution or <https://octave.org/copyright/>.
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	7 ##
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	8 ## This file is part of Octave.
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	9 ##
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 24102 diff changeset	10 ## Octave is free software: you can redistribute it and/or modify it
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	11 ## under the terms of the GNU General Public License as published by
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 24102 diff changeset	12 ## the Free Software Foundation, either version 3 of the License, or
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	13 ## (at your option) any later version.
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	14 ##
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	15 ## Octave is distributed in the hope that it will be useful, but
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	18 ## GNU General Public License for more details.
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	19 ##
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	20 ## You should have received a copy of the GNU General Public License
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	21 ## along with Octave; see the file COPYING. If not, see
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 24102 diff changeset	22 ## <https://www.gnu.org/licenses/>.
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	23 ##
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	24 ########################################################################
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	25
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	26 ## -- texinfo --
20852 516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20158 diff changeset	27 ## @deftypefn {} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb})
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20158 diff changeset	28 ## @deftypefnx {} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol})
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20158 diff changeset	29 ## @deftypefnx {} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol}, @var{quadf})
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20158 diff changeset	30 ## @deftypefnx {} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol}, @var{quadf}, @dots{})
12612 16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	31 ## Numerically evaluate the double integral of @var{f}.
20158 7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	32 ##
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	33 ## @var{f} is a function handle, inline function, or string containing the name
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	34 ## of the function to evaluate. The function @var{f} must have the form
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	35 ## @math{z = f(x,y)} where @var{x} is a vector and @var{y} is a scalar. It
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	36 ## should return a vector of the same length and orientation as @var{x}.
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	37 ##
12612 16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	38 ## @var{xa}, @var{ya} and @var{xb}, @var{yb} are the lower and upper limits of
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	39 ## integration for x and y respectively. The underlying integrator determines
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	40 ## whether infinite bounds are accepted.
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	41 ##
12642 f96b9b9f141b doc: Periodic grammarcheck and spellcheck of documentation. Rik <octave@nomad.inbox5.com> parents: 12612 diff changeset	42 ## The optional argument @var{tol} defines the absolute tolerance used to
24545 ba8b828ee4f2 doc: Replace @math{1e^{XXX}} sequences with raw 1eXXX (bug #52827). Rik <rik@octave.org> parents: 23219 diff changeset	43 ## integrate each sub-integral. The default value is 1e-6.
12612 16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	44 ##
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	45 ## The optional argument @var{quadf} specifies which underlying integrator
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	46 ## function to use. Any choice but @code{quad} is available and the default
12616 eb4afb6a1a51 dblquad.m,triplequad.m: Switch to quadcc as default integrator. Rik <octave@nomad.inbox5.com> parents: 12612 diff changeset	47 ## is @code{quadcc}.
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	48 ##
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	49 ## Additional arguments, are passed directly to @var{f}. To use the default
17281 bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted. Rik <rik@octave.org> parents: 14868 diff changeset	50 ## value for @var{tol} or @var{quadf} one may pass @qcode{':'} or an empty
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted. Rik <rik@octave.org> parents: 14868 diff changeset	51 ## matrix ([]).
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 23220 diff changeset	52 ## @seealso{integral2, integral3, triplequad, quad, quadv, quadl, quadgk,
c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 23220 diff changeset	53 ## quadcc, trapz}
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	54 ## @end deftypefn
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	55
12616 eb4afb6a1a51 dblquad.m,triplequad.m: Switch to quadcc as default integrator. Rik <octave@nomad.inbox5.com> parents: 12612 diff changeset	56 function q = dblquad (f, xa, xb, ya, yb, tol = 1e-6, quadf = @quadcc, varargin)
eb4afb6a1a51 dblquad.m,triplequad.m: Switch to quadcc as default integrator. Rik <octave@nomad.inbox5.com> parents: 12612 diff changeset	57
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	58 if (nargin < 5)
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	59 print_usage ();
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	60 endif
12616 eb4afb6a1a51 dblquad.m,triplequad.m: Switch to quadcc as default integrator. Rik <octave@nomad.inbox5.com> parents: 12612 diff changeset	61 if (isempty (tol))
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11562 diff changeset	62 tol = 1e-6;
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	63 endif
12616 eb4afb6a1a51 dblquad.m,triplequad.m: Switch to quadcc as default integrator. Rik <octave@nomad.inbox5.com> parents: 12612 diff changeset	64 if (isempty (quadf))
eb4afb6a1a51 dblquad.m,triplequad.m: Switch to quadcc as default integrator. Rik <octave@nomad.inbox5.com> parents: 12612 diff changeset	65 quadf = @quadcc;
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	66 endif
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	67
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	68 inner = @__dblquad_inner__;
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	69 if (ischar (f))
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	70 f = @(x,y) feval (f, x, y, varargin{:});
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	71 varargin = {};
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	72 endif
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	73
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7771 diff changeset	74 q = feval (quadf, @(y) inner (y, f, xa, xb, tol, quadf,
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	75 varargin{:}), ya, yb, tol);
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 20852 diff changeset	76
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	77 endfunction
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	78
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7771 diff changeset	79 function q = __dblquad_inner__ (y, f, xa, xb, tol, quadf, varargin)
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	80 q = zeros (size (y));
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	81 for i = 1 : length (y)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7771 diff changeset	82 q(i) = feval (quadf, @(x) f(x, y(i), varargin{:}), xa, xb, tol);
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	83 endfor
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	84 endfunction
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	85
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	86
19833 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19697 diff changeset	87 ## Nasty integrand to show quadcc off
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	88 %!assert (dblquad (@(x,y) 1 ./ (x+y), 0, 1, 0, 1), 2*log (2), 1e-6)
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	89
30330 01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599) Rik <rik@octave.org> parents: 29358 diff changeset	90 %!assert (dblquad (@(x,y) exp (-x.^2 - y.^2) , -1, 1, -1, 1, 1e-6, @quadgk),
01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599) Rik <rik@octave.org> parents: 29358 diff changeset	91 %! pi * erf (1).^2, 1e-6)
01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599) Rik <rik@octave.org> parents: 29358 diff changeset	92 %!assert (dblquad (@(x,y) exp (-x.^2 - y.^2) , -1, 1, -1, 1, 1e-6, @quadl),
01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599) Rik <rik@octave.org> parents: 29358 diff changeset	93 %! pi * erf (1).^2, 1e-6)
30400 168da23530b4 maint: strip trailing spaces from code base. Rik <rik@octave.org> parents: 30330 diff changeset	94 %!assert (dblquad (@(x,y) exp (-x.^2 - y.^2) , -1, 1, -1, 1, 1e-6, @quadv),
30330 01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599) Rik <rik@octave.org> parents: 29358 diff changeset	95 %! pi * erf (1).^2, 1e-6)