octave: scripts/general/quadl.m annotate

annotate scripts/general/quadl.m @ 30893:e1788b1a315f

maint: Use "fcn" as preferred abbreviation for "function" in m-files. * accumarray.m, accumdim.m, quadl.m, quadv.m, randi.m, structfun.m, __is_function__.m, uigetfile.m, uimenu.m, uiputfile.m, doc_cache_create.m, colorspace_conversion_input_check.m, imageIO.m, argnames.m, vectorize.m, vectorize.m, normest1.m, inputname.m, nthargout.m, display_info_file.m, decic.m, ode15i.m, ode15s.m, ode23.m, ode23s.m, ode45.m, odeset.m, check_default_input.m, integrate_adaptive.m, ode_event_handler.m, runge_kutta_23.m, runge_kutta_23s.m, runge_kutta_45_dorpri.m, runge_kutta_interpolate.m, starting_stepsize.m, __all_opts__.m, fminbnd.m, fminsearch.m, fminunc.m, fsolve.m, fzero.m, sqp.m, fplot.m, plotyy.m, __bar__.m, __ezplot__.m, flat_entry.html, profexport.m, movfun.m, bicg.m, bicgstab.m, cgs.m, eigs.m, gmres.m, pcg.m, __alltohandles__.m, __sprand__.m, qmr.m, tfqmr.m, dump_demos.m: Replace "func", "fun", "fn" in documentation and variable names with "fcn".

author	Rik <rik@octave.org>
date	Mon, 04 Apr 2022 18:14:56 -0700
parents	796f54d4ddbf
children	597f3ee61a48

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: 30379 diff changeset	3 ## Copyright (C) 1998-2022 The Octave Project Developers
27918 b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 27800 diff changeset	4 ##
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	5 ## See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	6 ## distribution or <https://octave.org/copyright/>.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	7 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	8 ## This file is part of Octave.
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	9 ##
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 24208 diff changeset	10 ## Octave is free software: you can redistribute it and/or modify it
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	11 ## under the terms of the GNU General Public License as published by
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 24208 diff changeset	12 ## the Free Software Foundation, either version 3 of the License, or
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	13 ## (at your option) any later version.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	14 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	15 ## Octave is distributed in the hope that it will be useful, but
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe 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.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	19 ##
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	20 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 5838 diff changeset	21 ## along with Octave; see the file COPYING. If not, see
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 24208 diff changeset	22 ## <https://www.gnu.org/licenses/>.
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	23 ##
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	24 ########################################################################
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	25
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe 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: 20689 diff changeset	27 ## @deftypefn {} {@var{q} =} quadl (@var{f}, @var{a}, @var{b})
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20689 diff changeset	28 ## @deftypefnx {} {@var{q} =} quadl (@var{f}, @var{a}, @var{b}, @var{tol})
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20689 diff changeset	29 ## @deftypefnx {} {@var{q} =} quadl (@var{f}, @var{a}, @var{b}, @var{tol}, @var{trace})
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20689 diff changeset	30 ## @deftypefnx {} {@var{q} =} quadl (@var{f}, @var{a}, @var{b}, @var{tol}, @var{trace}, @var{p1}, @var{p2}, @dots{})
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	31 ## @deftypefnx {} {[@var{q}, @var{nfev}] =} quadl (@dots{})
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	32 ##
20158 7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	33 ## Numerically evaluate the integral of @var{f} from @var{a} to @var{b} using
25003 2365c2661b3c doc: Spellcheck documentation ahead of 4.4 release. Rik <rik@octave.org> parents: 24546 diff changeset	34 ## an adaptive @nospell{Lobatto} rule.
20158 7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	35 ##
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	36 ## @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: 19697 diff changeset	37 ## of the function to evaluate. The function @var{f} must be vectorized and
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	38 ## return a vector of output values when given a vector of input values.
12612 16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	39 ##
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	40 ## @var{a} and @var{b} are the lower and upper limits of integration. Both
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	41 ## limits must be finite.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	42 ##
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	43 ## The optional argument @var{tol} defines the absolute tolerance with which
24545 ba8b828ee4f2 doc: Replace @math{1e^{XXX}} sequences with raw 1eXXX (bug #52827). Rik <rik@octave.org> parents: 23219 diff changeset	44 ## to perform the integration. The default value is 1e-6.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	45 ##
12612 16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	46 ## The algorithm used by @code{quadl} involves recursively subdividing the
20158 7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	47 ## integration interval. If @var{trace} is defined then for each subinterval
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	48 ## display: (1) the total number of function evaluations, (2) the left end of
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	49 ## the subinterval, (3) the length of the subinterval, (4) the approximation of
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	50 ## the integral over the subinterval.
12612 16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	51 ##
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	52 ## Additional arguments @var{p1}, etc., are passed directly to the function
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	53 ## @var{f}. To use default values for @var{tol} and @var{trace}, one may pass
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	54 ## empty matrices ([]).
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	55 ##
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	56 ## The result of the integration is returned in @var{q}.
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	57 ##
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	58 ## The optional output @var{nfev} indicates the total number of function
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	59 ## evaluations performed.
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	60 ##
19040 0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 17744 diff changeset	61 ## Reference: @nospell{W. Gander and W. Gautschi}, @cite{Adaptive Quadrature -
27800 5a6a19a4e3da doc: Use Texinfo non-sentence ending periods in citations. Rik <rik@octave.org> parents: 26376 diff changeset	62 ## Revisited}, BIT Vol.@: 40, No.@: 1, March 2000, pp.@: 84--101.
25143 13fd0610480f doc: Use https whenever possible in @url entries. Rik <rik@octave.org> parents: 25054 diff changeset	63 ## @url{https://www.inf.ethz.ch/personal/gander/}
24208 eec262017c6a maint: Strip trailing whitespace from source files. John W. Eaton <jwe@octave.org> parents: 24156 diff changeset	64 ## @seealso{quad, quadv, quadgk, quadcc, trapz, dblquad, triplequad, integral,
24102 c723faa56ab4 Add missing functions integral2.m and integral3.m (bug #52074). Nicholas R. Jankowski <jankowskin@asme.org> parents: 24066 diff changeset	65 ## integral2, integral3}
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	66 ## @end deftypefn
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	67
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	68 ## Original Author: Walter Gautschi
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	69 ## Date: 08/03/98
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	70 ## Reference: Gander, Computermathematik, Birkhaeuser, 1992.
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	71
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	72 ## 2003-08-05 Shai Ayal
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	73 ## * permission from author to release as GPL
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	74
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	75 function [q, nfev] = quadl (f, a, b, tol = [], trace = false, varargin)
13008 85dac13a911b quadl.m: Fix integration with large error tolerances (Bug #33792) Rik <octave@nomad.inbox5.com> parents: 12802 diff changeset	76
85dac13a911b quadl.m: Fix integration with large error tolerances (Bug #33792) Rik <octave@nomad.inbox5.com> parents: 12802 diff changeset	77 if (nargin < 3)
85dac13a911b quadl.m: Fix integration with large error tolerances (Bug #33792) Rik <octave@nomad.inbox5.com> parents: 12802 diff changeset	78 print_usage ();
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	79 endif
13008 85dac13a911b quadl.m: Fix integration with large error tolerances (Bug #33792) Rik <octave@nomad.inbox5.com> parents: 12802 diff changeset	80
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	81 if (isa (a, "single") \|\| isa (b, "single"))
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	82 eps = eps ("single");
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	83 else
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	84 eps = eps ("double");
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7017 diff changeset	85 endif
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	86 if (isempty (tol))
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	87 tol = 1e-6;
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	88 elseif (! isscalar (tol) \|\| tol < 0)
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	89 error ("quadl: TOL must be a scalar >=0");
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	90 elseif (tol < eps)
24066 d9b0d8ae734f Update tolerances in BIST tests for quad functions. Rik <rik@octave.org> parents: 23220 diff changeset	91 warning ("quadl: TOL specified is smaller than machine precision, using %g",
d9b0d8ae734f Update tolerances in BIST tests for quad functions. Rik <rik@octave.org> parents: 23220 diff changeset	92 tol);
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	93 tol = eps;
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	94 endif
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	95 if (isempty (trace))
13008 85dac13a911b quadl.m: Fix integration with large error tolerances (Bug #33792) Rik <octave@nomad.inbox5.com> parents: 12802 diff changeset	96 trace = false;
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	97 endif
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	98
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	99 y = feval (f, [a, b], varargin{:});
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	100 nfev = 1;
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	101
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11562 diff changeset	102 fa = y(1);
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	103 fb = y(2);
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	104
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	105 h = b - a;
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	106
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	107 [q, nfev, hmin] = adaptlobstp (f, a, b, fa, fb, Inf, nfev, abs (h),
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	108 tol, trace, varargin{:});
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	109
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	110 if (nfev > 10_000)
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	111 warning ("quadl: maximum iteration count reached -- possible singular integral");
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	112 elseif (any (! isfinite (q(:))))
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	113 warning ("quadl: infinite or NaN function evaluations were returned");
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	114 elseif (hmin < (b - a) * eps)
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	115 warning ("quadl: minimum step size reached -- possible singular integral");
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	116 endif
13008 85dac13a911b quadl.m: Fix integration with large error tolerances (Bug #33792) Rik <octave@nomad.inbox5.com> parents: 12802 diff changeset	117
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	118 endfunction
55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	119
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	120 function [q, nfev, hmin] = adaptlobstp (f, a, b, fa, fb, q0, nfev, hmin,
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	121 tol, trace, varargin)
30379 363fb10055df maint: Style check m-files ahead of 7.1 release. Rik <rik@octave.org> parents: 29359 diff changeset	122
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	123 persistent alpha = sqrt (2/3);
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	124 persistent beta = 1 / sqrt (5);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	125
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	126 if (nfev > 10_000)
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	127 q = q0;
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	128 return;
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	129 endif
13008 85dac13a911b quadl.m: Fix integration with large error tolerances (Bug #33792) Rik <octave@nomad.inbox5.com> parents: 12802 diff changeset	130
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	131 h = (b - a) / 2;
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	132 m = (a + b) / 2;
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	133 mll = m - alpha*h;
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	134 ml = m - beta*h;
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	135 mr = m + beta*h;
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	136 mrr = m + alpha*h;
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	137 x = [mll, ml, m, mr, mrr];
13008 85dac13a911b quadl.m: Fix integration with large error tolerances (Bug #33792) Rik <octave@nomad.inbox5.com> parents: 12802 diff changeset	138 y = feval (f, x, varargin{:});
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	139 nfev += 1;
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11562 diff changeset	140 fmll = y(1);
13008 85dac13a911b quadl.m: Fix integration with large error tolerances (Bug #33792) Rik <octave@nomad.inbox5.com> parents: 12802 diff changeset	141 fml = y(2);
85dac13a911b quadl.m: Fix integration with large error tolerances (Bug #33792) Rik <octave@nomad.inbox5.com> parents: 12802 diff changeset	142 fm = y(3);
85dac13a911b quadl.m: Fix integration with large error tolerances (Bug #33792) Rik <octave@nomad.inbox5.com> parents: 12802 diff changeset	143 fmr = y(4);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	144 fmrr = y(5);
5838 376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	145 i2 = (h/6)(fa + fb + 5(fml+fmr));
376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe] jwe parents: 5837 diff changeset	146 i1 = (h/1470)(77(fa+fb) + 432(fmll+fmrr) + 625(fml+fmr) + 672*fm);
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	147
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	148 if (abs (b - a) < hmin)
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	149 hmin = abs (b - a);
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	150 endif
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	151
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	152 if (trace)
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	153 disp ([nfev, a, b-a, i1]);
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	154 endif
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	155
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	156 ## Force at least one adaptive step (nfev > 2 test).
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	157 if ((abs (i1-i2) < tol \|\| mll <= a \|\| b <= mrr) && nfev > 2)
12612 16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	158 q = i1;
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	159 else
24156 ce435b70fd94 quadl.m: Return single output when inputs are single (bug #52243). Rik <rik@octave.org> parents: 24102 diff changeset	160 q = zeros (6, 1, class (x));
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	161 [q(1), nfev, hmin] = adaptlobstp (f, a , mll, fa , fmll, q0/6, nfev, hmin,
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	162 tol, trace, varargin{:});
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	163 [q(2), nfev, hmin] = adaptlobstp (f, mll, ml , fmll, fml , q0/6, nfev, hmin,
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	164 tol, trace, varargin{:});
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	165 [q(3), nfev, hmin] = adaptlobstp (f, ml , m , fml , fm , q0/6, nfev, hmin,
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	166 tol, trace, varargin{:});
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	167 [q(4), nfev, hmin] = adaptlobstp (f, m , mr , fm , fmr , q0/6, nfev, hmin,
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	168 tol, trace, varargin{:});
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	169 [q(5), nfev, hmin] = adaptlobstp (f, mr , mrr, fmr , fmrr, q0/6, nfev, hmin,
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	170 tol, trace, varargin{:});
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	171 [q(6), nfev, hmin] = adaptlobstp (f, mrr, b , fmrr, fb , q0/6, nfev, hmin,
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	172 tol, trace, varargin{:});
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	173 q = sum (q);
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	174 endif
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	175
5837 55404f3b0da1 [project @ 2006-06-01 19:05:31 by jwe] jwe parents: diff changeset	176 endfunction
12802 412882f498b4 codesprint: Wrote 5 tests for quadl.m David Wells <drwells@vt.edu> parents: 12642 diff changeset	177
412882f498b4 codesprint: Wrote 5 tests for quadl.m David Wells <drwells@vt.edu> parents: 12642 diff changeset	178
412882f498b4 codesprint: Wrote 5 tests for quadl.m David Wells <drwells@vt.edu> parents: 12642 diff changeset	179 ## basic functionality
24066 d9b0d8ae734f Update tolerances in BIST tests for quad functions. Rik <rik@octave.org> parents: 23220 diff changeset	180 %!assert (quadl (@(x) sin (x), 0, pi), 2, 1e-6)
12802 412882f498b4 codesprint: Wrote 5 tests for quadl.m David Wells <drwells@vt.edu> parents: 12642 diff changeset	181
412882f498b4 codesprint: Wrote 5 tests for quadl.m David Wells <drwells@vt.edu> parents: 12642 diff changeset	182 ## the values here are very high so it may be unavoidable that this fails
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	183 %!assert (quadl (@(x) sin (3x).cosh (x).*sinh (x),10,15, 1e-3),
655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	184 %! 2.588424538641647e+10, 1e-3)
12802 412882f498b4 codesprint: Wrote 5 tests for quadl.m David Wells <drwells@vt.edu> parents: 12642 diff changeset	185
412882f498b4 codesprint: Wrote 5 tests for quadl.m David Wells <drwells@vt.edu> parents: 12642 diff changeset	186 ## extra parameters
412882f498b4 codesprint: Wrote 5 tests for quadl.m David Wells <drwells@vt.edu> parents: 12642 diff changeset	187 %!assert (quadl (@(x,a,b) sin (a + b*x), 0, 1, [], [], 2, 3),
28912 0de38a6ef693 maint: Use Octave convention of space after function name in scripts dir. Rik <rik@octave.org> parents: 28896 diff changeset	188 %! cos (2)/3 - cos (5)/3, 1e-6)
12802 412882f498b4 codesprint: Wrote 5 tests for quadl.m David Wells <drwells@vt.edu> parents: 12642 diff changeset	189
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13008 diff changeset	190 ## test different tolerances.
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	191 %!test
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	192 %! [q, nfev1] = quadl (@(x) sin (2 + 3*x).^2, 0, 10, 0.5, []);
28912 0de38a6ef693 maint: Use Octave convention of space after function name in scripts dir. Rik <rik@octave.org> parents: 28896 diff changeset	193 %! assert (q, (60 + sin (4) - sin (64))/12, 0.5);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	194 %! [q, nfev2] = quadl (@(x) sin (2 + 3*x).^2, 0, 10, 0.1, []);
28912 0de38a6ef693 maint: Use Octave convention of space after function name in scripts dir. Rik <rik@octave.org> parents: 28896 diff changeset	195 %! assert (q, (60 + sin (4) - sin (64))/12, 0.1);
30893 e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files. Rik <rik@octave.org> parents: 30564 diff changeset	196 %! assert (nfev2 > nfev1);
12802 412882f498b4 codesprint: Wrote 5 tests for quadl.m David Wells <drwells@vt.edu> parents: 12642 diff changeset	197
24156 ce435b70fd94 quadl.m: Return single output when inputs are single (bug #52243). Rik <rik@octave.org> parents: 24102 diff changeset	198 %!test # test single input/output
ce435b70fd94 quadl.m: Return single output when inputs are single (bug #52243). Rik <rik@octave.org> parents: 24102 diff changeset	199 %! assert (class (quadl (@sin, 0, 1)), "double");
ce435b70fd94 quadl.m: Return single output when inputs are single (bug #52243). Rik <rik@octave.org> parents: 24102 diff changeset	200 %! assert (class (quadl (@sin, single (0), 1)), "single");
ce435b70fd94 quadl.m: Return single output when inputs are single (bug #52243). Rik <rik@octave.org> parents: 24102 diff changeset	201 %! assert (class (quadl (@sin, 0, single (1))), "single");
ce435b70fd94 quadl.m: Return single output when inputs are single (bug #52243). Rik <rik@octave.org> parents: 24102 diff changeset	202
20689 655816377845 quadl.m: Overhal function and switch to absolute tolerance. Rik <rik@octave.org> parents: 20231 diff changeset	203 ## Test input validation
28896 90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 27923 diff changeset	204 %!error <Invalid call> quadl ()
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 27923 diff changeset	205 %!error <Invalid call> quadl (@sin)
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 27923 diff changeset	206 %!error <Invalid call> quadl (@sin,1)
24066 d9b0d8ae734f Update tolerances in BIST tests for quad functions. Rik <rik@octave.org> parents: 23220 diff changeset	207 %!error <TOL must be a scalar> quadl (@sin,0,1, ones (2,2))
d9b0d8ae734f Update tolerances in BIST tests for quad functions. Rik <rik@octave.org> parents: 23220 diff changeset	208 %!error <TOL must be .* .=0> quadl (@sin,0,1, -1)

Mercurial > octave

annotate scripts/general/quadl.m @ 30893:e1788b1a315f