Mercurial > octave
view scripts/general/quadl.m @ 31063:451fb63a10a0
update integral to call quadgk for 'ArrayValued' integrations (bug #62468)
* integral.m: Modify integrator selection so that calls with ‘ArrayValued’ go
to quadgk instead of quadv. Remove error checks for previously incompatible
parameter combinations. Update docstring to remove mention of quadv, point
'ArrayValued' reference to quadgk, change returned error parameter description
to match current behavior, and remove parameter incompatibility note. Add BIST
to verify combined parameter functionality, and change BISTs checking quadv
err parameter.
* quadgk.m: Correct parameter name in docstring.
* NEWS.8.md: Under General Improvements add note about quadgk now accepting
'ArrayValued' parameter and update integral improvement description of
optional returned error parameter. Under Matlab Compatibility add note about
integral now accepting all parameter combinations.
author | Nicholas R. Jankowski <jankowski.nicholas@gmail.com> |
---|---|
date | Thu, 02 Jun 2022 19:56:15 -0400 |
parents | e1788b1a315f |
children | 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 1998-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## This file is part of Octave. ## ## Octave is free software: you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {@var{q} =} quadl (@var{f}, @var{a}, @var{b}) ## @deftypefnx {} {@var{q} =} quadl (@var{f}, @var{a}, @var{b}, @var{tol}) ## @deftypefnx {} {@var{q} =} quadl (@var{f}, @var{a}, @var{b}, @var{tol}, @var{trace}) ## @deftypefnx {} {@var{q} =} quadl (@var{f}, @var{a}, @var{b}, @var{tol}, @var{trace}, @var{p1}, @var{p2}, @dots{}) ## @deftypefnx {} {[@var{q}, @var{nfev}] =} quadl (@dots{}) ## ## Numerically evaluate the integral of @var{f} from @var{a} to @var{b} using ## an adaptive @nospell{Lobatto} rule. ## ## @var{f} is a function handle, inline function, or string containing the name ## of the function to evaluate. The function @var{f} must be vectorized and ## return a vector of output values when given a vector of input values. ## ## @var{a} and @var{b} are the lower and upper limits of integration. Both ## limits must be finite. ## ## The optional argument @var{tol} defines the absolute tolerance with which ## to perform the integration. The default value is 1e-6. ## ## The algorithm used by @code{quadl} involves recursively subdividing the ## integration interval. If @var{trace} is defined then for each subinterval ## display: (1) the total number of function evaluations, (2) the left end of ## the subinterval, (3) the length of the subinterval, (4) the approximation of ## the integral over the subinterval. ## ## Additional arguments @var{p1}, etc., are passed directly to the function ## @var{f}. To use default values for @var{tol} and @var{trace}, one may pass ## empty matrices ([]). ## ## The result of the integration is returned in @var{q}. ## ## The optional output @var{nfev} indicates the total number of function ## evaluations performed. ## ## Reference: @nospell{W. Gander and W. Gautschi}, @cite{Adaptive Quadrature - ## Revisited}, BIT Vol.@: 40, No.@: 1, March 2000, pp.@: 84--101. ## @url{https://www.inf.ethz.ch/personal/gander/} ## @seealso{quad, quadv, quadgk, quadcc, trapz, dblquad, triplequad, integral, ## integral2, integral3} ## @end deftypefn ## Original Author: Walter Gautschi ## Date: 08/03/98 ## Reference: Gander, Computermathematik, Birkhaeuser, 1992. ## 2003-08-05 Shai Ayal ## * permission from author to release as GPL function [q, nfev] = quadl (f, a, b, tol = [], trace = false, varargin) if (nargin < 3) print_usage (); endif if (isa (a, "single") || isa (b, "single")) eps = eps ("single"); else eps = eps ("double"); endif if (isempty (tol)) tol = 1e-6; elseif (! isscalar (tol) || tol < 0) error ("quadl: TOL must be a scalar >=0"); elseif (tol < eps) warning ("quadl: TOL specified is smaller than machine precision, using %g", tol); tol = eps; endif if (isempty (trace)) trace = false; endif y = feval (f, [a, b], varargin{:}); nfev = 1; fa = y(1); fb = y(2); h = b - a; [q, nfev, hmin] = adaptlobstp (f, a, b, fa, fb, Inf, nfev, abs (h), tol, trace, varargin{:}); if (nfev > 10_000) warning ("quadl: maximum iteration count reached -- possible singular integral"); elseif (any (! isfinite (q(:)))) warning ("quadl: infinite or NaN function evaluations were returned"); elseif (hmin < (b - a) * eps) warning ("quadl: minimum step size reached -- possible singular integral"); endif endfunction function [q, nfev, hmin] = adaptlobstp (f, a, b, fa, fb, q0, nfev, hmin, tol, trace, varargin) persistent alpha = sqrt (2/3); persistent beta = 1 / sqrt (5); if (nfev > 10_000) q = q0; return; endif h = (b - a) / 2; m = (a + b) / 2; mll = m - alpha*h; ml = m - beta*h; mr = m + beta*h; mrr = m + alpha*h; x = [mll, ml, m, mr, mrr]; y = feval (f, x, varargin{:}); nfev += 1; fmll = y(1); fml = y(2); fm = y(3); fmr = y(4); fmrr = y(5); i2 = (h/6)*(fa + fb + 5*(fml+fmr)); i1 = (h/1470)*(77*(fa+fb) + 432*(fmll+fmrr) + 625*(fml+fmr) + 672*fm); if (abs (b - a) < hmin) hmin = abs (b - a); endif if (trace) disp ([nfev, a, b-a, i1]); endif ## Force at least one adaptive step (nfev > 2 test). if ((abs (i1-i2) < tol || mll <= a || b <= mrr) && nfev > 2) q = i1; else q = zeros (6, 1, class (x)); [q(1), nfev, hmin] = adaptlobstp (f, a , mll, fa , fmll, q0/6, nfev, hmin, tol, trace, varargin{:}); [q(2), nfev, hmin] = adaptlobstp (f, mll, ml , fmll, fml , q0/6, nfev, hmin, tol, trace, varargin{:}); [q(3), nfev, hmin] = adaptlobstp (f, ml , m , fml , fm , q0/6, nfev, hmin, tol, trace, varargin{:}); [q(4), nfev, hmin] = adaptlobstp (f, m , mr , fm , fmr , q0/6, nfev, hmin, tol, trace, varargin{:}); [q(5), nfev, hmin] = adaptlobstp (f, mr , mrr, fmr , fmrr, q0/6, nfev, hmin, tol, trace, varargin{:}); [q(6), nfev, hmin] = adaptlobstp (f, mrr, b , fmrr, fb , q0/6, nfev, hmin, tol, trace, varargin{:}); q = sum (q); endif endfunction ## basic functionality %!assert (quadl (@(x) sin (x), 0, pi), 2, 1e-6) ## the values here are very high so it may be unavoidable that this fails %!assert (quadl (@(x) sin (3*x).*cosh (x).*sinh (x),10,15, 1e-3), %! 2.588424538641647e+10, 1e-3) ## extra parameters %!assert (quadl (@(x,a,b) sin (a + b*x), 0, 1, [], [], 2, 3), %! cos (2)/3 - cos (5)/3, 1e-6) ## test different tolerances. %!test %! [q, nfev1] = quadl (@(x) sin (2 + 3*x).^2, 0, 10, 0.5, []); %! assert (q, (60 + sin (4) - sin (64))/12, 0.5); %! [q, nfev2] = quadl (@(x) sin (2 + 3*x).^2, 0, 10, 0.1, []); %! assert (q, (60 + sin (4) - sin (64))/12, 0.1); %! assert (nfev2 > nfev1); %!test # test single input/output %! assert (class (quadl (@sin, 0, 1)), "double"); %! assert (class (quadl (@sin, single (0), 1)), "single"); %! assert (class (quadl (@sin, 0, single (1))), "single"); ## Test input validation %!error <Invalid call> quadl () %!error <Invalid call> quadl (@sin) %!error <Invalid call> quadl (@sin,1) %!error <TOL must be a scalar> quadl (@sin,0,1, ones (2,2)) %!error <TOL must be .* .=0> quadl (@sin,0,1, -1)