Mercurial > octave
view scripts/general/trapz.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 | 796f54d4ddbf |
children | 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 2000-2022 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} =} trapz (@var{y}) ## @deftypefnx {} {@var{q} =} trapz (@var{x}, @var{y}) ## @deftypefnx {} {@var{q} =} trapz (@dots{}, @var{dim}) ## ## Numerically evaluate the integral of points @var{y} using the trapezoidal ## method. ## ## @w{@code{trapz (@var{y})}} computes the integral of @var{y} along the first ## non-singleton dimension. When the argument @var{x} is omitted an equally ## spaced @var{x} vector with unit spacing (1) is assumed. ## @code{trapz (@var{x}, @var{y})} evaluates the integral with respect to the ## spacing in @var{x} and the values in @var{y}. This is useful if the points ## in @var{y} have been sampled unevenly. ## ## If the optional @var{dim} argument is given, operate along this dimension. ## ## Application Note: If @var{x} is not specified then unit spacing will be ## used. To scale the integral to the correct value you must multiply by the ## actual spacing value (deltaX). As an example, the integral of @math{x^3} ## over the range [0, 1] is @math{x^4/4} or 0.25. The following code uses ## @code{trapz} to calculate the integral in three different ways. ## ## @example ## @group ## x = 0:0.1:1; ## y = x.^3; ## ## No scaling ## q = trapz (y) ## @result{} q = 2.5250 ## ## Approximation to integral by scaling ## q * 0.1 ## @result{} 0.25250 ## ## Same result by specifying @var{x} ## trapz (x, y) ## @result{} 0.25250 ## @end group ## @end example ## ## @seealso{cumtrapz} ## @end deftypefn function z = trapz (x, y, dim) if (nargin < 1) print_usage (); endif have_xy = have_dim = false; if (nargin == 3) have_xy = true; have_dim = true; elseif (nargin == 2) if (isscalar (y) && ! isscalar (x)) have_dim = true; dim = y; else have_xy = true; endif endif if (have_xy) nd = ndims (y); sz = size (y); else nd = ndims (x); sz = size (x); endif if (! have_dim) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (!(isscalar (dim) && dim == fix (dim)) || !(1 <= dim && dim <= nd)) error ("trapz: DIM must be an integer and a valid dimension"); endif endif n = sz(dim); idx1 = idx2 = {':'}(ones (nd, 1)); # repmat ({':'}, [nd, 1]), but faster idx1{dim} = 2 : n; idx2{dim} = 1 : (n - 1); if (! have_xy) z = 0.5 * sum (x(idx1{:}) + x(idx2{:}), dim); elseif (isscalar (x)) z = x * 0.5 * sum (y(idx1{:}) + y(idx2{:}), dim); elseif (isvector (x)) if (length (x) != n) error ("trapz: length of X and length of Y along DIM must match"); endif ## Reshape spacing vector x to point along dimension DIM shape = ones (nd, 1); shape(dim) = n; x = reshape (x, shape); z = 0.5 * sum (diff (x) .* (y(idx1{:}) + y(idx2{:})), dim); else if (! size_equal (x, y)) error ("trapz: X and Y must have same shape"); endif z = 0.5 * sum (diff (x, 1, dim) .* (y(idx1{:}) + y(idx2{:})), dim); endif endfunction %!assert (trapz (1:5), 12) %!assert (trapz (1, 1:5), 12) %!assert (trapz (0.5, 1:5), 6) %!assert (trapz ([1:5], [1:5]), 12) %!assert (trapz ([1:5], [1:5]'), 12) %!assert (trapz ([1:5]', [1:5]'), 12) %!assert (trapz ([1:5]', [1:5]), 12) %!assert (trapz (0:0.5:2,1:5), 6) %!assert (trapz ([1:5;1:5].', 1), [12, 12]) %!assert (trapz ([1:5;1:5], 2), [12; 12]) %!assert (trapz (repmat (reshape (1:5,1,1,5),2,2), 3), [12 12; 12 12]) %!assert (trapz ([0:0.5:2;1:5].', [1:5;1:5].', 1), [6, 12]) %!assert (trapz ([0:0.5:2;1:5], [1:5;1:5], 2), [6; 12]) %!assert (trapz (repmat (reshape ([0:0.5:2],1,1,5),2,2), ... %! repmat (reshape (1:5,1,1,5),2,2), 3), [6 6; 6 6]) %!assert (trapz (0:0.5:2, [(1:5)', (1:5)']), [6, 6]) %!assert (trapz (0:0.5:2, [(1:5); (1:5)], 2), [6; 6]) %!assert (trapz (0:0.5:2, repmat (reshape (1:5,1,1,5),2,2),3), [6 6; 6 6]) %!assert <*54277> (trapz (ones (1,3), 1), zeros (1,3)) %!assert <*54277> (trapz (ones (3,1), 2), zeros (3,1)) ## Test input validation %!error <Invalid call> trapz () %!error <DIM must be an integer> trapz (1, 2, [1 2]) %!error <DIM must be an integer> trapz (1, 2, 1.5) %!error <DIM must be .* a valid dimension> trapz (1, 2, 0) %!error <length of X and length of Y.*must match> trapz ([1 2], [1 2 3]) %!error <X and Y must have same shape> trapz (ones (2,3), ones (2,4))