Mercurial > octave
view scripts/general/rat.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 |
line wrap: on
line source
######################################################################## ## ## Copyright (C) 2001-2022 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{s} =} rat (@var{x}) ## @deftypefnx {} {@var{s} =} rat (@var{x}, @var{tol}) ## @deftypefnx {} {[@var{n}, @var{d}] =} rat (@dots{}) ## ## Find a rational approximation of @var{x} to within the tolerance defined by ## @var{tol}. ## ## If unspecified, the default tolerance is @code{1e-6 * norm (@var{x}(:), 1)}. ## ## When called with one output argument, return a string containing a ## continued fraction expansion (multiple terms). ## ## When called with two output arguments, return numeric matrices for the ## numerator and denominator of a fractional representation of @var{x} such ## that @code{@var{x} = @var{n} ./ @var{d}}. ## ## For example: ## ## @example ## @group ## s = rat (pi) ## @result{} s = 3 + 1/(7 + 1/16) ## ## [n, d] = rat (pi) ## @result{} n = 355 ## @result{} d = 113 ## ## n / d - pi ## @result{} 0.00000026676 ## @end group ## @end example ## ## Programming Note: With one output @code{rat} produces a string which is a ## continued fraction expansion. To produce a string which is a simple ## fraction (one numerator, one denominator) use @code{rats}. ## ## @seealso{rats, format} ## @end deftypefn function [n, d] = rat (x, tol) if (nargin < 1) print_usage (); endif if (! isfloat (x)) error ("rat: X must be a single or double array"); endif ## FIXME: This test should be removed when complex support is added. ## See bug #55198. if (iscomplex (x)) error ("rat: X must be a real, not complex, array"); endif y = x(:); ## Replace Inf with 0 while calculating ratios. inf_idx = isinf (x); y(inf_idx(:)) = 0; if (nargin == 1) ## default norm tol = 1e-6 * norm (y, 1); else if (! (isscalar (tol) && isnumeric (tol) && tol > 0)) error ("rat: TOL must be a numeric scalar > 0"); endif endif ## First step in the approximation is the integer portion ## First element in the continued fraction. n = round (y); d = ones (size (y)); frac = y - n; lastn = ones (size (y)); lastd = zeros (size (y)); nsz = numel (y); steps = zeros ([nsz, 0]); ## Grab new factors until all continued fractions converge. while (1) ## Determine which fractions have not yet converged. idx = find (y != 0 & abs (y - n./d) >= tol); if (isempty (idx)) if (isempty (steps)) steps = NaN (nsz, 1); endif break; endif ## Grab the next step in the continued fraction. flip = 1 ./ frac(idx); ## Next element in the continued fraction. step = round (flip); if (nargout < 2) tsteps = NaN (nsz, 1); tsteps(idx) = step; steps = [steps, tsteps]; endif frac(idx) = flip - step; ## Update the numerator/denominator. savedn = n; savedd = d; n(idx) = n(idx).*step + lastn(idx); d(idx) = d(idx).*step + lastd(idx); lastn = savedn; lastd = savedd; endwhile if (nargout <= 1) ## string output n = ""; nsteps = columns (steps); ## Loop over all values in array for i = 1:nsz if (inf_idx(i)) s = ifelse (x(i) > 0, "Inf", "-Inf"); elseif (y(i) == 0) s = "0"; else ## Create partial fraction expansion of one value s = [int2str(y(i)), " "]; j = 1; while (true) step = steps(i, j++); if (isnan (step)) break; endif if (j > nsteps || isnan (steps(i, j))) if (step < 0) s = [s(1:end-1), " + 1/(", int2str(step), ")"]; else s = [s(1:end-1), " + 1/", int2str(step)]; endif break; else s = [s(1:end-1), " + 1/(", int2str(step), ")"]; endif endwhile s = [s, repmat(")", 1, j-2)]; endif ## Append result to output n_nc = columns (n); s_nc = columns (s); if (n_nc > s_nc) s(:, s_nc+1:n_nc) = " "; elseif (s_nc > n_nc && n_nc != 0) n(:, n_nc+1:s_nc) = " "; endif n = cat (1, n, s); endfor else ## numerator, denominator output ## Move the minus sign to the numerator. n .*= sign (d); d = abs (d); ## Return the same shape as the input. n = reshape (n, size (x)); d = reshape (d, size (x)); ## Use 1/0 for Inf. n(inf_idx) = sign (x(inf_idx)); d(inf_idx) = 0; endif endfunction %!assert (rat (pi), "3 + 1/(7 + 1/16)") %!assert (rat (pi, 1e-2), "3 + 1/7") ## Test exceptional values %!assert (rat (0), "0") %!assert (rat (Inf), "Inf") %!assert (rat (-Inf), "-Inf") %!test %! [n, d] = rat ([0.5, 0.3, 1/3]); %! assert (n, [1, 3, 1]); %! assert (d, [2, 10, 3]); ## Test exceptional values %!test %! [n, d] = rat ([Inf, 0, -Inf]); %! assert (n, [1, 0, -1]); %! assert (d, [0, 1, 0]); %!assert <*43374> (eval (rat (0.75)), [0.75]) ## Test input validation %!error <Invalid call> rat () %!error <X must be a single or double array> rat (int8 (3)) %!error <X must be a real, not complex, array> rat (1+1i) %!error <TOL must be a numeric scalar> rat (1, "a") %!error <TOL must be a numeric scalar> rat (1, [1 2]) %!error <TOL must be a numeric scalar . 0> rat (1, -1)