Mercurial > octave-antonio
view scripts/general/rat.m @ 20158:7503499a252b stable
doc: Update docstrings to have one sentence summary as first line.
Update scripts in audio, elfun, general, geometry, and image directories.
* scripts/audio/@audioplayer/__get_properties__.m,
scripts/audio/@audioplayer/audioplayer.m, scripts/audio/@audioplayer/get.m,
scripts/audio/@audioplayer/isplaying.m, scripts/audio/@audioplayer/play.m,
scripts/audio/@audioplayer/playblocking.m, scripts/audio/@audioplayer/set.m,
scripts/audio/@audioplayer/subsasgn.m, scripts/audio/@audioplayer/subsref.m,
scripts/audio/@audiorecorder/audiorecorder.m,
scripts/audio/@audiorecorder/get.m,
scripts/audio/@audiorecorder/getaudiodata.m,
scripts/audio/@audiorecorder/getplayer.m,
scripts/audio/@audiorecorder/isrecording.m,
scripts/audio/@audiorecorder/play.m, scripts/audio/@audiorecorder/record.m,
scripts/audio/@audiorecorder/recordblocking.m,
scripts/audio/@audiorecorder/set.m, scripts/audio/@audiorecorder/stop.m,
scripts/audio/@audiorecorder/subsasgn.m,
scripts/audio/@audiorecorder/subsref.m, scripts/audio/lin2mu.m,
scripts/audio/mu2lin.m, scripts/audio/record.m, scripts/audio/sound.m,
scripts/audio/soundsc.m, scripts/audio/wavread.m, scripts/audio/wavwrite.m,
scripts/elfun/cosd.m, scripts/elfun/sind.m, scripts/elfun/tand.m,
scripts/general/accumarray.m, scripts/general/accumdim.m,
scripts/general/bitcmp.m, scripts/general/bitget.m, scripts/general/bitset.m,
scripts/general/blkdiag.m, scripts/general/cart2pol.m,
scripts/general/cart2sph.m, scripts/general/cell2mat.m,
scripts/general/celldisp.m, scripts/general/chop.m,
scripts/general/circshift.m, scripts/general/common_size.m,
scripts/general/cplxpair.m, scripts/general/cumtrapz.m,
scripts/general/dblquad.m, scripts/general/deal.m, scripts/general/del2.m,
scripts/general/display.m, scripts/general/divergence.m,
scripts/general/fieldnames.m, scripts/general/flip.m,
scripts/general/flipdim.m, scripts/general/fliplr.m, scripts/general/flipud.m,
scripts/general/gradient.m, scripts/general/interp3.m,
scripts/general/interpft.m, scripts/general/interpn.m,
scripts/general/loadobj.m, scripts/general/logspace.m,
scripts/general/methods.m, scripts/general/nargchk.m,
scripts/general/narginchk.m, scripts/general/nargoutchk.m,
scripts/general/nextpow2.m, scripts/general/nthargout.m,
scripts/general/num2str.m, scripts/general/pol2cart.m,
scripts/general/polyarea.m, scripts/general/postpad.m,
scripts/general/prepad.m, scripts/general/profile.m, scripts/general/quadgk.m,
scripts/general/quadl.m, scripts/general/quadv.m, scripts/general/randi.m,
scripts/general/rat.m, scripts/general/repmat.m, scripts/general/rot90.m,
scripts/general/rotdim.m, scripts/general/saveobj.m, scripts/general/shift.m,
scripts/general/shiftdim.m, scripts/general/sortrows.m,
scripts/general/sph2cart.m, scripts/general/structfun.m,
scripts/general/subsindex.m, scripts/general/trapz.m,
scripts/general/triplequad.m, scripts/geometry/delaunayn.m,
scripts/geometry/dsearch.m, scripts/geometry/dsearchn.m,
scripts/geometry/griddata.m, scripts/geometry/griddata3.m,
scripts/geometry/griddatan.m, scripts/geometry/inpolygon.m,
scripts/geometry/rectint.m, scripts/geometry/tsearchn.m,
scripts/geometry/voronoi.m, scripts/geometry/voronoin.m,
scripts/help/__unimplemented__.m, scripts/help/doc.m,
scripts/help/doc_cache_create.m, scripts/help/get_first_help_sentence.m,
scripts/help/help.m, scripts/help/lookfor.m, scripts/help/print_usage.m,
scripts/help/type.m, scripts/help/which.m, scripts/image/autumn.m,
scripts/image/bone.m, scripts/image/brighten.m, scripts/image/cmpermute.m,
scripts/image/colorcube.m, scripts/image/contrast.m, scripts/image/cool.m,
scripts/image/copper.m, scripts/image/cubehelix.m, scripts/image/flag.m,
scripts/image/gmap40.m, scripts/image/gray.m, scripts/image/gray2ind.m,
scripts/image/hot.m, scripts/image/hsv.m, scripts/image/image.m,
scripts/image/imagesc.m, scripts/image/imfinfo.m, scripts/image/imformats.m,
scripts/image/imread.m, scripts/image/imshow.m, scripts/image/imwrite.m,
scripts/image/iscolormap.m, scripts/image/jet.m, scripts/image/lines.m,
scripts/image/ntsc2rgb.m, scripts/image/ocean.m, scripts/image/pink.m,
scripts/image/prism.m, scripts/image/rainbow.m, scripts/image/rgb2ntsc.m,
scripts/image/spinmap.m, scripts/image/spring.m, scripts/image/summer.m,
scripts/image/white.m, scripts/image/winter.m:
Update docstrings to have one sentence summary as first line.
Re-structure to have line lengths <= 80 chars.
author | Rik <rik@octave.org> |
---|---|
date | Sun, 03 May 2015 09:36:20 -0700 |
parents | 4197fc428c7d |
children |
line wrap: on
line source
## Copyright (C) 2001-2015 Paul Kienzle ## ## 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 ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{s} =} rat (@var{x}, @var{tol}) ## @deftypefnx {Function File} {[@var{n}, @var{d}] =} rat (@var{x}, @var{tol}) ## ## Find a rational approximation to @var{x} within the tolerance defined by ## @var{tol} using a continued fraction expansion. ## ## For example: ## ## @example ## @group ## rat (pi) = 3 + 1/(7 + 1/16) = 355/113 ## rat (e) = 3 + 1/(-4 + 1/(2 + 1/(5 + 1/(-2 + 1/(-7))))) ## = 1457/536 ## @end group ## @end example ## ## When called with two output arguments return the numerator and denominator ## separately as two matrices. ## @seealso{rats} ## @end deftypefn function [n,d] = rat (x,tol) if (nargin != [1,2] || nargout > 2) print_usage (); endif y = x(:); ## Replace Inf with 0 while calculating ratios. y(isinf(y)) = 0; ## default norm if (nargin < 2) tol = 1e-6 * norm (y,1); 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)); nd = ndims (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 (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. nextn = n; nextd = d; n(idx) = n(idx).*step + lastn(idx); d(idx) = d(idx).*step + lastd(idx); lastn = nextn; lastd = nextd; endwhile if (nargout == 2) ## Move the minus sign to the top. n = n .* sign (d); d = abs (d); ## Return the same shape as you receive. n = reshape (n, size (x)); d = reshape (d, size (x)); ## Use 1/0 for Inf. n(isinf (x)) = sign (x(isinf (x))); d(isinf (x)) = 0; ## Reshape the output. n = reshape (n, size (x)); d = reshape (d, size (x)); else n = ""; nsteps = columns (steps); for i = 1: nsz 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)]; 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 endif endfunction %!test %! [n, d] = rat ([0.5, 0.3, 1/3]); %! assert (n, [1, 3, 1]); %! assert (d, [2, 10, 3]); ## bug #43374 %!assert (eval (rat (0.75)), [0.75]) %!error rat (); %!error rat (1, 2, 3);