Mercurial > octave
view scripts/plot/draw/fplot.m @ 30564:796f54d4ddbf stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
In all .txi and .texi files except gpl.txi and gpl.texi in the
doc/liboctave and doc/interpreter directories, change the copyright
to "Octave Project Developers", the same as used for other source
files. Update copyright notices for 2022 (not done since 2019). For
gpl.txi and gpl.texi, change the copyright notice to be "Free Software
Foundation, Inc." and leave the date at 2007 only because this file
only contains the text of the GPL, not anything created by the Octave
Project Developers.
Add Paul Thomas to contributors.in.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 7854d5752dd2 |
children | e1788b1a315f |
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######################################################################## ## ## Copyright (C) 2005-2022 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 {} {} fplot (@var{fn}) ## @deftypefnx {} {} fplot (@var{fn}, @var{limits}) ## @deftypefnx {} {} fplot (@dots{}, @var{tol}) ## @deftypefnx {} {} fplot (@dots{}, @var{n}) ## @deftypefnx {} {} fplot (@dots{}, @var{fmt}) ## @deftypefnx {} {} fplot (@dots{}, @var{property}, @var{value}, @dots{}) ## @deftypefnx {} {} fplot (@var{hax}, @dots{}) ## @deftypefnx {} {[@var{x}, @var{y}] =} fplot (@dots{}) ## Plot a function @var{fn} within the range defined by @var{limits}. ## ## @var{fn} is a function handle, inline function, or string containing the ## name of the function to evaluate. ## ## The limits of the plot are of the form @w{@code{[@var{xlo}, @var{xhi}]}} or ## @w{@code{[@var{xlo}, @var{xhi}, @var{ylo}, @var{yhi}]}}. If no limits ## are specified the default is @code{[-5, 5]}. ## ## The next three arguments are all optional and any number of them may be ## given in any order. ## ## @var{tol} is the relative tolerance to use for the plot and defaults ## to 2e-3 (.2%). ## ## @var{n} is the minimum number of points to use. When @var{n} is specified, ## the maximum stepsize will be @code{(@var{xhi} - @var{xlo}) / @var{n}}. More ## than @var{n} points may still be used in order to meet the relative ## tolerance requirement. ## ## The @var{fmt} argument specifies the linestyle to be used by the plot ## command. ## ## Multiple property-value pairs may also be specified, but they must appear ## in pairs. These arguments are applied to the line objects drawn by ## @code{plot}. ## ## The full list of line properties is documented at ## @ref{Line Properties}. ## ## If the first argument @var{hax} is an axes handle, then plot into this axes, ## rather than the current axes returned by @code{gca}. ## ## With no output arguments, the results are immediately plotted. With two ## output arguments, the 2-D plot data is returned. The data can subsequently ## be plotted manually with @code{plot (@var{x}, @var{y})}. ## ## Example: ## ## @example ## @group ## fplot (@@cos, [0, 2*pi]) ## fplot ("[cos(x), sin(x)]", [0, 2*pi]) ## @end group ## @end example ## ## Programming Notes: ## ## @code{fplot} works best with continuous functions. Functions with ## discontinuities are unlikely to plot well. This restriction may be removed ## in the future. ## ## @code{fplot} performance is better when the function accepts and returns a ## vector argument. Consider this when writing user-defined functions and use ## element-by-element operators such as @code{.*}, @code{./}, etc. ## ## @seealso{ezplot, plot} ## @end deftypefn function [X, Y] = fplot (varargin) [hax, varargin, nargin] = __plt_get_axis_arg__ ("fplot", varargin{:}); if (nargin < 1 || nargin > 5) print_usage (); endif fn = varargin{1}; if (isa (fn, "inline")) fn = vectorize (inline (fn)); nam = formula (fn); elseif (is_function_handle (fn)) nam = func2str (fn); elseif (all (isalnum (fn))) nam = fn; elseif (ischar (fn)) fn = vectorize (inline (fn)); nam = formula (fn); else error ("fplot: FN must be a function handle, inline function, or string"); endif if (nargin > 1 && isnumeric (varargin{2})) limits = varargin{2}; if (iscomplex (limits) || (numel (limits) != 2 && numel (limits) != 4)) error ("fplot: LIMITS must be a real vector with 2 or 4 elements"); endif i = 3; else limits = [-5, 5]; i = 2; endif n = 5; tol = 2e-3; fmt = {}; prop_vals = {}; while (i <= numel (varargin)) arg = varargin{i}; if (ischar (arg)) [~, valid_fmt] = __pltopt__ ("fplot", arg, false); if (valid_fmt) fmt(end+1) = arg; else if (i == numel (varargin)) error ("fplot: bad input in position %d", i); endif prop_vals(end+(1:2)) = varargin([i, i+1]); i++; # Skip PROPERTY. endif elseif (isnumeric (arg) && isscalar (arg) && arg > 0) if (arg == fix (arg)) n = arg; else tol = arg; endif else error ("fplot: bad input in position %d", i); endif i++; endwhile if (n != 5) ## n was specified x0 = linspace (limits(1), limits(2), n/2 + 1)'; else x0 = linspace (limits(1), limits(2), 5)'; n = 8; endif try y0 = feval (fn, x0); if (isscalar (y0)) warning ("fplot: FN is not a vectorized function which reduces performance"); fn = @(x) arrayfun (fn, x); # Create a new fn that accepts vectors y0 = feval (fn, x0); endif catch ## feval failed, maybe it is because the function is not vectorized? fn = @(x) arrayfun (fn, x); # Create a new fn that accepts vectors y0 = feval (fn, x0); warning ("fplot: FN is not a vectorized function which reduces performance"); end_try_catch x = linspace (limits(1), limits(2), n)'; y = feval (fn, x); if (rows (x0) == rows (y0)) fcn_transpose = false; elseif (rows (x0) == columns (y0)) fcn_transpose = true; y0 = y0.'; y = y.'; else error ("fplot: invalid function FN (# of outputs not equal to inputs)"); endif err0 = Inf; ## FIXME: This algorithm should really use adaptive scaling as ## the numerical quadrature algorithms do so that extra points are ## used where they are needed and not spread evenly over the entire ## x-range. Try any function with a discontinuity, such as ## fplot (@tan, [-2, 2]) or fplot ("1./x", [-3, 2]), to see the ## problems with the current solution. while (n < 2^18) # Something is wrong if we need more than 250K points yi = interp1 (x0, y0, x, "linear"); ## relative error calculation using average of [yi,y] as reference ## since neither estimate is known a priori to be better than the other. err = 0.5 * max (abs ((yi - y) ./ (yi + y + eps))(:)); if (err < tol || abs (err - err0) < tol/2) ## Either relative tolerance has been met OR ## algorithm has stopped making any reasonable progress per iteration. break; endif x0 = x; y0 = y; err0 = err; n = 2 * (n - 1) + 1; x = linspace (limits(1), limits(2), n)'; y = feval (fn, x); if (fcn_transpose) y = y.'; endif endwhile if (nargout == 2) X = x; Y = y; else if (isempty (hax)) hax = gca (); endif hl = plot (hax, x, y, fmt{:}); if (isempty (get (hl(1), "displayname"))) ## Set displayname for legend if FMT did not contain a name. if (isvector (y)) set (hl, "displayname", nam); else for i = 1:columns (y) nams{i} = sprintf ("%s(:,%i)", nam, i); endfor set (hl, {"displayname"}, nams(:)); endif endif ## Properties passed as input arguments override other properties. if (! isempty (prop_vals)) set (hl, prop_vals{:}); endif axis (hax, limits); legend (hax, "show"); endif endfunction %!demo %! clf; %! fplot (@cos, [0, 2*pi]); %! title ("fplot() single function"); %!demo %! clf; %! fplot ("[cos(x), sin(x)]", [0, 2*pi]); %! title ("fplot() multiple functions"); %!demo %! clf; %! fh = @(x) sin (pi*x) ./ (pi*x); %! fplot (fh, [-5, 5]); %! title ("fplot() sinc function (possible division by 0, near 0)"); %!test %! ## Multi-valued function %! [x, y] = fplot ("[cos(x), sin(x)]", [0, 2*pi]); %! assert (columns (y) == 2); %! assert (rows (x) == rows (y)); %! assert (y, [cos(x), sin(x)], -2e-3); %!test %! ## Function requiring transpose %! fn = @(x) 2 * x(:).'; %! [x, y] = fplot (fn, [-1, 1]); %! assert (columns (y) == 1); %! assert (rows (x) == rows (y)); %! assert (y, 2*x); %!test %! ## Constant value function %! fn = @(x) 0; %! [x, y] = fplot (fn, [-1, 1]); %! assert (columns (y) == 1); %! assert (rows (x) == rows (y)); %! assert (y, repmat ([0], size (x))); %!test <*59274> %! ## Manual displayname overrides automatic legend entry %! hf = figure ("visible", "off"); %! unwind_protect %! fplot (@sin, [0, 3], "displayname", "mysin"); %! hl = legend (); %! assert (get (hl, "string"), {"mysin"}); %! unwind_protect_cleanup %! close (hf); %! end_unwind_protect %!test <*59274> %! ## displayname in format string overrides automatic legend entry %! hf = figure ("visible", "off"); %! unwind_protect %! fplot (@sin, [0, 3], "+;mysin;"); %! hl = legend (); %! assert (get (hl, "string"), {"mysin"}); %! unwind_protect_cleanup %! close (hf); %! end_unwind_protect ## Test input validation %!error <Invalid call> fplot () %!error <Invalid call> fplot (1,2,3,4,5,6) %!error <FN must be a function handle> fplot (1, [0 1]) %!error <LIMITS must be a real vector> fplot (@cos, [i, 2*i]) %!error <LIMITS must be a real vector with 2 or 4> fplot (@cos, [1]) %!error <LIMITS must be a real vector with 2 or 4> fplot (@cos, [1 2 3]) %!error <bad input in position 2> fplot (@cos, "linewidth") %!error <bad input in position 3> fplot (@cos, [-1,1], {1}) %!warning <FN is not a vectorized function> %! fn = @(x) 0; %! [x,y] = fplot (fn, [-1,1]); %!error <invalid function FN> %! fn = @(x) [x;x]; %! fplot (fn, [-1,1]);