Mercurial > octave
annotate scripts/plot/draw/fplot.m @ 28942:fc4bb4bd1d5e
maint: Use '##' as lead-in for full-line comments.
* condeig.m, mustBeMember.m, runge_kutta_interpolate.m, lsqnonneg.m,
pqpnonneg.m, sqp.m, pkg.m, fplot.m, isosurface.m, __gnuplot_draw_axes__.m,
profexport.m, bicgstab.m, factorial.m, movmad.m, movmax.m, movmean.m,
movmedian.m, movmin.m, movprod.m, movstd.m, movsum.m, movvar.m, fA.m, fB.m,
fC.m, one.m, two.m, df_vr.m, u_vr.m, myclass2.m, foo_subsref_subsasgn.m,
Blork.m, CPrecedenceTester1.m, Cork.m, display.m, display.m, get.m, set.m,
display.m, Sneetch.m, Snork.m, Spork.m, jit.tst, line-continue.tst,
mk_bc_overloads_expected.m, arg_nest.m, no_closure.m, persistent_nest.m,
recursive_nest.m, recursive_nest2.m, scope0.m, scope1.m, scope2.m, scope3.m,
script_nest.m, script_nest_2.m, script_nest_script.m, script_nest_script_2.m,
pkg.tst:
Use '##' as lead-in for full-line comments.
author | Rik <rik@octave.org> |
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date | Thu, 15 Oct 2020 14:30:01 -0700 |
parents | 914816dd2f1a |
children | 7854d5752dd2 |
rev | line source |
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 2005-2020 The Octave Project Developers |
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4 ## |
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5 ## See the file COPYRIGHT.md in the top-level directory of this |
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6 ## distribution or <https://octave.org/copyright/>. |
5820 | 7 ## |
8 ## This file is part of Octave. | |
9 ## | |
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10 ## Octave is free software: you can redistribute it and/or modify it |
5820 | 11 ## under the terms of the GNU General Public License as published by |
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12 ## the Free Software Foundation, either version 3 of the License, or |
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13 ## (at your option) any later version. |
5820 | 14 ## |
15 ## Octave is distributed in the hope that it will be useful, but | |
16 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 ## GNU General Public License for more details. |
5820 | 19 ## |
20 ## You should have received a copy of the GNU General Public License | |
7016 | 21 ## along with Octave; see the file COPYING. If not, see |
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22 ## <https://www.gnu.org/licenses/>. |
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23 ## |
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24 ######################################################################## |
5820 | 25 |
26 ## -*- texinfo -*- | |
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27 ## @deftypefn {} {} fplot (@var{fn}) |
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28 ## @deftypefnx {} {} fplot (@var{fn}, @var{limits}) |
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29 ## @deftypefnx {} {} fplot (@dots{}, @var{tol}) |
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30 ## @deftypefnx {} {} fplot (@dots{}, @var{n}) |
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31 ## @deftypefnx {} {} fplot (@dots{}, @var{fmt}) |
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32 ## @deftypefnx {} {} fplot (@dots{}, @var{property}, @var{value}, @dots{}) |
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33 ## @deftypefnx {} {} fplot (@var{hax}, @dots{}) |
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34 ## @deftypefnx {} {[@var{x}, @var{y}] =} fplot (@dots{}) |
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35 ## Plot a function @var{fn} within the range defined by @var{limits}. |
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36 ## |
17479 | 37 ## @var{fn} is a function handle, inline function, or string containing the |
38 ## name of the function to evaluate. | |
39 ## | |
40 ## The limits of the plot are of the form @w{@code{[@var{xlo}, @var{xhi}]}} or | |
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41 ## @w{@code{[@var{xlo}, @var{xhi}, @var{ylo}, @var{yhi}]}}. If no limits |
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42 ## are specified the default is @code{[-5, 5]}. |
17479 | 43 ## |
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44 ## The next three arguments are all optional and any number of them may be |
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45 ## given in any order. |
17479 | 46 ## |
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47 ## @var{tol} is the relative tolerance to use for the plot and defaults |
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48 ## to 2e-3 (.2%). |
17479 | 49 ## |
50 ## @var{n} is the minimum number of points to use. When @var{n} is specified, | |
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51 ## the maximum stepsize will be @code{(@var{xhi} - @var{xlo}) / @var{n}}. More |
17479 | 52 ## than @var{n} points may still be used in order to meet the relative |
53 ## tolerance requirement. | |
54 ## | |
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55 ## The @var{fmt} argument specifies the linestyle to be used by the plot |
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56 ## command. |
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57 ## |
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58 ## Multiple property-value pairs may also be specified, but they must appear |
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59 ## in pairs. These arguments are applied to the line objects drawn by |
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60 ## @code{plot}. |
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61 ## |
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62 ## The full list of line properties is documented at |
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63 ## @ref{Line Properties}. |
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64 ## |
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65 ## If the first argument @var{hax} is an axes handle, then plot into this axes, |
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66 ## rather than the current axes returned by @code{gca}. |
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67 ## |
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68 ## With no output arguments, the results are immediately plotted. With two |
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69 ## output arguments, the 2-D plot data is returned. The data can subsequently |
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70 ## be plotted manually with @code{plot (@var{x}, @var{y})}. |
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71 ## |
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72 ## Example: |
5820 | 73 ## |
74 ## @example | |
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75 ## @group |
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76 ## fplot (@@cos, [0, 2*pi]) |
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77 ## fplot ("[cos(x), sin(x)]", [0, 2*pi]) |
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78 ## @end group |
5820 | 79 ## @end example |
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80 ## |
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81 ## Programming Notes: |
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82 ## |
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83 ## @code{fplot} works best with continuous functions. Functions with |
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84 ## discontinuities are unlikely to plot well. This restriction may be removed |
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85 ## in the future. |
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86 ## |
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87 ## @code{fplot} performance is better when the function accepts and returns a |
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88 ## vector argument. Consider this when writing user-defined functions and use |
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89 ## element-by-element operators such as @code{.*}, @code{./}, etc. |
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90 ## |
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91 ## @seealso{ezplot, plot} |
5820 | 92 ## @end deftypefn |
93 | |
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94 function [X, Y] = fplot (varargin) |
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95 |
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96 [hax, varargin, nargin] = __plt_get_axis_arg__ ("fplot", varargin{:}); |
5820 | 97 |
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98 if (nargin < 1 || nargin > 5) |
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99 print_usage (); |
6781 | 100 endif |
101 | |
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102 fn = varargin{1}; |
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103 if (isa (fn, "inline")) |
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104 fn = vectorize (inline (fn)); |
6699 | 105 nam = formula (fn); |
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106 elseif (is_function_handle (fn)) |
6699 | 107 nam = func2str (fn); |
5820 | 108 elseif (all (isalnum (fn))) |
6781 | 109 nam = fn; |
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110 elseif (ischar (fn)) |
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111 fn = vectorize (inline (fn)); |
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112 nam = formula (fn); |
5820 | 113 else |
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114 error ("fplot: FN must be a function handle, inline function, or string"); |
6781 | 115 endif |
116 | |
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117 if (nargin > 1 && isnumeric (varargin{2})) |
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118 limits = varargin{2}; |
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119 if (iscomplex (limits) || (numel (limits) != 2 && numel (limits) != 4)) |
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120 error ("fplot: LIMITS must be a real vector with 2 or 4 elements"); |
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121 endif |
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122 i = 3; |
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123 else |
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124 limits = [-5, 5]; |
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125 i = 2; |
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126 endif |
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127 |
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128 n = 5; |
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129 tol = 2e-3; |
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130 fmt = {}; |
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131 prop_vals = {}; |
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132 while (i <= numel (varargin)) |
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133 arg = varargin{i}; |
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134 if (ischar (arg)) |
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135 [~, valid_fmt] = __pltopt__ ("fplot", arg, false); |
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136 if (valid_fmt) |
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137 fmt(end+1) = arg; |
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138 else |
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139 if (i == numel (varargin)) |
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140 error ("fplot: bad input in position %d", i); |
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141 endif |
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142 prop_vals(end+(1:2)) = varargin([i, i+1]); |
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143 i++; # Skip PROPERTY. |
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144 endif |
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145 elseif (isnumeric (arg) && isscalar (arg) && arg > 0) |
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146 if (arg == fix (arg)) |
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147 n = arg; |
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148 else |
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149 tol = arg; |
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150 endif |
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151 else |
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152 error ("fplot: bad input in position %d", i); |
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153 endif |
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154 i++; |
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155 endwhile |
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156 |
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157 if (n != 5) |
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158 ## n was specified |
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159 x0 = linspace (limits(1), limits(2), n/2 + 1)'; |
6781 | 160 else |
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161 x0 = linspace (limits(1), limits(2), 5)'; |
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162 n = 8; |
5820 | 163 endif |
164 | |
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165 try |
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166 y0 = feval (fn, x0); |
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167 if (isscalar (y0)) |
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168 warning ("fplot: FN is not a vectorized function which reduces performance"); |
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169 fn = @(x) arrayfun (fn, x); # Create a new fn that accepts vectors |
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170 y0 = feval (fn, x0); |
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171 endif |
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172 catch |
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173 ## feval failed, maybe it is because the function is not vectorized? |
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174 fn = @(x) arrayfun (fn, x); # Create a new fn that accepts vectors |
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175 y0 = feval (fn, x0); |
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176 warning ("fplot: FN is not a vectorized function which reduces performance"); |
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177 end_try_catch |
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178 |
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179 x = linspace (limits(1), limits(2), n)'; |
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180 y = feval (fn, x); |
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181 |
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182 if (rows (x0) == rows (y0)) |
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183 fcn_transpose = false; |
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184 elseif (rows (x0) == columns (y0)) |
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185 fcn_transpose = true; |
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186 y0 = y0.'; |
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187 y = y.'; |
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188 else |
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189 error ("fplot: invalid function FN (# of outputs not equal to inputs)"); |
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190 endif |
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191 |
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192 err0 = Inf; |
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193 |
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194 ## FIXME: This algorithm should really use adaptive scaling as |
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195 ## the numerical quadrature algorithms do so that extra points are |
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196 ## used where they are needed and not spread evenly over the entire |
17479 | 197 ## x-range. Try any function with a discontinuity, such as |
198 ## fplot (@tan, [-2, 2]) or fplot ("1./x", [-3, 2]), to see the | |
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199 ## problems with the current solution. |
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200 |
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201 while (n < 2^18) # Something is wrong if we need more than 250K points |
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202 yi = interp1 (x0, y0, x, "linear"); |
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203 ## relative error calculation using average of [yi,y] as reference |
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204 ## since neither estimate is known a priori to be better than the other. |
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205 err = 0.5 * max (abs ((yi - y) ./ (yi + y + eps))(:)); |
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206 if (err < tol || abs (err - err0) < tol/2) |
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207 ## Either relative tolerance has been met OR |
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208 ## algorithm has stopped making any reasonable progress per iteration. |
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209 break; |
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210 endif |
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211 x0 = x; |
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212 y0 = y; |
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213 err0 = err; |
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214 n = 2 * (n - 1) + 1; |
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215 x = linspace (limits(1), limits(2), n)'; |
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216 y = feval (fn, x); |
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217 if (fcn_transpose) |
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218 y = y.'; |
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219 endif |
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220 endwhile |
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221 |
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222 if (nargout == 2) |
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223 X = x; |
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224 Y = y; |
6781 | 225 else |
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226 if (isempty (hax)) |
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227 hax = gca (); |
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228 endif |
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229 hl = plot (hax, x, y, fmt{:}); |
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230 if (isempty (get (hl(1), "displayname"))) |
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231 ## Set displayname for legend if FMT did not contain a name. |
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232 if (isvector (y)) |
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233 set (hl, "displayname", nam); |
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234 else |
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235 for i = 1:columns (y) |
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236 nams{i} = sprintf ("%s(:,%i)", nam, i); |
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237 endfor |
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238 set (hl, {"displayname"}, nams(:)); |
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239 endif |
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240 endif |
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241 ## Properties passed as input arguments override other properties. |
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242 if (! isempty (prop_vals)) |
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243 set (hl, prop_vals{:}); |
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244 endif |
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245 axis (hax, limits); |
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246 legend (hax, "show"); |
6781 | 247 endif |
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248 |
5820 | 249 endfunction |
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251 | |
252 %!demo | |
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253 %! clf; |
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254 %! fplot (@cos, [0, 2*pi]); |
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255 %! title ("fplot() single function"); |
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256 |
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257 %!demo |
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258 %! clf; |
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259 %! fplot ("[cos(x), sin(x)]", [0, 2*pi]); |
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260 %! title ("fplot() multiple functions"); |
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261 |
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262 %!demo |
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263 %! clf; |
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264 %! fh = @(x) sin (pi*x) ./ (pi*x); |
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265 %! fplot (fh, [-5, 5]); |
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266 %! title ("fplot() sinc function (possible division by 0, near 0)"); |
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267 |
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268 %!test |
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269 %! ## Multi-valued function |
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270 %! [x, y] = fplot ("[cos(x), sin(x)]", [0, 2*pi]); |
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271 %! assert (columns (y) == 2); |
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272 %! assert (rows (x) == rows (y)); |
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273 %! assert (y, [cos(x), sin(x)], -2e-3); |
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274 |
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275 %!test |
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276 %! ## Function requiring transpose |
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277 %! fn = @(x) 2 * x(:).'; |
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278 %! [x, y] = fplot (fn, [-1, 1]); |
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279 %! assert (columns (y) == 1); |
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280 %! assert (rows (x) == rows (y)); |
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281 %! assert (y, 2*x); |
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282 |
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283 %!test |
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284 %! ## Constant value function |
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285 %! fn = @(x) 0; |
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286 %! [x, y] = fplot (fn, [-1, 1]); |
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287 %! assert (columns (y) == 1); |
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288 %! assert (rows (x) == rows (y)); |
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289 %! assert (y, repmat ([0], size (x))); |
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290 |
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291 %!test <*59274> |
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292 %! ## Manual displayname overrides automatic legend entry |
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293 %! hf = figure ("visible", "off"); |
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294 %! unwind_protect |
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295 %! fplot (@sin, [0, 3], "displayname", "mysin"); |
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296 %! hl = legend (); |
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297 %! assert (get (hl, "string"), {"mysin"}); |
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298 %! unwind_protect_cleanup |
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299 %! close (hf); |
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300 %! end_unwind_protect |
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301 |
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302 %!test <*59274> |
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303 %! ## displayname in format string overrides automatic legend entry |
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304 %! hf = figure ("visible", "off"); |
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305 %! unwind_protect |
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306 %! fplot (@sin, [0, 3], "+;mysin;"); |
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307 %! hl = legend (); |
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308 %! assert (get (hl, "string"), {"mysin"}); |
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309 %! unwind_protect_cleanup |
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310 %! close (hf); |
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311 %! end_unwind_protect |
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312 |
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313 ## Test input validation |
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314 %!error <Invalid call> fplot () |
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315 %!error <Invalid call> fplot (1,2,3,4,5,6) |
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316 %!error <FN must be a function handle> fplot (1, [0 1]) |
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317 %!error <LIMITS must be a real vector> fplot (@cos, [i, 2*i]) |
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318 %!error <LIMITS must be a real vector with 2 or 4> fplot (@cos, [1]) |
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319 %!error <LIMITS must be a real vector with 2 or 4> fplot (@cos, [1 2 3]) |
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320 %!error <bad input in position 2> fplot (@cos, "linewidth") |
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321 %!error <bad input in position 3> fplot (@cos, [-1,1], {1}) |
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322 %!warning <FN is not a vectorized function> |
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323 %! fn = @(x) 0; |
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324 %! [x,y] = fplot (fn, [-1,1]); |
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325 %!error <invalid function FN> |
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326 %! fn = @(x) [x;x]; |
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327 %! fplot (fn, [-1,1]); |