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fplot.m: Document requirement of accepting vector inputs (bug #42050). fplot.m: Document requirement of accepting vector inputs.
author Rik <rik@octave.org>
date Tue, 19 May 2015 12:13:22 -0700
parents 9fc020886ae9
children 5b7643257978
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4197fc428c7d maint: Update copyright notices for 2015.
John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 2005-2015 Paul Kienzle
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} fplot (@var{fn}, @var{limits})
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21 ## @deftypefnx {Function File} {} fplot (@dots{}, @var{tol})
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22 ## @deftypefnx {Function File} {} fplot (@dots{}, @var{n})
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23 ## @deftypefnx {Function File} {} fplot (@dots{}, @var{fmt})
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24 ## @deftypefnx {Function File} {[@var{x}, @var{y}] =} fplot (@dots{})
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25 ## Plot a function @var{fn} within the range defined by @var{limits}.
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26 ##
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27 ## @var{fn} is a function handle, inline function, or string containing the
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28 ## name of the function to evaluate.
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29 ##
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30 ## The limits of the plot are of the form @w{@code{[@var{xlo}, @var{xhi}]}} or
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31 ## @w{@code{[@var{xlo}, @var{xhi}, @var{ylo}, @var{yhi}]}}.
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32 ##
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33 ## The next three arguments are all optional and any number of them may be
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34 ## given in any order.
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35 ##
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36 ## @var{tol} is the relative tolerance to use for the plot and defaults
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37 ## to 2e-3 (.2%).
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38 ##
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39 ## @var{n} is the minimum number of points to use. When @var{n} is specified,
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40 ## the maximum stepsize will be @code{@var{xhi} - @var{xlo} / @var{n}}. More
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41 ## than @var{n} points may still be used in order to meet the relative
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42 ## tolerance requirement.
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43 ##
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44 ## The @var{fmt} argument specifies the linestyle to be used by the plot
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45 ## command.
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46 ##
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47 ## If the first argument @var{hax} is an axes handle, then plot into this axis,
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48 ## rather than the current axes returned by @code{gca}.
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49 ##
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50 ## With no output arguments the results are immediately plotted. With two
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51 ## output arguments the 2-D plot data is returned. The data can subsequently
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52 ## be plotted manually with @code{plot (@var{x}, @var{y})}.
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53 ##
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54 ## Example:
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55 ##
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56 ## @example
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57 ## @group
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58 ## fplot (@@cos, [0, 2*pi])
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59 ## fplot ("[cos(x), sin(x)]", [0, 2*pi])
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60 ## @end group
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61 ## @end example
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62 ##
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63 ## Programming Notes:
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64 ##
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65 ## @code{fplot} works best with continuous functions. Functions with
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66 ## discontinuities are unlikely to plot well. This restriction may be removed
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67 ## in the future.
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68 ##
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69 ## @code{fplot} requires that the function accept and return a vector argument.
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70 ## Consider this when writing user-defined functions and use @code{.*},
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71 ## @code{./}, etc. See the function @code{vectorize} for potentially
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72 ## converting inline or anonymous functions to vectorized versions.
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73 ##
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74 ## @seealso{ezplot, plot, vectorize}
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75 ## @end deftypefn
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76
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77 ## Author: Paul Kienzle <pkienzle@users.sf.net>
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78
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79 function [X, Y] = fplot (varargin)
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80
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81 [hax, varargin, nargin] = __plt_get_axis_arg__ ("fplot", varargin{:});
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82
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83 if (nargin < 2 || nargin > 5)
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84 print_usage ();
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85 endif
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86
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87 fn = varargin{1};
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88 limits = varargin{2};
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89 varargin = varargin(3:end);
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90
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91 if (strcmp (typeinfo (fn), "inline function"))
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92 fn = vectorize (fn);
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93 nam = formula (fn);
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94 elseif (isa (fn, "function_handle"))
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95 nam = func2str (fn);
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96 elseif (all (isalnum (fn)))
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97 nam = fn;
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98 elseif (ischar (fn))
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99 fn = vectorize (inline (fn));
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100 nam = formula (fn);
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101 else
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102 error ("fplot: FN must be a function handle, inline function, or string");
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103 endif
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104
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105 if (iscomplex (limits) || (numel (limits) != 2 && numel (limits) != 4))
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106 error ("fplot: LIMITS must be a real vector with 2 or 4 elements");
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107 endif
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108
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109 n = 5;
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110 tol = 2e-3;
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111 fmt = "";
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112 for i = 1:numel (varargin)
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113 arg = varargin{i};
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114 if (ischar (arg))
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115 fmt = arg;
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116 elseif (isnumeric (arg) && isscalar (arg) && arg > 0)
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117 if (arg == fix (arg))
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118 n = arg;
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119 else
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120 tol = arg;
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121 endif
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122 else
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123 error ("fplot: bad input in position %d", i+2);
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124 endif
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125 endfor
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126
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127 if (n != 5)
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128 ## n was specified
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129 x0 = linspace (limits(1), limits(2), n/2 + 1)';
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130 y0 = feval (fn, x0);
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131 x = linspace (limits(1), limits(2), n)';
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132 y = feval (fn, x);
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133 else
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134 x0 = linspace (limits(1), limits(2), 5)';
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135 y0 = feval (fn, x0);
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136 n = 8;
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137 x = linspace (limits(1), limits(2), n)';
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138 y = feval (fn, x);
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139 endif
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140
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141 if (rows (x0) != rows (y0))
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142 ## FN is a constant value function
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143 y0 = repmat (y0, size (x0));
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144 y = repmat (y, size (x));
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145 endif
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146
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147 err0 = Inf;
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148
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149 ## FIXME: This algorithm should really use adaptive scaling as the
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150 ## the numerical quadrature algorithms do so that extra points are
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151 ## used where they are needed and not spread evenly over the entire
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152 ## x-range. Try any function with a discontinuity, such as
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153 ## fplot (@tan, [-2, 2]) or fplot ("1./x", [-3, 2]), to see the
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154 ## problems with the current solution.
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155
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156 while (n < 2^18) # Something is wrong if we need more than 250K points
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157 yi = interp1 (x0, y0, x, "linear");
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158 ## relative error calculation using average of [yi,y] as reference
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159 ## since neither estimate is known a priori to be better than the other.
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160 err = 0.5 * max (abs ((yi - y) ./ (yi + y))(:));
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161 if (err < tol || abs (err - err0) < tol/2)
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162 ## Either relative tolerance has been met OR
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163 ## algorithm has stopped making any reasonable progress per iteration.
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164 break;
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165 endif
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166 x0 = x;
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167 y0 = y;
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168 err0 = err;
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169 n = 2 * (n - 1) + 1;
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170 x = linspace (limits(1), limits(2), n)';
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171 y = feval (fn, x);
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172 endwhile
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173
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174 if (nargout == 2)
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175 X = x;
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176 Y = y;
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177 else
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178 if (isempty (hax))
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179 hax = gca ();
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180 endif
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181 plot (hax, x, y, fmt);
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182 axis (hax, limits);
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183 if (isvector (y))
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184 legend (hax, nam);
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185 else
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186 for i = 1:columns (y)
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187 nams{i} = sprintf ("%s(:,%i)", nam, i);
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188 endfor
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189 legend (hax, nams{:});
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190 endif
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191 endif
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192
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193 endfunction
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194
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195
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196 %!demo
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197 %! clf;
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198 %! fplot (@cos, [0, 2*pi]);
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199 %! title ('fplot() single function');
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200
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201 %!demo
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202 %! clf;
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203 %! fplot ('[cos(x), sin(x)]', [0, 2*pi]);
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204 %! title ('fplot() multiple functions');
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205
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206 %!demo
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207 %! clf;
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208 %! %% sinc function
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209 %! fh = @(x) sin (pi*x) ./ (pi*x);
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210 %! fplot (fh, [-5, 5]);
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211 %! title ('fplot() sinc function');
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212
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213 %!test
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214 %! [x, y] = fplot ("[cos(x), sin(x)]", [0, 2*pi]);
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215 %! assert (columns (y) == 2);
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216 %! assert (rows (x) == rows (y));
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217 %! assert (y, [cos(x), sin(x)], -2e-3);
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218
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219 ## Test input validation
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220 %!error fplot (1)
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221 %!error fplot (1,2,3,4,5,6)
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222 %!error <FN must be a function handle> fplot (1, [0 1])
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223 %!error <LIMITS must be a real vector> fplot (@cos, [i, 2*i])
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224 %!error <LIMITS must be a real vector with 2 or 4> fplot (@cos, [1])
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225 %!error <LIMITS must be a real vector with 2 or 4> fplot (@cos, [1 2 3])
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226 %!error <bad input in position 3> fplot (@cos,[-1,1], {1})
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227