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1 @c Copyright (C) 1996 John W. Eaton |
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2 @c This is part of the Octave manual. |
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3 @c For copying conditions, see the file gpl.texi. |
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4 |
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5 @node Plotting, Image Processing, Statistics, Top |
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6 @chapter Plotting |
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7 |
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8 All of Octave's plotting functions use @code{gnuplot} to handle the |
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9 actual graphics. There are two low-level functions, @code{gplot} and |
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10 @code{gsplot}, that behave almost exactly like the corresponding |
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11 @code{gnuplot} functions @code{plot} and @samp{splot}. A number of |
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12 other higher level plotting functions, patterned after the graphics |
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13 functions found in @sc{Matlab} version 3.5, are also available. |
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14 These higher level functions are all implemented in terms of the two |
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15 low-level plotting functions. |
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16 |
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17 @menu |
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18 * Two-Dimensional Plotting:: |
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19 * Three-Dimensional Plotting:: |
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20 * Miscellaneous Plotting Functions:: |
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21 @end menu |
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22 |
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23 @node Two-Dimensional Plotting, Three-Dimensional Plotting, Plotting, Plotting |
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24 @section Two-Dimensional Plotting |
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25 |
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26 @deffn {Command} gplot @var{ranges} @var{expression} @var{using} @var{title} @var{style} |
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27 Generate a 2-dimensional plot. |
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28 |
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29 The @var{ranges}, @var{using}, @var{title}, and @var{style} arguments |
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30 are optional, and the @var{using}, @var{title} and @var{style} |
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31 qualifiers may appear in any order after the expression. You may plot |
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32 multiple expressions with a single command by separating them with |
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33 commas. Each expression may have its own set of qualifiers. |
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34 |
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35 The optional item @var{ranges} has the syntax |
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36 |
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37 @example |
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38 [ x_lo : x_up ] [ y_lo : y_up ] |
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39 @end example |
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40 |
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41 @noindent |
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42 and may be used to specify the ranges for the axes of the plot, |
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43 independent of the actual range of the data. The range for the y axes |
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44 and any of the individual limits may be omitted. A range @code{[:]} |
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45 indicates that the default limits should be used. This normally means |
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46 that a range just large enough to include all the data points will be |
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47 used. |
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48 |
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49 The expression to be plotted must not contain any literal matrices |
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50 (e.g. @code{[ 1, 2; 3, 4 ]}) since it is nearly impossible to |
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51 distinguish a plot range from a matrix of data. |
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52 |
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53 See the help for @code{gnuplot} for a description of the syntax for the |
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54 optional items. |
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55 |
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56 By default, the @code{gplot} command plots the second column of a matrix |
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57 versus the first. If the matrix only has one column, it is taken as a |
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58 vector of y-coordinates and the x-coordinate is taken as the element |
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59 index, starting with zero. For example, |
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60 |
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61 @example |
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62 gplot rand (100,1) with linespoints |
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63 @end example |
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64 |
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65 @noindent |
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66 will plot 100 random values and connect them with lines. When |
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67 @code{gplot} is used to plot a column vector, the indices of the |
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68 elements are taken as x values. |
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69 |
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70 If there are more than two columns, you can |
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71 choose which columns to plot with the @var{using} qualifier. For |
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72 example, given the data |
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73 |
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74 @example |
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75 x = (-10:0.1:10)'; |
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76 data = [x, sin(x), cos(x)]; |
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77 @end example |
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78 |
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79 @noindent |
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80 the command |
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81 |
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82 @example |
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83 gplot [-11:11] [-1.1:1.1] data with lines, data using 1:3 with impulses |
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84 @end example |
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85 |
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86 @noindent |
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87 will plot two lines. The first line is generated by the command |
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88 @code{data with lines}, and is a graph of the sine function over the |
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89 range -10 to 10. The data is taken from the first two columns of the |
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90 matrix because columns to plot were not specified with the @var{using} |
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91 qualifier. |
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92 |
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93 The clause @code{using 1:3} in the second part of this plot command |
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94 specifies that the first and third columns of the matrix @code{data} |
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95 should be taken as the values to plot. |
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96 |
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97 In this example, the ranges have been explicitly specified to be a bit |
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98 larger than the actual range of the data so that the curves do not touch |
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99 the border of the plot. |
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100 @end deffn |
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101 |
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102 @deffn {Command} set options |
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103 @deffnx {Command} show options |
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104 @deffnx {Command} replot options |
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105 In addition to the basic plotting commands, the whole range of |
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106 @code{set} and @code{show} commands from @code{gnuplot} are available, |
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107 as is @code{replot}. |
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108 |
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109 The @code{set} and @code{show} commands allow you to set and show |
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110 @code{gnuplot} parameters. For more information about the set and show |
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111 commands, see the @code{gnuplot} user's guide (also available on line if |
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112 you run @code{gnuplot} directly, instead of running it from Octave). |
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113 |
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114 The @code{replot} command allows you to force the plot to be |
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115 redisplayed. This is useful if you have changed something about the |
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116 plot, such as the title or axis labels. The @code{replot} command also |
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117 accepts the same arguments as @code{gplot} or @code{gsplot} (except for |
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118 data ranges) so you can add additional lines to existing plots. |
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119 |
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120 For example, |
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121 |
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122 @example |
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123 set term tek40 |
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124 set output "/dev/plotter" |
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125 set title "sine with lines and cosine with impulses" |
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126 replot "sin (x) w l" |
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127 @end example |
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128 |
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129 will change the terminal type for plotting, add a title to the current |
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130 plot, add a graph of sin (x) to the plot, and force the new plot to be |
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131 sent to the plot device. This last step is normally required in order |
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132 to update the plot. This default is reasonable for slow terminals or |
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133 hardcopy output devices because even when you are adding additional |
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134 lines with a replot command, gnuplot always redraws the entire plot, and |
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135 you probably don't want to have a completely new plot generated every |
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136 time something as minor as an axis label changes. |
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137 @end deffn |
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138 |
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139 @defvr {Built-in Variable} automatic_replot |
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140 You can tell Octave to redisplay the plot each time anything about it |
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141 changes by setting the value of the builtin variable |
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142 @code{automatic_replot} to a nonzero value. Since this is fairly |
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143 inefficient, the default value is 0. |
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144 @end defvr |
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145 |
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146 Note that NaN values in the plot data are automatically omitted, and |
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147 Inf values are converted to a very large value before calling gnuplot. |
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148 |
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149 @c XXX FIXME XXX -- add info about what to do to get plots on remote X |
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150 @c terminals. People often forget how to properly set DISPLAY and run |
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151 @c xhost. |
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152 |
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153 @c XXX FIXME XXX -- add info about getting paper copies of plots. |
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154 |
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155 The @sc{Matlab}-style two-dimensional plotting commands are: |
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156 |
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157 @cindex plotting |
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158 @cindex graphics |
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159 |
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160 @deftypefn {Function File} {} plot (@var{args}) |
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161 This function produces two-dimensional plots. Many different |
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162 combinations of arguments are possible. The simplest form is |
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163 |
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164 @example |
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165 plot (y) |
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166 @end example |
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167 |
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168 @noindent |
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169 where the argument is taken as the set of @var{y} coordinates and the |
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170 @var{x} coordinates are taken to be the indices of the elements, |
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171 starting with 1. |
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172 |
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173 If more than one argument is given, they are interpreted as |
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174 |
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175 @example |
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176 plot (x [, y] [, fmt] ...) |
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177 @end example |
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178 |
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179 @noindent |
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180 where @var{y} and @var{fmt} are optional, and any number of argument |
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181 sets may appear. The @var{x} and @var{y} values are |
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182 interpreted as follows: |
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183 |
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184 @itemize @bullet |
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185 @item |
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186 If a single data argument is supplied, it is taken as the set of @var{y} |
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187 coordinates and the @var{x} coordinates are taken to be the indices of |
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188 the elements, starting with 1. |
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189 |
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190 @item |
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191 If the first argument is a vector and the second is a matrix, the |
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192 the vector is plotted versus the columns (or rows) of the matrix. |
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193 (using whichever combination matches, with columns tried first.) |
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194 |
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195 @item |
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196 If the first argument is a matrix and the second is a vector, the |
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197 the columns (or rows) of the matrix are plotted versus the vector. |
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198 (using whichever combination matches, with columns tried first.) |
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199 |
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200 @item |
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201 If both arguments are vectors, the elements of @var{y} are plotted versus |
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202 the elements of @var{x}. |
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203 |
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204 @item |
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205 If both arguments are matrices, the columns of @var{y} are plotted |
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206 versus the columns of @var{x}. In this case, both matrices must have |
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207 the same number of rows and columns and no attempt is made to transpose |
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208 the arguments to make the number of rows match. |
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209 |
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210 If both arguments are scalars, a single point is plotted. |
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211 @end itemize |
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212 |
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213 The @var{fmt} argument, if present is interpreted as follows. If |
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214 @var{fmt} is missing, the default gnuplot line style is assumed. |
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215 |
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216 @table @asis |
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217 @item @samp{-} |
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218 Set lines plot style (default). |
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219 |
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220 @item @samp{.} |
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221 Set dots plot style. |
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222 |
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223 @item @samp{@@} |
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224 Set points plot style. |
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225 |
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226 @item @samp{-@@} |
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227 Set linespoints plot style. |
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228 |
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229 @item @samp{^} |
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230 Set impulses plot style. |
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231 |
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232 @item @samp{L} |
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233 Set steps plot style. |
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234 |
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235 @item @samp{#} |
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236 Set boxes plot style. |
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237 |
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238 @item @samp{~} |
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239 Set errorbars plot style. |
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240 |
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241 @item @samp{#~} |
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242 Set boxerrorbars plot style. |
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243 |
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244 @item @samp{n} |
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245 Interpreted as the plot color if @var{n} is an integer in the range 1 to |
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246 6. |
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247 |
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248 @item @samp{nm} |
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249 If @var{nm} is a two digit integer and @var{m} is an integer in the |
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250 range 1 to 6, @var{m} is interpreted as the point style. This is only |
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251 valid in combination with the @code{@@} or @code{-@@} specifiers. |
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252 |
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253 @item @samp{c} |
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254 If @var{c} is one of @var{"r"}, @var{"g"}, @var{"b"}, @var{"m"}, |
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255 @var{"c"}, or @var{"w"}, it is interpreted as the plot color (red, |
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256 green, blue, magenta, cyan, or white). |
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257 |
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258 @item @samp{+} |
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259 @itemx @samp{*} |
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260 @itemx @samp{o} |
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261 @itemx @samp{x} |
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262 Used in combination with the points or linespoints styles, set the point |
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263 style. |
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264 @end table |
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265 |
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266 The color line styles have the following meanings on terminals that |
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267 support color. |
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268 |
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269 @example |
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270 Number Gnuplot colors (lines)points style |
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271 1 red * |
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272 2 green + |
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273 3 blue o |
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274 4 magenta x |
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275 5 cyan house |
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276 6 brown there exists |
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277 @end example |
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278 |
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279 Here are some plot examples: |
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280 |
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281 @example |
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282 plot (x, y, "@@12", x, y2, x, y3, "4", x, y4, "+") |
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283 @end example |
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284 |
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285 This command will plot @var{y} with points of type 2 (displayed as |
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286 @code{+}) and color 1 (red), @var{y2} with lines, @var{y3} with lines of |
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287 color 4 (magenta) and @var{y4} with points displayed as @code{+}. |
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288 |
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289 @example |
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290 plot (b, "*") |
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291 @end example |
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292 |
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293 This command will plot the data in @var{b} will be plotted with points |
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294 displayed as @code{*}. |
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295 @end deftypefn |
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296 |
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297 @deftypefn {Function File} {} hold @var{args} |
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298 Tell Octave to `hold' the current data on the plot when executing |
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299 subsequent plotting commands. This allows you to execute a series of |
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300 plot commands and have all the lines end up on the same figure. The |
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301 default is for each new plot command to clear the plot device first. |
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302 For example, the command |
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303 |
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304 @example |
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305 hold on |
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306 @end example |
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307 |
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308 @noindent |
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309 turns the hold state on. An argument of @code{off} turns the hold state |
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310 off, and @code{hold} with no arguments toggles the current hold state. |
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311 @end deftypefn |
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312 |
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313 @deftypefn {Function File} {} ishold |
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314 Returns 1 if the next line will be added to the current plot, or 0 if |
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315 the plot device will be cleared before drawing the next line. |
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316 @end deftypefn |
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317 |
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318 @deftypefn {Function File} {} loglog (@var{args}) |
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319 Make a two-dimensional plot using log scales for both axes. See the |
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320 description of @code{plot} above for a description of the arguments that |
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321 @code{loglog} will accept. |
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322 @end deftypefn |
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323 |
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324 @deftypefn {Function File} {} semilogx (@var{args}) |
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325 Make a two-dimensional plot using a log scale for the @var{x} axis. See |
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326 the description of @code{plot} above for a description of the arguments |
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327 that @code{semilogx} will accept. |
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328 @end deftypefn |
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329 |
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330 @deftypefn {Function File} {} semilogy (@var{args}) |
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331 Make a two-dimensional plot using a log scale for the @var{y} axis. See |
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332 the description of @code{plot} above for a description of the arguments |
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333 that @code{semilogy} will accept. |
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334 @end deftypefn |
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335 |
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336 @deftypefn {Function File} {} contour (@var{z}, @var{n}, @var{x}, @var{y}) |
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337 Make a contour plot of the three-dimensional surface described by |
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338 @var{z}. Someone needs to improve @code{gnuplot}'s contour routines |
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339 before this will be very useful. |
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340 @end deftypefn |
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341 |
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342 @deftypefn {Function File} {} polar (@var{theta}, @var{rho}) |
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343 Make a two-dimensional plot given polar the coordinates @var{theta} and |
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344 @var{rho}. |
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345 @end deftypefn |
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346 |
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347 @node Three-Dimensional Plotting, Miscellaneous Plotting Functions, Two-Dimensional Plotting, Plotting |
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348 @section Three-Dimensional Plotting |
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349 |
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350 @deffn {Command} gsplot @var{ranges} @var{expression} @var{using} @var{title} @var{style} |
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351 Generate a 3-dimensional plot. |
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352 |
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353 The @var{ranges}, @var{using}, @var{title}, and @var{style} arguments |
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354 are optional, and the @var{using}, @var{title} and @var{style} |
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355 qualifiers may appear in any order after the expression. You may plot |
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356 multiple expressions with a single command by separating them with |
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357 commas. Each expression may have its own set of qualifiers. |
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358 |
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359 The optional item @var{ranges} has the syntax |
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360 |
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361 @example |
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362 [ x_lo : x_up ] [ y_lo : y_up ] [ z_lo : z_up ] |
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363 @end example |
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364 |
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365 @noindent |
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366 and may be used to specify the ranges for the axes of the plot, |
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367 independent of the actual range of the data. The range for the y and z |
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368 axes and any of the individual limits may be omitted. A range |
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369 @code{[:]} indicates that the default limits should be used. This |
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370 normally means that a range just large enough to include all the data |
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371 points will be used. |
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372 |
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373 The expression to be plotted must not contain any literal matrices (e.g. |
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374 @code{[ 1, 2; 3, 4 ]}) since it is nearly impossible to distinguish a |
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375 plot range from a matrix of data. |
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376 |
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377 See the help for @code{gnuplot} for a description of the syntax for the |
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378 optional items. |
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379 |
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380 By default, the @code{gsplot} command plots each column of the |
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381 expression as the z value, using the row index as the x value, and the |
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382 column index as the y value. The indices are counted from zero, not |
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383 one. For example, |
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384 |
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385 @example |
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386 gsplot rand (5, 2) |
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387 @end example |
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388 |
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389 @noindent |
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390 will plot a random surface, with the x and y values taken from the row |
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391 and column indices of the matrix. |
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392 |
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393 If parametric plotting mode is set (using the command |
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394 @samp{set parametric}, then @code{gsplot} takes the columns of the |
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395 matrix three at a time as the x, y and z values that define a line in |
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396 three space. Any extra columns are ignored, and the x and y values are |
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397 expected to be sorted. For example, with @samp{parametric} set, it |
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398 makes sense to plot a matrix like |
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399 @iftex |
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400 @tex |
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401 $$ |
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402 \left[\matrix{ |
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403 1 & 1 & 3 & 2 & 1 & 6 & 3 & 1 & 9 \cr |
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404 1 & 2 & 2 & 2 & 2 & 5 & 3 & 2 & 8 \cr |
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405 1 & 3 & 1 & 2 & 3 & 4 & 3 & 3 & 7}\right] |
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406 $$ |
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407 @end tex |
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408 @end iftex |
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409 @ifinfo |
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410 |
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411 @example |
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412 1 1 3 2 1 6 3 1 9 |
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413 1 2 2 2 2 5 3 2 8 |
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414 1 3 1 2 3 4 3 3 7 |
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415 @end example |
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416 @end ifinfo |
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417 |
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418 @noindent |
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419 but not @code{rand (5, 30)}. |
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420 @end deffn |
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421 |
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422 The @sc{Matlab}-style three-dimensional plotting commands are: |
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423 |
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424 @deftypefn {Function File} {} mesh (@var{x}, @var{y}, @var{z}) |
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425 Plot a mesh given matrices @code{x}, and @var{y} from @code{meshdom} and |
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426 a matrix @var{z} corresponding to the @var{x} and @var{y} coordinates of |
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427 the mesh. |
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428 @end deftypefn |
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429 |
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430 @deftypefn {Function File} {} meshdom (@var{x}, @var{y}) |
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431 Given vectors of @var{x} and @var{y} coordinates, return two matrices |
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432 corresponding to the @var{x} and @var{y} coordinates of the mesh. |
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433 |
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434 See the file @file{sombrero.m} for an example of using @code{mesh} and |
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435 @code{meshdom}. |
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436 @end deftypefn |
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437 |
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438 @defvr {Built-in Variable} gnuplot_binary |
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439 The name of the program invoked by the plot command. The default value |
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440 is @code{"gnuplot"}. @xref{Installation}. |
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441 @end defvr |
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442 |
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443 @defvr {Built-in Variable} gnuplot_has_frames |
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444 If the value of this variable is nonzero, Octave assumes that your copy |
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445 of gnuplot has support for multiple frames that is included in recent |
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446 3.6beta releases. It's initial value is determined by configure, but it |
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447 can be changed in your startup script or at the command line in case |
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448 configure got it wrong, or if you upgrade your gnuplot installation. |
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449 @end defvr |
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450 |
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451 @defvr {Built-in Variable} gnuplot_has_multiplot |
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452 If the value of this variable is nonzero, Octave assumes that your copy |
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453 of gnuplot has the multiplot support that is included in recent |
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454 3.6beta releases. It's initial value is determined by configure, but it |
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|
455 can be changed in your startup script or at the command line in case |
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|
456 configure got it wrong, or if you upgrade your gnuplot installation. |
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457 @end defvr |
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458 |
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459 @node Miscellaneous Plotting Functions, , Three-Dimensional Plotting, Plotting |
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460 @section Miscellaneous Plotting Functions |
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461 |
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462 @deftypefn {Function File} {} bar (@var{x}, @var{y}) |
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463 Given two vectors of x-y data, @code{bar} produces a bar graph. |
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464 |
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465 If only one argument is given, it is taken as a vector of y-values |
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466 and the x coordinates are taken to be the indices of the elements. |
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467 |
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|
468 If two output arguments are specified, the data are generated but |
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469 not plotted. For example, |
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470 |
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471 @example |
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472 bar (x, y); |
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473 @end example |
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474 |
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475 @noindent |
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476 and |
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477 |
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478 @example |
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479 [xb, yb] = bar (x, y); |
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|
480 plot (xb, yb); |
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481 @end example |
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482 |
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|
483 @noindent |
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|
484 are equivalent. |
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485 @end deftypefn |
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|
486 |
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|
487 @deftypefn {Function File} {} grid |
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488 For two-dimensional plotting, force the display of a grid on the plot. |
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|
489 @end deftypefn |
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490 |
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491 @deftypefn {Function File} {} stairs (@var{x}, @var{y}) |
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492 Given two vectors of x-y data, bar produces a `stairstep' plot. |
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|
493 |
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|
494 If only one argument is given, it is taken as a vector of y-values |
|
|
495 and the x coordinates are taken to be the indices of the elements. |
|
|
496 |
|
|
497 If two output arguments are specified, the data are generated but |
|
|
498 not plotted. For example, |
|
|
499 |
|
|
500 @example |
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|
501 stairs (x, y); |
|
|
502 @end example |
|
|
503 |
|
|
504 @noindent |
|
|
505 and |
|
|
506 |
|
|
507 @example |
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|
508 [xs, ys] = stairs (x, y); |
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|
509 plot (xs, ys); |
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|
510 @end example |
|
|
511 |
|
|
512 @noindent |
|
|
513 are equivalent. |
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|
514 @end deftypefn |
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|
515 |
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|
516 @deftypefn {Function File} {} title (@var{string}) |
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2333
|
517 Specify a title for the plot. If you already have a plot displayed, use |
|
|
518 the command @code{replot} to redisplay it with the new title. |
|
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|
519 @end deftypefn |
|
2333
|
520 |
|
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|
521 @deftypefn {Function File} {} xlabel (@var{string}) |
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|
522 @deftypefnx {Function File} {} ylabel (@var{string}) |
|
2333
|
523 Specify x and y axis labels for the plot. If you already have a plot |
|
|
524 displayed, use the command @code{replot} to redisplay it with the new |
|
|
525 labels. |
|
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|
526 @end deftypefn |
|
2333
|
527 |
|
2449
|
528 @deftypefn {Function File} {} sombrero (@var{n}) |
|
2333
|
529 Display a classic three-dimensional mesh plot. The parameter @var{n} |
|
|
530 allows you to increase the resolution. |
|
2449
|
531 @end deftypefn |
|
2333
|
532 |
|
2449
|
533 @deftypefn {Function File} {} clearplot |
|
|
534 @deftypefnx {Function File} {} clg |
|
2333
|
535 Clear the plot window and any titles or axis labels. The name |
|
|
536 @code{clg} is aliased to @code{clearplot} for compatibility with @sc{Matlab}. |
|
|
537 |
|
|
538 The commands @samp{gplot clear}, @samp{gsplot clear}, and @samp{replot |
|
|
539 clear} are equivalent to @samp{clearplot}. (Previously, commands like |
|
|
540 @samp{gplot clear} would evaluate @samp{clear} as an ordinary expression |
|
|
541 and clear all the visible variables.) |
|
2449
|
542 @end deftypefn |
|
2333
|
543 |
|
2449
|
544 @deftypefn {Function File} {} closeplot |
|
2333
|
545 Close stream to the @code{gnuplot} subprocess. If you are using X11, |
|
|
546 this will close the plot window. |
|
2449
|
547 @end deftypefn |
|
2333
|
548 |
|
2449
|
549 @deftypefn {Function File} {} purge_tmp_files |
|
2333
|
550 Delete the temporary files created by the plotting commands. |
|
|
551 |
|
|
552 Octave creates temporary data files for @code{gnuplot} and then sends |
|
|
553 commands to @code{gnuplot} through a pipe. Octave will delete the |
|
|
554 temporary files on exit, but if you are doing a lot of plotting you may |
|
|
555 want to clean up in the middle of a session. |
|
|
556 |
|
|
557 A future version of Octave will eliminate the need to use temporary |
|
|
558 files to hold the plot data. |
|
2449
|
559 @end deftypefn |
|
2333
|
560 |
|
2449
|
561 @deftypefn {Function File} {} axis (@var{limits}) |
|
2333
|
562 Sets the axis limits for plots. |
|
|
563 |
|
|
564 The argument @var{limits} should be a 2, 4, or 6 element vector. The |
|
|
565 first and second elements specify the lower and upper limits for the x |
|
|
566 axis. The third and fourth specify the limits for the y axis, and the |
|
|
567 fifth and sixth specify the limits for the z axis. |
|
|
568 |
|
|
569 With no arguments, @code{axis} turns autoscaling on. |
|
|
570 |
|
|
571 If your plot is already drawn, then you need to use @code{replot} before |
|
|
572 the new axis limits will take effect. You can get this to happen |
|
|
573 automatically by setting the built-in variable @code{automatic_replot} |
|
2449
|
574 to a nonzero value. |
|
|
575 @end deftypefn |
|
2333
|
576 |
|
2449
|
577 @deftypefn {Function File} {} hist (@var{y}, @var{x}) |
|
2333
|
578 Produce histogram counts or plots. |
|
|
579 |
|
|
580 With one vector input argument, plot a histogram of the values with |
|
|
581 10 bins. The range of the histogram bins is determined by the range |
|
|
582 of the data. |
|
|
583 |
|
|
584 Given a second scalar argument, use that as the number of bins. |
|
|
585 |
|
|
586 Given a second vector argument, use that as the centers of the bins, |
|
|
587 with the width of the bins determined from the adjacent values in |
|
|
588 the vector. |
|
|
589 |
|
|
590 Extreme values are lumped in the first and last bins. |
|
|
591 |
|
|
592 With two output arguments, produce the values @var{nn} and @var{xx} such |
|
|
593 that @code{bar (@var{xx}, @var{nn})} will plot the histogram. |
|
2449
|
594 @end deftypefn |
