Plotting
********

All of Octave's plotting functions use gnuplot to handle the actual graphics.  There are two low-level functions, gplot and gsplot, that behave almost exactly like the corresponding gnuplot functions plot and splot.  A number of other higher level plotting functions, patterned after the graphics functions found in MATLAB version 3.5, are also available. These higher level functions are all implemented in terms of the two low-level plotting functions.

Two-Dimensional Plotting
========================

 -- Command: gplot RANGES EXPRESSION USING TITLE STYLE
     Generate a 2-dimensional plot.

     The RANGES, USING, TITLE, and STYLE arguments are optional, and the USING, TITLE and STYLE qualifiers may appear in any order after the expression.  You may plot multiple expressions with a single command by separating them with commas.  Each expression may have its own set of qualifiers.

     The optional item RANGES has the syntax

          [ x_lo : x_up ] [ y_lo : y_up ]

     and may be used to specify the ranges for the axes of the plot, independent of the actual range of the data.  The range for the y axes and any of the individual limits may be omitted.  A range [:] indicates that the default limits should be used.  This normally means that a range just large enough to include all the data points will be used.

     The expression to be plotted must not contain any literal matrices (e.g. [ 1, 2; 3, 4 ]) since it is nearly impossible to distinguish a plot range from a matrix of data.

     See the help for gnuplot for a description of the syntax for the optional items.

     By default, the gplot command plots the second column of a matrix versus the first.  If the matrix only has one column, it is taken as a vector of y-coordinates and the x-coordinate is taken as the element index, starting with zero.  For example,

          gplot rand (100,1) with linespoints

     will plot 100 random values and connect them with lines.  When gplot is used to plot a column vector, the indices of the elements are taken as x values.

     If there are more than two columns, you can choose which columns to plot with the USING qualifier. For example, given the data

          x = (-10:0.1:10)';
          data = [x, sin(x), cos(x)];

     the command

          gplot [-11:11] [-1.1:1.1] \
            data with lines, data using 1:3 with impulses

     will plot two lines.  The first line is generated by the command data with lines, and is a graph of the sine function over the range -10 to 10.  The data is taken from the first two columns of the matrix because columns to plot were not specified with the USING qualifier.

     The clause using 1:3 in the second part of this plot command specifies that the first and third columns of the matrix data should be taken as the values to plot.

     In this example, the ranges have been explicitly specified to be a bit larger than the actual range of the data so that the curves do not touch the border of the plot.

 -- Command: gset options
 -- Command: gshow options
 -- Command: replot options
     In addition to the basic plotting commands, the whole range of gset and gshow commands from gnuplot are available, as is replot.

     Note that in Octave 2.0, the set and show commands were renamed to gset and gshow in order to allow for compatibility with the MATLAB graphics and GUI commands in a future version of Octave.  (For now, the old set and show commands do work, but they print an annoying warning message to try to get people to switch to using gset and gshow.)

     The gset and gshow commands allow you to set and show gnuplot parameters.  For more information about the gset and gshow commands, see the documentation for set and show in the gnuplot user's guide (also available on line if you run gnuplot directly, instead of running it from Octave).

     The replot command allows you to force the plot to be redisplayed.  This is useful if you have changed something about the plot, such as the title or axis labels.  The replot command also accepts the same arguments as gplot or gsplot (except for data ranges) so you can add additional lines to existing plots.

     For example,

          gset term tek40
          gset output "/dev/plotter"
          gset title "sine with lines and cosine with impulses"
          replot "sin (x) w l"

     will change the terminal type for plotting, add a title to the current plot, add a graph of sin (x) to the plot, and force the new plot to be sent to the plot device.  This last step is normally required in order to update the plot.  This default is reasonable for slow terminals or hardcopy output devices because even when you are adding additional lines with a replot command, gnuplot always redraws the entire plot, and you probably don't want to have a completely new plot generated every time something as minor as an axis label changes.

     The command shg is equivalent to executing replot without any arguments.

 -- Built-in Variable: automatic_replot
     You can tell Octave to redisplay the plot each time anything about it changes by setting the value of the builtin variable automatic_replot to a nonzero value.  Since this is fairly inefficient, the default value is 0.

Note that NaN values in the plot data are automatically omitted, and Inf values are converted to a very large value before calling gnuplot.

The MATLAB-style two-dimensional plotting commands are:

 -- Function File: plot (ARGS)
     This function produces two-dimensional plots.  Many different combinations of arguments are possible.  The simplest form is

          plot (Y)

     where the argument is taken as the set of Y coordinates and the X coordinates are taken to be the indices of the elements, starting with 1.

     If more than one argument is given, they are interpreted as

          plot (X, Y, FMT ...)

     where Y and FMT are optional, and any number of argument sets may appear.  The X and Y values are interpreted as follows:

       * If a single data argument is supplied, it is taken as the set of Y coordinates and the X coordinates are taken to be the indices of the elements, starting with 1.

       * If the first argument is a vector and the second is a matrix, the the vector is plotted versus the columns (or rows) of the matrix. (using whichever combination matches, with columns tried first.)

       * If the first argument is a matrix and the second is a vector, the the columns (or rows) of the matrix are plotted versus the vector. (using whichever combination matches, with columns tried first.)

       * If both arguments are vectors, the elements of Y are plotted versus the elements of X.

       * If both arguments are matrices, the columns of Y are plotted versus the columns of X.  In this case, both matrices must have the same number of rows and columns and no attempt is made to transpose the arguments to make the number of rows match.

          If both arguments are scalars, a single point is plotted.

     The FMT argument, if present is interpreted as follows.  If FMT is missing, the default gnuplot line style is assumed.

     -
          Set lines plot style (default).

     .
          Set dots plot style.

     @
          Set points plot style.

     -@
          Set linespoints plot style.

     ^
          Set impulses plot style.

     L
          Set steps plot style.

     #
          Set boxes plot style.

     ~
          Set errorbars plot style.

     #~
          Set boxerrorbars plot style.

     N
          Interpreted as the plot color if N is an integer in the range 1 to 6.

     NM
          If NM is a two digit integer and M is an integer in the range 1 to 6, M is interpreted as the point style.  This is only valid in combination with the @ or -@ specifiers.

     C
          If C is one of "r", "g", "b", "m", "c", or "w", it is interpreted as the plot color (red, green, blue, magenta, cyan, or white).

     +
     *
     o
     x
          Used in combination with the points or linespoints styles, set the point style.

     The color line styles have the following meanings on terminals that support color.

          Number  Gnuplot colors  (lines)points style
            1       red                   *
            2       green                 +
            3       blue                  o
            4       magenta               x
            5       cyan                house
            6       brown            there exists

     Here are some plot examples:

          plot (x, y, "@12", x, y2, x, y3, "4", x, y4, "+")

     This command will plot y with points of type 2 (displayed as +) and color 1 (red), y2 with lines, y3 with lines of color 4 (magenta) and y4 with points displayed as +.

          plot (b, "*")

     This command will plot the data in the variable b will be plotted with points displayed as *.

 -- Function File: hold ARGS
     Tell Octave to `hold' the current data on the plot when executing subsequent plotting commands.  This allows you to execute a series of plot commands and have all the lines end up on the same figure.  The default is for each new plot command to clear the plot device first. For example, the command

          hold on

     turns the hold state on.  An argument of off turns the hold state off, and hold with no arguments toggles the current hold state.

 -- Function File: ishold
     Return 1 if the next line will be added to the current plot, or 0 if the plot device will be cleared before drawing the next line.

 -- Function File: clearplot
 -- Function File: clg
     Clear the plot window and any titles or axis labels.  The name clg is aliased to clearplot for compatibility with MATLAB.

     The commands gplot clear, gsplot clear, and replot clear are equivalent to clearplot.  (Previously, commands like gplot clear would evaluate clear as an ordinary expression and clear all the visible variables.)

 -- Function File: closeplot
     Close stream to the gnuplot subprocess.  If you are using X11, this will close the plot window.

 -- Function File: purge_tmp_files
     Delete the temporary files created by the plotting commands.

     Octave creates temporary data files for gnuplot and then sends commands to gnuplot through a pipe.  Octave will delete the temporary files on exit, but if you are doing a lot of plotting you may want to clean up in the middle of a session.

     A future version of Octave will eliminate the need to use temporary files to hold the plot data.

 -- Function File: axis (LIMITS)
     Sets the axis limits for plots.

     The argument LIMITS should be a 2, 4, or 6 element vector.  The first and second elements specify the lower and upper limits for the x axis.  The third and fourth specify the limits for the y axis, and the fifth and sixth specify the limits for the z axis.

     With no arguments, axis turns autoscaling on.

     If your plot is already drawn, then you need to use replot before the new axis limits will take effect.  You can get this to happen automatically by setting the built-in variable automatic_replot to a nonzero value.

Specialized Two-Dimensional Plots
=================================

 -- Function File: bar (X, Y)
     Given two vectors of x-y data, bar produces a bar graph.

     If only one argument is given, it is taken as a vector of y-values and the x coordinates are taken to be the indices of the elements.

     If two output arguments are specified, the data are generated but not plotted.  For example,

          bar (x, y);

     and

          [xb, yb] = bar (x, y);
          plot (xb, yb);

     are equivalent.

 -- Function File: contour (Z, N, X, Y)
     Make a contour plot of the three-dimensional surface described by Z.  Someone needs to improve gnuplot's contour routines before this will be very useful.

 -- Function File: hist (Y, X)
     Produce histogram counts or plots.

     With one vector input argument, plot a histogram of the values with 10 bins.  The range of the histogram bins is determined by the range of the data.

     Given a second scalar argument, use that as the number of bins.

     Given a second vector argument, use that as the centers of the bins, with the width of the bins determined from the adjacent values in the vector.

     Extreme values are lumped in the first and last bins.

     With two output arguments, produce the values NN and XX such that bar (XX, NN) will plot the histogram.

 -- Function File: loglog (ARGS)
     Make a two-dimensional plot using log scales for both axes.  See the description of plot above for a description of the arguments that loglog will accept.

 -- Function File: polar (THETA, RHO)
     Make a two-dimensional plot given polar the coordinates THETA and RHO.

 -- Function File: semilogx (ARGS)
     Make a two-dimensional plot using a log scale for the X axis.  See the description of plot above for a description of the arguments that semilogx will accept.

 -- Function File: semilogy (ARGS)
     Make a two-dimensional plot using a log scale for the Y axis.  See the description of plot above for a description of the arguments that semilogy will accept.

 -- Function File: stairs (X, Y)
     Given two vectors of x-y data, bar produces a `stairstep' plot.

     If only one argument is given, it is taken as a vector of y-values and the x coordinates are taken to be the indices of the elements.

     If two output arguments are specified, the data are generated but not plotted.  For example,

          stairs (x, y);

     and

          [xs, ys] = stairs (x, y);
          plot (xs, ys);

     are equivalent.

Three-Dimensional Plotting
==========================

 -- Command: gsplot RANGES EXPRESSION USING TITLE STYLE
     Generate a 3-dimensional plot.

     The RANGES, USING, TITLE, and STYLE arguments are optional, and the USING, TITLE and STYLE qualifiers may appear in any order after the expression.  You may plot multiple expressions with a single command by separating them with commas.  Each expression may have its own set of qualifiers.

     The optional item RANGES has the syntax

          [ x_lo : x_up ] [ y_lo : y_up ] [ z_lo : z_up ]

     and may be used to specify the ranges for the axes of the plot, independent of the actual range of the data.  The range for the y and z axes and any of the individual limits may be omitted.  A range [:] indicates that the default limits should be used.  This normally means that a range just large enough to include all the data points will be used.

     The expression to be plotted must not contain any literal matrices (e.g. [ 1, 2; 3, 4 ]) since it is nearly impossible to distinguish a plot range from a matrix of data.

     See the help for gnuplot for a description of the syntax for the optional items.

     By default, the gsplot command plots each column of the expression as the z value, using the row index as the x value, and the column index as the y value.  The indices are counted from zero, not one.  For example,

          gsplot rand (5, 2)

     will plot a random surface, with the x and y values taken from the row and column indices of the matrix.

     If parametric plotting mode is set (using the command gset parametric, then gsplot takes the columns of the matrix three at a time as the x, y and z values that define a line in three space.  Any extra columns are ignored, and the x and y values are expected to be sorted.  For example, with parametric set, it makes sense to plot a matrix like

          1 1 3 2 1 6 3 1 9
          1 2 2 2 2 5 3 2 8
          1 3 1 2 3 4 3 3 7

     but not rand (5, 30).

The MATLAB-style three-dimensional plotting commands are:

 -- Function File: mesh (X, Y, Z)
     Plot a mesh given matrices x, and Y from meshdom and a matrix Z corresponding to the X and Y coordinates of the mesh.

 -- Function File: meshdom (X, Y)
     Given vectors of X and Y coordinates, return two matrices corresponding to the X and Y coordinates of the mesh.

     See the file sombrero.m for an example of using mesh and meshdom.

 -- Built-in Variable: gnuplot_binary
     The name of the program invoked by the plot command.  The default value is "gnuplot".  See Installation.

 -- Built-in Variable: gnuplot_has_frames
     If the value of this variable is nonzero, Octave assumes that your copy of gnuplot has support for multiple frames that is included in recent 3.6beta releases.  It's initial value is determined by configure, but it can be changed in your startup script or at the command line in case configure got it wrong, or if you upgrade your gnuplot installation.

 -- Function File: figure (N)
     Set the current plot window to plot window N.  This function currently requires X11 and a version of gnuplot that supports multiple frames.

 -- Built-in Variable: gnuplot_has_multiplot
     If the value of this variable is nonzero, Octave assumes that your copy of gnuplot has the multiplot support that is included in recent 3.6beta releases.  It's initial value is determined by configure, but it can be changed in your startup script or at the command line in case configure got it wrong, or if you upgrade your gnuplot installation.

Plot Annotations
================

 -- Function File: grid
     For two-dimensional plotting, force the display of a grid on the plot.

 -- Function File: title (STRING)
     Specify a title for the plot.  If you already have a plot displayed, use the command replot to redisplay it with the new title.

 -- Function File: xlabel (STRING)
 -- Function File: ylabel (STRING)
 -- Function File: zlabel (STRING)
     Specify x, y, and z axis labels for the plot.  If you already have a plot displayed, use the command replot to redisplay it with the new labels.

Multiple Plots on One Page
==========================

The following functions all require a version of gnuplot that supports the multiplot feature.

 -- Function File: mplot (X, Y)
 -- Function File: mplot (X, Y, FMT)
 -- Function File: mplot (X1, Y1, X2, Y2)
     This is a modified version of the plot function that works with the multiplot version of gnuplot to plot multiple plots per page. This plot version automatically advances to the next subplot position after each set of arguments are processed.

     See the description of the PLOT function for the various options.

 -- Function File: multiplot (XN, YN)
     Sets and resets multiplot mode.

     If the arguments are non-zero, multiplot will set up multiplot mode with XN, YN subplots along the X and Y axes.  If both arguments are zero, multiplot closes multiplot mode.

 -- Function File: oneplot ()
     If in multiplot mode, switches to single plot mode.

 -- Function File: plot_border (...)
     Multiple arguments allowed to specify the sides on which the border is shown.  Allowed arguments include:

     "blank"
          No borders displayed.

     "all"
          All borders displayed

     "north"
          North Border

     "south"
          South Border

     "east"
          East Border

     "west"
          West Border

     The arguments may be abbreviated to single characters.  Without any arguments, plot_border turns borders off.

 -- Function File: subplot (ROWS, COLS, INDEX)
 -- Function File: subplot (RCN)
     Sets gnuplot in multiplot mode and plots in location given by index (there are COLS by ROWS subwindows).

     Input:

     rows
          Number of rows in subplot grid.

     columns
          Number of columns in subplot grid.

     index
          Index of subplot where to make the next plot.

     If only one argument is supplied, then it must be a three digit value specifying the location in digits 1 (rows) and 2 (columns) and the plot index in digit 3.

     The plot index runs row-wise.  First all the columns in a row are filled and then the next row is filled.

     For example, a plot with 4 by 2 grid will have plot indices running as follows:

          +-----+-----+-----+-----+
          |  1  |  2  |  3  |  4  |
          +-----+-----+-----+-----+
          |  5  |  6  |  7  |  8  |
          +-----+-----+-----+-----+

 -- Function File: subwindow (XN, YN)
     Sets the subwindow position in multiplot mode for the next plot.  The multiplot mode has to be previously initialized using the multiplot function, otherwise this command just becomes an alias to multiplot

 -- Function File: top_title (STRING)
 -- Function File: bottom_title (STRING)
     Makes a title with text STRING at the top (bottom) of the plot.