Figures, Graphs, and Plots in Octave

This twelfth article of the mathematical journey through open source, shows the mathematical visualization in octave.

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Mathematics is incomplete without visualization, without drawing the results, and without plotting the graphs. octave uses the powerful gnuplot as the backend of its plotting functionality. And in the frontend provides various plotting functions. Let’s look at the most beautiful ones.

Basic 2D Plotting

The most basic plotting is using the plot() function, which takes the Cartesian x & y values. Additionally, you may pass, as how to plot, i.e. as points or lines, their style, their colour, label, etc. Supported point styles are: +, *, o, x, ^, and lines are represented by -. Supported colours are: k (black), r (red), g (green), b (blue), y (yellow), m (magenta), c (cyan), w (white). With this background, here is how you plot a sine curve, and Figure 12 shows the plot.

$ octave -qf
octave:1> x = 0:0.1:2*pi;
octave:2> y = sin(x);
octave:3> plot(x, y, "^b");
octave:4> xlabel("x ->");
octave:5> ylabel("y = sin(x) ->");
octave:6> title("Basic plot");
octave:7>
Figure 12: Basic plotting in octave

Figure 12: Basic plotting in octave

xlabel(), and ylabel() adds the corresponding labels, and title() adds the title. Multiple plots can be done on the same axis as follows, and Figure 13 shows the plots. Note the usage of legend() to mark the multiple plots.

$ octave -qf
octave:1> x = 0:0.1:2*pi;
octave:2> plot(x, sin(x), "*", x, 1 + sin(x), "-", x, cos(x), "o");
octave:3> xlabel("x ->");
octave:4> ylabel("y ->");
octave:5> legend("sine", "1 + sine", "cosine");
octave:6> title("Multiple plots");
octave:7>
Figure 13: Multiple plots on the same axis

Figure 13: Multiple plots on the same axis

Advanced 2D Figures

Now, if we want to have the multiple graphs on the same sheet but with different axes as shown in Figure 14, here is how to do that:

octave:1> t = 0:0.1:6*pi;
octave:2> subplot(2, 1, 1);
octave:3> plot(t, 325 * sin(t));
octave:4> xlabel("t (sec)");
octave:5> ylabel("V_{ac} (V)");
octave:6> title("AC voltage curve");
octave:7> grid("on");
octave:8> subplot(2, 1, 2);
octave:9> plot(t, 5 * cos(t));
octave:10> xlabel("t (sec)");
octave:11> ylabel("I_{ac} (A)");
octave:12> title("AC current curve");
octave:13> grid("on");
octave:14> print("-dpng", "multiple_plots_on_a_sheet.png");
octave:15>
Figure 14: Multiple plots on a sheet

Figure 14: Multiple plots on a sheet

Note the usage of subplot(), taking the matrix dimensions (row, column) and the plot number to create the matrix of plots. In the example above, it created a 2×1 matrix of plots. As add-ons, we have used the grid(“on”) to show up the dotted grid lines, and print() to save the generated figure as a .png file.

It is not always easy to plot everything in Cartesian co-ordinates, or rather many things are easier to plot in polar co-ordinates, e.g. a spiral, circle, heart, etc. The following code & Figure 15 shows a few such examples. Shown along with is a technique of modifying the figure properties, after drawing the figure using the set() function. Here it modifies the line thickness.

octave:1> th = 0:0.1:2*pi;
octave:2> r1 = 1.1 .^ th;
octave:3> r2 = 7 * cos(th);
octave:4> r3 = 5 * (1 - cos(th));
octave:5> r = [r1; r2; r3];
octave:6> ph = polar(th, r, "-");
octave:7> set(ph, "LineWidth", 4);
octave:8> legend("spiral", "circle", "heart");
octave:9>
Figure 15: Polar plots

Figure 15: Polar plots

There are many other possible ways of drawing various interesting 2-D figures for all kind of mathematical & scientific requirements. So, before closing on 2-D plotting, let’s look into just one more often needed drawing – plotting with log axis, and more over with two y-axes on a single plot. The function for that is plotyy(). Note the plotyy() calling the corresponding function pointers @plot, @semilogy passed to it, in the following code segment. Figure 16 shows the output.

octave:1> x = 0:0.1:2*pi;
octave:2> y1 = sin(x);
octave:3> y2 = exp(exp(x));
octave:4> ax = plotyy(x, y1, x, y2, @plot, @semilogy);
octave:5> xlabel("x ->");
octave:6> ylabel(ax(1), "sine ->");
octave:7> ylabel(ax(2), "e^{e^x} ->");
octave:8> title("Mixed plots");
octave:9>
Figure 16: Mixed plots with semi log axis

Figure 16: Mixed plots with semi log axis

3D Visualization

And finally, let’s do some 3-D plotting. plot3() is the simplest octave function to do a simple 3-D drawing, taking the set of (x, y, z) points. Here’s the sample code to draw the dwindling sinusoidal curve shown in Figure 17:

octave:1> x = -10:0.1:10;
octave:2> y = 10:-0.1:-10;
octave:3> z = x .* sin(x - y); 
octave:4> plot3(x, y, z, "-", "LineWidth", 4); 
octave:5> xlabel("x ->");
octave:6> ylabel("y ->");
octave:7> zlabel("z ->");
octave:8> title("Dwindling sinusoidal");
octave:9> grid("on");
octave:10>
Figure 17: 3-D plot of a dwindling sinusoidal

Figure 17: 3-D plot of a dwindling sinusoidal

In case, we want to plot the values of a 2-D matrix against its indices (x, y), it could be done using mesh(), one of the many other 3-D plotting functions. Figure 18 shows the same, created using the following code:

octave:1> x = 0:0.1:2*pi;
octave:2> y = 0:0.1:2*pi;
octave:3> z = sin(x)' * sin(y);
octave:4> mesh(x, y, z); 
octave:5> xlabel("x ->");
octave:6> ylabel("y ->");
octave:7> zlabel("z ->");
octave:8> title("3-D waves");
octave:9>
Figure 18: 3-D waves

Figure 18: 3-D waves

What’s next?

Hope you enjoyed the colours of drawing. Next, we would look into octave from a statisticians perspective.

Thirteenth Article >>

Anil Kumar Pugalia Anil Kumar Pugalia (106 Posts)

The author is a hobbyist in open source hardware and software, with a passion for mathematics, and philosopher in thoughts. A gold medallist from the Indian Institute of Science, Linux, mathematics and knowledge sharing are few of his passions. He experiments with Linux and embedded systems to share his learnings through his weekend workshops. Learn more about him and his experiments at https://sysplay.in.


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6 thoughts on “Figures, Graphs, and Plots in Octave

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  3. David Nelson

    Thank you, Anil,

    I would like to eliminate the gridlines on the plot and see–and save–just color information.

    From advice elsewhere, I tried separately:
    surface(x,y,z,’linestyle’,’none’), shading(‘interp’), colormap(gray);
    surface(x,y,z,’edgecolor’,’none’), shading(‘interp’), colormap(gray);
    (because I really only want intensities) and both do result in plots which visually do not show
    visible lines between the values of the mesh. (I understand that the ‘interp’ shading interpolates missing values).

    However, when I “Save-as” the result as a ‘png’, the image always contains residual evidence of the lines.

    Also, if I may, is there a way to lock the aspect ratio of resulting plots? Despite the fact that my x,y values are symmetric, the plots are always over a rectangular grid, instead of square.

    Reply
    1. Anil Kumar PugaliaAnil Kumar Pugalia Post author

      David, I am getting it perfectly fine. Just try “graphics_toolkit(“gnuplot”);”, the first thing when you start octave, and then do your drawings, prints, etc. Let us know, if it helps.

      Regarding the aspect ratio, you may try pbaspect() for plot box and daspect() for data. Without parameter, they return the current corresponding aspect ratios. With a 3-D vector, they change the corresponding aspect ratios.

      Reply
  4. lakshmikruthiga

    sir, I have following code, The values of displ in stage1 and stage2 are plotted in displ vs time graph. Thus a single curve is obtained.

    displ=zeros(100,2)
    tim=zeros(100,1)
    for i=2:100
    v=5;
    dt=1*10^-4;
    function [displ_f]=stage1(displ_i)
    dt=1*10^-4;
    v=5;
    displ_f=displ_i+v*dt;
    endfunction
    function [displ_f]=stage2(displ_i)
    dt=1*10^-4;
    v=5;
    displ_f=displ_i+v*dt;
    endfunction
    if (displ(i-1,1)=0)
    disp(“IN stage 1”);
    [displ(i,1)]=stage1(displ(i-1,1));
    displ(i,2)=v;
    tim(i,1)=tim(i-1)+dt;
    elseif (displ(i-1,1)>=0.020 && displ(i-1,1)==0)
    disp(“IN stage 2″);
    [displ(i,1)]=stage2(displ(i-1,1));
    displ(i,2)=displ(i-1,2);
    tim(i,1)=tim(i-1)+dt;
    end
    end
    disp(” displ vs tim”)
    plot(tim(:,1),displ(:,1));

    How will I get stage1 curve in orange color and stage2 curve in blue color in the same plot to know which stage has which displ values? kindly help me.

    Reply

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