Gnuplotting

Create scientific plots using gnuplot

August 13th, 2010 | 5 Comments

In Gnuplot it is easy to define a continuous and differentiable function such as f(x) = x, but what to do if we need a function that fulfill non of these conditions?
For example let us consider a step function. Typically a step function is given by

           / 1   if x > a
step(x) = -|
           \ 0   else

In Gnuplot this can be achieved by using the ternary operator:

step(x) = x>a ? 1 : 0

Which is a simple if-else statement and means step(x)=1 if x>a else step(x)=0.

If we plot this function we get Fig. 1.

step function

Fig. 1 Continuous plot of the step function (code to produce this figure)

As you can see this will result in a continuous plot. If we want a discontinuity in the plot, we have to create two separate functions that are only piecewise defined. This can be achieved by using 1/0 that will result in a undefined value.

f(x) = x<a  ? 1 : 1/0
g(x) = x>=a ? 1 : 1/0 

Plotting both functions will result in Fig. 2.

step function

Fig. 2 Discontinuous plot of the step function (code to produce this figure)

The ternary operator can also be used in an iterative way. For example if we want to define a rectangular function that is given by

           / 0     if abs(x) > 0.5
rect(x) = -| 0.5   if abs(x) = 0.5
           \ 1     if abs(x) < 0.5

we can use the following statement in Gnuplot to define it:

rect(x) = abs(x)>0.5 ? 0 : abs(x)<0.5 ? 1 : 0.5

In Fig. 3 you can see a plot of this function. To produce the sharp edges of the rectangular function we use a higher number of sampling points (also in Fig. 1 for the step function). In order to plot a function Gnuplot calculates 100 points of the given function and draw a line through them. This can be set to another value with the set samples <value> command.

rectangular function

Fig. 3 Plot of the above defined rect(x) function (code to produce this figure)

5 Comments

  1. Tony says:

    Very helpful!!!
    Thanks ;)

  2. Sascha says:

    Very helpful indeed, thank you very much!

  3. Owen says:

    Very useful! :)

    Is it possible to use these discontinuous functions in ‘fit’- I can’t seem to get it work myself.

  4. hagen says:

    What is not so easy is to get the range values of the different parts of the step functions, but the actual y values worked well for me.

    For example, for step_data.txt try:

    rect(x) = abs(x)>0.5 ? a : abs(x)<0.5 ? b : b/2.0
    fit rect(x) 'step_data.txt' u 1:2 via a,b
    plot 'step_data.txt' u 1:2 w p ls 1, \
         rect(x)               w l ls 2
    
  5. Rose says:

    Thanks SO much! I have been looking everywhere for a way of plotting a “discontinuous” step function as above. How very nice to find one :-)

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