# Gnuplotting

Create scientific plots using gnuplot

August 13th, 2010 | 7 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.

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.

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.

1. Tony says:

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 :-)

6. Kuti says:

Many thanks!

7. JGarcia177 says:

Very useful! Thanks