Tutorial 2: Studying functions in Haskell

3 Tutorial 2: Studying functions in Haskell

3.1 Worked example

pict

Figure 1: Plot of

f (x) = 2 x^{2} - 4 x

We can use Haskell to study the behaviour of mathematical functions. The function $f (x)$ is defined as

f (x) = 2 x^{2} - 4 x

and plotted in Figure 1.

1.

To study the function, we need to define it as a function. Create a module in a file NumTutorial.hs, with the following definition

module NumTutorial where 
 
f :: Double −> Double 
f x = 2*x**2 − 4*x

2.

In this exercise, we will use the easyplot library. We install it with the following commands before we start GHCi.

cabal update 
cabal install easyplot

3.

easyplot depends on gnuplot, which you also have to install. If you run Debian/Ubuntu, try the following.

apt−get install gnuplot

Otherwise please google for installation instructions for your OS.

4.

Open GHCi

ghci

5.

Load the module

:l NumTutorial

6.

Test the function f

f 0 
f 1 
f (−1)

Do the results look reasonable?

7.

We import the EasyPlot library so that we can use it

import Graphics.EasyPlot

You will see that the prompt changes, to indicate loaded modules.

8.

The following command plots the function f.

plot X11 ( Function2D [] [] f )

The second argument to plot is a data set. The Function2D function creates such a data set from a function.

Note If you run Windows you need to replace X11 with Windows (unless you have an X server running). There is a similar Aqua option for Mac OS, but Mac ofthen has an X server as well.

If the plot window closes before you manage to see it, try the following variant instead (Windows):

plot’ [Interactive] Windows ( Function2D [] [] f )

9.

The two empty brackets in the arguments for Function2D are lists of options. We can add a title and restrict the range, as follows:

:set +m 
plot X11 ( Function2D 
           [Title "The f function"] 
           [Range (−20) (20)] f )

The :set +m command is necessary to allow one statement to span multiple lines. The plot statement has been split over three lines just to make it easier to read.

10.

The X11 argument to plot says that the plot be shown in an X11 window. It is possible to plot to file, as follows:

:set +m 
plot (PDF "fplot.pdf") ( Function2D 
           [Title "The f function"] 
           [Range (−20) (20)] f )

11.

Leave GHCi (use the :q command).

12.

Open the PDF plot, using

okular fplot.pdf &

If you want to learn more about EasyPlot, you find documentation on Hackage.

3.2 Practice Problem

pict

Figure 2: Plot of

g (x) = x^{5} + x^{4} \cdot 2 + x^{2} \cdot 4 + x - 10

Let’s study a second function $g (x)$ . A plot is shown in Figure 2, and the definition is

g (x) = x^{5} + x^{4} \cdot 2 + x^{2} \cdot 4 + x - 10

Please implement and plot this function in Haskell, as follows:

1.: Add a definition for a function g in the file NumTutorial.hs.
2.: Open GHCi and load NumTutorial.
3.: Evaluate $g (0)$ , $g (1)$ , and $g (- 1)$ to test the function g. Do the results look reasonable?
4.: Import Graphics.EasyPlot
5.: Plot the function g on the range $- 10 \geq x \geq 10$ in a window. Give the curve a meaningful title.
6.: Plot the g function to a PDF file (gplot.pdf).
7.: Leave GHCi (use the :q command) and open the PDF plot in okular (or another PDF viewer).

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