1 The Scilab environment

To start Scilab:

Double-click the Scilab icon on the PC desktop, or

Go to Start / All Programs / Scilab / scilab (do not select scilab console).

Start Scilab.

Starting Scilab opens the Scilab command window, see the figure below.

The Scilab command window

Scilab commands are executed at the command line by entering the command, and

then clicking the Enter button on the keyboard.

Execute 1+1 (type 1+1 at the command line, and finish with Enter-button).

The result is shown in the command window (see the figure above).

2 Scilab Help

Open Scilab Help by clicking the Help button in the toolbar (the button with the question mark).

The Help window is shown below.

Scilab Help window

As you see from the Help window, the commands and functions are organized in a

number of categories.

As an example, click the Elementary Functions category to see the functions in that category.

The functions are as shown in the figure above.

To get detailed help text about a specific function, click that function.

Click the abs function (in the Elementary Functions category).

The detailed help text for the abs function is shown in the figure below.

The detailed help text for the abs function

You can also search for a function by first clicking the Search button in the Help

window (the magnifying glass button).

Search for sine.

The result of the search is a list of relevant functions, see the figure below.

The result of the search for sine

3 Basic Scilab operations

Typically you use variables in your calculations. To create the variable a and

assigning to it the result of 1+1:

a=1+1 (Enter)

Hereafter, (Enter) will not be shown, but it is assumed that you click the Enter button.

The response is shown in the command window (but shown here). Now, try

(remember to type the semicolon):

b=1+2;

The response is not shown in the command window. The command was actually

executed, but because of the semicolon the response was not shown. To verify that the

variable b actually exists:

b

As you will see, it exists.

If you omit the variable name, the result is assigned to the inbuilt variable ans:

2+2

The response shows that the variable ans has got the value 4.

You can execute one or more commands - separated by semicolon or comma - on one

line:

c=2+3, d=2+4

Scilab is case-sensitive. For example, d and D are two different variables:

d, D

As you see from the response (not shown here), d exists, while D does not exist (since

we have not created D).

Scilab variables exists in the workspace. There are two ways to see the contents of a

workspace:

Executing the command who at the command line, which just lists the variables

in the command window.

Menu Applications / Browser Variables, which opens the Browser Variables

window.

Execute the command who.

The response should be similar to what is shown in the figure below. (The user-

defined variables are shown among many other variables.)

The response of the command who

Select the menu Applications / Browser Variables.

This opens the Browser Variables window, see the figure below.

Browser Variables window

The Browser Variables window contains at the bottom a number of utility buttons (not

described in detail here).

Note that if you exit from Scilab, the variables you created in the workspace are

deleted. You can save variables in a file using the save function. However, if you

really need to save variables that are a result of some Scilab expressions, then you

should consider writing these expressions in a Scilab script instead. More about

scripts soon.

There are various ways to enter numbers (the pi is an inbuilt constant). Here are some

illustrative examples (I assume that you see the principles from these examples):

0.1, 1e-1, 2^3, exp(1), pi

The response is shown in the figure below.

Various ways to enter numbers

You can determine how numbers are displayed in the command window with

the format function, but the internal representation of the number in Scilab

isindependent if the display format. We will not look at details. If you need to change

the display format, consult Scilab Help.

Scilab functions are vectorized, i.e. functions can be called with vectorial arguments.

(A vector is simply a one-dimensional matrix. We will return to vector- and matrix

operations in a later section.) In the following example, first a vector of name t is

created, then this vector is used as an argument in the sine function (thesine function

assumes the argument is an angle in radians).

t=[0:10]', sin(0.1*t)

The response is shown in the figure below.

The result of the vectorized function call sin(0.1*t) where t is a vector

4 Scripts

A Scilab script is a text file of name *.sce containing Scilab commands. You can edit

the script using the inbuilt Scipad editor. (Scripts can also have names *.sci. The

default name when saving a fle in Scipad is *.sce.)

You should use scripts even for small tasks because in this way you have all your

"projects" saved in files which is good for documentation and also very convenient

when you want to run all your commands after some changes.

We will now create a simple script, and then run it. Running a script is the same as

executing all the commands (from top to bottom in the script) at the command line

one by one.

Launch the Scipad editor by selecting the Editor menu (or by executing the scipad command).

Then enter the commands shown in the figure below.

The Scipad editor is shown in the figure below. Note that double slashes (//) are used

to start comments in the script.

Scilab script of name script1.sce opened in the Scipad editor

Note that you can open several scripts in the same Scipad window with the File /

New menu.

Save the script with name script1.sce (of course some other name can be used) in the directory

(folder) C:\temp or in any other directory you prefer.

There are two ways to run the script1.sce script:

With the Execute / Load into Scilab menu in Scipad

By executing the command exec script1.sce at the command line

Let us try the Execute menu first:

Select the Execute / Load into Scilab menu in Scipad.

The result is shown in the command window.

Now let us try the exec command:

Execute the command exec script1.sce at the command line.

Scilab responds with an error! See below.

Scilab responds with an error when after executing the command exec script1.sce

The error comes because script1.sce is not in the Current directory of Scilab. The

Current directory is the directory where Scilab looks for your script when you try to

execute it with the exec command. What is then the present Current directory?

Excute the menu File / Get Current Directory.

The response (in the command window) may be different on different PCs. On my PC

the response is

C:\Documents and Settings\User\SciLab

We saved script1.sce in the C:\temp directory which is different from the present

Current Directory. Let us change the Current Directory to C:\temp, and then execute

the script:

Excute the menu File / Change Directory. This opens a window in which you select to become

the Current directory.

Execute the command exec script1.sce at the command line.

Now the script should run without errors.

5 Matrix operations

In Scilab numbers are in general stored in matrices, which can be regarded as a table.

Matrices with only one column or only one row are denoted vectors. (Matrices and

vectors are very similar to arrays as used in programming languages as C, Visual

Basic etc.)

Creating matrices. Retrieving data from matrices

Let us create a 2x2 matrix of name A. In general, comma (or space) is used to separate

numers on a row (or line), and semicolon is used to separate rows.

A=[1,2;3,4]

The figure below shows A as displayed in the command window.

Creating and displaying the matrix A

Create a row vector with first element 0, last element 1 and increment (step size) 0.2:

r=[0:0.2:1]

Create a column vector, note the apostrophe to transpose:

c=[0:0.2:1]'

Create matrix B from given column vectors x and y:

x=[1,2,3]'; y=[4,5,6]'; B=[x,y]

Get the size (dimensions) of matrix B:

size(B)

Get the first element of vector r. Note that 1 (not 0) is the first index!

r(1)

Now try

r(0)

You get an error because index number 0 can not be used.

Get the second column in matrix B, and assign the values to vector v:

v=B(:,2)

Some special matrices

Create an identity matrix of dimension 2x2:

C=eye(2,2)

Create a matrix of dimension 3x2 consisting of ones:

D=ones(3,2)

Create a matrix of dimension 3x2 consisting of zeros:

E=zeros(3,2)

Matrix calculations

Matrices can be used in matrix calculations.

Add two matrices (assuming A and C have been created as explained above):

F=A+C

Multiply two matrices:

G=A*C

Take the inverse of a matrix:

H=inv(A)

Elementwise calculations

Elementwise calculations are made with the dot operator. As an example, to perform

elemenwise multiplication of two vectors:

v1=[1,2], v2=[3,4], z=v1.*v2

The result is shown in the figure below. Element z(1) is v1(1)*v2(1), and element z(2)

is v1(2)*v2(2).

Elementwise multiplication of two vectors

6 Plotting

The basic command for plotting data in a figure is plot. In the following are a number

of examples demonstrating various plotting options. (It is of course up to you if

you type the code from scratch on the command line or in Scipad, or if you

just copy the code. If you type the commands, you may omit the comments which is

the text following the // sign to save time.)

First, let us generate some data that will be used in the following examples.

t=[0:.1:10]'; //t is a column vector

u=-1+0.2*t; //u is a column vector

y=sin(2*t); //y is a column vector

Very basic plotting:

scf(1); //Opens (new) figure with ID 1. (scf = set current fig)

plot(y) //Plots y against y-indexes (integers along x-axis)

Below is shown the Scilab figure with the plot. Along the x-axis are the indexes of the

y vector. The indexes are integers from 1 to 101.

Before we continue with more plotting commands, let us take a look at some buttons

and menus in the Graphics window.

Click the GED button in the figure window.

This opens the Clicking the GED button opens the Graphics Editor, see the figure

below.

The Graphics Editor

With the graphics editor you can change line colours, line style, add labels to the axis,

add grid, etc. The various options will not be described here because it is rather easy

to investigate the possibilities by yourself. Many of the options in the Graphics Editor

can alternatively be set with options to the plot command. This will be shown in

subsequent examples.

You can produce various graphics files from the plot:

Select the menu File / Export in the figure window.

This opens the Export dialog window shown below.

The Export dialog in the figure window

If you want to create a graphis file to put into a document processor, as MS Word or

Scientific Workplace, you should select Enhanced Meta File (EMF), whch is a

vectorized graphics format which means that the picture can be enlarged and still look

sharp. However, EMF files can not be used in native web documents, e.g. in HTML-

files to be displayed in a web browser. In this case you should select the GIF format

(this format does not give you vectorized graphics).

We continue with looking at more options to the plot command.

Assume that we will plot y against t in Figure 1 which is the same figure as we used

above. This is done with the command plot(t,y) where it is of course assumed that

vectors t and y have the same length (same number of elements).

If you just use the plot command, the new plot adds to the previous plot, showing two

(or more curves). Typically, this is not what you want. To clear the previous plot, we

use the clf (clear figure) command before we use the plot command.

//Clears a plot, and plots in the same figure:

scf(1); //Sets figure 1 to become current figure

clf; //clears the figure

plot(t,y) //Plots in figure 1

The result is shown in the figure below. Observe that the x-axis now contains

the t values.

Suppose you want to show the plot in a new Figure 2 in stead of the previously

opened Figure 1:

scf(2); //Sets figure 2 to become current figure

plot(t,y) //Plots in figure 1

To clear Figure 2:

Just close the Figure 2 window by clicking the close button in the upper right corner of the

window (or with the menu File / Close in the window).

To plot with with grid and plot title and labels:

scf(1); //Opens (new) figure with ID 1. (scf = set current fig)

plot(t,y) //Plots u against t

ax1=gca();ax1.grid=[0,0];//Adds grid. (gca=get current axes)

//[0,0] is colour code for x and y grid, resp. [0,0] is black.

title('Experiment 1')

xlabel('t [s]')

ylabel('y [V]')

The resulting plot is shown in the figure below. (If you think the

code ax1=gca();ax1.grid=[0,0]; is too cumbersome for generating a grid, you can in

stead use the Graphics Editor (by clicking the GED button in the figure window).)

To plot two curves in one plot (note the ordering of the vectors in the plot command):

scf(1);clf; //Opens figure 1 and clears its present content

plot(t,y,t,u) //Plots y against t, and u against t

The result is shown in the figure below.

To plot two curves with options for the line style and colours:

scf(1); clf; //Opens and clears figure 1

plot(t,y,'r--',t,u,'b') //'r--' is red and dashes. 'b' is blue.

(Many more options can be found from Help linespec.) The result is shown in the

figure below.

To plot several subplots in one figure:

scf(1); clf; //Opens and clears figure 1

subplot(211) //Plot number 1 in a 2x1 "table" of plots

plot(t,u)

subplot(212) //Plot number 2 in the 2x1 "table" of plots

plot(t,y)

The result is shown in the figure below.

Subplots