MatLab01.pdf

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LABORATORIUM MECHATRONIKI, DIAGNOSTYKI
I BEZPIECZEŃSTWA TECHNICZNEGO
INSTYTUT POJAZDÓW
WYDZIAŁ SAMOCHODÓW I MASZYN ROBOCZYCH
POLITECHNIKA WARSZAWSKA
ul. Narbutta 84, 02-524 Warszawa
Tel. (22) 234-8117 do 8119
e-mail :msekretariat@mechatronika.net.pl
http://www.mechatronika.net.pl
Laboratorium Inżynierii Oprogramowania
Matlab Tutorial
Introduction to Vectors in Matlab
This is the basic introduction to Matlab. Creation of vectors is included with a few basic
operations. Topics include the following:
1.
Defining a vector
2.
Accessing elements within a vector
3.
Basic operations on vectors
Defining a Vector
Matlab is a software package that makes it easier for you to enter matrices and vectors, and
manipulate them. The interface follows a language that is designed to look a lot like the
notation use in linear algebra. In the following tutorial, we will discuss some of the basics of
working with vectors.
If you are running Windows, you can start Matlab by choosing it from the menu. This will start
up the software, and it will wait for you to enter your commands. In the text that follows, any
line that starts with two greater than signs (>>) is used to denote the Matlab command line.
This is where you enter your commands.
Almost all of Matlab's basic commands revolve around the use of vectors. A vector is defined
by placing a sequence of numbers within square braces:
>> v = [3 1]
v=
3
1
This creates a row vector which has the label "v". The first entry in the vector is a 3 and the
second entry is a 1. Note that matlab printed out a copy of the vector after you hit the enter
key. If you do not want to print out the result put a semi-colon at the end of the line:
>> v = [3 1];
>>
This tutorial was originally written by
Kelly Black.
Modified by
Jędrzej Mączak.
It is licensed under a
Creative Commons Attribution-ShareAlike 2.5 License
If you want to view the vector just type its label:
>> v
v=
3
1
You can define a vector of any size in this manner:
>> v = [3 1 7 -21 5 6]
v=
3
1 7 -21 5 6
Notice, though, that this always creates a row vector. If you want to create a column vector
you need to take the transpose of a row vector. The transpose is defined using an apostrophe
("'"):
>> v = [3 1 7 -21 5 6]'
v=
3
1
7
-21
5
6
A common task is to create a large vector with numbers that fit a repetitive pattern. Matlab
can define a set of numbers with a common increment using colons. For example, to define a
vector whose first entry is 1, the second entry is 2, the third is three, up to 8 you enter the
following:
>> v = = [1:8]
v=
1
2
3
4
5
6
7
8
If you wish to use an increment other than one that you have to define the start number, the
value of the increment, and the last number. For example, to define a vector that starts with 2
and ends in 4 with steps of .25 you enter the following:
>> v = [2:.25:4]
v=
2
Columns 1 through 7
2.0000 2.2500 2.5000 2.7500 3.0000 3.2500 3.5000
Columns 8 through 9
3.7500 4.0000
Accessing elements within a vector
You can view individual entries in this vector. For example to view the first entry just type in
the following:
>> v(1)
ans =
2
This command prints out entry 1 in the vector. Also notice that a new variable called
ans
has
been created. Any time you perform an action that does not include an assignment matlab
will put the label
ans
on the result.
To simplify the creation of large vectors, you can define a vector by specifying the first entry,
an increment, and the last entry. Matlab will automatically figure out how many entries you
need and their values. For example, to create a vector whose entries are 0, 2, 4, 6, and 8, you
can type in the following line:
>> 0:2:8
ans =
0
2
4
6
8
Matlab also keeps track of the last result. In the previous example, a variable "ans" is created.
To look at the transpose of the previous result, enter the following:
>> ans'
ans =
0
2
4
6
8
To be able to keep track of the vectors you create, you can give them names. For example, a
row vector v can be created:
>> v = [0:2:8]
3
v=
0
>> v
v=
0
>> v;
>> v'
ans =
0
2
4
6
8
2
4
6
8
2
4
6
8
Note that in the previous example, if you end the line with a semi-colon, the result is not
displayed. This will come in handy later when you want to use Matlab to work with very large
systems of equations.
Matlab will allow you to look at specific parts of the vector. If you want to only look at the first
three entries in a vector you can use the same notation you used to create the vector:
>> v(1:3)
ans =
0
2
4
>> v(1:2:4)
ans =
0
4
>> v(1:2:4)'
ans =
0
4
Basic operations on vectors
Once you master the notation you are free to perform other operations:
>> v(1:3)-v(2:4)
4
ans =
-2 -2 -2
For the most part Matlab follows the standard notation used in linear algebra. We will see
later that there are some extensions to make some operations easier. For now, though, both
addition subtraction are defined in the standard way. For example, to define a new vector
with the numbers from 0 to -4 in steps of -1 we do the following:
>> u = [0:-1:4]
u = [0:-1:-4]
u=
0 -1 -2 -3 -4
We can now add u and v together in the standard way:
>> u+v
ans =
0
1
2
3
4
Additionally, scalar multiplication is defined in the standard way. Also note that scalar division
is defined in a way that is consistent with scalar multiplication:
>> -2*u
ans =
0
>> v/3
ans =
0 0.6667 1.3333 2.0000 2.6667
2
4
6
8
With these definitions linear combinations of vectors can be easily defined and the basic
operations combined:
>> -2*u+v/3
ans =
0 2.6667 5.3333 8.0000 10.6667
You will need to be careful. These operations can only be carried out when the dimensions of
the vectors allow it. You will likely get used to seeing the following error message which
follows from adding two vectors whose dimensions are different:
5

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