MatLab03.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
Vector Functions
Matlab makes it easy to create vectors and matrices. The real power of Matlab is the ease in
which you can manipulate your vectors and matrices. Here we assume that you know the
basics of defining and manipulating vectors and matrices. In particular we assume that you
know how to create vectors and matrices and know how to index into them. For more
information on those topics see our tutorial on either
vectors
or
matrices.
In this tutorial we will first demonstrate simple manipulations such as addition, subtraction,
and multiplication. Following this basic "element-wise" operations are discussed. Once these
operations are shown, they are put together to demonstrate how relatively complex
operations can be defined with little effort.
First, we will look at simple addition and subtraction of vectors. The notation is the same as
found in most linear algebra texts. We will define two vectors and add and subtract them:
>> v = [1 2 3]'
v=
1
2
3
>> b = [2 4 6]'
b=
2
4
6
>> v+b
ans =
3
6
9
>> v-b
This tutorial was originally written by
Kelly Black.
Modified by
Jędrzej Mączak.
It is licensed under a
Creative Commons Attribution-ShareAlike 2.5 License
[Wpisz tekst]
ans =
-1
-2
-3
Multiplication of vectors and matrices must follow strict rules. Actually, so must addition. In
the example above, the vectors are both column vectors with three entries. You cannot add
a row vector to a column vector. Multiplication, though, can be a bit trickier. The number of
columns of the thing on the left must be equal to the number of rows of the thing on the
right of the multiplication symbol:
>> v*b
??? Error using ==> *
Inner matrix dimensions must agree.
>> v*b'
ans =
2 4 6
4 8 12
6 12 18
>> v'*b
ans =
28
There are many times where we want to do an operation to every entry in a vector or
matrix. Matlab will allow you to do this with "element-wise" operations. For example,
suppose you want to multiply each entry in vector v with its cooresponding entry in vector b.
In other words, suppose you want to find v(1)*b(1), v(2)*b(2), and v(3)*b(3). It would be nice
to use the "*" symbol since you are doing some sort of multiplication, but since it already
has a definition, we have to come up with something else. The programmers who came up
with Matlab decided to use the symbols ".*" to do this. In fact, you can put a period in front
of any math symbol to tell Matlab that you want the operation to take place on each entry
of the vector.
>> v.*b
ans =
2
8
18
>> v./b
2
[Wpisz tekst]
ans =
0.5000
0.5000
0.5000
Since we have opened the door to non-linear operations, why not go all the way? If you pass
a vector to a predefined math function, it will return a vector of the same size, and each
entry is found by performing the specified operation on the cooresponding entry of the
original vector:
>> sin(v)
ans =
0.8415
0.9093
0.1411
>> log(v)
ans =
0
0.6931
1.0986
The ability to work with these vector functions is one of the advantages of Matlab. Now
complex operations can be defined that can be done quickly and easily. In the following
example a very large vector is defined and can be easily manipulated. (Notice that the
second command has a ";" at the end of the line. This tells Matlab that it should not print out
the result.)
>> x = [0:0.1:100]
x=
Columns 1 through 7
0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000
[stuff deleted]
Columns 995 through 1001
99.4000 99.5000 99.6000 99.7000 99.8000 99.9000 100.0000
>> y = sin(x).*x./(1+cos(x));
3
[Wpisz tekst]
Through this simple manipulation of vectors, Matlab will also let you graph the results. The
following example also demonstrates one of the most useful commands in Matlab, the
"help" command.
>> plot(x,y)
>> plot(x,y,'rx')
>> help plot
PLOT Linear plot.
PLOT(X,Y) plots vector Y versus vector X. If X or Y is a matrix,
then the vector is plotted versus the rows or columns of the matrix,
whichever line up. If X is a scalar and Y is a vector, length(Y)
disconnected points are plotted.
PLOT(Y) plots the columns of Y versus their index.
If Y is complex, PLOT(Y) is equivalent to PLOT(real(Y),imag(Y)).
In all other uses of PLOT, the imaginary part is ignored.
Various line types, plot symbols and colors may be obtained with
PLOT(X,Y,S) where S is a character string made from one element
from any or all the following 3 columns:
b
g
r
c
m
y
k
blue
. point
-
green
o circle
:
red
x x-mark
-.
cyan
+ plus
--
magenta
* star
yellow
s square
black
d diamond
v triangle (down)
^ triangle (up)
< triangle (left)
> triangle (right)
p pentagram
h hexagram
solid
dotted
dashdot
dashed
For example, PLOT(X,Y,'c+:') plots a cyan dotted line with a plus
at each data point; PLOT(X,Y,'bd') plots blue diamond at each data
point but does not draw any line.
PLOT(X1,Y1,S1,X2,Y2,S2,X3,Y3,S3,...) combines the plots defined by
the (X,Y,S) triples, where the X's and Y's are vectors or matrices
and the S's are strings.
For example, PLOT(X,Y,'y-',X,Y,'go') plots the data twice, with a
solid yellow line interpolating green circles at the data points.
The PLOT command, if no color is specified, makes automatic use of
the colors specified by the axes ColorOrder property. The default
ColorOrder is listed in the table above for color systems where the
default is blue for one line, and for multiple lines, to cycle
through the first six colors in the table. For monochrome systems,
PLOT cycles over the axes LineStyleOrder property.
PLOT returns a column vector of handles to LINE objects, one
handle per line.
4
[Wpisz tekst]
The X,Y pairs, or X,Y,S triples, can be followed by
parameter/value pairs to specify additional properties
of the lines.
See also SEMILOGX, SEMILOGY, LOGLOG, PLOTYY, GRID, CLF, CLC, TITLE,
XLABEL, YLABEL, AXIS, AXES, HOLD, COLORDEF, LEGEND, SUBPLOT, STEM.
Overloaded methods
help idmodel/plot.m
help iddata/plot.m
>> plot(x,y,'y',x,y,'go')
>> plot(x,y,'y',x,y,'go',x,exp(x+1),'m--')
>> whos
Name Size
Bytes Class
ans
b
v
x
y
3x1
3x1
3x1
1x1001
1x1001
24 double array
24 double array
24 double array
8008 double array
8008 double array
Grand total is 2011 elements using 16088 bytes
The compact notation will let you tell the computer to do lots of calculations using few
commands. For example, suppose you want to calculate the divided differences for a given
equation. Once you have the grid points and the values of the function at those grid points,
building a divided difference table is simple:
>> coef = zeros(1,1001);
>> coef(1) = y(1);
>> y = (y(2:1001)-y(1:1000))./(x(2:1001)-x(1:1000));
>> whos
Name
Size
Bytes Class
ans
3x1
b
3x1
coef
1x1001
v
3x1
x
1x1001
y
1x1000
24 double array
24 double array
8008 double array
24 double array
8008 double array
8000 double array
Grand total is 3008 elements using 24064 bytes
>> coef(2) = y(1);
>> y(1)
ans =
0.0500
>> y = (y(2:1000)-y(1:999))./(x(3:1001)-x(1:999));
5

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