Date post: | 20-Jan-2016 |
Category: |
Documents |
Upload: | garey-jennings |
View: | 215 times |
Download: | 0 times |
Lecture 2 - Matlab Introduction
CVEN 302
August 29, 2001
Lecture Goals
• Scalar Operations
• Vectors Operations
• Matrix Operations
• Plot & Graphics
• Matlab files
• Matlab controls
Scalar OperationsScalar Operations
• Addition - a + b
• Subtraction - a - b
• Multiplication - a * b
• Right Division - a / b
• Left Division - b \ a
• Exponential - a^b
Order of Precedence of Order of Precedence of Arithmetic OperationsArithmetic Operations
Precedence( 1 ) - Parenthesis
( 2 ) - Exponential from left to right
( 3 ) - Multiplication and division from left to right.
( 4 ) - Addition and subtraction from left to right.
Vector
A vector is defined as a combination of variables values to with components of xj , where j = 1,…n values.
3
2
1
T
321 ,...,,
x
x
x
x
xxxx
Vectors
• Matlab is designed for vector and matrix manipulation some of the basic commands are given as
]6
6
4
1
t [1;4;6] or t 4
1 [
6
4
3
1
t 6,4,3,1
t
t
Vectors
• t’ represents the transpose of the vector “t”.• Individual components can be represented by
t = [ 4,5,6,9], where t(3) = 6.• [ ] represent the start and finish of the vector
and/or matrix. ( ) represent components of the vector.
• A period “.” represent an elemental set of functions, such as multiplication, division,etc.
Vector element Operations
• Individual addition A + B A + B• Individual subtraction A – B A - B• Individual multiplication A*B A.*B• Individual division (left) A/B A./B• Individual division (right) A\B A.\B
• Individual power AB A.^B
Hierarchy of the vector operations
Precedence( 1 ) - Parenthesis
( 2 ) - Exponential from left to right
( 3 ) - Multiplication and division from left to right.
( 4 ) - Addition and subtraction from left to right.
Vector Operations
• Vector product - A is 1 x n vector
• The magnitude of the vector is a dot product of the vector.
nn x n x 1*1n x A'*A
1 x 11n x *n x 1A'*A
'A*AA
1 x 11n x *n x 1A'*A
Vector Examples
Matrix
• A matrix is a two dimensional arrays, where the matrix B is represented by a [ m x n ]
nm,m,1
n1,1,1
bb
bb
B
Matrix Operations
• For addition and subtraction, the matrix sizes must match up. If you are adding to each component of the matrix you can do a simple scalar addition.
• Examples: [A] + [B] = [C] [A] + 3 = [D]
Matrix Operation
• Multiplication of matrices will need to match up the columns to the row values of the following matrix. Scalar multiplication will work.
• Division is different. You will either divide member by member, where the matrices are the same size or you will need to find the inverse of the matrix.
Matrix Multiplication Examples
Graphical Representation
• Matlab has a function known as “plot( ), where the values are plotted on an x-y plane.
• General format of the graph is given as,plot(x,y,’symbols’)
• The symbols represent the color, point shape, and the line type.
Plot symbols commandsColors Symbols Lines
y – yellow . – point - – solid line
m – mag o – circle : – dots
c – cyan x – xmark -. – line dot
r – red + – plus - - – dashes
g – green * – star
b – blue s – square
w – white d – diamond
k – black v – triangle down^ – triangle up< – left
< – right
p – pentagram
h – hexagram
Plot Commands
t = linspace(0, 2*pi); - results in 100 data points
y1 = cos(t); - cosine of the points
y2 = sin(t); - sine of the points
y3 = y1.*y2; - cos(t)*sin(t)
plot(t,y1,’-’) ; - plots cosine verse t with a straight line.
plot(t,y3,’r:’) - plots cosine*sine verse t with red dots.
Plot Commands
Example:
plot(t,y1,’-’,t,y2,’g*’,t,y3,’r-.’) - plots all 3
axis( [0 2*pi -1.5 1.5]) - adds axes
legend(‘cos(t)’,’sin(t)’,’cos(t)*sin(t)’) - legend
Note that the [ ] represent an array and ( ) represent a function, and ‘ ‘ represent the symbols.
Matlab commands for file management
The files can be written as a script, which can be loaded into the memory. From the command line:
• “echo” - causes the file to be echoed to the screen.• “what” - shows the type of file in the current
directory.
• “type” - will present show the file contents
Matlab Files
There are three types of files:• Data files
– Matlab files have their own format for saving data
– ascii files are standard text files, which can be printed out or used in excel files.
• m-files represent the program files.
• function files are functions similar to ‘sin(x)’, cos(x), etc.
Data Files
Data files can be written in two forms:
• Matlab format
• ascii format
Matlab data format
MatLab generates a data
file, which will have
look like:
“filename”.mat
File can be loaded into
the memory with:
load “filename”
t = linspace(0, 2*pi)
x = cos(t)
save data1 t x
clear
what
data1.mat
load data1
ACSII format
An ascii file type can be
created by adding a flag
on the end of the save
command
save “filename”.dat -ascii
t = linspace(0 2*pi)
x = sin(t)
save data2.dat t x -ascii
dir
data2.dat
clear
load data2.dat -ascii
Loading Data Files
Matlab Files
load “filename”
The file will load the file into
the same format as it was
saved.
ASCII Files
load “filename.dat” -ascii
The file will be loaded as an
data array and will require
you to modify to obtained the
data vectors.
Data file example
t=linspace(0,2*pi);
y1 = sin(x);
save data1 t y1;
clear
(created data1.mat and
will show up in home
directory.)
load data1;
(data1 will have created
t and y1 vectors.)
save data2.dat t y1 -ascii
clear
(created a ascii file with
the data)
load data2 -ascii
Data file example continued
(loaded an ascii file into
memory as data2 array)
whos
data2 2X100 double array
t= data2(1,:);
y1= data2(2,:);
: assigns the row to the
vector
Homework
• Check the Homework files– create a data file– input a simple program– run the program– plot the results