Transcript Introduction to Matlab

What is MATLAB?
• MATrix LABoratory
• Developed by The Mathworks, Inc (http://www.mathworks.com(
• Interactive, integrated, environment
– for numerical computations
– for symbolic computations
– for scientific visualizations
• It is a high-level programming language
Characteristics of MATLAB
• Programming language based (principally) on matrices .
– Slow - an interpreted language ,i.e .not pre-compiled.
Avoid for loops; instead use vector form whenever
possible .
– Automatic memory management, i.e., you don't have
to declare arrays in advance .
– Intuitive, easy to use .
– Shorter program development time than traditional
programming languages such as Fortran and C .
– Can be converted into C code via MATLAB compiler
for better efficiency .
• Many application-specific toolboxes available .
Start menu
Matlab
“>>” – ‫שורת הפקודה‬
<< date
MATLAB
Getting Help
<< help date
>> helpwin date
helpwin gives you the same information as help, but in a different window.
Getting Help
<< doc date
<< lookfor date % search for keywords that best describe the function
>> Ctrl+C % stop Matlab from running
>> clc % clear screen
Special characters
• >> % default command prompt
• % % comment - MATLAB simply ignores anything to the
right of this sign (till the end of the line).
>> % my comment
• ;
% semicolon at the end of the line will prevent MATLAB
from echoing the information you type on the screen.
>> a=20
>> B=20;
Creating Variables
•
•
•
•
•
Matlab as a calculator:
>>2+5
>>7*10+8
>>5^2
‘ans’ - "answer", used in MATLAB as the default variable.
Defining Your Own Variables
• When Matlab comes across a new variable name - it
automatically creates it.
• Begins with a LETTER, e.g., A2z.
• Can be a mix of letters, digits, and underscores (e.g.,
vector_A, but not vector-A)
• Not longer than 31 characters.
• No spaces
• Different mixes of capital and small letters = different
variables.
For example: "A_VaRIAbLe", "a_variable",
"A_VARIABLE", and "A_variablE
• >> String=‘this is a string’
Listing & Clearing Variables
<< a=10
<< b = 20
<< the_average = (a + b ) / 2
<< whos
<< clear, clear all
%clear variables from memory
Creating vectors
Row separator:
space/coma (,)
Creating sequences:
• From : jump: till
• linespec(X1, X2, N)
generates N points between
X1 and X2.
Coulmn separator:
Semicolon (;)
Creating Matrices
• Matrices must be rectangular.
• Creating random matrices:
2-by-4 random matrix
(2 rows and 4 columns).
Creating Matrices
• You can combine existing vectors as matrix elements:
• You can combine existing matrices as matrix elements:
Indexing Into a Matrix
>> B=A(3,1);
>> A(:,end)=[1;7;3;8;4];
• The row number is first, followed by the column number.
Linear Algebra Operations
Matrix Multiplication
• Inner dimensions must be equal
• Dimension of resulting matrix = outermost
dimensions of multiplied matrices
• Resulting elements = dot product of the rows of
the 1st matrix with the columns of the 2nd matrix
Vector Multiplication
Type the following:
>>a=[2 3]
>>b=[3 2]
>>a*b
>>a.*b
>>a.*b’
>>a*b’
String Arrays
• Created using single quote delimiter (')
• Indexing is the same as for numeric arrays
String Array Concatenation
Working with String Arrays
Example: Solving Equations
• Solve this set of simultaneous equations: Ax=B, x=?
Creating Scripts with MATLAB
Editor/Debugger
• Automatically saves files as ASCII text files for you.
• Scripts in MATLAB has the ".m" suffix.
• They are also called "M-files".
Open Matlab Editor:
• File
New
• >> edit
M-file OR:
Run
Add path
• >> addpath
• Set path
C:\EMEM899\Somedirectory
Script M-files
•
•
•
Standard ASCII text files
Contain a series of MATLAB expressions
A script does not define a new workspace
% Comments start with "%" character
pause
% Suspend execution - hit any key to continue.
keyboard % Pause & return control to command line.
% Type "return" to continue.
break
return
% Terminate execution of current loop/file.
%
%
Continue %
Input
%
Exit current function
Return to invoking function/command line.
go to next iteration
Prompt for user input
A Simple Script
Write a program which receives a number from the user,
calculates it’s square root (use ‘sqrt’ command) and displays
the result.
save the script as "square_root_script.m" in your own folder
% a simple MATLAB m-file to calculate the
% square root of an input numbers.
my_num=input('insert a number');
% now calculate the square root of the number and print
it out:
square_root = sqrt(my_num)
Running Scripts
•
>> square_root_script
• The header - comments you place at the beginning of your scripts will be
returned to users when they get help for your script.
•
>> help square_root_script
• Note: The variables defined in the script remain in the workspace even
after the script finishes running.
• Creating comments: ctrl+r, or right click on the mouse, or
%{
coment
coment
%}
Running Scripts (2)
• Find and Replace – ctrl+F
• Key words
• Wrong use of key words
• Indenting: Ctrl+I
Flow Control Constructs
•
•
Logic Control:
–
–
IF / ELSEIF / ELSE
SWITCH / CASE / OTHERWISE
Iterative Loops:
–
–
FOR
WHILE
The if, elseif and else statements
•
•
Works on Conditional statements
Logic condition is ‘true’ if its different then 0.
if I == J
A(I,J) = 2;
else if abs(I-J) == 1
A(I,J) = -1;
else
A(I,J) = 0;
end %else if
end %if
•
if I == J
A(I,J) = 2;
elseif abs(I-J) == 1
A(I,J) = -1;
else
A(I,J) = 0;
end
ELSEIF does not need a matching END, while ELSE IF
does.
Boolean Operators & Indexing
Switch, Case, and Otherwise
•
•
More efficient than elseif statements
Only the first matching case is executed
switch input_num
case -1
input_str = 'minus one';
case 0
input_str = 'zero';
case 1
input_str = 'plus one';
case {-10,10}
input_str = '+/- ten';
otherwise
input_str = 'other value';
end
Problem
• Build a program which receives a variable x and its units
(mm, cm, inch, meter) and calculates Y- it’s value in
centimeters units.
• Use switch case.
• 1 Inch = 2.54 cm
• Write a comment for error case.
• Save the file under units.m
Solution
x = 3.0;
units = 'mm';
switch units
case {'in','inch'}
y = 2.54*x
% converts to centimeters
case {'m','meter'}
y = x*100
% converts to centimeters
case { 'millimeter','mm'}
y = x/10;
disp
([num2str(x) '
in
' units ' converted
to cm is :' num2str(y)])
case {'cm','centimeter'}
y = x
otherwise
disp
(['unknown units:' units])
y = nan;
end
The for loop
•
•
•
•
Similar to other programming languages
Repeats loop a set number of times (based on index)
Can be nested
Each loop is closed with end.
N=10;
for I = 1:2:N
for J = 1:N
A(I,J) = 1/(I+J-1);
end
end
The while loop
•
•
•
•
Similar to other programming languages
Repeats loop until logical condition returns FALSE.
Can be nested.
Stopping infinity loop:
I=1; N=10;
Ctrl+C
while I<=N
Ctrl+break
J=1;
while J<=N
A(I,J)=1/(I+J-1);
J=J+1;
end
I=I+1;
end
Array Operations
Line Plots in Two Dimensions
• Plot (x,y)
• makes a two-dimensional line plot for each point in X and its
corresponding point in Y: (X(1),Y(1)), (X(2),Y(2)), (X(3),Y(3)), etc.,
and then connect all these points together with line.
• Example:
• >> x=1:1:5;
• >>Y=[2 7 0 -8 6];
• >> plot (x,y);
• >> xlabel (‘label for x-axis’)
• >> ylabel (‘label for y-axis’)
• >> title (‘title’)
Multiple Plots
Check the following:
x_points = [-10 : .05 : 10];
plot(x_points, exp(x_points)); % plot in Blue (default)
grid on
hold on
plot(x_points, exp(.95 .* x_points), 'm'); % plot in Magenta
plot(x_points, exp(.85 .* x_points), 'g'); % plot in Green
plot(x_points, exp(.75 .* x_points), 'p'); % plot a star
hold off
xlabel('x-axis'); ylabel('y-axis');
title('Comparing Exponential Functions');
legend ('1', '2', '3', '4')
2.5
x 10
4
Comparing Exponential Functions
1
2
3
4
2
1.5
y-axis
•
•
•
•
•
•
•
•
•
•
•
•
1
0.5
0
-10
-5
0
5
10
Subplots
• multiple plots in the same window, each with their own
axes.
• Subplot (M,N,P)
• M – rows
• N - columns
• P – number of subplot
in the figure
Subplot (2,2,1)
More about figures
•
•
•
•
Figure % Open a new figure without closing old figures
Figure (i) % Open the i-th figure
Close all % close all open figures
axis ([xmin xmax ymin ymax]) % sets scaling for the xand y-axes on the current plot.
Special Graph Annotations (TeX)
Plot Editor Toolbar
Exercise
Create the following:
Merav's graph
2
sin(x)
log(x)
1.5
y
1
0.5
0
-0.5
-1
•
•
•
•
•
1
1.5
2
2.5
3
x
3.5
4
x = (1, 1.05, 1.1, 1.15… 5)
Y=sin(x)
Z=log(x)
Put your name in the title
Hint: check the doc on function “LineSpec”.
4.5
5
Solution
•
•
•
•
•
•
•
•
•
•
•
x=1:0.05:5;
y=sin(x);
z=log(x);
hold on
plot (x,y,'-.r*')
plot (x,z,'-.go')
hold off
title ('Merav''s graph');
xlabel ('x')
ylabel ('y')
legend ('sin(x)', 'log(x)');
More exercise
• Make a 3 three-dimensional graph of (x,y,z) – use Matlab help.
• Make two separate 2-D graphs, with separate axis, in the same
window: y vs. x, and z vs. x.
• Use the same x,y,z as defined in the previous exercise
3D graph
sin(x)
log(x)
1
1.8
0.8
1.6
0.6
2
1.4
1.5
0.4
1.2
0
z
1
1
z
y=sin(x)
0.2
0.8
0.5
-0.2
0.6
-0.4
0
1
0.4
-0.6
0.5
0.2
-0.8
5
4
0
3
-0.5
-1
1
2
3
x
4
5
0
1
2
3
x
4
5
y
2
-1
1
x
Solution
•
•
•
•
•
•
•
3-D graph:
>> plot3(x,y,z)
>> grid
>> xlabel ('x')
>> ylabel('y')
>> zlabel('z')
>> title ('3D graph')
• Subplots
>> subplot (1,2,1);
>> plot(x,y);
>> title ('sin(x)');
>> xlabel('x');
>> ylabel('y=sin(x)');
>> grid;
>> subplot (1,2,2);
>> plot(x,z);
>> xlabel('x');
>> title ('log(x)');
>> grid;
>> ylabel ('z');