Getting started with MATLAB
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% Introduction to Matlab
% This course is adapted from MIT, Stanford, U Delaware Matlab crash
% courses.
% I have used the documents written by Stefan Roth and Tobin Driscoll
% besides the Matlab online tutorial. Azadeh Samadani 01/10/2007
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Useful links: The Getting Started with MATLAB manual is a very good place to get a more gentle and
thorough introduction:
http://www.mathworks.com/access/helpdesk/help/techdoc/learn_matlab/
http://www.mathworks.com/academia/student_center/tutorials/
Basics:
If you type in a valid expression and press Enter, MATLAB will immediately execute it and return the
result, just like a calculator.
>> 2+2
ans =
4
>> 4ˆ2
ans =
16
>> sin(pi/2)
ans =
1
>> 1/0
Warning: Divide by zero.
ans =
Inf
>> exp(i*pi)
ans =
-1.0000 + 0.0000i
Notice some of the special expressions here: pi for , Inf for ∞, and i for  1 . Another special value is
NaN, which stands for not a number. NaN is used to express an undefined value. For example,
>> Inf/Inf
ans = NaN
* Challenge: Calculate the following statements:  
1 5
2
and sin
1
(1 / 2) and tan(e) (Hint:
>>help exp).
Here are a few other demonstration statements.
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x = rand(2,2);
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s = ’Hello world’;
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t = 1 + 2 + 3 + ...
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Anything after a % sign is a comment.
; means "don’t print out result"
single quotes enclose a string
... means continue a line
4 + 5 + 6 % ...
Here are a few useful commands:
who
cd
pwd
dir
ls
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gives you your variables
Change current working directory.
Show (print) current working directory.
List directory.
List directory.
A = [1 2; 3 4];
B = [1,2; 3,4];
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Creates a 2x2 matrix
The simplest way to create a matrix is
to list its entries in square brackets.
The ";" symbol separates rows;
the (optional) "," separates columns.
N
v
v
v
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A scalar
A row vector
A column vector
Transpose a vector (row to column or
column to row)
A vector filled in a specified range:
[start:stepsize:end], brackets are
optional
Empty vector
* Type why in your command window
Creating matrices and vectors
=
=
=
=
5
[1 0 0]
[1; 2; 3]
v'
v = 1:0.5:3
v = pi*[-4:4]/4
v = []
Creating special matrices
1ST parameter is ROWS, 2ND parameter is COLS
m
v
m
v
=
=
=
=
zeros(2, 3)
ones(1, 3)
eye(3)
rand(3, 1)
m = zeros(3)
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Creates a 2x3 matrix of zeros
Creates a 1x3 matrix (row vector)of ones
Identity matrix (3x3)
Randomly filled 3x1 matrix (column
vector); see also randn
Creates a 3x3 matrix (!) of zeros
* Challenge: Without using a for loop, make a 4x4 matrix with zeros in lower left triangle and ones in
upper right triangle (Hint: >>doc triu, >>doc tril). Then find the size of the matrix, number of
dimensions and its nonzero elements. (Hint: >>doc size, >>doc ndims, >>doc find)
* Challenge: Create a 3x1 matrix with random elements between 0 and 5. (Hint: >>doc rand)
* Challenge: Create random nxn symmetric and antisymmetric matrices. (symmetric: a = transpose(a).
antisymmetric: a = -transpose(a) )
* Challenge: Without using a for loop, create the 5x5 matrix A = [1 2 3 4 5; 6 7 8 9 10; 11…].(Hint:
>>doc reshape)
* Challenge: Find the row-wise sum of the elements of A. Find the column-wise product of the elements of
A. (Hint: >>doc sum)
Indexing vectors and matrices
% Warning: Indices always start at 1 and *NOT* at 0!
v = [1 2 3];
v(3)
% Access a vector element
m = [1 2 3 4; 5 7 8 8, 9 10 11 12; 13 14 15 16]
m(1, 3)
% Access a matrix element
% matrix(ROW #, COLUMN #)
m(2, :)
% Access a whole matrix row (2nd row)
m(:, 1)
% Access a whole matrix column(1st column)
m(1, 1:3)
% Access elements 1 through 3 of the 1st
% row
m(2:3, 2)
% Access elements 2 through 3 of the
% 2nd column
m(2:end, 3)
% Keyword "end" accesses the remainder of
% a column or row
m = [1 2 3; 4 5 6]
size(m)
% Returns the size of a matrix
size(m, 1)
% Number of rows
size(m, 2)
% Number of columns
m1 = zeros(size(m))
% Create a new matrix with the size of m
*Challenge: Create a 5x3 matrix with random elements and access the (3x2) elements on the lower right
hand corner. (Hint: >>help end)
Remember to check the help system often! It is really easy! If you know the command that you want to
obtain some info about it is as easy as typing help command where command is the command that you
are interested in.
Simple operations and the “dot” modifier
a
2
a
b
a
a
a
a
= [1 2 3 4]';
* a
/ 4
= [5 6 7 8]';
+ b
- b
.^ 2
.* b
a ./ b
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A column vector
Scalar multiplication
Scalar division
Another column vector
Vector addition
Vector subtraction
Element-wise squaring (note the ".")
Element-wise multiplication (note the
".")
Element-wise division (note the ".")
* Challenge: Define two arbitrary vectors A and B with same dimensions. Calculate A*B, A.*B and
A*B’? What is the answer to A/B and A./B? Which operations do not make sense?
Vector operations
% Built-in Matlab functions that operate on vectors
sum(a)
mean(a)
std(a)
% Sum of vector elements
% Mean of vector elements
% Standard deviation
max(a)
min(a)
% Maximum
% Minimum
* Challenge: Without using a for loop, calculate the sum of all prime numbers less than 100.
(Hint:>>help isprime)
% If a matrix is given, then these functions will operate on each
column of the matrix and return a row vector as result
a = [1 2 3; 4 5 6]
mean(a)
max(a)
max(max(a))
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%
A matrix
Mean of each column
Max of each column
Obtaining the max of a matrix
x = [0 1 2 3 4];
plot(x);
pause
plot(x, 2*x);
axis([0 4 0 8]);
%
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%
%
%
Basic plotting
Plot x versus its index values
Wait for key press
Plot 2*x versus x
Adjust visible rectangle
figure;
x = pi*[-24:24]/24;
plot(x, sin(x));
xlabel('radians');
ylabel('sin value');
title('dummy');
% Open new figure
Graphics (2D plotting)
figure;
subplot(1, 2, 1);
plot(x, sin(x));
axis square;
subplot(1, 2, 2);
plot(x, 2*cos(x));
axis square;
figure;
plot(x, sin(x));
hold on;
plot(x, 2*cos(x), '--');
legend('sin', 'cos');
hold off;
figure;
m = rand(64,64);
imagesc(m)
%colormap gray;
axis image;
axis off;
% Assign label for x-axis
% Assign label for y-axis
% Assign plot title
% Multiple functions in separate graphs
% (see "help subplot")
% Make visible area square
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Multiple functions in single graph
'--' chooses different line pattern
Assigns names to each plot
Stop putting multiple figures in current
graph
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Plot matrix as image
Choose gray level colormap
Show pixel coordinates as axes
Remove axes
%You may zoom in to particular portions of a plot by clicking on the
%magnifying glass icon in the figure and drawing a rectangle.
* Challenge: Plot functions x (blue squares and line), x^2 (red circles and line) and x^1/2 (green diamonds
and line) between (0,2) on the same plot.
Let’s do Exercise 1!
Creating scripts and functions using m-files
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Matlab scripts are files with ".m" extension containing Matlab
commands. Variables in a script file are global and will change the
value of variables of the same name in the environment of the current
Matlab session. A script with name "script1.m" can be invoked by
typing "script1" in the command window.
* Challenge: Create a script called “myfirstscript.m” to prints out today’s date. (Hint: >>help date)
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Functions are also m-files. The first line in a function file must be
of this form:
function [out_1,..., out_m] = myfunction(in_1,..., in_n)
The function name should be the same as that of the file
(i.e. function "myfunction" should be saved in file "myfunction.m").
Have a look at myfunction.m for examples.
a = [1 2 3 4];
b = myfunction(2 * a)
% Global variable a
% Call myfunction which has local
% variable a
>>a
function y = myfunction(x)
% Function of one argument with one return value
a = [-2 -1 0 1];
% Have a global variable of the same name
y = a + x;
>>help myfunction
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Functions are executed using local workspaces: there is no risk of
conflicts with the variables in the main workspace. At the end of a
function execution only the output arguments will be visible in the
main workspace.
If we create a file named f.m in the current working directory with
this code
%f.m
function y = f(x, a)
% Returns the square of the first argument times the second
y = a * x ^ 2;
% Then, from the command window we can just evaluate the function
f(3, 4)
ans = 36
% In the command window type: >>help f
* Challenge: Define a new function called stat.m that calculates the mean and standard deviation of a
vector x.
* Challenge: Define a new function called bellcurve.m that creates 10000 normally distributed random
numbers with mean 3 and standard deviation 2. Make a histogram to verify the bell curve. (Hint:>>
help randn and >>help hist)
Time for Exercise 2 and 3!
Syntax of flow control statements (for, while and if expressions)
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for VARIABLE = EXPR
STATEMENT
...
STATEMENT
end
EXPR is a vector here, e.g. 1:10 or -1:0.5:1 or [1 4 7]
while EXPRESSION
STATEMENTS
end
if EXPRESSION
STATEMENTS
elseif EXPRESSION
STATEMENTS
else
STATEMENTS
end
(elseif and else clauses are optional, the "end" is required)
EXPRESSIONs are usually made of relational clauses, e.g. a < b
The operators are <, >, <=, >=, ==, ~=(almost like in C(++))
* Challenge: Write a function that takes two variables and prints a statement indicating whether the first
variable is smaller, larger, or equal to the second variable.
200
* Challenge: Write a function that calculates
 (n
0
3
 n2 )