Advanced MATLAB
Vectors and matrices
fprintf
Cell arrays
Structures
Flow of control
Vectorization
Functions
1
Using an Index to Address Elements of an Array
In the C/C++ programming language, an index starts at 0 and
elements of an array are addressed with square brackets [∙]:
8
2
-3
7
-1
↑
↑
↑
↑
↑
x[0]
x[1]
x[2]
x[3]
x[4]
In MATLAB, an index starts at 1 and elements of an array are
addressed with parentheses (∙):
8
2
-3
7
-1
↑
↑
↑
↑
↑
x(3)
x(4)
x(5)
x(1)
x(2)
2
Columns, Rows, and Pages
for a 2-Dimensional Array (Matrix)
x(m,n)
m is the row number
n is the column number
x(m,n) is the element of the matrix x that is:
in the mth row
in the nth column
3
Columns, Rows, and Pages
for a 3-Dimensional Array
x(m,n,p)
m is the row number
n is the column number
p is the page number
x(m,n,p) is the element of the 3-dimensional array x that is:
in the mth row
in the nth column
on the pth page
4
% scalars, vectors, matrices, 3-dimensional arrays
a1 = zeros(1,1); % scalar
disp(['a1: ',num2str(size(a1))])
a2 = zeros(1,4); % vector
disp(['a2: ',num2str(size(a2))])
disp(a2)
a3 = zeros(2,2); % matrix
disp(['a3: ',num2str(size(a3))])
disp(a3)
a4 = zeros(2,2,3); % 3-dimensional array
disp(['a4: ',num2str(size(a4))])
a1:
a2:
a3:
a4:
1
1
0
1
4
2
0
0
2
2
2
0
0
0
3
0
0
Exercise
1. Create a row vector of length 5. Use any values you want
for the elements.
2. Display the size of this vector.
3. Create a matrix of all 1s that has 3 rows and 4 columns.
(Use the function ones.)
4. Display the size of this matrix.
6
% Editing arrays with parentheses ()
B = [1 2 3 4; 5 6 7 8];
disp('before:')
disp(B)
b = [0 0]';
B(:,4) = b;
disp('after:')
disp(B)
before:
1
5
2
6
3
7
4
8
after:
1
5
2
6
3
7
0
0
7
Exercises
Create a matrix of zeros with 3 rows and 4 columns.
Create a matrix with 2 rows and 2 columns, with all elements
equal to 5.
Insert the smaller matrix into the lower right-hand corner of
the larger matrix.
Hints:
zeros()
5*ones()
8
% array versus matrix multiplication
a = [1 2; 3 4];
disp(a*a) % matrix multiplication
disp(a.*a) % array multiplication
7
15
10
22
1
9
4
16
% array multiplication, division, and power
x = [1 4; 9 8];
y = [1 2; 3 4];
disp(x.*y) % array multiplication: .*
disp(x./y) % array division:
./
disp(x.^2) % array power:
.^
1
27
8
32
1
3
2
2
1
81
16
64
10
Exercise
1. Create a row vector containing 4 elements. Use any values
you want.
2. Create a second row vector of the same length, using any
values you want.
3. Show the result of an array multiplication of these two
vectors.
4. Show the result of doing an array division of one of these
vectors by the other.
11
MATLAB Documentation for fprintf
fprintf
Write data to text file
Syntax
fprintf(fileID,formatSpec,A1,...,An)
My comments:
fileID not used when printing to Command Window
formatSpec enclosed in single quote marks: ‘string’
A1,…,An are variables (or numbers) to be printed
12
% print pi to 7 decimal places
fprintf('%9.7f\n',pi)
% f
fixed-point number
% a.b
field width = a characters
%
b digits to the right of decimal point
% \n
newline
3.1415927
13
% print a column of numbers
x = [1.34, -2.45, 0.91];
fprintf('%5.2f\n',x) % There can be 2 characters on left.
1.34
-2.45
0.91
14
Exercise
Print 𝜋 as a fixed-point number to 12 decimal places.
15
% print signed integers with field width 4
x = [198, -230, 3];
fprintf('%4d\n',x)
198
-230
3
16
Exercise
Create a vector containing the (integer) elements: 0, -1, 2, -3.
Print these numbers in a column with right justification.
17
Cell Arrays
A cell array can combine different data having different data
types all in one array.
A cell within a cell array is referenced by an index.
A cell array is frequently an input argument of a function.
This permits a collection of data (even of different data
types) to be input to the function using a single argument.
18
% create a cell array using braces {}
y = {'scores',[73,38,81,55]};
y{3} = 'success';
celldisp(y)
y{1} =
scores
y{2} =
73
38
81
55
y{3} =
success
19
% What is in the second cell of the cell array y?
disp(y(2))
[1x4 double]
20
% What values are in the second cell of the cell array y?
disp(y{2})
73
38
81
55
21
% print values in the cell array y
fprintf('%s: ',y{1})
fprintf('%2d ',y{2})
fprintf('\n')
scores: 73 38 81 55
22
% create a cell array using the function cell()
x = cell(1,2);
x{1} = 'salary';
x{2} = 45000;
celldisp(x)
x{1} =
salary
x{2} =
45000
23
Exercise
1. Create a cell array that contains three cells:
A string containing your first name,
An unsigned integer (uint8) containing your age, and
A vector containing any two numbers between 0 and 1.
2. Use celldisp to display the contents of the cell array.
3. Extract the string in the first cell.
4. Extract your age.
5. Extract the first number in the vector.
24
Structures
A structure can combine different data having different data
types under one banner.
Each component of a structure is called a field.
A structure array is an array, each element of which is a
structure, and all structures in the structure array have the
same set of fields.
25
% simple structure
a.label = 'x';
a.vect = 0:5;
disp(a)
label: 'x'
vect: [0 1 2 3 4 5]
26
Exercise
1. Create a structure that contains two fields: a name (string)
and a number. Place any values you want into these fields.
2. Use disp to display the fields of this structure.
27
% create structure array using function struct()
c = struct('label',{'x','y'},'vect',{0:5,0:10});
disp(c)
disp(c(1))
disp(c(2))
1x2 struct array with fields:
label
vect
label: 'x'
vect: [0 1 2 3 4 5]
label: 'y'
vect: [0 1 2 3 4 5 6 7 8 9 10]
28
% create 1 x 2 structure array
c = struct('class',{71,72},'language',{'C','MATLAB'});
for n = 1:2
fprintf('ECE %2d: %s\n',c(n).class,c(n).language)
end
ECE 71: C
ECE 72: MATLAB
29
% structure array
b(1).label = 'x';
b(2).label = 'y';
b(1).vect = 0:5;
b(2).vect = 0:10;
disp(b)
disp(b(1))
disp(b(2))
1x2 struct array with fields:
label
vect
label: 'x'
vect: [0 1 2 3 4 5]
label: 'y'
vect: [0 1 2 3 4 5 6 7 8 9 10]
30
Exercise
1. Create a 1x2 structure array that contains two fields:
a string containing a first name, and
a number containing an age (in years)
Provide a value for each field of each structure in the
structure array.
2. Use a loop and the fprintf function to print the data in
the structure array.
31
Flow of Control
Redirection
if
else
elseif
Loops
for
32
Relational Operators
x ==
x ~=
x <
x <=
x >
x >=
y
y
y
y
y
y
equal to
not equal to
less than
less than or equal to
greater than
greater than or equal to
33
Logical Operators
&&
||
(short-circuit) and
(short-circuit) or
34
% if
for k = 0:3
if k == 2
disp(k)
end
end
2
35
% if and else
for k = 0:3
if k >= 2
disp(k)
else
disp([num2str(k),' < 2'])
end
end
0 < 2
1 < 2
2
3
36
% elseif
for k = 0:3
if k < 2
disp([num2str(k),' < 2'])
elseif k == 2
disp(k)
else
disp([num2str(k),' > 2'])
end
end
0 < 2
1 < 2
2
3 > 2
37
% or
for k = 0:4
if k < 2 || k > 3
disp(k)
end
end
0
1
4
38
% and (input number is 3)
x = input('number: ');
if x >= 1 && x <= 5
disp('between 1 and 5')
end
between 1 and 5
39
Exercise
Create a script that does the following:
1. Get a number (x) from the user.
2. If x is less than or equal to 3, set y to 3.
3. If x is greater than or equal to 6, set y to 6.
4. Otherwise, set y to x.
5. Display y.
40
% Compare 2 methods of printing a vector
tic
for k = 0:9 % within this loop, k is a scalar
fprintf('%1d ',k)
end
fprintf('\n')
toc
tic
m = 0:9;
fprintf('%1d ',m) % This is preferred.
fprintf('\n')
toc
0 1 2 3
Elapsed
0 1 2 3
Elapsed
4 5 6 7
time is
4 5 6 7
time is
It is faster.
8 9
0.000264 seconds.
8 9
0.000077 seconds.
41
% Add all even integers 0 through 100
x = 0;
for m = 2:2:100 % even integers, 2 through 100
x = x + m;
end
fprintf('%4d\n',x)
2550
42
Exercise
Calculate the sum of all odd integers from 1 through 101.
43
Vectorization
Preallocation of memory
Vectorizing Loops
44
% Preallocation of memory
tic % SLOW: frequent lengthening of x
x(1) = 1;
x(2) = 1;
for n = 3:100000
x(n) = x(n-1)*x(n-2);
end
toc
tic % FAST: preallocation of memory for x
y = ones(1,100000);
for n = 3:10000
y(n) = y(n-1)*y(n-2);
end
toc
Elapsed time is 0.526046 seconds.
Elapsed time is 0.021451 seconds.
45
% Vectorizing a loop: linspace
tic % slow
phi = 0;
dphi = 2*pi/100;
g = zeros(1,1001);
for n = 1:1001
g(n) = sin(phi);
phi = phi + dphi;
end
toc
tic % fast
phi = linspace(0,20*pi,1001);
h = sin(phi);
toc
Elapsed time is 0.002522 seconds.
Elapsed time is 0.000136 seconds.
46
Exercise
Here is one way to generate samples of a sinewave:
for n = 1:8
x(n) = sin(pi*(n-1)/4);
end
Enter the above code and display the results. Then vectorize this
code and verify that your vectorized code gives the same results.
47
Functions
Function m-file
Local variables
Functions with multiple inputs/outputs
48
function v = sphereVol(r)
% calculates the volume of a sphere
% input r = radius
% output v = volume
c = 4/3;
v = c*pi*(r^3);
end % sphereVol
49
Local Variables
Variables appearing in a function are local. These local variables do
not appear in the MATLAB workspace and are not visible outside of
the function in which they occur. For example, a variable c in the
MATLAB workspace will be unaffected by a (local) variable c that
appears within a function. Within the function, the local c is
recognized and the workspace c is not. When the function returns,
the local c is forgotten and the workspace c is again recognized.
The input arguments of a function have local names. When the
function returns, these local names are forgotten.
The output variables of a function have local names. The values of
these output variables are returned to the caller; however, the local
names of these output variables are forgotten.
50
% Script that calls the function sphereVol
c = 2;
radius = 1;
vol = sphereVol(radius);
fprintf('c = %3.1f, vol = %5.2f\n',c,vol)
whos
c = 2.0, vol = 4.19
Name
Size
c
radius
vol
1x1
1x1
1x1
Bytes
8
8
8
Class
Attributes
double
double
double
51
Exercise
1. Create a function m-file that computes the surface area of a
sphere. There will be one input, the radius, and one output,
the surface area.
𝐴 = 4𝜋𝑟 2
2. Create a script m-file that calls your function m-file.
52
function [radius, angle] = rect2polar(x, y)
% converts the (x,y) coordinates to polar coordinates
% inputs: rectangular coordinates x and y
% outputs:
% radius = distance from origin
% angle = angle (rad) measured counterclockwise from x axis
radius = sqrt(x.^2 + y.^2);
angle = atan2(y,x);
end % rect2polar
53
% Rectangular to polar coordinate conversions
x = linspace(1,0,5);
y = linspace(0,1,5);
[r,theta] = rect2polar(x,y);
table = [x; y; r; theta];
fprintf('
x
y
r
fprintf('%5.2f %5.2f %5.3f
x
1.00
0.75
0.50
0.25
0.00
y
0.00
0.25
0.50
0.75
1.00
r
1.000
0.791
0.707
0.791
1.000
theta\n')
%5.3f\n',table)
theta
0.000
0.322
0.785
1.249
1.571
54
Exercise
1. Create a function m-file that takes two inputs and produces two
outputs, where the inputs are the polar coordinates (𝑟 and 𝜃)
of a point in 2-dimensional space and the outputs are the
rectangular coordinates (𝑥 and 𝑦).
𝑥 = 𝑟 ∙ cos(𝜃)
𝑦 = 𝑟 ∙ sin(𝜃)
2. Make sure to include some comment lines, including an H1 line.
3. Create a script m-file that calls your function m-file.
55