Introduction to MATLAB
MATLAB is all of the following:
1. Computational environment
2. Plotting software
3. Programming language
Typical applications:
1.
2.
3.
4.
Calculations
Engineering/Scientific programs
Audio processing
Image processing
1
% Scalars
x = 1.23;
y = pi;
disp(x)
format long
disp(y)
format short
disp(y)
1.2300
3.141592653589793
3.1416
2
% Scalar arithmetic
x = 3;
y = 2;
disp(x+y)
disp(x-y)
disp(x*y)
disp(x/y)
disp(x^y)
%
%
%
%
%
addition:
subtraction:
multiplication:
division:
power:
+
*
/
^
5
1
6
1.5000
9
3
Exercise
1.
Calculate 4 times 5.
2.
Raise 2 to the power 10.
Hints:
*
(multiplication)
^
(raising to a power)
4
% vectors
x = [1,2,3]; % row vector
x = [1 2 3]; % commas can be replaced by spaces
disp(x)
disp(length(x))
disp(size(x))
y = [1;2;3]; % column vector
disp(y)
disp(size(y))
1
2
3
3
1
3
1
2
3
3
1
5
% Transpose
x = [1 2 3];
y = x'; % transpose of real vector x
disp(y)
z = y';
disp(z)
1
2
3
1
2
3
6
Exercise
1.
2.
Create a row vector consisting of the whole numbers
(integers) from 0 to 5. Display it.
Have MATLAB identify the size of this “matrix.”
3.
Convert your row vector into a column vector. Display it.
4.
Have MATLAB identify the size of this new “matrix.”
Hints:
size()
'
(transpose)
7
% Concatenation of row vectors
x = [1 2 3];
y = [4 5 6];
z = [x y];
% concatenate row vectors
disp(z)
z = cat(2,x,y); % concatenate by adding columns
% this accomplishes the same thing as above
disp(z)
1
2
3
4
5
6
1
2
3
4
5
6
8
% Concatenation of column vectors
x = [1; 2];
y = [3; 4];
z = [x; y];
% concatenate column vectors
disp(z)
z = cat(1,x,y); % concatenate by adding rows
% this accomplishes the same thing as above
disp(z)
1
2
3
4
1
2
3
4
9
Exercise
1.
Create a row vector consisting of the whole numbers
(integers) from 1 to 5 and a second row vector consisting
of the whole numbers 6 to 8.
2.
Concatenate these two row vectors into one long row
vector using two different methods:
square brackets
the function cat
3.
Create the transpose of each of the two component row
vectors that you created in step 1.
Concatenate these two column vectors into one long
column vector using two different methods:
square brackets
the function cat
4.
10
MATLAB Documentation for sum
sum
Sum of array elements
Syntax
B = sum(A)
B = sum(A,dim)
My comments:
A is a matrix, and dim is either 1 or 2.
If A is a vector, then a scalar (the sum of all elements) results.
If A is a matrix (with at least 2 rows and at least 2 columns), then
either a row (dim = 1) or a column (dim = 2) vector results.
11
% sum function with vector argument
x = [1 2 3 4]; % row vector
disp(x)
disp(sum(x))
y = [1; 2; 3]; % column vector
disp(y)
disp(sum(y))
1
2
3
4
10
1
2
3
6
12
% The functions maximum and minimum
x = [1 2 3];
% The functions maximum and minimum work equally well for
% row and column vectors.
disp(max(x))
disp(max(x'))
disp(min(x))
disp(min(x'))
3
3
1
1
13
Exercise
Create a column vector consisting of the whole numbers 0 to 10.
Have MATLAB find the length of this vector, the sum of its
elements, the maximum and minimum elements.
Hints:
length()
sum()
max()
min()
14
% Create vectors with the functions zeros and ones
x = zeros(1,5);
disp(x)
y = zeros(2,1);
disp(y)
y = ones(1,4);
disp(y)
0
0
0
0
1
1
1
0
0
0
1
15
% Create row vectors with the colon operator
a = 0:2:10; % start at 0, increment by 2, end at 10
disp(a)
b = 0:5; % by default, increment by 1
disp(b)
c = 0:-1:-5;
disp(c)
0
2
4
6
8
10
0
1
2
3
4
5
0
-1
-2
-3
-4
-5
16
% Create row vectors with linspace and logspace
x = linspace(0,1,5); % 5 values: 0 through 1
disp(x)
y = logspace(0,4,5); % 5 values: 10^0 through 10^4
disp(y)
0
0.2500
1
0.5000
10
0.7500
100
1.0000
1000
10000
17
Exercise
1.
Create a column vector of length 6, with each element a 0.
2.
Create a row vector consisting of the odd integers 1
through 11, using the colon operator.
3.
Create a row vector of 21 equally-spaced values between 0
and 10.
Create a row vector of 7 logarithmically-spaced values
between 1 and 1,000,000.
4.
Hints:
zeros()
linspace()
logspace()
18
% Vector input to built-in mathematical function
x = linspace(0,pi,5);
disp(x)
y = sin(x); % because x is a vector, sin produces a vector
disp(y)
0
0.7854
1.5708
2.3562
3.1416
0
0.7071
1.0000
0.7071
0.0000
19
% Basic plot
x = linspace(0,4,41);
y = sqrt(x);
figure(1)
plot(x,y,'-b')
axis([0 4 0 2])
saveas(1,'basic','png')
% Bigger font size and thicker lines
x = linspace(0,4,41);
y = sqrt(x);
figure(2);
plot(x,y,'-b')
axis([0 4 0 2])
set(gca,'FontSize',24)
set(findobj(2,'LineWidth',0.5),'LineWidth',2) % thick lines
saveas(2,'better','png')
Exercise
Create a plot of the squaring function (𝑦 = 𝑥 2 ).
Experiment with different ranges for the axes. For example,
you could start with:
axis([0 2 0 4])
For this exercise, you needn’t worry about appearance. In
other words, you don’t have to set font size or line thickness.
Hint. Recall that we plotted square-root like this:
x = linspace(0,4,41);
y = sqrt(x);
figure(2);
plot(x,y,'-b')
axis([0 4 0 2])
22
Color Specifiers
r
g
b
c
m
y
k
w
red
green
blue
cyan
magenta
yellow
black
‘white’
23
Line Style Specifiers
‘-’ solid line
‘--’ dashed line
‘:’ dotted line
‘-.’ dash-dot line
24
Exercise
Create a plot of the common logarithm (base 10 logarithm),
𝑦 = log(𝑥). In MATLAB the common logarithm function is
log10.
Experiment with using different line style specifiers and
different colors.
Hint. Recall that we plotted square-root like this:
x = linspace(0,4,41);
y = sqrt(x);
figure(2);
plot(x,y,'-b')
axis([0 4 0 2])
25
% Two curves
x = linspace(0,4,41);
y = sqrt(x);
z = x./2;
figure(5);
plot(x,y,'-k',x,z,'--b') % 2 curves on same axes
axis([0 4 0 2])
set(gca,'FontSize',24)
set(findobj(5,'LineWidth',0.5),'LineWidth',2)
saveas(5,'curves','png')
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)
27
Square Brackets in MATLAB
In MATLAB, square brackets [∙] are used for building arrays, such
as vectors, matrices, and three-dimensional arrays.
For example,
x = [1 2 3];
y = [4 5 6];
z = [x y];
disp(z)
1
2
% concatenate row vectors
3
4
5
6
28
% Indices (spelling lesson: 1 index, 2 or more indices)
x = zeros(1,5);
x(1) = 8;
% change element with index 1 (first element)
disp(x)
x(2:5) = 7; % change elements having indices 2 through 5
disp(x)
y = 1:4;
x(2:5) = y;
disp(x)
8
0
0
0
0
8
7
7
7
7
8
1
2
3
4
29
Exercise
1.
Create a row vector of length 8, with each element a 0.
2.
Create a row vector consisting of the whole numbers 1 to 4.
3.
In the row vector of step 1, replace the last 4 elements with
the vector of step 2.
30