Variables and Expressions
3-1
Matrix Calculation with MATLAB
MATLAB® Fundamentals
Pony Lai
[email protected]
© 2012 MathWorks, Inc.
3-2
Variables and Expressions
The MATLAB® Desktop
Desktop controls
Current folder
Commands entered
& results returned
Files in the
current folder
Variables
(data) in
memory
Previously
entered
commands
Variables and Expressions
Interactive Importing
3-3
3-4
Variables and Expressions
Read and Write data from EXCEL

XLSREAD
–
–
–
–
–

num = xlsread('filename')
num = xlsread('filename', -1)
num = xlsread('filename', 'sheet')
num = xlsread('filename', 'range')
[num, txt] = xlsread('filename',
'sheet', 'range')
XLSWRITE
–
–
–
–
xlswrite('filename',
xlswrite('filename',
xlswrite('filename',
xlswrite('filename',
'range')
M)
M, 'sheet')
M, 'range')
M, 'sheet',
Variables and Expressions
Saving and Loading Variables
3-5
3-6
Variables and Expressions
Plotting the Data
 Automatic code
3-7
Variables and Expressions
Plot Tools
Axis labels -2
Units -1
4/10
Select plot
components
Add plot
elements
Change properties
3-8
Variables and Expressions
Multiple Plots
1
3
2
Variables and Expressions
Exporting to Another Application
3-9
3 - 10
Variables and Expressions
Script Files
H1 line
%
%
%
%
%
%
CALLMODEL Models a blue whale B call.
Uses a model of the form y = A.*y0
where A = A0*exp(-B*t).*sin(2*pi*fm*t)
and y0 is a sum of harmonics
yn = sin(2*pi*n*f0*t)
Help
% Create the time base for the signal.
fs = 4000;
t = 0:(1/fs):1.5;
Code
% Set the fundamental frequency of the call.
f0 = 175;
Comments
% Create the harmonics.
y0 = sin(2*pi*f0*t) + sin(2*pi*2*f0*t) + sin(2*pi*3*f0*t);
callmodel.m
3 - 11
Variables and Expressions
Assignment
>> no_of_penguins = x*sin(pi*t);
1. evaluate right-hand side
2. assign resulting value to
variable on left-hand side
create new variable or
overwrite old one,
as appropriate
3 - 12
Variables and Expressions
Creating Vectors
Arbitrary data
>> x = [2,3,5,7,11,13];
Equally-spaced values
n subdivision points
x
a
b
dx
>> x = a:dx:b;
>> x = linspace(a,b,n);
3 - 13
Variables and Expressions
Creating Matrices
>> A = [1,2,3; 4,5,6; 7,8,9];
or
>> A = [1 2 3; 4 5 6; 7 8 9];
or
>> A = [1 2 3
4 5 6
7 8 9]
data entry
mode
1 2 3
4 5 6
7 8 9
3 - 14
Variables and Expressions
Multidimensional Arrays
i
5
2
7
4
1

3
j
6

8
k
>> A(:,:,2) = [5, 6; 7, 8];
>> B = rand(2,2,3);
>> A(:,2,1)
ans =
2
4
Variables and Expressions
Matrix Creation Functions
3 - 15
compan
eye
gallery
hadamard
hankel
hilb
invhilb
magic
ones
pascal
rand
randi
randn
rosser
toeplitz
vander
wilkinson
zeros
3 - 16
Variables and Expressions
Row, Column Indexing
>> gasprices(1,2)
>> gasprices(3,6)
>> gasprices(end,2)
>> gasprices(2,end)
>> gasprices(end,end)
3 - 17
Variables and Expressions
Multiple Row, Column Indices
>> Year = gasprices(:,1)
>> gasprices([3,4],6:9)
>> gp08 = gasprices(end,2:end)
3 - 18
Variables and Expressions
Indexed Assignment
>> x = gasprices(1,2)
reference
>> x = 1.96;
>> gasprices(1,2) = x
assignment
3 - 19
Variables and Expressions
Characters and Strings
>> y = x
>> y = 'x'
variable
character
>> MarkA = 'Friends, Romans, countrymen, lend me your ears';
1-by-46 char array
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
'F'
'r'
'i'
'e'
'n'
'd'
's'
','
' '
'R'
'o'
'm'
'a'
'n'
's'
','
' '
'c'
>> FriendNationality = MarkA(10:15)
3 - 20
Variables and Expressions
Determining Size
Prices
size
length
numel
1.96
1.96
1.89
1.73
1.84
1.95
2.12
2.05
1.63
1.72
1.94
1.71
1.76
2.19
2.72
3.23
3.54
3.85
4.45
1.87
1.92
1.73
1.57
1.45
1.53
1.61
1.62
1.38
1.52
1.86
1.72
1.69
1.99
2.37
2.89
3.26
3.59
4.08
3.63
3.45
3.56
3.41
3.59
4.26
4.41
4.00
3.87
3.85
3.80
3.51
3.62
4.35
4.99
5.46
5.88
6.60
7.51
2.65
2.90
3.27
3.07
3.52
3.96
3.94
3.53
3.34
3.42
3.45
3.40
3.67
4.59
5.24
5.66
6.03
6.88
7.75
4.59
4.50
4.53
3.68
3.70
4.00
4.39
4.07
3.84
3.87
3.77
3.57
3.74
4.53
5.29
5.74
6.10
6.73
7.63
3.16
3.46
3.58
4.16
4.36
4.43
3.64
3.26
2.82
3.27
3.65
3.27
3.15
3.47
3.93
4.28
4.47
4.49
5.74
1.00
1.30
1.50
1.56
1.48
1.11
1.25
1.47
1.49
1.79
2.01
2.20
2.24
2.04
2.03
2.22
2.31
2.40
2.45
2.05
2.49
2.65
2.88
2.87
2.94
3.18
3.34
3.04
3.80
4.18
3.76
3.84
4.11
4.51
5.28
5.92
6.21
5.83
2.82
3.01
3.06
2.84
2.99
3.21
3.34
3.83
4.06
4.29
4.58
4.13
4.16
4.70
5.56
5.97
6.36
7.13
7.42
1.16
1.14
1.13
1.11
1.11
1.15
1.23
1.23
1.06
1.17
1.51
1.46
1.36
1.59
1.88
2.30
2.59
2.80
3.27
[19, 10]
max
19
190
*
3 - 21
Variables and Expressions
Matrix Operations
WAvgPrices
215.4
226.6
235.0
233.4
241.4
252.4
252.1
244.7
227.1
247.7
271.9
257.1
257.5
293.1
334.9
376.0
406.2
440.1
497.1
Prices
=
1.96
1.96
1.89
1.73
1.84
1.95
2.12
2.05
1.63
1.72
1.94
1.71
1.76
2.19
2.72
3.23
3.54
3.85
4.45
1.87
1.92
1.73
1.57
1.45
1.53
1.61
1.62
1.38
1.52
1.86
1.72
1.69
1.99
2.37
2.89
3.26
3.59
4.08
3.63
3.45
3.56
3.41
3.59
4.26
4.41
4.00
3.87
3.85
3.80
3.51
3.62
4.35
4.99
5.46
5.88
6.60
7.51
2.65
2.90
3.27
3.07
3.52
3.96
3.94
3.53
3.34
3.42
3.45
3.40
3.67
4.59
5.24
5.66
6.03
6.88
7.75
4.59
4.50
4.53
3.68
3.70
4.00
4.39
4.07
3.84
3.87
3.77
3.57
3.74
4.53
5.29
5.74
6.10
6.73
7.63
3.16
3.46
3.58
4.16
4.36
4.43
3.64
3.26
2.82
3.27
3.65
3.27
3.15
3.47
3.93
4.28
4.47
4.49
5.74
1.00
1.30
1.50
1.56
1.48
1.11
1.25
1.47
1.49
1.79
2.01
2.20
2.24
2.04
2.03
2.22
2.31
2.40
2.45
2.05
2.49
2.65
2.88
2.87
2.94
3.18
3.34
3.04
3.80
4.18
3.76
3.84
4.11
4.51
5.28
5.92
6.21
5.83
2.82
3.01
3.06
2.84
2.99
3.21
3.34
3.83
4.06
4.29
4.58
4.13
4.16
4.70
5.56
5.97
6.36
7.13
7.42
1.16
1.14
1.13
1.11
1.11
1.15
1.23
1.23
1.06
1.17
1.51
1.46
1.36
1.59
1.88
2.30
2.59
2.80
3.27
rpop
*
2.1
3.7
7.1
9.0
6.6
13.9
11.8
5.3
6.7
33.6
334.9 = 2.72*2.1 + 2.37*3.7 + 4.99*7.1 + 5.24*9.0 + 5.29*6.6 + 3.93*13.9 + 2.03*11.8 + 4.51*5.3 + 5.56*6.7 + 1.88*33.6
3 - 22
Variables and Expressions
Mathematical Operations
Performed on all elements of a matrix
 a b   sin( a) sin( b) 
  

sin 
 c d   sin( c) sin( d ) 
The operation is vectorized
1

3
2

4
sin
™
 0.8415 0.9093 


 0.1411  0.7568 
sin
sind
sinh
asin
exp
log
log2
log10
sqrt
nthroot
abs
angle
floor
ceil
round
mod
3 - 23
Variables and Expressions
Statistical Operations
Performed on an entire vector
or on the columns of a matrix
a b 
  mean (v1) mean (v2 ) 
mean 
c d 
v1 v2
1

3
2

4
mean
Data is in the form:
observations x variables
2 3
max
min
mean
median
std
sum
prod
diff
gradient
cumsum
cumprod
corrcoef
cov
filter
conv
fft
ifft
3 - 24
Variables and Expressions
Concatenation
>> C = [A,B]
C =
>> A
A =
1 2 3 1 0 0
1 2 3
4 5 6
7 8 9
>> B
B =
4 5 6 0 1 0
7 8 9 0 0 1
>> D = [A;B]
1 0 0
0 1 0
0 0 1
D =
1 2 3
4 5 6
7 8 9
1 0 0
0 1 0
0 0 1
[]