ADVANCED MATRIX OPERATIONS

ADVANCED MATRIX OPE RATIONS

• Advanced matrix operations fall under the
fol lowing categories .

• Building larger matrices
• Relational operations (larger/smaller)
• Logical operators (and ,or)
• Subscripting
• Manipulating matrices
• Reshaping

BUILDING LARGER MATRICES

• We can form larger matrices from smaller
matrices.

• Let a=[1 2 3;4 5 6;7 8 9] and b=[4 5 6] then
c=[a,b’]

adds a 4th column to a. c looks like this . Try
this and see for yourself
1 2 3 4
4 5 6 5
7 8 9 6

MATRIX MULTIPLICATION

• MATLAB multiplies two matrices provided
rows and column numbers agree .
• Let

A=[1 2 3;4 5 6;7 8 9]
B=[7 8 9;4 5 6;1 2 3]

• Multiplication of A by B is simply A *B. The
answer is

Try it!

• To ap preciate size restrictions, try to
multiply a=[1 2 3] by b=[4 5 6] using a*b.
What do you get and why?.
• Try the multiplication given in the previous
slide and check your answer.
• Now do a term-by- term multiplication like
a.*b. Explain why this is different from
a*b?

RELATIONAL OPERATIONS

• Relational operators are used for
comparison of two arrays . They are defined
as follows

WHAT DO THEY DO?

• The response of a relational operator is
another vector
• This vector is binary (0,1) and of the same
length as the data vector
• The 1 locations indicate places where the
relational operator is TRUE

Example

• We have two arrays

• If you say c=a>b, then

Try it!

• Define the following row vector
v=[1 3 4 9 8 6 7 0 2 6]

• Do the following and look at the result.
Explain what is happening.

x=v<5, x=v<=4, x=v>3, x=v>=0, x=v==6
x=v~=6

How many times a was larger
than b? introducing sum

• Application: compare the closing prices of
two stocks over a one year period. How
many times one closed higher than the
other?

• sum(x) sums of all elements of x and
produces one number
• Let x=[1 2 3 4 5], then sum(x)=15

sum over a matrix

• If x is an NxN matrix, then sum(x) is a 1xN
array. Each term is the sum of the
corresponding column

Stock comparison question

• Let stockA and stockB be 1x365 arrays.
Define
comp=[stockA>stockB]

• Comp is now a 0/1 array with 1 anytime A
exceeded B. Connect the dots. How many
days did A closed higher than B?

find command

• There are many instances where we want
to know the locations of non-zero entries
• For example, v > 5 is a logical array where
all non-zero entries correspond to positions
where v exceeds 5
• find(v>5) gives the exact locations where
the elements of v exceed 5

Try it!

• Take the v vector defined in slide 9. Find
all locations where v is
• Less than 5
• Larger than 3
• Less than or equal 9

LOGICAL OPERATORS

• Logical expressions can be compared
using logical operators. There are 3 logical
operators:
not...~
and...&
or......|

Using logical AND (&)

• Let’s try the & operator. Define
a=[1 9 8], b=[ 2 9 7] and c=[ 2 5 4 ].
• If we say a>b we get [0 0 1] which says
that in the third position, a>b is true. a>c
gets us [ 0 1 1].
• What we want is this: where both of these
expressions are true at the same time
[a>b & a>c]

The answer is...

• Here is the code
a=[1 9 8];
b=[ 2 9 7];
c=[ 2 5 4 ];
p=[a>b&a>c]
• p is then equal to [0 0 1]. Notice that in
the third position the joint condition was
true

Using logical OR ( | )

• The vertical bar is logical OR. a>b | a>c
looks for locations where a>b OR a>c is
true
• The answer is the 2nd and 3rd locations
where meets the condition

How many times a signal exceeds
a fixed threshold?

Random number generator

• We frequently need numbers to test things.
• One easy way of getting them is through
random number generators
• rand (1,N) generates N random numbers
between 0 and 1
• rand (N) generates an NXN matrix of
random numbers between 0 and 1

Try it!

• Give these commands a try in MATLAB and
see what you get
• rand(1,10)
• rand(10,1)
• rand(5)
• rand(3,4)

Using find: removing noise spike
from data

• First we generate a 1000 point signal then
plant a spike right in the middle. The code
to do this:
• x=rand(1,1000);
• x(500)=5;
• plot(x)

Graph of spike

Sample code

In-class practice

• Generate a 1x1000 array of normal random
numbers using randn
• Find all locations (indices) where x>.6
• How many times does x exceed .3?
• How many times does does x lie
between 0.2 and 0.4?
• How many times does x exceed .8 or
drop below .2?

Importing data

• Data that is saved as .mat file can be read
by Matlab using load command
• For example we have bond.mat on the
server. When you do load bond.mat, your
workspace will show an array m which
contains the imported data

Homework

• Load bond.mat. This is an audio clip
sampled at 8000 samples/sec.
• Plot its amplitude vs. time( not number of samples)
• Find how many times amplitude exceeds 0.2 volts
• Find how many times amplitude lies between -0.1 and
+0.2 volts
• At what times does the amplitude goes above 0.2
volts?