14:440:127– Introduction to Computers for Engineers
Notes for Lecture 03
Rutgers University, Fall 2009
Instructor Blase E. Ur
1
Functions for Matrices and Vectors
1.1
Max, Min
There are also functions to find the maximum and minimum values of a vector or matrix.
These are
the creatively named
max
and
min
functions. For vectors, they return a single scalar with the absolute
maximum number. For matrices, they return the maximum or minimum number
in each column
. Thus,
as with the
sum
and
prod
functions, to find the absolute largest number in a matrix
M
, you would use
max(max(M))
.
The
max
and
min
functions can also be used to identify the location of the maximum or minimum number
inside a vector (or, with a little bit more trouble, a matrix). If you write a statement like
[a,b] = max(V)
,
where
a
and
b
are names of variables and
V
is a vector, then
a
will contain the largest value and
b
will
contain the location of that largest value inside the vector V. Note that [a,b] is essentially just a vector
of two variables. Also note that if the largest value is found more than one time inside the vector,
b
will
contain the first location where it is found.
V = [ 5 7 6 1 2 ];
[a,b] = min(V)
a = 1
% The smallest element is 1
b = 4
% 1 is the 4th element of V
What if you wanted to find the row and column in which the maximum or minimum is located?
We
can use a bit of a trick, as in the example below. We could also use the find function, which you’ll hear
about in a second.
NOTE, ERROR from last week’s lecture notes FIXED in example below
V = [ 5 7; 6 1; 2 3];
[smallC,rowsC] = min(V)
smallC = [2 1]
% The smallest element IN EACH COLUMN
rowsC = [3 2]
% The ROWs which contains the smallest elementS
[smallO,column] = min(smallC)
smallO = 1
%
The overall smallest element
column = 2
% The COLUMN containing the overall smallest element
row = rowsC(column)
% Column 2 contains the smallest overall element.
% Check which ROW in Column 2 contains the smallest element.
row = 2
1.2
Mean, Median
The
mean
and
median
functions operate on vectors just as you’d expect from statistics. The
mean
cal
culates the average, the sum of the elements of a vector divided by the number of elements. The
median
identifies the middle number if the vector were to be ordered from smallest to largest element.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
As with the other matrix functions, calculating the mean or median of a matrix calculates the mean
or median of each column.
Thus, to find the mean of a matrix
M
, use
mean(mean(M))
. However, this
wouldn’t work for the median– think about why!
Instead, use
median(M(:))
, which first converts the
matrix
M
to a vector (by making a vector containing ALL of the elements) and then finding the me
dian.
NOTE, ERROR from the printed lecture notes FIXED for median(M(:)) in the above
paragraph
1.3
Sort, Sortrows
You can also sort the elements of a vector in ascending (smallest to largest) order by using the
sort
func
tion. For matrices, the
sort
function sorts each column individually.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 blase
 matlab

Click to edit the document details