3.12: Common Vector Operations

Rounding Functions

Rounding functions convert floating-point values to nearby integer values, but each function follows a different rule.

Function	Description
ceil(x)	Rounds each element up to the nearest integer greater than or equal to the element
floor(x)	Rounds each element down to the nearest integer less than or equal to the element
fix(x)	Rounds each element toward zero
round(x)	Rounds each element to the nearest integer

 

Example \(\PageIndex{1}\)

Using rounding functions.

array1 = [2.1, 5.7, -3.7, -1.2];

value_1 = ceil(array1)

value_2 = floor(array1)

value_3 = fix(array1)

value_4 = round(array1)

 

Solution

value_1 =

    3 6 -3 -1


value_2 =

    2 5 -4 -2


value_3 =

    2 5 -3 -1


value_4 =

    2 6 -4 -1

 

 

 

Caution

Think carefully with negative numbers: ceil, floor, and fix behave differently for negative values. Try the examples above and compare the results.

 

Remainder and Modulus

MATLAB has two functions for computing remainders: rem and mod.  Both functions return the remainder of a division operation. They often produce the same result for positive numbers, but they can differ when negative numbers are involved.

 

Example \(\PageIndex{2}\)

Using rem and mod functions.

x = [5, 10, 12, -13];
y = 2;

value_1 = rem(x, y)
value_2 = mod(x, y)

Solution

value_1 =

     1     0     0    -1


value_2 =

     1     0     0     1

In the value_1 and value_2 arrays, notice the difference in the remainder when -13 is divided by 2 using the rem and mod functions. The rem function returns -1, while the mod function returns 1.

 

A common use of mod is to test whether a number is even, odd, or divisible by another number.

 

Example \(\PageIndex{3}\)

Using rem and mod functions.

values = 1:10;
evens = values(mod(values, 2) == 0)
odds  = values(mod(values, 2) == 1)

 

Solution

evens =

     2     4     6     8    10


odds =

     1     3     5     7     9

 

 

Statistics Functions for Arrays

MATLAB includes many built-in functions for basic statistical analysis. These functions are especially useful when working with experimental data.

Function	Description
mean(x)	Average value
std(x)	Standard deviation, a measure of spread around the mean
median(x)	Middle value after sorting
mode(x)	Most frequently occurring value
max(x)	Largest value
min(x)	Smallest value

 

Example \(\PageIndex{4}\)

Add example text here.

data = [9, 50, 51, 49, 100];
value_1 = mean(data)
value_2 = std(data)
value_3 = median(data)
value_4 = mode(data)

 

Solution

value_1 = 51.8000

value_2 = 32.2754

value_3 = 50

value_4 = 9

 

 

Random Numbers

Random numbers are useful for simulations, testing programs, games, and probability experiments. MATLAB has two commonly used random-number functions: rand and randi.

Function	Description
rand	Creates a random number between 0 and 1
rand(m,n)	Creates an m-by-n array of random decimal values between 0 and 1
randi(maxVal,m,n)	Creates an m-by-n array of random integers from 1 to maxVal

 

Example \(\PageIndex{5}\)

Add example text here.

value_1 = rand
value_2 = rand(3)
value_3 = rand(3, 1)
value_4 = rand(1, 3)
value_5 = randi(5, 3, 1)
value_6 = randi(5, 3)

 

Solution

value_1 = 0.8147


value_2 =

    0.9058    0.6324    0.5469
    0.1270    0.0975    0.9575
    0.9134    0.2785    0.9649


value_3 =

    0.1576
    0.9706
    0.9572


value_4 =

    0.4854    0.8003    0.1419


value_5 =

     3
     5
     4


value_6 =

     5     5     4
     4     5     4
     1     4     2

 

Random Numbers in a Specific Range

To create random decimal numbers between 4 and 9, start with rand, which gives values between 0 and 1, stretch the range by multiplying by 5, and then shift the range by adding 4.

Example \(\PageIndex{6}\)

randomDecimals = 4 + 5 * rand(1, 4)

Solution

randomDecimals =

    7.2774 4.8559 7.5302 4.1592

 

To create random integers between 4 and 9, use randi carefully. Since there are six integers from 4 through 9, generate integers from 1 through 6 and then shift them by adding 3.

 

Example \(\PageIndex{7}\)

randomIntegers = 3 + randi(6, 1, 4)

Solution

randomIntegers =

     5     4     4     8