For-loop

Let's start with an example, in which we want to compute $a=1+1+1+1+1$. This can be obtained by repeating a = a + 1 five times with the initial value a = 0:

a = 0;
a = a + 1;
a = a + 1;
a = a + 1;
a = a + 1;
a = a + 1;

Alternatively, this can be achieved by using a for-loop with fewer lines of code:

a = 0;
for i = 1:5
	a = a + 1;
end

The vector 1:5 here controls how many times the statement a = a + 1 will be repeated.

The example below computes

A naive way is to repeat the addition five times:

S = 0;
s = s + 1/2^1;
s = s + 1/2^2;
s = s + 1/2^3;
s = s + 1/2^4;
s = s + 1/2^5;

Actually, it evaluates the statement s = s + 1/2^i repeatedly with i equal to 1, 2, ..., 5. This observation leads us to using the loop below:

s = 0;
for i = 1:5 
    s = s + 1/2^i; 
end

For convenience of our discussion, let's call statements sandwiched by for and end the body. The vector 1:5 has 5 elements, hence the loop body will be executed 5 times. The value of i is taken from an element of the vector, in such a way that

• i takes the first element (i.e., 1) when the body is evaluated for the first time,
• i takes the second element (i.e., 2) when the body is evaluated for the second time,
• and so on.

To demonstrate that

converges to 1, you may use i = 1:40 as shown below. It returns a sum extremely close to 1.

Input

clear
s = 0;
for i = 1:40
    s = s + 1/2^i; 
end
s

Output

All variables cleared
s = 1e-1 × 
 9.999999999990905

Syntax

A for-loop takes the following general form:

for variable = vector
		statement_1
		statement_2
		...
		statement_n
end

Here, vector is a row or column vector. If vector is empty, none of the statements in the body will be executed. The vector vector is usually constructed in the for line by the colon : operator. Nevertheless, it can also be constructed elsewhere, as shown in the example below.

In the example below, the vector v is constructed before entering the loop.

Input

s = 0;
% v is a vector of integers from 1 to 40.
v = 1:40;
for i = v 
    s = s + 1/2^i; 
end
s

Output

s = 1e-1 × 
 9.999999999990905

Instead of looping through the integers $i=1,2,\ldots,40$ as we did in the above code, we can loop through the numbers

The following implementation gives exactly the same result.

Input

s = 0;
% v is a vector of the numbers 1/2^1, 1/2^2, ..., 1/2^40.
v = 1./2.^(1:40);
for i = v 
    s = s + i;
end
s

Output

s = 1e-1 × 
 9.999999999990905

One-line Form

The general syntax shown here is the most common form. Nevertheless, a for-loop can also be written in one single line using separators , or ;. All of the examples below give the same a as the final results.

Input

disp('Example 1. Using separators , and ,')
a = 0;
for i = 1:3, a = a + i, end
a

disp('Example 2. Using separators ; and ;')
a = 0;
for i = 1:3; a = a + i; end
a

disp('Example 3. Using separators , and ;')
a = 0;
for i = 1:3, a = a + i; end
a

Output

Example 1. Using separators , and ,

a = 
 1.0000

a = 
 3.0000

a = 
 6.0000

a = 
 6.0000

Example 2. Using separators ; and ;

a = 
 6.0000

Example 3. Using separators , and ;

a = 
 6.0000

In the above example, different components of the for-loop are separated by separators. A separator can be a comma, a semicolon, or a newline character.

⚠️⚠️⚠️ The end keyword should be followed by a newline character. This is different from MATLAB in which the end can be followed by other separators.

Loop Within Loops

A loop can be embedded within another loop, as shown in the example below.

• We compute the vector $[p_1,p_2,p_3]$, where $p_i=1^i+2^i+\cdots+N^i$ for $i=1,2,3$. This can be achieved by using a for-loop within another for-loop. The outer loop loops through the numbers $i=1,2,3$, and the inner loop computes the sum $p_i=1^i+2^i+\cdots+N^i$ for a particular $i$.

Input

N = 6;
for i = 1:3
    p(i) = 0.0;
    for j = 1:N
        p(i) = p(i) + j^i;
    end
end
p

Output

p = 
 21.000   91.000   441.00

More Examples

• Looping through a vector of complex Numbers.

Input

v= rand(1,5) + rand(1,5)*i
for i = v
    % Computing the length.
    abs(i)
end

Output

ans = 
 1.2290

ans = 1e-1 × 
 8.4194

ans = 1e-1 × 
 6.7398

ans = 1e-1 × 
 7.2952

ans = 1e-1 × 
 7.1020

• Looping through a character vector

Input

v='loop through characters'
for c = v
    disp(c)
end

Output

l
o
o
p
 
t
h
r
o
u
g
h
 
c
h
a
r
a
c
t
e
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s