6.6: Nested Loops

A nested loop is a loop inside another loop. The outside loop is called the outer loop, and the inside loop is called the inner loop.

Nested loops are useful when working with two-dimensional data, such as matrices. The outer loop can move through the rows, and the inner loop can move through the columns.

Example: Adding All Numbers in a Matrix

function outSum = findMatSum(mat)
% findMatSum adds all numbers in a matrix.

outSum = 0;
[row, col] = size(mat);

for i = 1:row
    for j = 1:col
        outSum = outSum + mat(i,j);
    end
end

end

Here, size(mat) returns the number of rows and columns in the matrix. The outer loop controls the row index i. For each row, the inner loop controls the column index j. The expression mat(i,j) refers to the element in row i and column j.

 

Note

Reading Nested Loops

For every value of the outer loop, the inner loop completes all of its repetitions. If a matrix has 3 rows and 4 columns, the inner statement runs 3 x 4 = 12 times.

 

Tracing a Nested Loop

Consider this matrix:

A = [2 4 6; 1 3 5];

This matrix has 2 rows and 3 columns. The nested loop visits the elements in this order:

Iteration	i (row)	j (column)	Element
1	1	1	A(1,1) = 2
2	1	2	A(1,2) = 4
3	1	3	A(1,3) = 6
4	2	1	A(2,1) = 1
5	2	2	A(2,2) = 3
6	2	3	A(2,3) = 5

 

Note

MATLAB Note

MATLAB has a built-in way to sum all elements in a matrix using sum(A, all) in newer versions, or sum(A(:)) in many versions. But nested loops help us understand how matrix processing works.