Find Indices of Maximum and Minimum Value of Matrix in MATLAB

Matrices in MATLAB are 2-dimensional arrays that store mostly numeric data at different indices. Now, to find the indices of maximum and minimum values of a given matrix, MATLAB does not provide any direct functionality however, we can do the same by using two other functionalities. Firstly, we will find the maximum or minimum value of a given matrix and then, we will find the indices of those two values. In this scenario, MATLAB does offer simple functions to perform the former tasks. In this article, we shall see how to do the same for a magic square.

Maximum and Minimum Values in a Matrix:

The max() and min() functions find the maximum and minimum values respectively in an array, along a given dimension. The output of these commands will be a row vector(default) which will have max/min values of each column in that array/matrix. Then we can apply the max()/min() function again to find the max/min values from that 1D vector. 

Syntax:

To get row vectors with extreme values

max-row = max(matrix)

min-row = min(matrix)

To get extreme value from a given row vector of extreme values

max(max-row)

min(min-row)

Now let us see the same in action.

Maximum Value:

We will create a 5x5 magic square and find its maximum value, which should be 25.

Example 1:

% MATLAB code 
matrix = magic(5)
% Nesting the max command 
% for finding maximum value
max_val = max(max(matrix))

Output:

Minimum Value:

Similarly, we will now find the minimum value of the same magic square, which should be 1.

Example 2:

% MATLAB code for find min_val
matrix = magic(5)
min_val = min(min(matrix))

Output:

Finding Indices of Max/Min Values in the Same Magic Square:

Now we will use the find() function to get the indices of the max/min values.

Syntax:

max-index = find(matrix==max_val)

min-index = find(matrix==min_val)

Example 3:

% Finding Indices of Max/Min
% Values in the Same Magic Square 
matrix = magic(5);

% Getting max and min values
min_val = min(min(matrix));
max_val = max(max(matrix));

% Getting indices of min and max values in (row, col)
[minx,miny] = find(matrix==min_val);
[maxx,maxy] = find(matrix==max_val);

% Displaying the indices
fprintf("minimum index")
disp([minx,miny])
fprintf("maximum index")
disp([maxx,maxy])

Output:

Finding Max/Min Values With Multiple Occurrences:

We can also find the indices of all occurrences of the max/min value of a matrix in a similar way. See the following code for understanding the same.

Example 4:

% Finding Max/Min Values With Multiple Occurrences
matrix = [1 2 3; 
        1 23 4;
        2 23 5]

%Getting values
min_val = min(min(matrix));
max_val = max(max(matrix));

% Getting indices as vectors
% All of minx, miny, maxx, maxy are vectors

[minx,miny] = find(matrix==min_val);
[maxx,maxy] = find(matrix==max_val);

% Displaying the values
fprintf("minimum index\n")
disp([minx,miny])
fprintf("maximum index\n")
disp([maxx,maxy])

Output:

As can be seen, the minimum value 1 occurs at (1,1) and (2,1), and the maximum value 23 occurs at (2,2) and (3,2) indices. The same results are given by the above code.