In this article, we will discuss how to find the permutation of the rows and columns in a Matrix with the help of multiple approaches
Method 1
In this approach, we are simply permuting the rows and columns of the matrix in the specified format of rows and columns respectively. For column permutation, we take an example of a 3*3 matrix being permuted in such a way that its first column becomes the second one, the second becomes the third one and lastly, the third becomes the first column.
Example 1:
% MATLAB code for column permutation
% and specifying a 3*3 matrix
A = [1 2 3
4 5 6
7 8 9]
% Initializing a list of columns (Index)
% in which above matrix need to be
% permuted
index = [3 1 2]
% Getting the column permuted matrix B
B = A(:, index)
Output:
A = 1 2 3 4 5 6 7 8 9 index = 3 1 2 B = 3 1 2 6 4 5 9 7 8
Example 2:
% MATLAB code for rows permutation.
% Specifying a 3*3 matrix
A = [1 2 3
4 5 6
7 8 9]
% Initializing a list of rows (Index)
% in which above matrix need to be
% permuted
index = [3 1 2]
% Getting the rows permuted matrix B
B = A(index, :)
Output:
A = 1 2 3 4 5 6 7 8 9 index = 3 1 2 B = 7 8 9 1 2 3 4 5 6
Method 2
The perms() function returns a matrix that contains all the possible permutations of the elements of the specified vector "v" in reverse lexicographic order. Here each row of the returned matrix contains a different permutation of the "n" elements of the specified vector "v". The returned matrix has the same data type as the given vector "v" and has n! rows and n columns.
Syntax:
perms(v)
Parameters: This function accepts a parameter which is illustrated below:
- v: This is the specified vector containing the "n" number of elements.
Return Value: It returns a matrix that contains all the possible permutations of the elements of the specified vector "v" in reverse lexicographic order.
Example 1:
% MATLAB code for perms()
% Initializing a vector of some elements
vector = [1 2 3];
% Calling the perms() function over the
% above vector as its parameter whose
% elements are going to be permuted
P = perms(vector)
Output:
P = 3 2 1 3 1 2 2 3 1 2 1 3 1 3 2 1 2 3
Example 2:
% MATLAB code for perms()
% Initializing a vector of some complex numbers
vector = [1+2i 3+4i 5+6i];
% Calling the perms() function over the
% above vector as its parameter whose
% elements are going to be permuted
P = perms(vector)
Output:
P = 5 + 6i 3 + 4i 1 + 2i 5 + 6i 1 + 2i 3 + 4i 3 + 4i 5 + 6i 1 + 2i 3 + 4i 1 + 2i 5 + 6i 1 + 2i 5 + 6i 3 + 4i 1 + 2i 3 + 4i 5 + 6i
Method 3
The permute() function rearranges the dimensions of the specified array in the order specified by the vector dimorder.
Syntax:
permute(A, dimorder)
Parameters: This function accepts two parameters, which are illustrated below:
- A: This is the specified array matrix.
- dimorder: This is the specified vector order in which permutation is being done.
Return Value: It returns the permuted matrix.
Example 1:
% MATLAB code for permute()
% Creating a random 2*3 matrix
A = rand(2, 3)
% Calling the permute() function
% over the above matrix in the
% dimension order of [2 1]
B = permute(A, [2 1])
Output:
A = 0.32773 0.12633 0.67752 0.26285 0.91283 0.42994 B = 0.32773 0.26285 0.12633 0.91283 0.67752 0.42994
Example 2:
% MATLAB code for permute ()
% Creating 2-by-3-by-2 random array matrix
A = rand(3, 3, 2)
% Calling the permute() function
% over the above matrix in the
% dimension order of [2 3 1]
B = permute(A, [2 3 1])
Output:
A = ans(:,:,1) = 0.53364 0.65671 0.32496 0.82471 0.36042 0.31604 0.82714 0.84231 0.70248 ans(:,:,2) = 0.424538 0.498572 0.972245 0.069400 0.799598 0.754885 0.722046 0.807107 0.392804 B = ans(:,:,1) = 0.53364 0.42454 0.65671 0.49857 0.32496 0.97224 ans(:,:,2) = 0.824706 0.069400 0.360418 0.799598 0.316038 0.754885 ans(:,:,3) = 0.82714 0.72205 0.84231 0.80711 0.70248 0.39280
