How to Permute the Rows and Columns in a Matrix on MATLAB?

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

% 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

% 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

% 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

% 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

% 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

% 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