Creating permutations from rows of a matrix

I have a matrix

X=[2-i 3+4i 5+7i; 7+8i 4-9i 7+9i; 2+i 4+8i 3-9i]

I would like to generate the following matrix (P) from X. Matrix P has six rows in total (3!), where by each row is composed of all the rows in X combined in a different order.

 P=[2.0000 + 1.0000i   4.0000 + 8.0000i   3.0000 - 9.0000i   7.0000 + 8.0000i   4.0000 - 9.0000i   7.0000 + 9.0000i
   2.0000 + 1.0000i   4.0000 + 8.0000i   3.0000 - 9.0000i   2.0000 - 1.0000i   3.0000 + 4.0000i   5.0000 + 7.0000i
   7.0000 + 8.0000i   4.0000 - 9.0000i   7.0000 + 9.0000i   2.0000 + 1.0000i   4.0000 + 8.0000i   3.0000 - 9.0000i
   7.0000 + 8.0000i   4.0000 - 9.0000i   7.0000 + 9.0000i   2.0000 - 1.0000i   3.0000 + 4.0000i   5.0000 + 7.0000i
   2.0000 - 1.0000i   3.0000 + 4.0000i   5.0000 + 7.0000i   2.0000 + 1.0000i   4.0000 + 8.0000i   3.0000 - 9.0000i
   2.0000 - 1.0000i   3.0000 + 4.0000i   5.0000 + 7.0000i   7.0000 + 8.0000i   4.0000 - 9.0000i   7.0000 + 9.0000i

  Columns 7 through 9

   2.0000 - 1.0000i   3.0000 + 4.0000i   5.0000 + 7.0000i
   7.0000 + 8.0000i   4.0000 - 9.0000i   7.0000 + 9.0000i
   2.0000 - 1.0000i   3.0000 + 4.0000i   5.0000 + 7.0000i
   2.0000 + 1.0000i   4.0000 + 8.0000i   3.0000 - 9.0000i
   7.0000 + 8.0000i   4.0000 - 9.0000i   7.0000 + 9.0000i
   2.0000 + 1.0000i   4.0000 + 8.0000i   3.0000 - 9.0000i]

 

[Walter Roberson]

You happen to be using a square matrix, X -- it is 3 x 3. Will your input X always be 3 x 3? Will your input X always be square? If X were 3 x 4 what would the expected output be like?

You can write it up like a prototype: if the original matrix were [11 12 13 14; 21 22 23 24; 31 32 33 34] then what would the expected output be?

[Roland Niwareeba]

X will not always be Square. Forexample

if

X=[1 4 3 2; 2 9 7 6];

then

P =

[2 9 7 6 1 4 3 2

1 4 3 2 2 9 7 6];

The number of rows here in P is 2! obtained through possible permutations from the X rows.

if X= [11 12 13 14; 21 22 23 24; 31 32 33 34];

then P =

31 32 33 34 21 22 23 24 11 12 13 14

31 32 33 34 11 12 13 14 21 22 23 24

21 22 23 24 31 32 33 34 11 12 13 14

21 22 23 24 11 12 13 14 31 32 33 34

11 12 13 14 31 32 33 34 21 22 23 24

11 12 13 14 21 22 23 24 31 32 33 34

Number of rows in P is 3! which is 6. Each row contains rows in X arranged in a different order.

Answer 1

[Bruno Luong]

This question is almost like what you ask in this thread

Only the formating of the input is different (in one case you split the sequences in different variables, in other case they are grouped as rows of an array).

The difference is not big enough the create 2 separate threads IMO, and you better think finding solution as combining of separate smaller steps if smaller problem.

% Input
X = [2-i 3+4i 5+7i; 7+8i 4-9i 7+9i; 2+i 4+8i 3-9i];

P = cell2mat(perms(num2cell(X,2)))

Here

num2cell(X,2)

and

{X1 X2 X3} % on the answer of other question

return the same cell for two different input storage schemes. You might reduce your question to this simply formatage.

Answer 2

[Walter Roberson]

idx = reshape(nchoosek(1:size(X,1),2).',[],1);
P = X(idx,:);