How permutate 2-by-2 matrices in a single matrix

Hello everyone

I have three matrices as:

a = [1,2;3,4]; b = [2,5;1,6]; c = [3,7;2,4];

and collect them in a single M matrix as, M = [a,b,c]. Now I want to have permutation of these three matrices in M_P matrix as:

M_P = [a b c;
    a c b;
    b a c; 
    b c a; 
    c a b;
    c b a].

When I use M_P = perms(M), I could not obtain the [M_P] written above. it permutation all the value inside the matirices, however I just want permutation just matrices (a,b,c) then, place the values of matrices. I would appriciate it you can help me

Thanks in advance

Answer 1

[Bruno Luong]

a = [1,2;3,4]; b = [2,5;1,6]; c = [3,7;2,4];

abc=  {a,b,c};
abc=perms(abc)

abc = 6×3 cell array
    {2×2 double}    {2×2 double}    {2×2 double}
    {2×2 double}    {2×2 double}    {2×2 double}
    {2×2 double}    {2×2 double}    {2×2 double}
    {2×2 double}    {2×2 double}    {2×2 double}
    {2×2 double}    {2×2 double}    {2×2 double}
    {2×2 double}    {2×2 double}    {2×2 double}

abc=cell2mat(abc)

abc = 12×6

3 7 2 5 1 2 2 4 1 6 3 4 3 7 1 2 2 5 2 4 3 4 1 6 2 5 3 7 1 2 1 6 2 4 3 4 2 5 1 2 3 7 1 6 3 4 2 4 1 2 3 7 2 5 3 4 2 4 1 6

[Peiman Khandar]

Thank you so much for you great answer. You helped me a lot. However, I encounter with another problem now how can do mathematic operation on them. For example:

2*(abc(1,1))

or cos(2*(abc(1,1)))

since this is a cell array it did not let to do any operation on them

Thanks in advance

[Bruno Luong]

Take a look at cellfun

It's funny that you ask to create data in format that you don't know how to work with. It is better that you don't jump quickly and think more about the data structure that you know how to manipulate downstream.

Might be what you need is 4D array and not a 2D array of all permulations clump together.

[Peiman Khandar]

I see. So in that case are you recommending an otherway to obtain my permutation function cause I need to do mathematical operations on it

Answer 2

[Rik]

You're close. You just need to store a, b, and c in a cell array and use perms to create indices.

The benefit of this approach is that you can extend it to more or fewer elements (although you will run into memory constraints fast with a larger number of matrices).

a = [1,2;3,4]; b = [2,5;1,6]; c = [3,7;2,4];
collation = {a,b,c};
inds = perms(1:numel(collation))

inds = 6×3

3 2 1 3 1 2 2 3 1 2 1 3 1 3 2 1 2 3

M_P = collation(inds)

M_P = 6×3 cell array
    {2×2 double}    {2×2 double}    {2×2 double}
    {2×2 double}    {2×2 double}    {2×2 double}
    {2×2 double}    {2×2 double}    {2×2 double}
    {2×2 double}    {2×2 double}    {2×2 double}
    {2×2 double}    {2×2 double}    {2×2 double}
    {2×2 double}    {2×2 double}    {2×2 double}

M_P = cell2mat(M_P)

M_P = 12×6

3 7 2 5 1 2 2 4 1 6 3 4 3 7 1 2 2 5 2 4 3 4 1 6 2 5 3 7 1 2 1 6 2 4 3 4 2 5 1 2 3 7 1 6 3 4 2 4 1 2 3 7 2 5 3 4 2 4 1 6

[Peiman Khandar]

Dear Rik

Thank you so much for you nice comment. You were a great help me a lot.

However, I have another challenging in my calculations.

How can do mathematic operations on them. For example:

2*(abc(1,1))

since this is a cell array it did not let to do any operation on them

Thanks in advance

[Rik]

What do you mean by that operation? What is abc(1,1)?

[Peiman Khandar]

I mean 2 times the first row and first column of overall matrix [abc] where it contains a matrix

[Bruno Luong]

"I mean 2 times the first row and first column of overall matrix [abc] where it contains a matrix"

Then litterally it is 2*abc(1,1), that means 2*3 = 6

but I guess this is NOT what you want. Describtion verbally and innacurately is the last thing you would do to ask question.

[Peiman Khandar]

Yes you are right I cannot explain explicitly. The abc matrix containt rows and column where it contains matrices. Now I want to multply 2 to first row first column of matix abc which is:

[3 7;2 4]. However, I cannot write code for that since it is a cell array.

2.*(abc(1,1))

[Bruno Luong]

a = [1,2;3,4]; b = [2,5;1,6]; c = [3,7;2,4];
abc=  {a,b,c};
abc=perms(abc);
2*abc{1,1}

ans = 2×2

6 14 4 8

[Peiman Khandar]

Thanks a lot Bruno (sorry for confusion)