how to scramble positions of a matrix?

Hello, I've been trying to scramble the positions of a matrix. I have generated two sequences which help us to scramble the positions of the matrix. Eg;

 X=[1 3 2 4]
 Y=[3 4 1 2]
ie (X,Y) is used to scramble the positions of  a 4x4 matrix
 Let A= 56 77 228 99
        88 31 52  21
        32 74 90  28
        66 99 42  33
now using the above two vectors i have the following order 

    B= (1,3) (1,4) (1,1) (1,2)
       (3,3) (3,4) (3,1) (3,2)
       (2,3) (2,4) (2,1) (2,2)
       (4,3) (4,4) (4,1) (4,2)
ie
    B= 228 99 56 77
       90  28 32 74
       52  21 88 31
       42  33 66 99.

in addition i would also like to know how i can reverse the positions again ie th first element should be placed at (1,3). please help thanks in advance

Answer 1

[Roger Stafford]

Just use the inverses of X and Y:

   X2 = zeros(1,4); X2(X) = 1:4;
   Y2 = zeros(1,4); Y2(Y) = 1:4;
   A2 = B(X2,Y2);

[Abirami]

Thank u sir..I got the results..but im not able to understand what this X2(X) is given for..I'm new to Matlab sir..Can u please explain it..

[Roger Stafford]

Every permutation always has an inverse. Writing "X2(X) = 1:4" causes X2 to be the inverse permutation of X. For example, if X = [3 2 4 1], then X2 will be [4 2 1 3] which is its inverse. That is, X2(X) = X(X2) = 1:4.

      X     X2
   1 --> 3 --> 1
   2 --> 2 --> 2
   3 --> 4 --> 3
   4 --> 1 --> 4

By being the two inverses of X and Y, that causes X2 and Y2 to do this:

 A2 = B(X2,Y2) = A(X(X2),Y(Y2)) = A(X2(X),Y2(Y)) = A(1:4,1:4) = A

and you are back to A again.

Doing the previous X2 = zeros(1,4) is essential in creating an X2 of the correct size. It doesn't matter what it has in it, but if it is not created ahead of time, matlab will give an error. I could have written X2 = rand(1,4) instead and the result of X2(X) = 1:4 would still be the same.

[Abirami]

Thank u very much sir....

Answer 2

[Andrei Bobrov]

Aout = B(X,Y)

[Roger Stafford]

That works only because the two permutations Abirami selected each happened to be their own inverse. Of the 24 possible permutations of 1:4 fourteen are not their own inverse. For example, if X is [4 1 3 2], then X(X) is [2 4 3 1], therefore X is not its own inverse, and B(X,Y) would not return A.