How to track elements in a matrix that switch their position when converting into another matrix?

Hi, Could you please help me find a solution to this problem:

Matrix A gives the index of a set of 2 particles (i;ii) distributed in 10 columns (2*10). Matrix B gives the index of these particles after 1 second and Matrix C gives their index after 2 seconds. For instance, if particle i is introduced at position 7 in matrix A, it would get to position 4 after t time; particle i from 4th column in matrix B would end in column 9 in Matrix C. I would like to track the trajectory of these particles as a function of time and their initial position (see Xi and Xii). For instance, the trajectory of particle i that is introduced at 7th is : from column 7 to column 4 and from 4 to 9 after 2 seconds.

A = [1 2 3 4 5 6 7 8 9 10;1 2 3 4 5 6 7 8 9 10]

B = [1 1 1 1 2 3 4 5 6 7;1 1 1 1 1 1 1 1 2 3]

C= [6 7 8 9 10 10 10 10 10 10;4 5 6 7 8 9 10 10 10 10]

Thanks in advance

Maryam

Answer 1

[Stephen23]

>> A = [1,2,3,4,5,6,7,8,9,10;1,2,3,4,5,6,7,8,9,10];
>> B = [1,1,1,1,2,3,4,5,6,7;1,1,1,1,1,1,1,1,2,3];
>> C = [6,7,8,9,10,10,10,10,10,10;4,5,6,7,8,9,10,10,10,10];

>> Xi = A([1,1,1],:); % preallocate
>> Xi(2,:) = B(1,Xi(1,:));
>> Xi(3,:) = C(1,Xi(2,:))
Xi =
    1    2    3    4    5    6    7    8    9   10
    1    1    1    1    2    3    4    5    6    7
    6    6    6    6    7    8    9   10   10   10
>> Xii = A([2,2,2],:); % preallocate
>> Xii(2,:) = B(2,Xii(1,:));
>> Xii(3,:) = C(2,Xii(2,:))
Xii =
    1    2    3    4    5    6    7    8    9   10
    1    1    1    1    1    1    1    1    2    3
    4    4    4    4    4    4    4    4    5    6

[Maryam Sadeghi]

Thanks, it works!