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

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Maryam S
Maryam S 2019-8-30
评论： Maryam Sadeghi 2019-8-30
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]
Screen Shot 2019-08-30 at 12.53.53 PM.png
Thanks in advance
Maryam

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采纳的回答

Stephen23
Stephen23 2019-8-30
>> 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

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