MATLAB: How to use matrix elements as indices to access elements of another matrix

indexingmatrix

I have a 5*4 matrix 'Id'
Id = [1 2 1 1; 
      1 2 2 2; 
      3 1 3 1;
      1 2 3 1; 
      2 2 3 3]
I have another matrix Values of size 5*4*3
Values(:,:,1) = [0 0 1 2;
                 2 2 1 1;
                 2 1 0 0;
                 1 1 2 1;
                 2 1 2 2]
Values(:,:,2) = [1 0 1 2;
                 2 0 2 1;
                 1 1 2 0;
                 1 0 2 1;
                 1 2 2 0]
Values(:,:,3) = [1 2 1 0;
                 2 0 2 1;
                 2 0 1 2;
                 0 0 2 1;
                 1 1 2 2]
I want the resultant matrix of size 5*4 to be using the value in Id as the index to pick corresponding elements from Values ie.
Result(i,j) = Values(i,j,Id(i,j)) 
Result = [0 0 1 2;
          2 0 2 1;
          2 1 1 0;
          1 0 2 1;
          1 2 2 2]
How do I do this without a for loop?

Best Answer

Values(:,:,1) = [0 0 1 2 
  2 2 1 1 
  2 1 0 0 
  1 1 2 1 
  2 1 2 2]
Values(:,:,2) = [1 0 1 2 
  2 0 2 1 
  1 1 2 0 
  1 0 2 1 
  1 2 2 0]
Values(:,:,3) = [1 2 1 0 
  2 0 2 1 
  2 0 1 2 
  0 0 2 1 
  1 1 2 2]
Id = [1 2 1 1 
  1 2 2 2 
  3 1 3 1 
  1 2 3 1 
  2 2 3 3]
[n,m]=size(Id)
[x,y]=ndgrid(1:n,1:m)
idl=sub2ind(size(Values),x,y,Id)
Result=Values(idl)
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