Matrix operations matlab to move values around - matlab

Question

I have a matrix that I'd like to create a new ordering of, for example,
vals = [1 2; 3 4]
I also have two matrices, new_x and new_y such that new_x(a,b) = j and new_x(a,b) = k means that I want the value at vals (a,b) to be mapped to new_vals(j,k).
For example, given
new_x = [1 2; 2 1]
new_y = [2 2; 1 1]
I'd want
new_vals = [4 3; 1 2]
I understand that I could just write two for loops to build the new array, but matlab is notoriously good at providing operations on entire matricies. My question is, how would I build new_vals without the for loops?

Answer 1

Basically you are trying to get a matrix that when indexed with new_x and new_y would give us vals, i.e. -
output(new_x(1,1),new_y(1,1)) must be equal to vals(1,1),
output(new_x(1,2),new_y(1,2)) must be equal to vals(1,2) and so on.
We will try to verify this later on. For now, here's one solution using linear indexing -
nrows = size(vals,1); %// Store number of rows
%// Calculate linear indices
idx = (new_x + (new_y-1)*nrows);
%// Trace/map back to sorted version of "1:numel(vals)"
[~,traced_back_idx] = sort(idx(:));
%// Index into vals with traced back linear indices & then reshape & transpose
out = reshape(vals(traced_back_idx),[],nrows).'
Here's another and possibly faster way -
out = nan(size(vals));
out((new_x + (new_y-1)*nrows)) = vals;
out = out.'
As discussed earlier for verification, let's index into out with new_x and new_y and that should match up with vals. Here's a code to do so -
for ii = 1:size(out,1)
for jj = 1:size(out,2)
check_back(ii,jj) = out(new_y(ii,jj),new_x(ii,jj));
end
end
Sample runs -
Case #1 (sample from question):
vals =
1 2
3 4
new_x =
1 2
2 1
new_y =
2 2
1 1
new_vals =
4 3
1 2
out =
4 3
1 2
check_back = (must be same as vals)
1 2
3 4
Case #2:
vals =
1 2 5
3 4 5
6 8 3
new_x =
1 2 3
3 1 2
3 2 1
new_y =
2 2 3
2 1 1
1 3 3
out =
4 5 6
1 2 3
3 8 5
check_back = (must be same as vals)
1 2 5
3 4 5
6 8 3

Answer 2

I think i see what you are trying to do here. new_x and new_y are just coordinates for the new_val matrix rigth? The problem is tha what you are trying to do only works for vectors, not for matrix, so the only way is to transform the matrix into a vector, reorder the values and then go back to matrix like:
vals = [1 ,2; 3, 4];
A=reshape(vals,1,4); % A is a vector [ 1 3 2 4]
new_coord=[2,3,4,1];
B(new_c)=A; %B is [4 1 3 2]
new_val=reshape(B,2,2) %back to matrix
Obtainig new_val=[4 3; 1 2]. Also B=A(new_c) is also allowed but with different coordinates, eventhoug is much easy to think the rigth coordinates in that way.
I am sure there must be a way to include the new_x matrix and transform everything into new_coord