sub2ind, picking specific values from a 3d matrix

I have a 500x8x4 matrix, lets call this X, and I have a 500x1 vector, lets call it Y, the latter contains numbers between 1 and 8. These numbers indicate the number in each row that I want from the matrix X. So by picking a number in each row of matrix X, I need to get a matrix that is 500x4, lets call it Z. I dont know how to get this vector Z, in a quick way (not using a loop). I know I should do it with sub2ind but I dont know how. Thank you for your help.

Answer 1

[Sean de Wolski]

sub2ind is slow, if you want performance, use a for-loop.

% Data
X = randn(500,8,4); % z
Y = randi(8,500,1); % idx

% Engine
szX = size(X);
Z = zeros(szX([1 3]));
for ii = 1:szX(1)
    Z(ii,:) = X(ii,Y(ii),:);
end

On my machine, the engine on here is taking about 1/1000 of a second.

Answer 2

[Dan Nussinson]

Sean is right when the matrices are small as in your example. For large for loops sub2ind is x10 faster on my system:

% Data

X = randn(50000,8,4); % z

Y = randi(8,50000,1); % idx

% Engine

szX = size(X);

tic

Z = zeros(szX([1 3]));

for ii = 1:szX(1)

Z(ii,:) = X(ii,Y(ii),:);

end

toc

%sub2ind

tic

ii = 1:szX(1);

linInds = sub2ind(szX([1 2]),ii',Y);

X2 = reshape(X,szX(1)*szX(2),[]);

Z2 = X2(linInds,:);

toc