Making a 3d array MATLAB

Question

In MATLAB I have

[Z,S]=meshgrid(0.01:0.01:1)

and I also have a 100000x2 matrix called X, each row has two sets of data - p is the first column and x is the 2nd.

I want to compute exp^(-S*X(j,2)).(*Z.^X(j,1)) where j indexes the row. The result should be a 100x100x100000 matrix. This will then be averaged along the 3rd dimension and a mesh plot will be produced. I've tried using a for loop

[Z,S]=meshgrid(0.01:0.01:1)
for j=1:100000
phi(j)=exp^(-S.*X(j,2)).*(Z.^X(j,1))
end

to produce the 100x100x100000 array I need. However this gives me the error

In an assignment  A(I) = B, the number of elements in B and I must be the same.
Error in phi (line 4)
phi(j)=exp(-S.*X(j,2)).*(Z.^X(j,1));

I'm not sure why this is happening? Can anyone figure out a better way of trying to find the result I want? Because I'm guessing there could be a fully vectorised solution (or least use of for loops)?

Answer 1

Assume that you are using two more nested loops to get Z and S , thus the code would have three nested loops in total.

Now, the vectorizing techniques haven't changed on vectorizable nested loops cases like these - Treat different parts of the code that involve different iterators separately . Thus, here you have three iterators, two of which are 100 in length and the third ones goes until 100000 . Putting the vectorizing ideas in a concise commented text and solving your case with bsxfun based code -

%// Get vectorized equivalent of exp(-S.*X(j,2)) and keeping in mind that
%// since the last (3rd) dimension of final output has length same as the 
%// number of elements in X(:,2), so "throw" this to 3rd dim with permute. 
%// Then, use bsxfun to let the broadcasting being taken care off by MATLAB.
p1 = exp(-bsxfun(@times,V.',permute(X(:,2),[3 2 1]))); %//'

%// Going with same philosophy as before, get vectorized (Z.^X(j,1))
p2 = bsxfun(@power,V,permute(X(:,1),[3 2 1]));

%// Finally "merge" earlier two parts for final output
phi_out = bsxfun(@times,p1,p2);