Alternative to reshape to multiply multidimensional arrays

I am working on a dynamic programming problem and after profiling my code I noticed that most of the computing time is spent using the reshape function to quickly multiply a value function by a probability array. This is faster than using for loops but not fast enough. The line using the reshape function takes almost 50% of the total computation time. Any suggestions would be very appreciated. Please let me know if the description/code is not clear. Thank you.

no_obs = 210;
EV = zeros(no_obs,4);
next_age = [9;1;1;1]; 
Vinit(pr1,pr2,pr3,next_age,action,no_obs)   
for action=1:4
   V = reshape(Vinit(:,:,:,next_age(action),action,:),[],no_obs);
   EV(:,action)=(P_array(:).' * V).';
end

Answer 1

[Walter Roberson]

NV = permute(Vinit, [1 2 3 6 4 5])

before you start, so that when you fill in the next_age(action) and action subscripts, you are taking a slice of contiguous memory NV(:,:,:,:, next_age(action), action).

Filling in the actual value for [] is measurably faster.

You might possibly get better performance by

NV = permute(Vinit, [6 1 2 3 4 5]);

and then

EV(:,action) = reshape( NV(:,:,:,:, next_age(action), action), no_obs, [] ) * P_array(:);

(except fill in [] with the actual value for better performance)

Especially if you can go back and create the Vinit in that order instead of permute()'ing it.

[Walter Roberson]

Also, you can do the P_array(:) before the loop and assign it into a variable.

[Raymundo Marcos-Martinez]

Thank you very much Mr. Robertson for sharing your knowledge. Your second permutation order is faster than the first one. In general, your suggestions allowed me to reduce the computation time around 8%. Thanks again.