Taking expectation of 3 dimension matrix

Hi,

I am trying to take the expectation of a function on two variables where the probabilities are markov process and it is 3dimension.

E(v(a',b',c'))= Sum(sum(v(a,b,c)*Q(b,b')*Q(c,c'))) where sums are on b and c and Q are the transition matrices.

I found it as below but i need to make it faster.

Nk=100, Nz=5, Ne=4

v_n=rand(Nk,Nz,Ne)

Q_z(Nz,Nz) is 5*5 transition matrix where sum of each row makes 1

Q_e(Ne,Ne) is 3*3 transition matrix where sum of each row makes 1

for ik=1:Nk

for iz=1:Nz

for ie=1:Ne

asd(ik,iz,ie)=dot(Q_e(ie,:),squeeze(v_n(ik,iz,:)));

end

end

end

for ik=1:NkPts

for iz=1:Nz

for ie=1:Ne

expv_n(ik,iz,ie)= dot(Q_z(iz,:),squeeze(asd(ik,:,ie)));

end

end

end

Answer 1

[Neelanshu]

Hi Mert Demir,

I understand that you are facing an issue related to finding a faster way to compute the expectation of 3 dimensional matrix.

The “for” loops in the code when converted to matrix operations will be much faster. For instance, replacing

for ie=1:Ne 
      asd(ik,iz,ie) = dot(Q_e(ie,:),squeeze(v_n(ik,iz,:)));          
end 

with

 asd(ik,iz,:) = dot(Q_e,repmat(squeeze(v_n(ik,iz,:))',4,1),2);

will improve the computation time significantly.

You can refer the following link to transform the remaining “for” loops with matrix operations: https://www.mathworks.com/help/matlab/matrices-and-arrays.html?s_tid=CRUX_lftnav

Hope it helps,

Regards,

Neelanshu