summation of products of matrices

I would like so have a fast solution to this problem

where is an p x m matrices and S is a symmetric matrices p x p, where m and p are very large

Answer 1

[Daniel Neubauer]

take a look at

Z = pagemtimes(X,Y)

is that what you need?

p=3;
m=4;
i=5;
E=ones(p,p,i);
A=rand(p,m,i);
Sum=sum(pagemtimes(pagemtimes(A,'C',E,'N'),A),3)

Sum = 4×4

16.1794 14.6014 11.9153 11.5921 14.6014 14.7036 11.2311 10.9738 11.9153 11.2311 9.4835 8.7488 11.5921 10.9738 8.7488 9.6928

[Bruno Luong]

pagemtimes(pagetranspose(A),E)

rather

pagemtimes(A,'C',E,'N')

[Daniel Neubauer]

thats true, thanks, I edited accordingly

[Pasquale Valentini]

thanks for your reply.

It is very useful, but it seems to me that using "pagemtimes" is not faster than using “For Loop Matlab"

[Daniel Neubauer]

I dont know if there is a fasther way then, sorry!