How to Vectorize a Nested Loop

I'm having trouble visualizing how to vectorize this set of loops. Any guidance would be appreciated. ``` ind_1 = [1,2,3]; ind_2 = [1,2,4]; K = zeros(3,3,3,3,3,3,3,3,3); pp = rand(4,4,4); for s = 1:3 for t = 1:3 for k = 1:3 for l = 1:3 for m = 1:3 for n = 1:3 for o = 1:3 for p = 1:3 for r = 1:3 % the following loops are singular valued except when % y=3 for ind_x(y) in this case for a_s = ind_1(s):ind_2(s) for a_t = ind_1(t):ind_2(t) for a_k = ind_1(k):ind_2(k) for a_l = ind_1(l):ind_2(l) for a_m = ind_1(m):ind_2(m) for a_n = ind_1(n):ind_2(n) for a_o = ind_1(o):ind_2(o) for a_p = ind_1(p):ind_2(p) for a_r = ind_1(r):ind_2(r) K(s,t,k,l,m,n,o,p,r) = K(s,t,k,l,m,n,o,p,r) + ... pp(a_s, a_t, a_r) * pp(a_k, a_l, a_r) * ... pp(a_n, a_m, a_s) * pp(a_o, a_n, a_t) * ... pp(a_p, a_o, a_k) * pp(a_m, a_p, a_l); end end end end end end end end end end end end end end end end end end ``` EDIT: The code is creating a rank-9 tensor with indices from 1 to 3 by summing the values of a product of `pp`s one or two times for each index, depending on the value of `ind_1` and `ind_2`. EDIT: Here is a 3d example, though bear in mind that the fact that the indices of `pp` are simply permuted is not preserved in the 9d version: ``` ind_1 = [1,2,3]; ind_2 = [1,2,4]; K = zeros(3,3,3); pp = rand(4,4,4); for s = 1:3 for t = 1:3 for k = 1:3 % the following loops are singular valued except when % y=3 for ind_x(y) in this case for a_s = ind_1(s):ind_2(s) for a_t = ind_1(t):ind_2(t) for a_k = ind_1(k):ind_2(k) K(s,t,k) = K(s,t,k) + ... pp(a_s, a_t, a_r) * pp(a_t, a_s, a_k) * ... pp(a_k, a_t, a_s) * pp(a_k, a_s, a_t); end end end end end end ```