如何使用 numpy 计算向量和矩阵的“克罗内克积”

Question

I need to compute the following forumula:

Fromula in TeX:

$\sum_n^N \sum_m^N a_n * a_m * C_{nm}$

Peudocode:

a = array of length N
C = NxN matrix
retval = 0
for n in range(N):
    for m in range(N):
         retval += a[n] * a[m] * C[n][m]

If a were a NxN matrix constructed as in the product above one could simply use np.kron for the Kronecker Matrix multiplication and then use np.sum to get the desired result. However I don't know a faster numpy way of constructing a matrix A as in the formula above.

Any ideas?

Answer 1

We could directly use those iterators for np.einsum string-notation -

retval = np.einsum('n,m,nm->',a,a,C)

Alternatively, withnp.dot -

retval = a.dot(C).dot(a)