np.tensordot function, how to multiply a tensor by successive slices of another?

Question

I want to multiply two 3D tensors in a specific way. The two tensors have shapes T1 = (a,b,c) and T2 = (d,b,c).

What I want is to multiply a times T2 by the successive 'slices' (b,c) of a. In other words, I want to have the same as this code :

import numpy as np

a=2
b=3
c=4
d=5

T1 = np.random.rand(a,b,c)
T2 = np.random.rand(d,b,c)


L= []
for j in range(a) :
    L+=[T1[j,:,:]*T2]
L = np.array(L)
L.shape

I have the iterative solution and I try with axes arguments but I didn't succeed in the second way.

Answer 1

Since the shapes:

In [26]: T1.shape, T2.shape
Out[26]: ((2, 3, 4), (5, 3, 4))

produce a:

In [27]: L.shape
Out[27]: (2, 5, 3, 4)

Let's try a broadcasted pair of arrays:

In [28]: res = T1[:,None]*T2[None,:]

Shape and values match:

In [29]: res.shape
Out[29]: (2, 5, 3, 4)    
In [30]: np.allclose(L,res)
Out[30]: True

tensordot, dot, or matmul don't apply; just plain elementwise multiplication, with broadcasting.

Answer 2

Ok, now I think I got the solution:

a=2
b=3
c=4
d=5

T1 = np.random.rand(a,b,c)
T2 = np.random.rand(d,b,c)

L = np.zeros(shape=(a,d,b,c))
for i1 in range(len(T1)):
    for i2 in range(len(T2)):
        L[i1,i2] = np.multiply(np.array(T1[i1]),np.array(T2[i2]))