# Einsum Matrix Multiplication Question

I currently have a tensor of size ([10, 5]) which represents 10 5-D vectors and a tensor of size ([10, 5, 5]) which represents 10 5x5 matrices. I would like to perform
V_i @ M_i @ V_i.T for each matrix and vector so it returns back a ([10, 1]) tensor and I think this could be done via einsum. Currently I can do this easily via a for loop but it is very slow and I am wondering if this calculation is possible to do using einsum or some other torch function?

Hi @armal,

Here are some example codes that solve your problem.

``````import torch

_ = torch.manual_seed(0)

V = torch.randn(10,5)
M = torch.randn(10,5,5)

def einsum_op(V, M):
out = torch.einsum("bi,bij,bj->b", V, M, V)
return out

def unsqueeze_op(V, M):
out = V.unsqueeze(-2) @ M @ V.unsqueeze(-1)
return out.squeeze() #reshape to size [B,]

out = einsum_op(V,M)
print(out)
#returns
#tensor([  4.7036,   6.2151,   1.1999,  -2.0412,  -6.3517,  -5.3721,  -2.5428,
#         -0.4131, -24.2325,  -2.3242])
out = unsqueeze_op(V, M)
print(out)
#returns
#tensor([  4.7036,   6.2151,   1.1999,  -2.0412,  -6.3517,  -5.3721,  -2.5428,
#         -0.4131, -24.2325,  -2.3242])
``````

If you want to run a function over batches of inputs, you might want to have a look at the functorch library (which is specifically built for this). Documentation here.

Thank you so much for this! I will definitely take a look at functorch as well, looks like exactly what I need.