I often find that I'd like like to do an operation between the last few dimensions of two arrays, where the first dimensions don't necessarily match. As an example I'd like to do something like:
a = np.random.randn(10, 10, 3, 3)
b = np.random.randn(5, 3)
c = np.einsum('...ij, ,,,j -> ...,,,i', a, b)
and the result should satisfy c.shape = (10, 10, 5, 3) and c[i, j, k] = a[i, j] @ b[k]. Is there a way to achieve this with the existing interface?
In [82]: c = np.einsum('...ij,...j->...i', a, b)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [82], in <cell line: 1>()
----> 1 c = np.einsum('...ij,...j->...i', a, b)
File <__array_function__ internals>:5, in einsum(*args, **kwargs)
File ~\anaconda3\lib\site-packages\numpy\core\einsumfunc.py:1359, in einsum(out, optimize, *operands, **kwargs)
1357 if specified_out:
1358 kwargs['out'] = out
-> 1359 return c_einsum(*operands, **kwargs)
1361 # Check the kwargs to avoid a more cryptic error later, without having to
1362 # repeat default values here
1363 valid_einsum_kwargs = ['dtype', 'order', 'casting']
ValueError: operands could not be broadcast together with remapped shapes
[original->remapped]: (10,10,3,3)->(10,10,3,3) (5,3)->(5,newaxis,3)
So it's trying to use broadcasting to match dimensions.
Let's make a (10,10,1,3,3) shape. That way the (10,10,1) part broadcasts with the (5,) of b:
In [83]: c = np.einsum('...ij,...j->...i', a[:,:,None], b)
In [84]: c.shape
Out[84]: (10, 10, 5, 3)
ended up getting around the issue with the following helper function
def batch_matvec(A, b):
product = np.einsum('...ij, ...kj->...ki', A, b.reshape(-1, b.shape[-1]))
return product.reshape((*A.shape[:-2], *b.shape[:-1], -1))
np.einsum('...ij,kj->...ki', a, b), with one more distinguishable axis.