object_einsum.py

import numpy as np

def object_einsum(string, *arrays):
    """Simplified object einsum, not as much error checking
    
    does not support "..." or list input and will see "...", etc. as three times
    an axes identifier, tries normal einsum first!
    
    NOTE: This is untested, and not fast, but object type is
    never really fast anyway...
    """
    try:
        return np.einsum(string, *arrays)
    except TypeError:
        pass
    
    s = string.split('->')
    in_op = s[0].split(',')
    out_op = None if len(s) == 1 else s[1].replace(' ', '')

    in_op = [axes.replace(' ', '') for axes in in_op]
    all_axes = set()

    for axes in in_op:
        all_axes.update(axes)

    if out_op is None:
        out_op = sorted(all_axes)
    else:
        all_axes.update(out_op)
    
    perm_dict = {_[1]: _[0] for _ in enumerate(all_axes)}
    
    dims = len(perm_dict)
    op_axes = []
    for axes in (in_op + list((out_op,))):
        op = [-1] * dims
        for i, ax in enumerate(axes):
           op[perm_dict[ax]] = i
        op_axes.append(op)
    
    op_flags = [('readonly',)] * len(in_op) + [('readwrite', 'allocate')]
    dtypes = [np.object_] * (len(in_op) + 1) # cast all to object

    nditer = np.nditer(arrays + (None,), op_axes=op_axes, flags=['buffered', 'delay_bufalloc', 'reduce_ok', 'grow_inner', 'refs_ok'], op_dtypes=dtypes, op_flags=op_flags)

    nditer.operands[-1][...] = 0
    nditer.reset()
    
    for vals in nditer:
        out = vals[-1]
        prod = vals[0]
        for value in vals[1:-1]:
            prod *= value
        out += prod
    
    return nditer.operands[-1]

I had to combine the changes made by @gugar20 and @wenlibin02 to get this to work correctly.