chainer.functions.einsumΒΆ

chainer.functions.einsum(*operands)[source]ΒΆ

Einstein summation

This function supports two formats of inputs:

  • einsum(subscripts, op0, op1, ...)
  • einsum(op0, sublist0, op1, sublist1, ..., [sublistout])

See also numpy.einsum()

Example

The following example computes a batched application of a bilinear function with weight w.

>>> x1 = np.arange(12).reshape(3, 4).astype(np.float32)
>>> x2 = np.arange(15).reshape(3, 5).astype(np.float32)
>>> w = np.arange(120).reshape(4, 5, 6).astype(np.float32)
>>> y = F.einsum('ij,ik,jkl->il', x1, x2, w)
>>> y.shape
(3, 6)

The batch axes can be denoted by .... If the string of output subscripts is omitted, the summation is taken over the subscript alphabets with two (or more) occurrences.

>>> np.allclose(y.array, F.einsum('...j,...k,jkl', x1, x2, w).array)
True

In the other format:

>>> y = F.einsum(x1, [0, 1], x2, [0, 2], w, [1, 2, 3], [0, 3])
>>> y.shape
(3, 6)
>>> y = F.einsum(x1, [Ellipsis, 1], x2, [Ellipsis, 2], w, [1, 2, 3])
>>> y.shape
(3, 6)