logsumexp

logsumexp#

Signature#

nabla.logsumexp(arg: 'Array', axis: 'int | None', keep_dims: 'bool') -> 'Array'

Description#

Computes the log of the sum of exponentials of input elements.

This function computes log(sum(exp(x))) in a numerically stable way by using the identity: logsumexp(x) = max(x) + log(sum(exp(x - max(x)))). This avoids overflow errors that can occur when exp(x) is very large.

Parameters#

  • arg (Array): The input array.

  • axis (int | None, optional): The axis or axes along which to compute the logsumexp. If None (the default), the operation is performed over all elements of the array.

  • keep_dims (bool, optional): If True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. Defaults to False.

Returns#

  • Array: An array containing the result of the logsumexp operation.

Examples#

>>> import nabla as nb
>>> x = nb.array([1.0, 2.0, 3.0])
>>> nb.logsumexp(x)
Array([3.407606], dtype=float32)

>>> data = nb.array([[1, 2, 3], [4, 5, 6]])
>>> nb.logsumexp(data, axis=1)
Array([3.407606, 6.407606], dtype=float32)
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