# tfp.experimental.substrates.jax.math.reduce_weighted_logsumexp

Computes `log(abs(sum(weight * exp(elements across tensor dimensions))))`.

If all weights `w` are known to be positive, it is more efficient to directly use `reduce_logsumexp`, i.e., `tf.reduce_logsumexp(logx + tf.log(w))` is more efficient than `du.reduce_weighted_logsumexp(logx, w)`.

Reduces `input_tensor` along the dimensions given in `axis`. Unless `keep_dims` is true, the rank of the tensor is reduced by 1 for each entry in `axis`. If `keep_dims` is true, the reduced dimensions are retained with length 1.

If `axis` has no entries, all dimensions are reduced, and a tensor with a single element is returned.

This function is more numerically stable than log(sum(w * exp(input))). It avoids overflows caused by taking the exp of large inputs and underflows caused by taking the log of small inputs.

#### For example:

``````x = tf.constant([[0., 0, 0],
[0, 0, 0]])

w = tf.constant([[-1., 1, 1],
[1, 1, 1]])

du.reduce_weighted_logsumexp(x, w)
# ==> log(-1*1 + 1*1 + 1*1 + 1*1 + 1*1 + 1*1) = log(4)

du.reduce_weighted_logsumexp(x, w, axis=0)
# ==> [log(-1+1), log(1+1), log(1+1)]

du.reduce_weighted_logsumexp(x, w, axis=1)
# ==> [log(-1+1+1), log(1+1+1)]

du.reduce_weighted_logsumexp(x, w, axis=1, keep_dims=True)
# ==> [[log(-1+1+1)], [log(1+1+1)]]

du.reduce_weighted_logsumexp(x, w, axis=[0, 1])
# ==> log(-1+5)
``````

`logx` The tensor to reduce. Should have numeric type.
`w` The weight tensor. Should have numeric type identical to `logx`.
`axis` The dimensions to reduce. If `None` (the default), reduces all dimensions. Must be in the range ```[-rank(input_tensor), rank(input_tensor))```.
`keep_dims` If true, retains reduced dimensions with length 1.
`return_sign` If `True`, returns the sign of the result.
`name` A name for the operation (optional).

`lswe` The `log(abs(sum(weight * exp(x))))` reduced tensor.
`sign` (Optional) The sign of `sum(weight * exp(x))`.