tf.lbeta()

tf.lbeta(x, name='lbeta')

Computes ln(|Beta(x)|), reducing along the last dimension.

Given one-dimensional z = [z_0,...,z_{K-1}], we define

Beta(z) = \prod_j Gamma(z_j) / Gamma(\sum_j z_j)

And for n + 1 dimensional x with shape [N1, ..., Nn, K], we define lbeta(x)[i1, ..., in] = Log(|Beta(x[i1, ..., in, :])|). In other words, the last dimension is treated as the z vector.

Note that if z = [u, v], then Beta(z) = int_0^1 t^{u-1} (1 - t)^{v-1} dt, which defines the traditional bivariate beta function.

Args:

• x: A rank n + 1 Tensor with type float, or double.
• name: A name for the operation (optional).

Returns:

The logarithm of |Beta(x)| reducing along the last dimension.

Raises:

• ValueError: If x is empty with rank one or less.