torch.mvlgamma

torch.mvlgamma(input, p) → Tensor

Computes the multivariate log-gamma function) with dimension $p$ element-wise, given by

$$\log(\Gamma_{p}(a)) = C + \displaystyle \sum_{i=1}^{p} \log\left(\Gamma\left(a - \frac{i - 1}{2}\right)\right)$$

where $C = \log(\pi) \times \frac{p (p - 1)}{4}$ and $\Gamma(\cdot)$ is the Gamma function.

All elements must be greater than $\frac{p - 1}{2}$, otherwise an error would be thrown.

Parameters

• input (Tensor) – the tensor to compute the multivariate log-gamma function

• p (int) – the number of dimensions

Example:

>>> a = torch.empty(2, 3).uniform_(1, 2)
>>> a
tensor([[1.6835, 1.8474, 1.1929],
        [1.0475, 1.7162, 1.4180]])
>>> torch.mvlgamma(a, 2)
tensor([[0.3928, 0.4007, 0.7586],
        [1.0311, 0.3901, 0.5049]])