def batch_log_pdf(self, x):
"""
Ref: :py:meth:`pyro.distributions.distribution.Distribution.batch_log_pdf`
"""
# expand to patch size of input
mu = self.mu.expand(self.shape(x))
gamma = self.gamma.expand(self.shape(x))
x_0 = torch.pow((x - mu) / gamma, 2)
px = 2 / (np.pi * gamma * (1 + x_0))
batch_log_pdf_shape = self.batch_shape(x) + (1,)
return torch.sum(torch.log(px), -1).contiguous().view(batch_log_pdf_shape)
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