Bases: Module
  
      A multivariate Gaussian distribution with trainable mean and covariance 
matrix.
Arguments:
- mu: list of floats, the initial mean of the distribution.
- sigma: float, the initial standard deviation of the distribution.
    The covariance matrix is initialized as a diagonal matrix with this
    value on the diagonal.
- device: str, the device to use for the distribution.
              Source code in blackbirds/posterior_estimators.py
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40 | class TrainableGaussian(torch.nn.Module):
    """
    A multivariate Gaussian distribution with trainable mean and covariance 
    matrix.
    **Arguments:**
    - `mu`: list of floats, the initial mean of the distribution.
    - `sigma`: float, the initial standard deviation of the distribution.
        The covariance matrix is initialized as a diagonal matrix with this
        value on the diagonal.
    - `device`: str, the device to use for the distribution.
    """
    def __init__(self, mu=[0.0], sigma=1.0, device="cpu"):
        super().__init__()
        self.mu = torch.nn.Parameter(torch.tensor(mu, device=device))
        self.sigma = sigma * torch.eye(len(mu), device=device)
        self.sigma = torch.nn.Parameter(self.sigma)
    def clamp_sigma(self):
        sigma = self.sigma.clone()
        mask = torch.eye(len(self.mu), device=self.sigma.device).bool()
        sigma[mask] = torch.clamp(self.sigma[mask], min=1e-3)
        return sigma
    def log_prob(self, x):
        sigma = self.clamp_sigma()
        return torch.distributions.MultivariateNormal(self.mu, sigma).log_prob(x)
    def sample(self, n):
        sigma = self.clamp_sigma()
        dist = torch.distributions.MultivariateNormal(self.mu, sigma)
        sample = dist.rsample((n,))
        return sample, self.log_prob(sample.detach())
    def __call__(self, x=None):
        return self
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