projnormal.formulas.projected_normal_iso.probability
Probability density function (PDF) for the projected normal distribution with isotropic covariance of the unprojected Gaussian.
Functions
|
Compute the log-pdf at points y for the distribution of the variable \(y = x/\sqrt{x^T x}\), where \(x \sim \mathcal{N}(\mu_x, \Sigma_x)\) and \(\Sigma_x = \sigma^2 I\) (isotropic covariance matrix). |
|
Compute the pdf at points y for the distribution of the variable \(y = x/\sqrt{x^T x}\), where \(x \sim \mathcal{N}(\mu_x, \Sigma_x)\) and \(\Sigma_x = \sigma^2 I\) (isotropic covariance matrix). |
- log_pdf(mean_x, var_x, y)
Compute the log-pdf at points y for the distribution of the variable \(y = x/\sqrt{x^T x}\), where \(x \sim \mathcal{N}(\mu_x, \Sigma_x)\) and \(\Sigma_x = \sigma^2 I\) (isotropic covariance matrix).
- Parameters:
mean_x (
torch.Tensor) – Mean of x. Shape is(n_dim,).var_x (
torch.tensor) – variance of x. shape is().y (
torch.Tensor) – Points where to evaluate the PDF. Shape is(n_points, n_dim).
- Returns:
Log-PDF evaluated at each y. Shape is
(n_points,).- Return type:
torch.Tensor
- pdf(mean_x, var_x, y)
Compute the pdf at points y for the distribution of the variable \(y = x/\sqrt{x^T x}\), where \(x \sim \mathcal{N}(\mu_x, \Sigma_x)\) and \(\Sigma_x = \sigma^2 I\) (isotropic covariance matrix).
- Parameters:
mean_x (
torch.Tensor) – Mean of x. Shape is(n_dim,).var_x (
torch.tensor) – variance of x. shape is().y (
torch.Tensor) – Points where to evaluate the PDF. Shape is(n_points, n_dim).
- Returns:
PDF evaluated at each y. Shape is
(n_points,).- Return type:
torch.Tensor