projnormal.formulas.projected_normal_B.probability
Probability density function (PDF) for the general projected normal distribution.
Functions
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Compute the log-pdf at points y for the distribution of the variable \(y = x/\sqrt{x^T B x}\), where \(x \sim \mathcal{N}(\mu_x, \Sigma_x)\) and \(B\) is a symmetric positive definite matrix. |
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Compute the pdf at points y for the distribution of the variable \(y = x/\sqrt{x^T B x}\), where \(x \sim \mathcal{N}(\mu_x, \Sigma_x)\) and \(B\) is a symmetric positive definite matrix. |
- log_pdf(mean_x, covariance_x, y, B=None)
Compute the log-pdf at points y for the distribution of the variable \(y = x/\sqrt{x^T B x}\), where \(x \sim \mathcal{N}(\mu_x, \Sigma_x)\) and \(B\) is a symmetric positive definite matrix.
- Parameters:
mean_x (
torch.Tensor) – Mean of x. Shape is(n_dim,).covariance_x (
torch.Tensor) – Covariance of x. Shape is(n_dim, n_dim).y (
torch.Tensor) – Points where to evaluate the PDF. Shape is(n_points, n_dim).B (
torch.Tensor, optional) – Matrix B used in the denominator of the projection. If not provided, the identity matrix is used. Shape is(n_dim, n_dim).
- Returns:
Log-PDF evaluated at each y. Shape is
(n_points,).- Return type:
torch.Tensor
- pdf(mean_x, covariance_x, y, B=None)
Compute the pdf at points y for the distribution of the variable \(y = x/\sqrt{x^T B x}\), where \(x \sim \mathcal{N}(\mu_x, \Sigma_x)\) and \(B\) is a symmetric positive definite matrix.
- Parameters:
mean_x (
torch.Tensor) – Mean of x. Shape is(n_dim,).covariance_x (
torch.Tensor) – Covariance of x. Shape is(n_dim, n_dim).y (
torch.Tensor) – Points where to evaluate the PDF. Shape is(n_points, n_dim).B (
torch.Tensor, optional) – Matrix B used in the denominator of the projection. If not provided, the identity matrix is used. Shape is(n_dim, n_dim).
- Returns:
PDF evaluated at each y. Shape is
(n_points,).- Return type:
torch.Tensor