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Triangular Multivariate Normal¤

distreqx.distributions.MultivariateNormalTri(distreqx.distributions.AbstractMultivariateNormalFromBijector) ¤

Multivariate normal distribution on \(\mathbb{R}^k\).

The MultivariateNormalTri distribution is parameterized by a \(k\)-length location (mean) vector \(b\) and a (lower or upper) triangular scale matrix \(S\) of size \(k \times k\). The covariance matrix is \(C = SS^T\).

Note

The scale_tri matrix must have non-zero diagonal elements for the distribution to be valid. This class does not verify this condition.

__init__(loc: Array | None = None, scale_tri: Array | None = None, is_lower: bool = True) ¤

Initializes a MultivariateNormalTri distribution.

Arguments:

  • loc: Mean vector of the distribution of shape k. If not specified, it defaults to zeros.
  • scale_tri: The scale matrix S. It must be a k x k triangular matrix. If scale_tri is not triangular, the entries above or below the main diagonal will be ignored. The parameter is_lower specifies if scale_tri is lower or upper triangular. It is the responsibility of the user to make sure that scale_tri only contains non-zero elements in its diagonal; this class makes no attempt to verify that. If scale_tri is not specified, it defaults to the identity.
  • is_lower: Indicates if scale_tri is lower (if True) or upper (if False) triangular.