azula.linalg.covariance¶

Covariance matrices.

Classes¶

`Covariance`	Abstract covariance matrix.
`IsotropicCovariance`	Isotropic covariance matrix.
`DiagonalCovariance`	Diagonal covariance matrix.
`FullCovariance`	Full covariance matrix.
`DPLRCovariance`	Diagonal plus low-rank (DPLR) covariance matrix.
`KroneckerCovariance`	Kronecker-factorized covariance matrix.

class azula.linalg.covariance.IsotropicCovariance(lmbda)¶

Isotropic covariance matrix.

\[\lambda I\]

class azula.linalg.covariance.DiagonalCovariance(D)¶

Diagonal covariance matrix.

\[\mathrm{diag}(D)\]

class azula.linalg.covariance.FullCovariance(C)¶

Full covariance matrix.

\[C\]

class azula.linalg.covariance.DPLRCovariance(D, V, S=None)¶

Diagonal plus low-rank (DPLR) covariance matrix.

\[\mathrm{diag}(D) + V \Sigma V^\top\]

Wikipedia

class azula.linalg.covariance.KroneckerCovariance(C, Qs)¶

Kronecker-factorized covariance matrix.

\[(Q_1 \otimes \dots \otimes Q_n) \, C \, (Q_1 \otimes \dots \otimes Q_n)^\top\]

where \(Q_i\) are orthonormal matrices for each dimension and \(\otimes\) denotes the Kronecker product.

Wikipedia