FreeFormCov

class glimix_core.cov.FreeFormCov(dim)

General definite positive matrix, K = LLᵀ + ϵI.

A d×d covariance matrix K will have ((d+1)⋅d)/2 parameters defining the lower triangular elements of a Cholesky matrix L such that:

K = LLᵀ + ϵI,

for a very small positive number ϵ. That additional term is necessary to avoid singular and ill conditioned covariance matrices.

Example

>>> from glimix_core.cov import FreeFormCov
>>>
>>> cov = FreeFormCov(2)
>>> cov.L = [[1., .0], [0.5, 2.]]
>>> print(cov.gradient()["Lu"])
[[[0.  2.  0. ]
  [1.  0.5 0. ]]

 [[1.  0.5 0. ]
  [1.  0.  8. ]]]
>>> cov.name = "K"
>>> print(cov)
FreeFormCov(dim=2): K
  L: [[1.  0. ]
      [0.5 2. ]]

__init__(dim)

Constructor.

Parameters

dim (int) – Dimension d of the free-form covariance matrix.

Methods

__init__(dim)	Constructor.
eigh()	Eigen decomposition of K.
fix()	Disable parameter optimisation.
gradient()	Derivative of the covariance matrix over the parameters of L.
listen(func)	Listen to parameters change.
logdet()	Log of ｜K｜.
unfix()	Enable parameter optimisation.
value()	Covariance matrix.

Attributes

L	Lower-triangular matrix L such that K = LLᵀ + ϵI.
Lu	Lower-triangular, flat part of L.
name	Name of this function.
nparams	Number of parameters.
shape	Array shape.