pymixef.transforms module¶

Canonical constraints between optimizer and natural parameter scales.

class pymixef.transforms.BoundedTransform(lower=0.0, upper=1.0)[source]¶

Bases: Transform

Map to the open interval (lower, upper) using a logistic map.

Parameters:

lower (float)
upper (float)

lower: float¶

upper: float¶

name: ClassVar[str] = 'bounded'¶

forward(unconstrained)[source]¶

Map an unconstrained value to its natural scale.

Parameters:: unconstrained (ArrayLike)
Return type:: NDArray[float64]

inverse(natural)[source]¶

Map a natural-scale value to its unconstrained scale.

Parameters:: natural (ArrayLike)
Return type:: NDArray[float64]

log_abs_det_jacobian(unconstrained)[source]¶

Return the log absolute determinant of the forward Jacobian.

Parameters:: unconstrained (ArrayLike)
Return type:: float

class pymixef.transforms.CholeskyCovarianceTransform(dimension)[source]¶

Bases: Transform

Map packed unconstrained Cholesky entries to an SPD covariance matrix.

Parameters:: dimension (int)

dimension: int¶

name: ClassVar[str] = 'cholesky-covariance'¶

property unconstrained_size: int¶

factor(unconstrained)[source]¶

Parameters:: unconstrained (ArrayLike)
Return type:: NDArray[float64]

forward(unconstrained)[source]¶

Map an unconstrained value to its natural scale.

Parameters:: unconstrained (ArrayLike)
Return type:: NDArray[float64]

inverse(natural)[source]¶

Map a natural-scale value to its unconstrained scale.

Parameters:: natural (ArrayLike)
Return type:: NDArray[float64]

log_abs_det_jacobian(unconstrained)[source]¶

Return the log absolute determinant of the forward Jacobian.

Parameters:: unconstrained (ArrayLike)
Return type:: float

class pymixef.transforms.IdentityTransform[source]¶

Bases: Transform

No constraint.

name: ClassVar[str] = 'identity'¶

forward(unconstrained)[source]¶

Map an unconstrained value to its natural scale.

Parameters:: unconstrained (ArrayLike)
Return type:: NDArray[float64]

inverse(natural)[source]¶

Map a natural-scale value to its unconstrained scale.

Parameters:: natural (ArrayLike)
Return type:: NDArray[float64]

log_abs_det_jacobian(unconstrained)[source]¶

Return the log absolute determinant of the forward Jacobian.

Parameters:: unconstrained (ArrayLike)
Return type:: float

class pymixef.transforms.LogTransform[source]¶

Bases: Transform

Strictly-positive transform using exp.

name: ClassVar[str] = 'log'¶

forward(unconstrained)[source]¶

Map an unconstrained value to its natural scale.

Parameters:: unconstrained (ArrayLike)
Return type:: NDArray[float64]

inverse(natural)[source]¶

Map a natural-scale value to its unconstrained scale.

Parameters:: natural (ArrayLike)
Return type:: NDArray[float64]

log_abs_det_jacobian(unconstrained)[source]¶

Return the log absolute determinant of the forward Jacobian.

Parameters:: unconstrained (ArrayLike)
Return type:: float

class pymixef.transforms.OrderedTransform[source]¶

Bases: Transform

Map a vector to a strictly increasing vector.

name: ClassVar[str] = 'ordered'¶

forward(unconstrained)[source]¶

Map an unconstrained value to its natural scale.

Parameters:: unconstrained (ArrayLike)
Return type:: NDArray[float64]

inverse(natural)[source]¶

Map a natural-scale value to its unconstrained scale.

Parameters:: natural (ArrayLike)
Return type:: NDArray[float64]

log_abs_det_jacobian(unconstrained)[source]¶

Return the log absolute determinant of the forward Jacobian.

Parameters:: unconstrained (ArrayLike)
Return type:: float

class pymixef.transforms.SimplexTransform[source]¶

Bases: Transform

Additive-log-ratio map from R^(K-1) to a K-simplex.

name: ClassVar[str] = 'simplex'¶

forward(unconstrained)[source]¶

Map an unconstrained value to its natural scale.

Parameters:: unconstrained (ArrayLike)
Return type:: NDArray[float64]

inverse(natural)[source]¶

Map a natural-scale value to its unconstrained scale.

Parameters:: natural (ArrayLike)
Return type:: NDArray[float64]

log_abs_det_jacobian(unconstrained)[source]¶

Return the log absolute determinant of the forward Jacobian.

Parameters:: unconstrained (ArrayLike)
Return type:: float

class pymixef.transforms.SoftplusTransform[source]¶

Bases: Transform

Smooth strictly-positive transform with a near-linear upper tail.

name: ClassVar[str] = 'softplus'¶

forward(unconstrained)[source]¶

Map an unconstrained value to its natural scale.

Parameters:: unconstrained (ArrayLike)
Return type:: NDArray[float64]

inverse(natural)[source]¶

Map a natural-scale value to its unconstrained scale.

Parameters:: natural (ArrayLike)
Return type:: NDArray[float64]

log_abs_det_jacobian(unconstrained)[source]¶

Return the log absolute determinant of the forward Jacobian.

Parameters:: unconstrained (ArrayLike)
Return type:: float

class pymixef.transforms.Transform[source]¶

Bases: ABC

Abstract optimizer-to-natural-scale transform.

name: ClassVar[str]¶

abstractmethod forward(unconstrained)[source]¶

Map an unconstrained value to its natural scale.

Parameters:: unconstrained (ArrayLike)
Return type:: NDArray[float64]

abstractmethod inverse(natural)[source]¶

Map a natural-scale value to its unconstrained scale.

Parameters:: natural (ArrayLike)
Return type:: NDArray[float64]

abstractmethod log_abs_det_jacobian(unconstrained)[source]¶

Return the log absolute determinant of the forward Jacobian.

Parameters:: unconstrained (ArrayLike)
Return type:: float

jacobian(unconstrained)[source]¶

Return a finite-difference Jacobian for general vector transforms.

Parameters:: unconstrained (ArrayLike)
Return type:: NDArray[float64]

pymixef.transforms.get_transform(name, **options)[source]¶

Construct a canonical transform by stable name.

Parameters:

name (str)
options (object)

Return type:

Transform