bijx.CubicRational

class bijx.CubicRational

Bases: ScalarBijection

Modified rational transform with learnable parameters.

Type: [-∞, ∞] → [-∞, ∞] Transform: x + α*x/(1 + β*x²) with constrained α ∈ [-1,8], β > 0.

__init__(loc=(), alpha=(), beta=(), alpha_transform=SigmoidTransform(low=-1, high=8, eps_low=0.001, eps_high=0.001), beta_transform=SoftplusTransform(eps=0.1), loc_transform=None, *, rngs=None)

Parameters:

• loc (Variable | Array | ndarray | Sequence[int | Any])

• alpha (Variable | Array | ndarray | Sequence[int | Any])

• beta (Variable | Array | ndarray | Sequence[int | Any])

• alpha_transform (Callable | None)

• beta_transform (Callable | None)

• loc_transform (Callable | None)

Methods

forward(x, log_density, **kwargs)	Apply forward transformation with log-density update.
fwd(x, **kwargs)	Apply forward transformation.
invert()	Create an inverted version of this bijection.
log_jac(x, y)	Compute log absolute determinant of the Jacobian.
rev(y, **kwargs)	Apply reverse (inverse) transformation.
reverse(y, log_density, **kwargs)	Apply reverse transformation with log-density update.

log_jac(x, y)

Compute log absolute determinant of the Jacobian.

Parameters:

• x – Input values where Jacobian is computed.

• y – Output values corresponding to x (i.e., y = fwd(x)).

• **kwargs – Additional transformation-specific arguments.

Returns:

Log absolute Jacobian determinant \(\log \abs{f'(x)}\) with same shape as x.

fwd(x, **kwargs)

Apply forward transformation.

Parameters:

• x – Input values to transform.

• **kwargs – Additional transformation-specific arguments.

Returns:

Transformed values \(y = f(x)\) with same shape as \(x\).

rev(y, **kwargs)

Apply reverse (inverse) transformation.

Parameters:

• y – Output values to inverse-transform.

• **kwargs – Additional transformation-specific arguments.

Returns:

Inverse-transformed values \(x = f^{-1}(y)\) with same shape as \(y\).