Cauchy

class pylit.models.Cauchy(tau, mu, sigma)

Bases: LinearRegressionModel

This is the linear regression model with Cauchy model functions.

kernel(omega, param)

Evaluate the Cauchy kernel function for a given set of parameters.

This method overrides kernel().

Parameters:

• omega (ndarray[float64]) – Discrete frequency axis.

• param (List[float]) – Parameter tuple [mu, sigma].

Return type:

ndarray

Returns:

Values of the Cauchy kernel

\[K(\omega; \mu, \sigma) = \frac{\sigma}{\pi ((\omega-\mu)^2 + \sigma^2)}.\]

ltransform(tau, param)

Evaluate the Laplace-transformed Cauchy kernel at the discrete time axis.

This method overrides ltransform().

Parameters:

• tau (ndarray[float64]) – Discrete time axis.

• param (List[float]) – Parameter tuple [mu, sigma].

Return type:

ndarray[float64]

Returns:

Laplace-transformed kernel

\[\widehat K(\tau; \mu, \sigma) = \exp(-\mu \tau - \sigma |\tau|).\]