Laplace#
- class pylit.models.Laplace(tau, mu, sigma)#
Bases:
LinearRegressionModelThis is the linear regression model with Gaussian model functions.
- kernel(omega, param)#
Evaluate the Laplacian 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 Laplacian kernel
\[K(\omega; \mu, \sigma) = \frac{1}{2 \sigma} \exp\Big(-\frac{|\omega-\mu|}{\sigma}\Big).\]
- ltransform(tau, param)#
Evaluate the Laplace-transformed Laplacian 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:
Values of the Laplace-transformed Laplacian kernel
\[\widehat{K}(\tau; \mu, \sigma) = \frac{\exp(-\mu \tau)}{1 - \sigma^2 \tau^2}.\]