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