spleaf.term.MEPKernel

class spleaf.term.MEPKernel(sig, P, rho, eta)

The Matérn 3/2 exponential periodic (MEP) kernel is a rank 6 kernel roughly approximating the squared-exponential periodic (SEP) kernel.

The exact SEP kernel is written as

\[k(\Delta t) = \sigma^2 \exp \left(- \frac{\Delta t^2}{2 \rho^2} - \frac{\sin^2 \left( \frac{\pi \Delta t }{P}\right) }{2 \eta^2}\right),\]

while the MEP kernel approximates it with

\[k(\Delta t) = \sigma^2\frac{k_{3/2}(\Delta t) + f k_{\mathrm{SHO,\,fund.}}(\Delta t) + \frac{f^2}{4} k_{\mathrm{SHO,\,harm.}}(\Delta t)}{1+f+\frac{f^2}{4}},\]

where

\[\begin{split}\begin{align} \nu &= \frac{2\pi}{P},\\ f &= \frac{1}{4\eta^2},\\ k_{3/2}(\Delta t) &= \exp\left(-\frac{\sqrt{3}\Delta t}{\rho}\right) \left(1+\frac{\sqrt{3}\Delta t}{\rho}\right),\\ k_{\mathrm{SHO,\,fund.}}(\Delta t) &= \exp\left(-\frac{\Delta t}{\rho}\right) \left(\cos\left(\nu \Delta t\right) +\frac{1}{\nu\rho}\sin\left(\nu \Delta t\right)\right),\\ k_{\mathrm{SHO,\,harm.}}(\Delta t) &= \exp\left(-\frac{\Delta t}{\rho}\right) \left(\cos\left(2\nu \Delta t\right) +\frac{1}{2\nu\rho}\sin\left(2\nu \Delta t\right)\right). \end{align}\end{split}\]

Parameters:

sigfloat

Amplitude (std).

Pfloat

Period.

rhofloat

Scale.

etafloat

Scale of oscillations.

Methods

eval(dt[, series_id])	Evaluate the kernel at lag dt.
set_conditional_coef(*args, **kwargs)	Set the coefficients used for the conditional computations.