Module `HawkesPyLib.core.kernel`

Functions

def uvhp_expo_kernel(t: numpy.ndarray, eta: float, theta: float) ‑> numpy.ndarray

Computes values of the single exponential Hawkes process memory kernel.

t : np.ndarray: Single time value or 1d array containing all the times at which the kernel value will be computed. Must be positive.
eta : float: The branching ratio, 0 < eta > 1
theta : float: 1d array of theta decay parameters, theta > 0

np.ndarray: Single value or 1d array containing the kernel values at the given times.

def uvhp_sum_expo_kernel(t: numpy.ndarray, eta: float, theta_vec: float) ‑> numpy.ndarray

Computes values of the P-sum exponential Hawkes process memory kernel.

t : np.ndarray: Single time value or 1d array containing all the times at which the kernel value will be computed. Must be positive.
eta : float: The branching ratio, 0 < eta > 1
theta_vec : float: 1d array of theta decay parameters, theta_k > 0

np.ndarray: Single value or 1d array containing the kernel values at the given times.

def uvhp_approx_powl_cutoff_kernel(t: numpy.ndarray, eta: float, alpha: float, tau: float, m: float, M: int) ‑> numpy.ndarray

Computes values of the Approximate power-law memory kernel with smooth cutoff component.

t : np.ndarray: Single time value or 1d array containing all the times at which the kernel value will be computed. Must be positive.
eta : float: Branching ratio of the Hawkes process, 0 > eta < 1
alpha : float: Power-law coefficient, alpha > 0
tau : float: Approximate location of cutoff, tau > 0
m : float: Approximate power-law parameter, m > 0
M : int: Number of weighted exponential kernels that approximate the power-law

np.ndarray: Single value or 1d array containing the kernel values at the given times.

def uvhp_approx_powl_kernel(t: numpy.ndarray, eta: float, alpha: float, tau: float, m: float, M: int) ‑> numpy.ndarray

Computes values of the Approximate power-law memory kernel.

t : np.ndarray: Single time value or 1d array containing all the times at which the kernel value will be computed. Must be positive.
eta : float: Branching ratio of the Hawkes process, 0 > eta < 1
alpha : float: Power-law coefficient, alpha > 0
tau : float: Approximate location of cutoff, tau > 0
m : float: Approximate power-law parameter, m > 0
M : int: Number of weighted exponential kernels that approximate the power-law

np.ndarray: Single value or 1d array containing the kernel values at the given times.