pysindy.differentiation.FiniteDifference

class pysindy.differentiation.FiniteDifference(order: int = 2, d: int = 1, axis: int = 0, is_uniform: bool = False, drop_endpoints: bool = False, periodic: bool = False)[source]

Finite difference derivatives.

Only centered differences are implemented, for even order and left-off-centered differences for odd order. See wikipedia for the coefficient formula used.

Parameters:

  • order (int, optional (default 2)) – The accuracy big-O exponent of the finite difference method to be used.

  • d (int, optional (default 1)) – The order of derivative to take. Must be positive integer.

  • axis (int, optional (default 0)) – The axis to differentiate along.

  • is_uniform (boolean, optional (default False)) – Parameter to tell the differentiation that, although a N-dim grid is passed, it is uniform so can use dx instead of the full grid array.

  • drop_endpoints (boolean, optional (default False)) – Whether or not derivatives are computed for endpoints. If False, endpoints will be set to np.nan. Note that which points are endpoints depends on the method being used.

  • periodic (boolean, optional (default False)) – Whether to use periodic boundary conditions for endpoints. Use forward differences for periodic=False and periodic boundaries with centered differences for periodic=True on the boundaries. No effect if drop_endpoints=True

  • Attributes – n_stencil: the number of coefficients in the finite difference expression.

Examples

>>> import numpy as np
>>> from pysindy.differentiation import FiniteDifference
>>> t = np.linspace(0, 1, 5)
>>> X = np.vstack((np.sin(t), np.cos(t))).T
>>> fd = FiniteDifference()
>>> fd._differentiate(X, t)
array([[ 1.00114596,  0.00370551],
       [ 0.95885108, -0.24483488],
       [ 0.8684696 , -0.47444711],
       [ 0.72409089, -0.67456051],
       [ 0.53780339, -0.84443737]])

Methods