pysindy.differentiation.SmoothedFiniteDifference

class pysindy.differentiation.SmoothedFiniteDifference(smoother=<function savgol_filter>, smoother_kws={}, save_smooth=True, **kwargs)[source]

Smoothed finite difference derivatives.

Perform differentiation by smoothing input data then applying a finite difference method.

Parameters:

smoother (function, optional (default savgol_filter)) – Function to perform smoothing. Must be compatible with the following call signature: x_smoothed = smoother(x, **smoother_kws)
smoother_kws (dict, optional (default {})) – Arguments passed to smoother when it is invoked.
save_smooth (bool) – Whether to save the smoothed coordinate values or not.
**kwargs (kwargs) – Additional parameters passed to the pysindy.FiniteDifference.__init__ function.

Examples

>>> import numpy as np
>>> from pysindy.differentiation import SmoothedFiniteDifference
>>> t = np.linspace(0,1,10)
>>> X = np.vstack((np.sin(t),np.cos(t))).T
>>> sfd = SmoothedFiniteDifference(smoother_kws={'window_length': 5})
>>> sfd._differentiate(X, t)
array([[ 1.00013114e+00,  7.38006789e-04],
       [ 9.91779070e-01, -1.10702304e-01],
       [ 9.73376491e-01, -2.20038119e-01],
       [ 9.43001496e-01, -3.26517615e-01],
       [ 9.00981354e-01, -4.29066632e-01],
       [ 8.47849424e-01, -5.26323977e-01],
       [ 7.84260982e-01, -6.17090177e-01],
       [ 7.11073255e-01, -7.00180971e-01],
       [ 6.29013295e-01, -7.74740601e-01],
       [ 5.39752150e-01, -8.41980082e-01]])

Methods