pysindy.differentiation.SpectralDerivative

class pysindy.differentiation.SpectralDerivative(d=1, axis=0)[source]

Spectral derivatives. Assumes uniform grid, and utilizes FFT to approximate a derivative. Works well for derivatives in periodic dimensions. Equivalent to a maximal-order finite difference, but runs in O(NlogN).

Parameters:

d (int) – The order of derivative to take
axis (int, optional (default 0)) – The axis to differentiate along

Examples

>>> import numpy as np
>>> from pysindy.differentiation import SpectralDerivative
>>> t = np.arange(0,1,0.1)
>>> X = np.vstack((np.sin(t), np.cos(t))).T
>>> sd = SpectralDerivative()
>>> sd._differentiate(X, t)
array([[ 6.28318531e+00,  2.69942771e-16],
   [ 5.08320369e+00, -3.69316366e+00],
   [ 1.94161104e+00, -5.97566433e+00],
   [-1.94161104e+00, -5.97566433e+00],
   [-5.08320369e+00, -3.69316366e+00],
   [-6.28318531e+00,  7.10542736e-16],
   [-5.08320369e+00,  3.69316366e+00],
   [-1.94161104e+00,  5.97566433e+00],
   [ 1.94161104e+00,  5.97566433e+00],
   [ 5.08320369e+00,  3.69316366e+00]])

Methods