Return weights for an Np-point central derivative.
Assumes equally-spaced function points.
If weights are in the vector w, then derivative is w * f(x-ho*dx) + … + w[-1] * f(x+h0*dx)
Number of points for the central derivative.
- ndivint, optional
Number of divisions. Default is 1.
Weights for an Np-point central derivative. Its size is Np.
Can be inaccurate for a large number of points.
We can calculate a derivative value of a function.
>>> from scipy.misc import central_diff_weights >>> def f(x): ... return 2 * x**2 + 3 >>> x = 3.0 # derivative point >>> h = 0.1 # differential step >>> Np = 3 # point number for central derivative >>> weights = central_diff_weights(Np) # weights for first derivative >>> vals = [f(x + (i - Np/2) * h) for i in range(Np)] >>> sum(w * v for (w, v) in zip(weights, vals))/h 11.79999999999998
This value is close to the analytical solution: f’(x) = 4x, so f’(3) = 12