`scipy.stats._finite_differences:_central_diff_weights`

source: /scipy/stats/_finite_differences.py :5

Signature

def _central_diff_weights ( Np , ndiv = 1 )

Summary

Return weights for an Np-point central derivative.

Extended Summary

Assumes equally-spaced function points.

If weights are in the vector w, then derivative is w[0] * f(x-ho*dx) + ... + w[-1] * f(x+h0*dx)

Parameters

Np : int: Number of points for the central derivative.
ndiv : int, optional: Number of divisions. Default is 1.

Returns

w : ndarray: Weights for an Np-point central derivative. Its size is Np.

Notes

Can be inaccurate for a large number of points.

Examples

We can calculate a derivative value of a function.

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

✗

This value is close to the analytical solution: f'(x) = 4x, so f'(3) = 12

Aliases

scipy.stats._finite_differences._central_diff_weights