scipy.misc.central_diff_weights

scipy.misc.central_diff_weights(Np, ndiv=1)

Return weights for an Np-point central derivative.

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

Npint

Number of points for the central derivative.

ndivint, optional

Number of divisions. Default is 1.

Returns

wndarray

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

Notes

Can be inaccurate for a large number of points.

References

1

https://en.wikipedia.org/wiki/Finite_difference

Examples

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