cmlabs.interpolate.forward_differences

cmlabs.interpolate.forward_differences(yvals)

Return the forward differences list for \(f(x_0)\).

\[\begin{gather} \Delta^k f(x_i) = \Delta^{k-1} f(x_{i+1}) - \Delta^{k-1} f(x_i) \end{gather}\]

Parameters:

yvals (array_like, 1-D) – The y-coordinates of the data points.

Returns:

res – The forward differences list.

Return type:

array_like, 1-D

Notes

The output is the list with following structure:

\[[\Delta^0 f(x_0), \Delta^1 f(x_0), \Delta^2 f(x_0), \ldots, \Delta^n f(x_0)]\]

where n = len(yvals) - 1.

The forward differences list is used to compute the coefficients of the Newton Forward-Difference Formula

Examples

>>> import numpy as np
>>> from cmlabs.interpolate import forward_differences
>>> yvals = np.array([1, 3, 2, 5])
>>> forward_differences(yvals)
>>> [1, 2, -3, 7]