N-Point Central Differencing

Computes an n-point central difference of function f with spacing h.

Computes an n-point central difference of function f with spacing h.

Returns a vector df of same size as f.
Input f must be a vector with evenly spaced points.
Input n must be 3,5,7, or 9.

Differences for points near the edges are calculated with lower order.
For example, if n=5 and length(f)=10, then 3-point central differencing is used to calculate values at points 2 and 9, 2-point forward differencing is used for point 1, 2-point backward differencing is used for point 10, and 5-point central differencing is used for points 3-7.

Differencing formulae from: http://www.holoborodko.com/pavel/numerical-methods/numerical-derivative/central-differences/ Accessed 4/10/12.