diffpoly-matlab

Compute the derivative of y(x) by computing the derivative of the the fitting polynomial of degree POLYDEG on a stencil of width w. At the boundaries of the domain, the stencil has always the same size but it is not centered.

Usage

dy = diffpoly(x, y, w, p)

Inputs

• x: points where the function y(x) has been computed
• y: values of the function y(x)
• w: width of the stencil (must be odd)
• p: degree of the interpolating polynomial

All inputs are mandatory, none are optional

Output

• dy: estimate of dy/dx computed in the points in x

Limitations

• The stencil is always symmetric (from -(w-1)/2 to (w-1)/2); this doesn't mean the points in the stencil need to be equally spaced
• x and y must be vectors, with x increasing
• y has no NaNs

Algorithm

  for x0 in x:
      define a neighbourhood of x0 of radius w
      if the distance of x0 from the boundary is less than w:
          make the neighb. not centered around x0 but keep width = w
      compute the best fitting polynomial of degree p in the neighb.
      estimate dydx(x0) as the derivative of the poynomial computed

Usage

Check file usage.m for proper usage and comparison with Matlab's gradient function.