title: Python finite difference functions?
body: <p>I've been looking around in Numpy/Scipy for modules containing finite difference functions.  However, the closest thing I've found is <code>numpy.gradient()</code>, which is good for 1st-order finite differences of 2nd order accuracy, but not so much if you're wanting higher-order derivatives or more accurate methods.  I haven't even found very many specific modules for this sort of thing; most people seem to be doing a "roll-your-own" thing as they need them.  So my question is if anyone knows of any modules (either part of Numpy/Scipy or a third-party module) that are specifically dedicated to higher-order (both in accuracy and derivative) finite difference methods.  I've got my own code that I'm working on, but it's currently kind of slow, and I'm not going to attempt to optimize it if there's something already available.</p>
  
  <p>Note that I am talking about finite differences, not derivatives.  I've seen both <code>scipy.misc.derivative()</code> and <a href="https://pypi.python.org/pypi/Numdifftools">Numdifftools</a>, which take the derivative of an analytical function, which I don't have.</p>