[Scipy-tickets] [SciPy] #564: Change derivative() to return the gradient of multidimensional functions

SciPy scipy-tickets@scipy....
Mon Dec 17 09:16:39 CST 2007

#564: Change derivative() to return the gradient of multidimensional functions
 Reporter:  robfalck     |        Owner:  jarrod.millman
     Type:  enhancement  |       Status:  new           
 Priority:  normal       |    Milestone:  0.7           
Component:  scipy.misc   |      Version:                
 Severity:  minor        |   Resolution:                
 Keywords:               |  
Comment (by stefan):

 We need a docstring, something like

     Given a function, use a central difference formula with spacing dx to
     compute the nth derivative at x0.

         func : callable(x,*args)
             Function for which the derivative is calculated.
         x0 : float or ndarray of floats
             Point around which the derivative is calculated.
         dx : float
             Sample spacing.  To small a step size can lead to
             round-off error.
         n : int
             Calculate the n-th derivative.
         order : int
             Number of points to take into account.  Must be odd.

 The weights can be defined using dicts, and the order semi-automatically

     if order < n+1:
         d,m = divmod(n,2)
         order = d*2 + 1
     assert (order % 2 == 1), "Odd number of points only."
     # pre-computed for n=1 and 2 and low-order for speed.
     if n==1:
         weights = {3: array([-1,0,1])/2.0,
                    5: array([1,-8,0,8,-1])/12.0,
                    7: array([-1,9,-45,0,45,-9,1])/60.0,
                    9: array([3,-32,168,-672,0,672,-168,32,-3])/840.0}
     elif n==2:
         weights = {3: array([1,-2.0,1]),
                    5: array([-1,16,-30,16,-1])/12.0,
                    7: array([2,-27,270,-490,270,-27,2])/180.0,
         weights = {}

     weights = weights.get(order,central_diff_weights(order,n))

 I'd also replace the ">>" with "divmod", to make it clearer that there is
 division by two.

 Some tests + examples in the docstring would be really great too.

 I think the last for-loop can be vectorised.

Ticket URL: <http://scipy.org/scipy/scipy/ticket/564#comment:2>
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