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

SciPy scipy-tickets@scipy....
Sun Dec 16 19:13:23 CST 2007

```#564: Change derivative() to return the gradient of multidimensional functions
-------------------------+--------------------------------------------------
Reporter:  robfalck     |       Owner:  somebody
Type:  enhancement  |      Status:  new
Priority:  normal       |   Milestone:  0.7
Component:  scipy.misc   |     Version:
Severity:  minor        |    Keywords:
-------------------------+--------------------------------------------------
The following version of derivative in scipy.misc will return an array
representing the gradient of a multidimensional function.  Currently
derivative() only works for functions with a single independent variable.
The difference in computational speed for one-dimensional functions has
not been assessed.

{{{
def derivative(func,x0,dx=1.0,n=1,args=(),order=3):
"""Given a function, use a central difference formula with spacing dx
to
compute the nth derivative at x0.

order is the number of points to use and must be odd.

Warning: Decreasing the step size too small can result in
round-off error.
"""
assert (order >= n+1), "Number of points must be at least the
derivative order + 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:
if order == 3:
weights = array([-1,0,1])/2.0
elif order == 5:
weights = array([1,-8,0,8,-1])/12.0
elif order == 7:
weights = array([-1,9,-45,0,45,-9,1])/60.0
elif order == 9:
weights = array([3,-32,168,-672,0,672,-168,32,-3])/840.0
else:
weights = central_diff_weights(order,1)
elif n==2:
if order == 3:
weights = array([1,-2.0,1])
elif order == 5:
weights = array([-1,16,-30,16,-1])/12.0
elif order == 7:
weights = array([2,-27,270,-490,270,-27,2])/180.0
elif order == 9:
weights =
array([-9,128,-1008,8064,-14350,8064,-1008,128,-9])/5040.0
else:
weights = central_diff_weights(order,2)
else:
weights = central_diff_weights(order, n)

ho = order >> 1
ax0 = asfarray(x0).flatten()
lx0 = len(ax0)
derivs = zeros(lx0)
for i in range(lx0):
val = 0.0
for k in range(order):