[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
adx = zeros(lx0)
adx[i] = dx
for k in range(order):
val += weights[k]*func(x0+(k-ho)*adx,*args)
derivs[i] = val / product((dx,)*n,axis=0)
return derivs
}}}
--
Ticket URL: <http://scipy.org/scipy/scipy/ticket/564>
SciPy <http://www.scipy.org/>
SciPy is open-source software for mathematics, science, and engineering.
More information about the Scipy-tickets
mailing list