CODEWITHSUNDEEP
pythonscipy
ash
ash

Reputation: 3474

scipy misc.derivative result is incorrect

I'm wondering what I'm doing wrong here...

I am experimenting with a simple and contrived function, taking it's derivative for certain values of x:

f(x) = x^3, then evaluating the derivative f'(x) = 3x^2 for values of x at 1, 2, 3

>>> from scipy import misc
>>> def x2(x): return x*x*x
...
>>> misc.derivative(x2,1)
4.0
>>> misc.derivative(x2,2)
13.0
>>> misc.derivative(x2,3)
28.0

problem: the results are incorrect, they are all +1 greater than they should be (they should be 3, 12 and 27 respectively).

Upvotes: 3

Views: 2252

Answers (2)

blue_zinc
blue_zinc

Reputation: 2500

If you specify dx or the spacing to a small enough number you'll get a decent approximation. 

>>> from scipy import misc
>>> def f(x): return x*x*x
... 
>>> misc.derivative(f,2,dx=0.1)
12.010000000000009

>>> round(misc.derivative(f,2,dx=0.1),0)
12.0

Upvotes: 1

user2357112
user2357112

Reputation: 280291

scipy.misc.derivative is not exact. It uses a central difference formula to compute the derivative. The default spacing is 1.0, which is pretty high for a lot of applications. Reducing it gives more accurate results:

>>> from scipy import misc
>>> def x3(x): return x*x*x
... 
>>> misc.derivative(x3, 1)
4.0
>>> misc.derivative(x3, 1, dx=0.5)
3.25
>>> misc.derivative(x3, 1, dx=0.25)
3.0625
>>> misc.derivative(x3, 1, dx=1.0/2**16)
3.0000000002328306

Upvotes: 6

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