Scipy derivative

Question

I have a question about the derivative function of Scipi. I used it last night and got some weird answers. This morning I tried some simple functions and got the correct answers and some errors. Here are my tests:

In [1]: def poly1(x): ...: return x**2 In [3]: derivative(poly1, 0) Out[3]: 0.0 In [4]: def poly2(x): ...: return (x-3)**2 In [6]: derivative(poly2, 3) Out[6]: 0.0 In [8]: def sin1(x): ...: return sin(x) In [14]: derivative(sin1, pi/2) Out[14]: 5.5511151231257827e-17 In [15]: def poly3(x): ....: return 3*x**4 + 2*x**3 - 10*x**2 + 15*x - 2 In [19]: derivative(poly3, -2) Out[19]: -39.0 In [20]: derivative(poly3, 2) Out[20]: 121.0 In [22]: derivative(poly3, 0) Out[22]: 17.0 

I checked the poly3 values ​​manually and -2 = 17, 2 = 95, 0 = 15. So I'm using the function incorrectly or something is wrong with the function. Thanks

Usage: Python 2.7.3, IPython 0.12.1, Numpy 1.6.1, Scipy 0.9.0, Linux Mint 13

Answer 1

As the documentation says for derivative :

 derivative(func, x0, dx=1.0, n=1, args=(), order=3) Find the n-th derivative of a function at point x0. Given a function, use a central difference formula with spacing `dx` to compute the n-th derivative at `x0`. 

You did not specify dx , so it used the default value of 1 , which is too large here. For instance:

 In [1]: from scipy.misc import derivative In [2]: derivative(lambda x: 3*x**4 + 2*x**3 - 10*x**2 + 15*x - 2, -2, dx=1) Out[2]: -39.0 In [3]: derivative(lambda x: 3*x**4 + 2*x**3 - 10*x**2 + 15*x - 2, -2, dx=0.5) Out[3]: -22.5 In [4]: derivative(lambda x: 3*x**4 + 2*x**3 - 10*x**2 + 15*x - 2, -2, dx=0.1) Out[4]: -17.220000000000084 In [5]: derivative(lambda x: 3*x**4 + 2*x**3 - 10*x**2 + 15*x - 2, -2, dx=0.01) Out[5]: -17.0022000000003 In [6]: derivative(lambda x: 3*x**4 + 2*x**3 - 10*x**2 + 15*x - 2, -2, dx=1e-5) Out[6]: -17.000000001843318 

Alternatively, you can increase the order:

 In [7]: derivative(lambda x: 3*x**4 + 2*x**3 - 10*x**2 + 15*x - 2, -2, dx=1, order=5) Out[7]: -17.0 

Taking numerical derivatives is always a bit troublesome.