Scipy Derivative

Question

我对Scipy的衍生功能有疑问.我昨晚用它并得到了一些奇怪的答案.我今天早上再次尝试了一些简单的功能,得到了一些正确的答案和一些错误.这是我的测试:

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

我用手检查了poly3的值,并且-2 = 17,2 = 95,0 = 15.所以我使用的函数是错误的,或者函数是否有问题.谢谢

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

Answer 1

正如文档derivative所说:

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`.

你没有指定dx,所以它使用了默认值1,这里太大了.例如:

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

或者,您可以增加订单:

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

采用数值导数总是有点麻烦.