How to calculate derivatives at the boundary in SciPy?

Question

I have a script drawing a set of (x,y) curves at various z.

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0,1,100)
z = np.linspace(0,30,30)

def y(z, x):
    return z**(1-x)

for i in z:
    plt.plot(x, y(i,x))

How can I draw dy/dx at x=0 versus z?

plt.plot(z, dy/dx at x=0)

In fact, I need to calculate the slope at the x=0 boundary for each (x,y) curve (shown below), then plot the slopes against z.

Answer 1

You must use the derivative function:

scipy.misc.derivative(func, x0, dx=1.0, n=1, args=(), order=3)

Find the n-th derivative of a function at a point.

Given a function, use a central difference formula with spacing dx to compute the n-th derivative at x0.

Parameters:

func : function Input function.

x0 : float The point at which n-th derivative is found.

dx : float, optional Spacing.

n : int,optional Order of the derivative. Default is 1.

args : tuple, optional Arguments order : int, optional Number of points to use, must be odd.

In your case:

import numpy as np
import matplotlib.pyplot as plt

from scipy.misc import derivative

x = np.linspace(0,1,100)
z = np.linspace(0,30,30)

x0 = 0

def y(z, x):
    return z**(1-x)

dydx = [derivative(lambda x : y(zi, x) , x0) for zi in z]

plt.plot(z, dydx)

plt.show()

Screenshot: