Solve an equation using a python numerical solver in numpy

Question

I have an equation, as follows:

R - ((1.0 - np.exp(-tau))/(1.0 - np.exp(-a*tau))) = 0.

I want to solve for tau in this equation using a

Answer 1

You can rewrite the equation as

• For integer a and non-zero R you will get a solutions in the complex space;
• There are analytical solutions for a=0,1,...4(see here);

So in general you may have one, multiple or no solution and some or all of them may be complex values. You may easily throw scipy.root at this equation, but no numerical method will guarantee to find all the solutions.

To solve in the complex space:

import numpy as np
from scipy.optimize import root

def poly(xs, R, a):
    x = complex(*xs)
    err = R * x - x + 1 - R
    return [err.real, err.imag]

root(poly, x0=[0, 0], args=(1.2, 6))