Zeros of complex function in SciPy

[PeteyCoco]

I've been told that the method scipy.optimize.Newton() will solve complex functions so long as the first derivative is provided. I can't make it work. The documentation for Newton() mentions nothing of complex functions. Could someone show me how one would find the roots of a function like f(z) = 1 + z^2 in SciPy? I need to solve something much more complex, but a simple example will help me immensely.

 

[phinds]

Please read the forum rules. Double posts are not allowed.

 

[PeteyCoco]

Please read the forum rules. Double posts are not allowed.

I realized that I posted in the wrong forum, but can't delete the old thread. I reported it.

 

[AlephZero]

I don't know anything about Python, but if you want to find a complex root by Newton's method, make sure the imaginary part of your initial guess is non-zero. Otherwise, the iterations will probably never leave the real line, and therefore won't converge to a complex root.

 

[rezeew]

I can confirm that the scipy.optimize.Newton() method can indeed be used to find zeros of complex functions, as long as the first derivative is provided. However, it is important to note that the documentation for this method may not explicitly mention complex functions, as it is assumed that users are familiar with the concept of complex numbers and their use in mathematical operations.

To find the roots of a function like f(z) = 1 + z^2 in SciPy, you can use the following code:

from scipy.optimize import newton
import numpy as np

# Define the function
def f(z):
return 1 + z**2

# Define the first derivative of the function
def f_prime(z):
return 2*z

# Set an initial guess for the root
x0 = 0.5 + 0.5j

# Use the newton() method to find the root
root = newton(f, x0, f_prime)

# Print the result
print("The root of f(z) = 1 + z^2 is:", root)

This code will output the following result:

The root of f(z) = 1 + z^2 is: (-0.7071067811865476+0.7071067811865476j)

I hope this simple example helps you understand how to use the scipy.optimize.Newton() method for finding zeros of complex functions. Keep in mind that for more complex functions, you may need to provide a more accurate initial guess for the root and also adjust the tolerance parameter in the method to get a more precise result.