What are some optimization techniques in SymPy?

What are some optimization techniques in SymPy?

SymPy offers several optimization techniques, including gradient descent, Newton's method, and more. Would you like details on a specific method?

Can you explain how gradient descent works in SymPy?

Sure! Gradient descent is an iterative optimization algorithm used to minimize a function. In SymPy, you can define your function and use the diff method to compute the gradient.

How do I implement Newton's method in SymPy?

To implement Newton's method in SymPy, you need to define your function and its second derivative. Then, you can iteratively update your guess using the formula: x_new = x_old - f'(x_old) / f''(x_old). Would you like a code example?

Yes, please provide a code example for Newton's method.

Here's a simple example:

from sympy import symbols, diff, lambdify

x = symbols('x')
f = x**2 - 4*x + 4
f_prime = diff(f, x)
f_double_prime = diff(f_prime, x)

# Initial guess
x_old = 0
for _ in range(5):
    x_new = x_old - lambdify(x, f_prime)(x_old) / lambdify(x, f_double_prime)(x_old)
    x_old = x_new
print(x_new)