変分法って何にでも使えるな

変分法って何にでも使えるな (44ﾚｽ)
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30: ご冗談でしょう？名無しさん [sage] 2024/08/03(土) 17:35:52.72 ID:???

>>26
import numpy as np
from scipy.optimize import minimize

def J(y, bc_type=None):
"""
Functional to be minimized.

Args:
y: Array representing the function y(x).
bc_type: Optional string specifying the boundary condition type.
- 'dirichlet': Enforces y(0) = y(1) = 0 (default).
- None: No boundary condition enforced.

Returns:
The value of the functional J evaluated at y.
"""
y_prime = np.gradient(y)
y_doubleprime = np.gradient(y_prime)
return np.trapz(y_doubleprime**2 + y**2 - 2*y*y_prime, np.linspace(0, 1, len(y)))

def bc_dirichlet(y):
"""
Constraint function for Dirichlet boundary conditions.

Args:
y: Array representing the function y(x).

Returns:
A list containing the constraint values (y(0) and y(1)).
"""
return [y[0], y[-1]]

# Define the problem with Dirichlet boundary conditions
bounds = ((0, None),) * len(np.linspace(0, 1, 101))  # No lower bound for y
cons = ({'type': 'eq', 'fun': bc_dirichlet})

# Solve the minimization problem
initial_guess = np.random.rand(101)  # Random initial guess
sol = minimize(J, initial_guess, method='SLSQP', bounds=bounds, constraints=cons)

# Extract the solution
y_opt = sol.x

# Print the minimum value of the functional
print("Minimum value of J:", J(y_opt))

# Plot the solution (optional)
import matplotlib.pyplot as plt

x = np.linspace(0, 1, len(y_opt))
plt.plot(x, y_opt)
plt.xlabel("x")
plt.ylabel("y(x)")
plt.title("Solution of the minimization problem")
plt.show()

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