import numpy as np
from scipy.optimize import minimize


def objective(values):
    x, y = values
    return (x - 2.0) ** 2 + (y + 1.0) ** 2 + 0.5


def gradient(values):
    x, y = values
    return np.array([2.0 * (x - 2.0), 2.0 * (y + 1.0)])


start = np.array([0.0, 0.0])
expected = np.array([2.0, -1.0])

result = minimize(
    objective,
    start,
    method="BFGS",
    jac=gradient,
    options={"gtol": 1e-10},
)

print(f"success: {result.success}")
print(f"message: {result.message}")
print(f"x: {result.x}")
print(f"fun: {result.fun:.6f}")
print(f"gradient_norm: {np.linalg.norm(result.jac):.2e}")
print(f"distance_to_expected: {np.linalg.norm(result.x - expected):.2e}")
print(f"iterations: {result.nit}")
print(f"function_calls: {result.nfev}")