stackoverflow hyperplane distance

hyp.py

import numpy as np
import scipy.optimize

np.random.seed(0)
V_orig = np.random.rand(50, 3)


def func(x):
    Vx = V_orig @ x
    return np.dot(Vx, Vx)


def con(t):
    return np.sum(t) - 1


x0 = np.zeros(3)
out = scipy.optimize.minimize(func, x0, constraints={"type": "eq", "fun": con})
print("optimization result:")
print(out)
print()


v0 = V_orig[:, 0]
V = np.column_stack(
    [
        V_orig[:, 1] - v0,
        V_orig[:, 2] - v0,
    ]
)
u = V.T @ V
v = np.array([v0 @ V[:, 0], v0 @ V[:, 1]])
r2 = np.dot(v0, v0) + v.T @ np.linalg.inv(u) @ v
print("user result:")
print(r2)
print()


e = np.ones(3)
VTVe = np.linalg.solve(V_orig.T @ V_orig, e)
# x = VTVe / np.dot(e, VTVe)
print("nschloe result:")
print(1 / (e @ VTVe))
print()