MATH_MOD

import numpy as np
import math
import copy
from scipy.optimize import minimize

def cor(V,x,eps):
    s = list()

    for i in V:
        s.append(1 / (np.linalg.norm(x - i, ord=2) + eps))

    S = list()

    for i in s:
        S.append(i / sum(s))

    print(S)
    print(V)
    return S[0] * V[0] + S[1] * V[1] + S[2] * V[2] + S[3] * V[3]

def coeffs(coef_lambda):
    c = list()

    for i in coef_lambda:
        c.append(sum(coef_lambda) / i)

    c1 = list()

    for i in c:
        c1.append(i / sum(c))

    return c1

def step_alg(A, eps):
    m = A.shape[1]
    w = np.array([[]])

    for i in range(m):
        w = np.append(w, [[1 / m]], axis=1)

    lam = pow(10, 10)
    k = 0
    w = w.T

    while True:
        k = k + 1
        w1 = copy.copy(w)
        w = np.dot(A, w)
        s = 0

        for i in range(A.shape[1]):
            s = s+w[i][0] / w1[i][0]

        lam1 = copy.copy(lam)
        lam = 1 / m * s
        m = max(w.T[0])

        for i in range(A.shape[1]):
            w[i][0] = w[i][0] / m

        if abs(lam - lam1) > eps:
            continue

        else:
            s=sum(w.T[0])

            for i in range(A.shape[1]):
                w[i][0] = w[i][0] / s

            break;
    return w

def St(x):
    sums = list()

    for i in V:
        sums.append(np.linalg.norm(x - i, ord=2))

    sums = np.array(sums)
    return sums

def Stein(x):
    return np.sum(C * St(x))

A1=np.array([[1, 3, 7, 9],
             [1/3, 1, 3, 1],
             [1/7, 1/3, 1, 1],
             [1/9, 1, 1, 1]])
A2=np.array([[1, 5, 7, 9],
             [1/5, 1, 3, 1],
             [1/7, 1/3, 1, 1],
             [1/9, 1, 1, 1]])
A3=np.array([[1, 3, 7, 3],
             [1/3, 1, 3, 1],
             [1/7, 1/3, 1, 1,],
             [1/3, 1, 1, 1]])
A4=np.array([[1, 3, 7, 5],
             [1/3, 1, 3, 1],
             [1/7, 1/3, 1, 1],
             [1/5, 1, 1, 1]])

w1=step_alg(A1, 0.0001)
w2=step_alg(A2, 0.0001)
w3=step_alg(A3, 0.0001)
w4=step_alg(A4, 0.0001)

V = copy.deepcopy(w1.T)

V = np.append(V, copy.deepcopy(w2.T), axis=0)
V = np.append(V, copy.deepcopy(w3.T), axis=0)
V = np.append(V, copy.deepcopy(w4.T), axis=0)

lambda1,v = np.linalg.eig(A1)
lambda2,v = np.linalg.eig(A2)
lambda3,v1 = np.linalg.eig(A3)
lambda4,v1 = np.linalg.eig(A4)

lambda1 = max(lambda1)
lambda2 = max(lambda2)
lambda3 = max(lambda3)
lambda4 = max(lambda4)
print(lambda1, lambda2, lambda3, lambda4)

C = np.array(coeffs([lambda1, lambda2, lambda3, lambda4]))

x0=np.array([0, 0, 0, 0])
x=minimize(Stein, x0, method='nelder-mead', options={'xtol':1e-3,'disp':True}).x
print(cor(V, x, 0.0001))