import numpy as np
from scipy.optimize import fsolve
from functools import lru_cache


class AutoRegression(object):
    def __init__(self, process, m):
        self.process = process
        self.m = m
        factors = list(fsolve(self.equations_system, np.ones(self.m + 1), factor=0.1))
        self.norm = np.linalg.norm(self.equations_system(factors))
        self.alpha = np.sqrt(factors.pop())
        self.betas = np.array(factors)

    @lru_cache(maxsize=None)
    def normalized_correlation(self, k):
        k = abs(k)
        if k <= self.m:
            return self.process.normalized_correlation(k)
        else:
            ncf = 0
            for i in range(1, self.m + 1):
                ncf += self.betas[i - 1] * self.normalized_correlation(k - i)
            return ncf

    @lru_cache(maxsize=None)
    def std(self, count=10):
        result = 0
        for i in range(1, count + 1):
            result += (self.normalized_correlation(i) - self.process.normalized_correlation(i)) ** 2
        return result

    def equations_system(self, beta):
        result = []
        temp = float()

        for i in range(1, self.m + 1):
            temp += beta[i - 1] * self.process.correlation_function(i)

        temp += beta[len(beta) - 1]
        temp -= self.process.correlation_function(0)
        result.append(temp)

        for i in range(1, self.m + 1):
            temp = float()
            for j in range(1, self.m + 1):
                temp += beta[j - 1] * self.process.correlation_function(i - j)
            temp -= self.process.correlation_function(i)
            result.append(temp)
        return result