from __future__ import annotations
import numpy as np
import numpy.random
from numpy.linalg import inv, det, slogdet
from matplotlib import pyplot as plt


class UnivariateGaussian:
    """
    Class for univariate Gaussian Distribution Estimator
    """

    def __init__(self, biased_var: bool = False) -> UnivariateGaussian:
        """
        Estimator for univariate Gaussian mean and variance parameters

        Parameters
        ----------
        biased_var : bool, default=False
            Should fitted estimator of variance be a biased or unbiased estimator

        Attributes
        ----------
        fitted_ : bool
            Initialized as false indicating current estimator instance has not been fitted.
            To be set as True in `UnivariateGaussian.fit` function.

        mu_: float
            Estimated expectation initialized as None. To be set in `UnivariateGaussian.fit`
            function.

        var_: float
            Estimated variance initialized as None. To be set in `UnivariateGaussian.fit`
            function.
        """
        self.biased_ = biased_var
        self.fitted_, self.mu_, self.var_ = False, None, None

    def fit(self, X: np.ndarray) -> UnivariateGaussian:
        """
        Estimate Gaussian expectation and variance from given samples

        Parameters
        ----------
        X: ndarray of shape (n_samples, )
            Training data

        Returns
        -------
        self : returns an instance of self.

        Notes
        -----
        Sets `self.mu_`, `self.var_` attributes according to calculated estimation (where
        estimator is either biased or unbiased). Then sets `self.fitted_` attribute to `True`
        """
        self.mu_ = np.average(X)
        self.var_ = np.var(X)
        self.fitted_ = True
        return self

    def pdf(self, X: np.ndarray) -> np.ndarray:
        """
        Calculate PDF of observations under Gaussian model with fitted estimators

        Parameters
        ----------
        X: ndarray of shape (n_samples, )
            Samples to calculate PDF for

        Returns
        -------
        pdfs: ndarray of shape (n_samples, )
            Calculated values of given samples for PDF function of N(mu_, var_)

        Raises
        ------
        ValueError: In case function was called prior fitting the model
        """
        if not self.fitted_:
            raise ValueError("Estimator must first be fitted before calling `pdf` function")
        exponent = np.exp(-1 * np.divide(np.power(X - self.mu_, 2), (2 * self.var_)))
        return np.multiply((1 / np.sqrt(2 * np.pi * self.var_)), exponent)

    @staticmethod
    def log_likelihood(mu: float, sigma: float, X: np.ndarray) -> float:
        """
        Calculate the log-likelihood of the data under a specified Gaussian model

        Parameters
        ----------
        mu : float
            Expectation of Gaussian
        sigma : float
            Variance of Gaussian
        X : ndarray of shape (n_samples, )
            Samples to calculate log-likelihood with

        Returns
        -------
        log_likelihood: float
            log-likelihood calculated
        """
        var = sigma ** 2
        exponent = np.exp(-1 * np.divide(np.power(X - mu, 2), (2 * var)))
        y = np.multiply((1 / np.sqrt(2 * np.pi * var)), exponent)
        summery = 0
        for elem in y:
            summery +=np.log2(elem)
        return summery


class MultivariateGaussian:
    """
    Class for multivariate Gaussian Distribution Estimator
    """

    def __init__(self):
        """
        Initialize an instance of multivariate Gaussian estimator

        Attributes
        ----------
        fitted_ : bool
            Initialized as false indicating current estimator instance has not been fitted.
            To be set as True in `MultivariateGaussian.fit` function.

        mu_: ndarray of shape (n_features,)
            Estimated expectation initialized as None. To be set in `MultivariateGaussian.fit`
            function.

        cov_: ndarray of shape (n_features, n_features)
            Estimated covariance initialized as None. To be set in `MultivariateGaussian.fit`
            function.
        """
        self.mu_, self.cov_ = None, None
        self.fitted_ = False

    def fit(self, X: np.ndarray) -> MultivariateGaussian:
        """
        Estimate Gaussian expectation and covariance from given samples

        Parameters
        ----------
        X: ndarray of shape (n_samples, n_features)
            Training data

        Returns
        -------
        self : returns an instance of self

        Notes
        -----
        Sets `self.mu_`, `self.cov_` attributes according to calculated estimation.
        Then sets `self.fitted_` attribute to `True`
        """
        self.mu_ = np.mean(X, axis=0)
        self.cov_ = np.cov(X.T)
        self.fitted_ = True
        return self

    def pdf(self, X: np.ndarray):
        """
        Calculate PDF of observations under Gaussian model with fitted estimators

        Parameters
        ----------
        X: ndarray of shape (n_samples, n_features)
            Samples to calculate PDF for

        Returns
        -------
        pdfs: ndarray of shape (n_samples, )
            Calculated values of given samples for PDF function of N(mu_, cov_)

        Raises
        ------
        ValueError: In case function was called prior fitting the model
        """
        if not self.fitted_:
            raise ValueError("Estimator must first be fitted before calling `pdf` function")
        d = len(self.mu_)
        divider = 1 / (((2 * np.pi) ** d) * det(self.cov_))
        f_arr = []
        for x in X:
            power = -0.5 * np.matmul(np.matmul((x - self.mu_).T, self.cov_.T), (x - self.mu_))
            f_arr.append(divider * np.exp(power.item()))
        return f_arr

    @staticmethod
    def log_likelihood(mu: np.ndarray, cov: np.ndarray, X: np.ndarray) -> float:
        """
        Calculate the log-likelihood of the data under a specified Gaussian model

        Parameters
        ----------
        mu : ndarray of shape (n_features,)
            Expectation of Gaussian
        cov : ndarray of shape (n_features, n_features)
            covariance matrix of Gaussian
        X : ndarray of shape (n_samples, n_features)
            Samples to calculate log-likelihood with

        Returns
        -------
        log_likelihood: float
            log-likelihood calculated over all input data and under given parameters of Gaussian
        """
        d = len(mu)
        divider = 1 / (((2 * np.pi) ** d) * det(cov))
        f_arr = []
        for x in X:
            power = -0.5 * np.matmul(np.matmul((x - mu).T, cov.T), (x - mu))
            f_arr.append(+divider * np.exp(power.item()))
        summery =0
        for i in range(len (f_arr)):
            summery += np.log2(f_arr[i])
        # if prod == 0:
        #     return 0
        # return prod
        return summery


if __name__ == "__main__":
    Q_3_array = np.array([1, 5, 2, 3, 8, -4, -2, 5, 1, 10, -10, 4, 5, 2, 7, 1, 1, 3, 2, -1, -3, 1, -4, 1, 2, 1,
                          -4, -4, 1, 3, 2, 6, -6, 8, 3, -6, 4, 1, -2, 3, 1, 4, 1, 4, -2, 3, -1, 0, 3, 5, 0, -2])
    print("mu=1 : {}".format(UnivariateGaussian.log_likelihood(1, 1, Q_3_array)))
    print("mu=10 : {}".format(UnivariateGaussian.log_likelihood(10, 1, Q_3_array)))
