from __future__ import annotations

import numpy as np
from numpy.linalg import inv, det, slogdet


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`
        """
        if self.biased_:  # ddof set to 0 - MLE of variance which is biased
            self.var_ = np.var(X)
        else:  # ddof set to 1 - unbiased estimator of var
            self.var_ = np.var(X, ddof=1)
        self.mu_ = np.mean(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")
        res = X.copy()
        cnt = 0
        for sample in X:
            res[cnt] = self.__calc_gauss(sample, self.var_, self.mu_)
            cnt += 1

        return res

    @staticmethod
    def __calc_gauss(x_i, variance, mu):

        sd = np.sqrt(variance)
        a = 1 / np.sqrt(2 * np.pi * variance)
        b = (((x_i - mu) / sd) ** 2)
        c = np.exp(-0.5 * b)
        return a * c

    @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 * sigma // written in the moodle that sigma is variance, although conventionally it is SD
        res = 0
        for x_i in X:
            res += np.log(UnivariateGaussian.__calc_gauss(x_i, sigma, mu))
        return res


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

    @staticmethod
    def __calc_mult_pdf(x_i, cov, mu, d):
        a = 1 / (np.sqrt(((2 * np.pi) ** d) * det(cov)))
        xi_i_mu = (x_i - mu)
        cov_inverted = inv(cov)
        p = -0.5 * np.matmul((np.matmul(xi_i_mu.T, cov_inverted)), xi_i_mu)
        res = a * np.exp(p)
        return res

    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`
        """
        # raise NotImplementedEror()
        self.mu_ = np.mean(X, axis=0)
        self.cov_ = np.cov(X, rowvar=False)
        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")
        pdfs = []
        d = X.shape[1]  # n_features
        cnt = 0
        for x in X:
            pdfs[cnt] = MultivariateGaussian.__calc_mult_pdf(x, self.cov_, self.mu_, d)
            cnt += 1
        return pdfs

    @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
        """

        x_mu_sig = np.sum((X-mu) @ inv(cov) * (X-mu))
        d = mu.shape[0]
        m = X.shape[0]
        almost = m * np.log((2 * np.pi) ** d * det(cov))
        final = -0.5 * (x_mu_sig + almost)
        return final
