import math
import matplotlib.pyplot as plt
from .Generaldistribution import Distribution


class Gaussian(Distribution):
    """Gaussian distribution class for calculating and
    visualizing a Gaussian distribution.

    Attributes:
        mean (float) representing the mean value of the distribution
        stdev (float) representing the standard deviation of the distribution
        data_list (list of floats) a list of floats extracted from the data file

    """

    def __init__(self, mu=0, sigma=1):

        Distribution.__init__(self, mu, sigma)

    def calculate_mean(self):
        """Function to calculate the mean of the data set.

        Args:
            None

        Returns:
            float: mean of the data set

        """

        avg = 1.0 * sum(self.data) / len(self.data)

        self.mean = avg

        return self.mean

    def calculate_stdev(self, sample=True):
        """Function to calculate the standard deviation of the data set.

        Args:
            sample (bool): whether the data represents a sample or population

        Returns:
            float: standard deviation of the data set

        """

        if sample:
            n = len(self.data) - 1
        else:
            n = len(self.data)

        mean = self.calculate_mean()

        sigma = 0

        for d in self.data:
            sigma += (d - mean) ** 2

        sigma = math.sqrt(sigma / n)

        self.stdev = sigma

        return self.stdev

    def plot_histogram(self):
        """Function to output a histogram of the instance variable data using
        matplotlib pyplot library.

        Args:
            None

        Returns:
            None

        """
        plt.hist(self.data)
        plt.title("Histogram of Data")
        plt.xlabel("data")
        plt.ylabel("count")

    def pdf(self, x):
        """Probability density function calculator for the gaussian distribution.

        Args:
            x (float): point for calculating the probability density function


        Returns:
            float: probability density function output
        """

        return (1.0 / (self.stdev * math.sqrt(2 * math.pi))) * math.exp(
            -0.5 * ((x - self.mean) / self.stdev) ** 2
        )

    def plot_histogram_pdf(self, n_spaces=50):
        """Function to plot the normalized histogram of the data and a plot of the
        probability density function along the same range

        Args:
            n_spaces (int): number of data points

        Returns:
            list: x values for the pdf plot
            list: y values for the pdf plot

        """

        mu = self.mean
        sigma = self.stdev

        min_range = min(self.data)
        max_range = max(self.data)

        # calculates the interval between x values
        interval = 1.0 * (max_range - min_range) / n_spaces

        x = []
        y = []

        # calculate the x values to visualize
        for i in range(n_spaces):
            tmp = min_range + interval * i
            x.append(tmp)
            y.append(self.pdf(tmp))

        # make the plots
        fig, axes = plt.subplots(2, sharex=True)
        fig.subplots_adjust(hspace=0.5)
        axes[0].hist(self.data, density=True)
        axes[0].set_title("Normed Histogram of Data")
        axes[0].set_ylabel("Density")

        axes[1].plot(x, y)
        axes[1].set_title(
            "Normal Distribution for \n Sample Mean and Sample Standard Deviation"
        )
        axes[0].set_ylabel("Density")
        plt.show()

        return x, y

    def __add__(self, other):
        """Function to add together two Gaussian distributions

        Args:
            other (Gaussian): Gaussian instance

        Returns:
            Gaussian: Gaussian distribution

        """

        result = Gaussian()
        result.mean = self.mean + other.mean
        result.stdev = math.sqrt(self.stdev**2 + other.stdev**2)

        return result

    def __repr__(self):
        """Function to output the characteristics of the Gaussian instance

        Args:
            None

        Returns:
            string: characteristics of the Gaussian

        """

        return "mean {}, standard deviation {}".format(self.mean, self.stdev)
