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.mean

		sigma = 0

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

		sigma = math.sqrt(sigma / n)

		self.stdev = sigma

		return self.stdev


	def read_data_file(self, file_name, sample=True):

		"""Function to read in data from a txt file. The txt file should have
		one number (float) per line. The numbers are stored in the data attribute.
		After reading in the file, the mean and standard deviation are calculated

		Args:
			file_name (string): name of a file to read from

		Returns:
			None

		"""

		with open(file_name) as file:
			data_list = []
			line = file.readline()
			while line:
				data_list.append(float(line))
				line = file.readline()
		file.close()

		self.data = data_list
		self.mean = self.calculate_mean()
		self.stdev = self.calculate_stdev(sample)


	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=.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)
