# -*- coding: utf-8 -*-
"""
Created on Sat Mar  7 10:41:51 2020

@author: Johan Rene van Dorp
"""

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import Dist_Library as dl

df = pd.read_csv('OldFaithFul.csv')
Durations = df["Duration (s)"]
WaitingTimes = df["Waiting Time (Min)"]

# Plotting Empirical Cumulative Distribution Functions

plt.rc('font', family='serif', size='10')
plt.figure(figsize=(10, 5))
ECDF_Figure = plt.figure()
ECDF_Figure.set_figwidth(9)
ECDF_Figure.set_figheight(4.5)
ECDF_Figure.subplots_adjust(hspace=0.4, wspace=0.4)
off_set_x = 10

# Plotting the Empirical CDF of the Durations

x_25, q_index, x_k, x_k_plus_1 = dl.empirical_quantile(Durations,0.25)
x_50, q_index, x_k, x_k_plus_1 = dl.empirical_quantile(Durations,0.50)
x_75, q_index, x_k, x_k_plus_1 = dl.empirical_quantile(Durations,0.75)
IQR = x_75 - x_25

n_d = len(Durations)
LB = 90
UB = 330
Durations.ordered = np.sort(Durations)
Durations.ordered = np.append(LB-off_set_x,Durations.ordered)
Durations.ordered = np.append(Durations.ordered,UB+off_set_x)
F = np.linspace(0,1,n_d)
F = np.append(0,F)
F = np.append(F,1)

x_lims = (LB-off_set_x,UB+off_set_x)
y_lims = (-0.05,1.1)
Panel = ECDF_Figure.add_subplot(1,2,1)
plt.step(Durations.ordered,F,lw = 1,color ='indianred')
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('Duration (in Sec)')
plt.ylabel('Empirical CDF $\hat{F}(d) = Pr(D \leq d)$')
plt.axvline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(1, lw=2, ls = ':',color = 'lightgray',alpha=0.5)
text_str = 'n = '+str(n_d)
plt.text(160,0.9,text_str,color = 'red',size = 10)

plt.vlines(x_25, 0, 0.25, color='black', linestyles='--', lw=1)
plt.vlines(x_50, 0, 0.50, color='black', linestyles=':', lw=1)
plt.vlines(x_75, 0, 0.75, color='black', linestyles='--', lw=1)

plt.hlines(0.25, 0, x_25, color='black', linestyles='--', lw=1)
plt.hlines(0.50, 0, x_50, color='black', linestyles=':', lw=1)
plt.hlines(0.75, 0, x_75, color='black', linestyles='--', lw=1)

text_str = '0.25'
plt.text(x_lims[0]+3,0.25+0.025,text_str,color = 'red')
text_str = '0.50'
plt.text(x_lims[0]+3,0.50+0.025,text_str,color = 'red')
text_str = '0.75'
plt.text(x_lims[0]+3,0.75+0.025,text_str,color = 'red')

text_str = f'{x_25:3.0f}'
plt.text(x_25+3, 0.025,text_str,color = 'red')
text_str = f'{x_50:3.0f}'
plt.text(x_50-40, 0.025,text_str,color = 'red')
text_str = f'{x_75:3.0f}'
plt.text(x_75+3, 0.025,text_str,color = 'red')

plt.arrow(x_25, 0.1, IQR, 0, lw = 0.1, color = 'blue',
         head_length = 15, head_width = 0.03, length_includes_head = True)
plt.arrow(x_25 + IQR, 0.1, -IQR, 0, lw = 0.1, color = 'blue',
         head_length = 15, head_width = 0.03, length_includes_head = True)

text_str = 'IQR = ' + f'{IQR:2.0f}'
plt.text((x_25+x_75)/2-28, 0.1+0.03,text_str,color = 'blue',size = 6)

# Plotting the Empirical CDF of the Waiting Times

x_25, q_index, x_k, x_k_plus_1 = dl.empirical_quantile(WaitingTimes,0.25)
x_50, q_index, x_k, x_k_plus_1 = dl.empirical_quantile(WaitingTimes,0.50)
x_75, q_index, x_k, x_k_plus_1 = dl.empirical_quantile(WaitingTimes,0.75)
IQR = x_75 - x_25

LB = 40
UB = 100
n_w = len(WaitingTimes)
WaitingTimes.ordered = np.sort(WaitingTimes)
WaitingTimes.ordered = np.append(LB-off_set_x,WaitingTimes.ordered)
WaitingTimes.ordered = np.append(WaitingTimes.ordered,UB+off_set_x)
F = np.linspace(0,1,n_d)
F = np.append(0,F)
F = np.append(F,1)

x_lims = (LB-off_set_x,UB+off_set_x)
y_lims = (-0.05,1.1)
Panel = ECDF_Figure.add_subplot(1,2,2)
plt.step(WaitingTimes.ordered,F,lw = 1,color ='skyblue')
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('Waiting Times (in Min)')
plt.ylabel('Empirical CDF $\hat{F}(w) = Pr(W \leq w)$')
plt.axvline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(1, lw=2, ls = ':',color = 'lightgray',alpha=0.5)
text_str = 'n = '+str(n_w)
plt.text(55,0.9,text_str,color = 'red',size = 10)

plt.vlines(x_25, 0, 0.25, color='black', linestyles='--', lw=1)
plt.vlines(x_50, 0, 0.50, color='black', linestyles=':', lw=1)
plt.vlines(x_75, 0, 0.75, color='black', linestyles='--', lw=1)

plt.hlines(0.25, 0, x_25, color='black', linestyles='--', lw=1)
plt.hlines(0.50, 0, x_50, color='black', linestyles=':', lw=1)
plt.hlines(0.75, 0, x_75, color='black', linestyles='--', lw=1)

text_str = '0.25'
plt.text(x_lims[0]+3,0.25+0.025,text_str,color = 'red')
text_str = '0.50'
plt.text(x_lims[0]+3,0.50+0.025,text_str,color = 'red')
text_str = '0.75'
plt.text(x_lims[0]+3,0.75+0.025,text_str,color = 'red')

text_str = f'{x_25:3.0f}'
plt.text(x_25, 0.025,text_str,color = 'red')
text_str = f'{x_50:3.0f}'
plt.text(x_50-10, 0.025,text_str,color = 'red')
text_str = f'{x_75:3.0f}'
plt.text(x_75, 0.025,text_str,color = 'red')

plt.arrow(x_25, 0.1, IQR, 0, lw = 0.1, color = 'blue',
         head_length = 4, head_width = 0.03, length_includes_head = True)
plt.arrow(x_25 + IQR, 0.1, -IQR, 0, lw = 0.1, color = 'blue',
         head_length = 4, head_width = 0.03, length_includes_head = True)
text_str = 'IQR = ' + f'{IQR:2.0f}'
plt.text((x_25+x_75)/2-8, 0.1+0.03,text_str,color = 'blue',size = 6)

ECDF_Figure.suptitle('Empirical CDFs Old Faithful Data and IQR',size='14')
plt.savefig('Old_Faithful_IQR.png', dpi=300)