#   scipy-yli: Helpful SciPy utilities and recipes
#   Copyright © 2022  Lee Yingtong Li (RunasSudo)
#
#   This program is free software: you can redistribute it and/or modify
#   it under the terms of the GNU Affero General Public License as published by
#   the Free Software Foundation, either version 3 of the License, or
#   (at your option) any later version.
#
#   This program is distributed in the hope that it will be useful,
#   but WITHOUT ANY WARRANTY; without even the implied warranty of
#   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#   GNU Affero General Public License for more details.
#
#   You should have received a copy of the GNU Affero General Public License
#   along with this program.  If not, see <https://www.gnu.org/licenses/>.

import numpy as np
from scipy import stats

import yli

def test_beta_ratio_cdf_vs_empirical():
	"""Compare beta_ratio.cdf with empirical distribution"""
	
	# Define the example beta distribution
	beta1 = stats.beta(3, 6)
	beta2 = stats.beta(12, 7)
	dist = yli.beta_oddsratio.from_scipy(beta1, beta2)
	
	# Compute empirical distribution
	samples_p1 = beta1.rvs(10_000, random_state=31415)
	samples_p2 = beta2.rvs(10_000, random_state=92653)
	sample = (samples_p1 / (1 - samples_p1)) / (samples_p2 / (1 - samples_p2))
	
	# Values to check
	x = np.linspace(0, 2, 10)
	y1 = dist.cdf(x)
	y2 = [(sample < xx).sum()/sample.size for xx in x]
	
	# Allow 0.01 tolerance
	assert (np.abs(y1 - y2) < 0.01).all()

def test_beta_ratio_ppf_vs_empirical():
	"""Compare beta_ratio.ppf with empirical distribution"""
	
	# Define the example beta distribution
	beta1 = stats.beta(3, 6)
	beta2 = stats.beta(12, 7)
	dist = yli.beta_oddsratio.from_scipy(beta1, beta2)
	
	# Compute empirical distribution
	samples_p1 = beta1.rvs(10_000, random_state=31415)
	samples_p2 = beta2.rvs(10_000, random_state=92653)
	sample = (samples_p1 / (1 - samples_p1)) / (samples_p2 / (1 - samples_p2))
	
	# Values to check
	x = np.linspace(0, 0.9, 10)
	y1 = dist.ppf(x)
	y2 = np.quantile(sample, x)
	
	# Allow 0.01 tolerance
	assert (np.abs(y1 - y2) < 0.01).all()

def test_beta_ratio_mean_vs_empirical():
	"""Compare beta_ratio.mean (vs _munp) with empirical mean"""
	
	# Define the example beta distribution
	beta1 = stats.beta(3, 6)
	beta2 = stats.beta(12, 7)
	dist = yli.beta_oddsratio.from_scipy(beta1, beta2)
	
	# Compute empirical mean
	samples_p1 = beta1.rvs(10_000, random_state=31415)
	samples_p2 = beta2.rvs(10_000, random_state=92653)
	sample = (samples_p1 / (1 - samples_p1)) / (samples_p2 / (1 - samples_p2))
	
	# Allow 0.01 tolerance
	assert np.abs(dist.mean() - sample.mean()) < 0.01

def test_beta_ratio_var_vs_empirical():
	"""Compare beta_ratio.var (vs _munp) with empirical variance"""
	
	# Define the example beta distribution
	beta1 = stats.beta(3, 6)
	beta2 = stats.beta(12, 7)
	dist = yli.beta_oddsratio.from_scipy(beta1, beta2)
	
	# Compute empirical mean
	samples_p1 = beta1.rvs(10_000, random_state=31415)
	samples_p2 = beta2.rvs(10_000, random_state=92653)
	sample = (samples_p1 / (1 - samples_p1)) / (samples_p2 / (1 - samples_p2))
	
	# Allow 0.01 tolerance
	assert np.abs(dist.var() - sample.var()) < 0.01