"""File: 03antitheticExplicit.py

 Author: Michel Bierlaire, EPFL
 Date: Wed Dec 11 17:04:40 2019

Calculation of a simple integral using Monte-Carlo integration. It
illustrates how to use antothetic draws, explicitly generared.
"""
# pylint: disable=invalid-name, undefined-variable

import pandas as pd
import biogeme.database as db
import biogeme.biogeme as bio
import biogeme.draws as draws
from biogeme.expressions import exp, bioDraws, MonteCarlo


# We create a fake database with one entry, as it is required to store the draws
pandas = pd.DataFrame()
pandas['FakeColumn'] = [1.0]
database = db.Database('fakeDatabase', pandas)

def halton13(sampleSize, numberOfDraws):
    """
    The user can define new draws. For example, Halton draws with base 13, skipping
    the first 10 draws.
    """
    return draws.getHaltonDraws(sampleSize,
                                numberOfDraws,
                                base=13,
                                skip=10)

mydraws = {'HALTON13': (halton13, 'Halton draws, base 13, skipping 10')}
database.setRandomNumberGenerators(mydraws)

U = bioDraws('U', 'UNIFORM')
integrand = exp(U) + exp(1 - U)
simulatedI = MonteCarlo(integrand) / 2.0

U_halton13 = bioDraws('U_halton13', 'HALTON13')
integrand_halton13 = exp(U_halton13) + exp(1 - U_halton13)
simulatedI_halton13 = MonteCarlo(integrand_halton13) / 2.0

U_mlhs = bioDraws('U_mlhs', 'UNIFORM_MLHS')
integrand_mlhs = exp(U_mlhs) + exp(1 - U_mlhs)
simulatedI_mlhs = MonteCarlo(integrand_mlhs) / 2.0

trueI = exp(1.0) - 1.0

R = 10000

error = simulatedI - trueI

error_halton13 = simulatedI_halton13 - trueI

error_mlhs = simulatedI_mlhs - trueI

simulate = {'Analytical Integral': trueI,
            'Simulated Integral': simulatedI,
            'Error             ': error,
            'Simulated Integral (Halton13)': simulatedI_halton13,
            'Error (Halton13)             ': error_halton13,
            'Simulated Integral (MLHS)': simulatedI_mlhs,
            'Error (MLHS)             ': error_mlhs}

biogeme = bio.BIOGEME(database, simulate, numberOfDraws=R)
biogeme.modelName = '03antitheticExplicit'
results = biogeme.simulate()
print(f"Analytical integral:{results.iloc[0]['Analytical Integral']:.6f}")
print(f"\t\tUniform (Anti)\t\tHalton13 (Anti)\t\tMLHS (Anti)")
print(f"Simulated\t{results.iloc[0]['Simulated Integral']:.6g}\t"
      f"{results.iloc[0]['Simulated Integral (Halton13)']:.6g}\t"
      f"{results.iloc[0]['Simulated Integral (MLHS)']:.6g}")
print(f"Error\t\t{results.iloc[0]['Error             ']:.6g}\t"
      f"{results.iloc[0]['Error (Halton13)             ']:.6g}\t"
      f"{results.iloc[0]['Error (MLHS)             ']:.6g}")