"""File 05normalMixture_simul.py

:author: Michel Bierlaire, EPFL
:date: Sat Sep  7 18:42:55 2019

 Example of a mixture of logit models, using Monte-Carlo integration, and
 used for simulatiom
 Three alternatives: Train, Car and Swissmetro
 SP data
"""
import numpy as np
import pandas as pd
import biogeme.database as db
import biogeme.biogeme as bio
import biogeme.models as models
import biogeme.results as res
from biogeme.expressions import Beta, DefineVariable,bioDraws, MonteCarlo
import matplotlib.pyplot as plt

# Read the data
df = pd.read_csv("swissmetro.dat",sep='\t')
database = db.Database("swissmetro",df)

# The Pandas data structure is available as database.data. Use all the
# Pandas functions to invesigate the database
#print(database.data.describe())

# The following statement allows you to use the names of the variable
# as Python variable.
globals().update(database.variables)

# Removing some observations can be done directly using pandas.
#remove = (((database.data.PURPOSE != 1) & (database.data.PURPOSE != 3)) | (database.data.CHOICE == 0))
#database.data.drop(database.data[remove].index,inplace=True)

# Here we use the "biogeme" way for backward compatibility
exclude = (( PURPOSE != 1 ) * (  PURPOSE   !=  3  ) +  ( CHOICE == 0 )) > 0
database.remove(exclude)


# Parameters to be estimated
ASC_CAR = Beta('ASC_CAR',0,None,None,0)
ASC_TRAIN = Beta('ASC_TRAIN',0,None,None,0)
ASC_SM = Beta('ASC_SM',0,None,None,1)
B_TIME = Beta('B_TIME',0,None,None,0)
B_TIME_S = Beta('B_TIME_S',0,None,None,0)
B_COST = Beta('B_COST',0,None,None,0)

# Define a random parameter, normally distributed, designed to be used
# for Monte-Carlo simulation
B_TIME_RND = B_TIME + B_TIME_S * bioDraws('B_TIME_RND','NORMAL')

# Definition of new variables
#If the person has a GA (season ticket) her incremental cost is actually 0 
#rather than the cost value gathered from the
# network data. 
SM_COST =  SM_CO   * (  GA   ==  0  ) 
TRAIN_COST =  TRAIN_CO   * (  GA   ==  0  )

# Definition of new variables: adding columns to the database 
# For numerical reasons, it is good practice to scale the data to
# that the values of the parameters are around 1.0. 
# A previous estimation with the unscaled data has generated
# parameters around -0.01 for both cost and time. Therefore, time and
# cost are multipled my 0.01.
TRAIN_TT_SCALED = DefineVariable('TRAIN_TT_SCALED',\
                                 TRAIN_TT / 100.0,database)
TRAIN_COST_SCALED = DefineVariable('TRAIN_COST_SCALED',\
                                   TRAIN_COST / 100,database)
SM_TT_SCALED = DefineVariable('SM_TT_SCALED', SM_TT / 100.0,database)
SM_COST_SCALED = DefineVariable('SM_COST_SCALED', SM_COST / 100,database)
CAR_TT_SCALED = DefineVariable('CAR_TT_SCALED', CAR_TT / 100,database)
CAR_CO_SCALED = DefineVariable('CAR_CO_SCALED', CAR_CO / 100,database)

# Definition of the utility functions
V1 = ASC_TRAIN + B_TIME_RND * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
V2 = ASC_SM + B_TIME_RND * SM_TT_SCALED + B_COST * SM_COST_SCALED
V3 = ASC_CAR + B_TIME_RND * CAR_TT_SCALED + B_COST * CAR_CO_SCALED

# Associate utility functions with the numbering of alternatives
V = {1: V1,
     2: V2,
     3: V3}

# Associate the availability conditions with the alternatives
CAR_AV_SP =  DefineVariable('CAR_AV_SP',CAR_AV  * (  SP   !=  0  ),database)
TRAIN_AV_SP =  DefineVariable('TRAIN_AV_SP',TRAIN_AV  * (  SP   !=  0  ),database)
av = {1: TRAIN_AV_SP,
      2: SM_AV,
      3: CAR_AV_SP}

# The estimation results are read from thr pickel file
results = res.bioResults(pickleFile='05normalMixture.pickle')


# Conditional to B_TIME_RND, we have a logit model (called the kernel)
prob = models.logit(V,av,CHOICE)

# We would like to simulate the value of the individual parameters
numerator = MonteCarlo(B_TIME_RND * prob)
denominator = MonteCarlo(prob)

simulate = {'Numerator': numerator,
            'Denominator': denominator}

# Create the Biogeme object
biosim  = bio.BIOGEME(database,simulate,numberOfDraws=1000)
biosim.modelName = "05normalMixture_simul"

# Simulate the requested quantities. The output is a Pandas data frame
simresults = biosim.simulate(results.data.betaValues)

# Post processing to obtain the individual parameters
simresults['beta'] = simresults['Numerator'] / simresults['Denominator']

#Plot the histogram of individual parameters
simresults['beta'].plot(kind='hist',density=True,bins=20)

# Plot the general distribution of beta
def normalpdf(x,mu=0.0,s=1.0):
    d = -(x-mu)*(x-mu)
    n = 2.0*s*s
    a = d/n
    num = np.exp(a)
    den = s*2.506628275
    p = num / den
    return p

betas = results.getBetaValues(['B_TIME','B_TIME_S'])
x = np.arange(simresults['beta'].min(),simresults['beta'].max(),0.01)
plt.plot(x,normalpdf(x,betas['B_TIME'],betas['B_TIME_S']),'-')
plt.show()