""" File: 06estimationIntegral.py

 Author: Michel Bierlaire, EPFL
 Date: Wed Dec 11 17:17:05 2019

Estimation of a mixtures of logit models where the integral is
calculated using numerical integration. 

"""

import pandas as pd
import biogeme.database as db
import biogeme.biogeme as bio
import biogeme.distributions as dist
import biogeme.models as models
from biogeme.expressions import Beta, DefineVariable, RandomVariable, Integrate, log

pandas = pd.read_csv("swissmetro.dat",sep='\t')
database = db.Database("swissmetro",pandas)

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

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)


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',1,None,None,0)
B_COST = Beta('B_COST',0,None,None,0)

# Define a random parameter, normally distirbuted, designed to be used
# for Monte-Carlo simulation

omega = RandomVariable('omega')
density = dist.normalpdf(omega) 
B_TIME_RND = B_TIME + B_TIME_S * omega 


# Utility functions

#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  )

# 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)

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 choice model is a logit, with availability conditions
condprob = models.logit(V,av,CHOICE)
prob = Integrate(condprob * density,'omega')
logprob = log(prob)

biogeme = bio.BIOGEME(database,logprob)

biogeme.modelName = '06estimationIntegral'

results = biogeme.estimate()
print(results)
results.writeLaTeX()