## This file is an updated version of 07problem.py, where
## the probabilities are simulated in order to
## investigate the numerical issue. 

import pandas as pd
import numpy as np
import biogeme.database as db
import biogeme.biogeme as bio
#import biogeme.models as models
import biogeme.loglikelihood as ll

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

from headers import *

exclude = (Choice == -1.0)
database.remove(exclude)



### Variables

ScaledIncome = DefineVariable('ScaledIncome',\
                              CalculatedIncome / 1000,database)
ContIncome_0_4000 = DefineVariable('ContIncome_0_4000',\
                                   bioMin(ScaledIncome,4),database)
ContIncome_4000_6000 = DefineVariable('ContIncome_4000_6000',\
                                      bioMax(0,bioMin(ScaledIncome-4,2)),database)
ContIncome_6000_8000 = DefineVariable('ContIncome_6000_8000',\
                                      bioMax(0,bioMin(ScaledIncome-6,2)),database)
ContIncome_8000_10000 = DefineVariable('ContIncome_8000_10000',\
                                       bioMax(0,bioMin(ScaledIncome-8,2)),database)
ContIncome_10000_more = DefineVariable('ContIncome_10000_more',\
                                       bioMax(0,ScaledIncome-10),database)

age_65_more = DefineVariable('age_65_more',age >= Numeric(65),database)
moreThanOneCar = DefineVariable('moreThanOneCar',NbCar > 1,database)
moreThanOneBike = DefineVariable('moreThanOneBike',NbBicy > 1,database)
individualHouse = DefineVariable('individualHouse',\
                                 HouseType == 1,database)
male = DefineVariable('male',Gender == 1,database)
haveChildren = DefineVariable('haveChildren',\
                              ((FamilSitu == 3)+(FamilSitu == 4)) > 0,database)
haveGA = DefineVariable('haveGA',GenAbST == 1,database)
highEducation = DefineVariable('highEducation', Education >= 6,database)

### Coefficients
coef_intercept = Beta('coef_intercept',0.0,None,None,0 )
coef_age_65_more = Beta('coef_age_65_more',0.0,None,None,0 )
coef_haveGA = Beta('coef_haveGA',0.0,None,None,0 )
coef_ContIncome_0_4000 = \
 Beta('coef_ContIncome_0_4000',0.0,None,None,0 )
coef_ContIncome_4000_6000 = \
 Beta('coef_ContIncome_4000_6000',0.0,None,None,0 )
coef_ContIncome_6000_8000 = \
 Beta('coef_ContIncome_6000_8000',0.0,None,None,0 )
coef_ContIncome_8000_10000 = \
 Beta('coef_ContIncome_8000_10000',0.0,None,None,0 )
coef_ContIncome_10000_more = \
 Beta('coef_ContIncome_10000_more',0.0,None,None,0 )
coef_moreThanOneCar = \
 Beta('coef_moreThanOneCar',0.0,None,None,0 )
coef_moreThanOneBike = \
 Beta('coef_moreThanOneBike',0.0,None,None,0 )
coef_individualHouse = \
 Beta('coef_individualHouse',0.0,None,None,0 )
coef_male = Beta('coef_male',0.0,None,None,0 )
coef_haveChildren = Beta('coef_haveChildren',0.0,None,None,0 )
coef_highEducation = Beta('coef_highEducation',0.0,None,None,0 )

### Latent variable: structural equation

# Note that the expression must be on a single line. In order to 
# write it across several lines, each line must terminate with 
# the \ symbol

CARLOVERS = \
coef_intercept +\
coef_age_65_more * age_65_more +\
coef_ContIncome_0_4000 * ContIncome_0_4000 +\
coef_ContIncome_4000_6000 * ContIncome_4000_6000 +\
coef_ContIncome_6000_8000 * ContIncome_6000_8000 +\
coef_ContIncome_8000_10000 * ContIncome_8000_10000 +\
coef_ContIncome_10000_more * ContIncome_10000_more +\
coef_moreThanOneCar * moreThanOneCar +\
coef_moreThanOneBike * moreThanOneBike +\
coef_individualHouse * individualHouse +\
coef_male * male +\
coef_haveChildren * haveChildren +\
coef_haveGA * haveGA +\
coef_highEducation * highEducation


### Measurement equations

INTER_Envir01 = Beta('INTER_Envir01',0,None,None,1)
INTER_Envir02 = Beta('INTER_Envir02',0.0,None,None,0 )
INTER_Envir03 = Beta('INTER_Envir03',0.0,None,None,0 )
INTER_Mobil11 = Beta('INTER_Mobil11',0.0,None,None,0 )
INTER_Mobil14 = Beta('INTER_Mobil14',0.0,None,None,0 )
INTER_Mobil16 = Beta('INTER_Mobil16',0.0,None,None,0 )
INTER_Mobil17 = Beta('INTER_Mobil17',0.0,None,None,0 )

B_Envir01_F1 = Beta('B_Envir01_F1',-1,None,None,1)
B_Envir02_F1 = Beta('B_Envir02_F1',0.0,None,None,0 )
B_Envir03_F1 = Beta('B_Envir03_F1',0.0,None,None,0 )
B_Mobil11_F1 = Beta('B_Mobil11_F1',0.0,None,None,0 )
B_Mobil14_F1 = Beta('B_Mobil14_F1',0.0,None,None,0 )
B_Mobil16_F1 = Beta('B_Mobil16_F1',0.0,None,None,0 )
B_Mobil17_F1 = Beta('B_Mobil17_F1',0.0,None,None,0 )



MODEL_Envir01 = INTER_Envir01 + B_Envir01_F1 * CARLOVERS
MODEL_Envir02 = INTER_Envir02 + B_Envir02_F1 * CARLOVERS
MODEL_Envir03 = INTER_Envir03 + B_Envir03_F1 * CARLOVERS
MODEL_Mobil11 = INTER_Mobil11 + B_Mobil11_F1 * CARLOVERS
MODEL_Mobil14 = INTER_Mobil14 + B_Mobil14_F1 * CARLOVERS
MODEL_Mobil16 = INTER_Mobil16 + B_Mobil16_F1 * CARLOVERS
MODEL_Mobil17 = INTER_Mobil17 + B_Mobil17_F1 * CARLOVERS

SIGMA_STAR_Envir01 = Beta('SIGMA_STAR_Envir01',1,None,None,1)
SIGMA_STAR_Envir02 = Beta('SIGMA_STAR_Envir02',0.01,None,None,0 )
SIGMA_STAR_Envir03 = Beta('SIGMA_STAR_Envir03',1,None,None,0 )
SIGMA_STAR_Mobil11 = Beta('SIGMA_STAR_Mobil11',1,None,None,0 )
SIGMA_STAR_Mobil14 = Beta('SIGMA_STAR_Mobil14',1,None,None,0 )
SIGMA_STAR_Mobil16 = Beta('SIGMA_STAR_Mobil16',1,None,None,0 )
SIGMA_STAR_Mobil17 = Beta('SIGMA_STAR_Mobil17',1,None,None,0 )

delta_1 = Beta('delta_1',0.1,0,10,0 )
delta_2 = Beta('delta_2',0.2,0,10,0 )
tau_1 = -delta_1 - delta_2
tau_2 = -delta_1 
tau_3 = delta_1
tau_4 = delta_1 + delta_2

Envir01_tau_1 = (tau_1-MODEL_Envir01) / SIGMA_STAR_Envir01
Envir01_tau_2 = (tau_2-MODEL_Envir01) / SIGMA_STAR_Envir01
Envir01_tau_3 = (tau_3-MODEL_Envir01) / SIGMA_STAR_Envir01
Envir01_tau_4 = (tau_4-MODEL_Envir01) / SIGMA_STAR_Envir01
IndEnvir01 = {
    1: bioNormalCdf(Envir01_tau_1),
    2: bioNormalCdf(Envir01_tau_2)-bioNormalCdf(Envir01_tau_1),
    3: bioNormalCdf(Envir01_tau_3)-bioNormalCdf(Envir01_tau_2),
    4: bioNormalCdf(Envir01_tau_4)-bioNormalCdf(Envir01_tau_3),
    5: 1-bioNormalCdf(Envir01_tau_4),
    6: 1.0,
    -1: 1.0,
    -2: 1.0
}

P_Envir01 = Elem(IndEnvir01, Envir01)


Envir02_tau_1 = (tau_1-MODEL_Envir02) / SIGMA_STAR_Envir02
Envir02_tau_2 = (tau_2-MODEL_Envir02) / SIGMA_STAR_Envir02
Envir02_tau_3 = (tau_3-MODEL_Envir02) / SIGMA_STAR_Envir02
Envir02_tau_4 = (tau_4-MODEL_Envir02) / SIGMA_STAR_Envir02
IndEnvir02 = {
    1: bioNormalCdf(Envir02_tau_1),
    2: bioNormalCdf(Envir02_tau_2)-bioNormalCdf(Envir02_tau_1),
    3: bioNormalCdf(Envir02_tau_3)-bioNormalCdf(Envir02_tau_2),
    4: bioNormalCdf(Envir02_tau_4)-bioNormalCdf(Envir02_tau_3),
    5: 1-bioNormalCdf(Envir02_tau_4),
    6: 1.0,
    -1: 1.0,
    -2: 1.0
}

P_Envir02 = Elem(IndEnvir02, Envir02)

Envir03_tau_1 = (tau_1-MODEL_Envir03) / SIGMA_STAR_Envir03
Envir03_tau_2 = (tau_2-MODEL_Envir03) / SIGMA_STAR_Envir03
Envir03_tau_3 = (tau_3-MODEL_Envir03) / SIGMA_STAR_Envir03
Envir03_tau_4 = (tau_4-MODEL_Envir03) / SIGMA_STAR_Envir03
IndEnvir03 = {
    1: bioNormalCdf(Envir03_tau_1),
    2: bioNormalCdf(Envir03_tau_2)-bioNormalCdf(Envir03_tau_1),
    3: bioNormalCdf(Envir03_tau_3)-bioNormalCdf(Envir03_tau_2),
    4: bioNormalCdf(Envir03_tau_4)-bioNormalCdf(Envir03_tau_3),
    5: 1-bioNormalCdf(Envir03_tau_4),
    6: 1.0,
    -1: 1.0,
    -2: 1.0
}

P_Envir03 = Elem(IndEnvir03, Envir03)

Mobil11_tau_1 = (tau_1-MODEL_Mobil11) / SIGMA_STAR_Mobil11
Mobil11_tau_2 = (tau_2-MODEL_Mobil11) / SIGMA_STAR_Mobil11
Mobil11_tau_3 = (tau_3-MODEL_Mobil11) / SIGMA_STAR_Mobil11
Mobil11_tau_4 = (tau_4-MODEL_Mobil11) / SIGMA_STAR_Mobil11
IndMobil11 = {
    1: bioNormalCdf(Mobil11_tau_1),
    2: bioNormalCdf(Mobil11_tau_2)-bioNormalCdf(Mobil11_tau_1),
    3: bioNormalCdf(Mobil11_tau_3)-bioNormalCdf(Mobil11_tau_2),
    4: bioNormalCdf(Mobil11_tau_4)-bioNormalCdf(Mobil11_tau_3),
    5: 1-bioNormalCdf(Mobil11_tau_4),
    6: 1.0,
    -1: 1.0,
    -2: 1.0
}

P_Mobil11 = Elem(IndMobil11, Mobil11)

Mobil14_tau_1 = (tau_1-MODEL_Mobil14) / SIGMA_STAR_Mobil14
Mobil14_tau_2 = (tau_2-MODEL_Mobil14) / SIGMA_STAR_Mobil14
Mobil14_tau_3 = (tau_3-MODEL_Mobil14) / SIGMA_STAR_Mobil14
Mobil14_tau_4 = (tau_4-MODEL_Mobil14) / SIGMA_STAR_Mobil14
IndMobil14 = {
    1: bioNormalCdf(Mobil14_tau_1),
    2: bioNormalCdf(Mobil14_tau_2)-bioNormalCdf(Mobil14_tau_1),
    3: bioNormalCdf(Mobil14_tau_3)-bioNormalCdf(Mobil14_tau_2),
    4: bioNormalCdf(Mobil14_tau_4)-bioNormalCdf(Mobil14_tau_3),
    5: 1-bioNormalCdf(Mobil14_tau_4),
    6: 1.0,
    -1: 1.0,
    -2: 1.0
}

P_Mobil14 = Elem(IndMobil14, Mobil14)

Mobil16_tau_1 = (tau_1-MODEL_Mobil16) / SIGMA_STAR_Mobil16
Mobil16_tau_2 = (tau_2-MODEL_Mobil16) / SIGMA_STAR_Mobil16
Mobil16_tau_3 = (tau_3-MODEL_Mobil16) / SIGMA_STAR_Mobil16
Mobil16_tau_4 = (tau_4-MODEL_Mobil16) / SIGMA_STAR_Mobil16
IndMobil16 = {
    1: bioNormalCdf(Mobil16_tau_1),
    2: bioNormalCdf(Mobil16_tau_2)-bioNormalCdf(Mobil16_tau_1),
    3: bioNormalCdf(Mobil16_tau_3)-bioNormalCdf(Mobil16_tau_2),
    4: bioNormalCdf(Mobil16_tau_4)-bioNormalCdf(Mobil16_tau_3),
    5: 1-bioNormalCdf(Mobil16_tau_4),
    6: 1.0,
    -1: 1.0,
    -2: 1.0
}

P_Mobil16 = Elem(IndMobil16, Mobil16)

Mobil17_tau_1 = (tau_1-MODEL_Mobil17) / SIGMA_STAR_Mobil17
Mobil17_tau_2 = (tau_2-MODEL_Mobil17) / SIGMA_STAR_Mobil17
Mobil17_tau_3 = (tau_3-MODEL_Mobil17) / SIGMA_STAR_Mobil17
Mobil17_tau_4 = (tau_4-MODEL_Mobil17) / SIGMA_STAR_Mobil17
IndMobil17 = {
    1: bioNormalCdf(Mobil17_tau_1),
    2: bioNormalCdf(Mobil17_tau_2)-bioNormalCdf(Mobil17_tau_1),
    3: bioNormalCdf(Mobil17_tau_3)-bioNormalCdf(Mobil17_tau_2),
    4: bioNormalCdf(Mobil17_tau_4)-bioNormalCdf(Mobil17_tau_3),
    5: 1-bioNormalCdf(Mobil17_tau_4),
    6: 1.0,
    -1: 1.0,
    -2: 1.0
}

P_Mobil17 = Elem(IndMobil17, Mobil17)

simulate = {'P_Envir01': P_Envir01,
            'P_Envir02': P_Envir02,
            'P_Envir03': P_Envir03,
            'P_Mobil11': P_Mobil11,
            'P_Mobil14': P_Mobil14,
            'P_Mobil16': P_Mobil16,
            'P_Mobil17': P_Mobil17}


biogeme  = bio.BIOGEME(database,simulate)
biogeme.modelName = "07problem_simul"
simulatedValues = biogeme.simulate()
zeroValues = simulatedValues.where(simulatedValues == 0,other='')
print(zeroValues)
