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        "#%%\n",
        "\"\"\"File 01logit_simul.py\n",
        "\n",
        ":author: Michel Bierlaire, EPFL\n",
        ":date: Sat Sep  7 18:06:08 2019\n",
        "\n",
        " Example of simulation with a logit model\n",
        " Three alternatives: Train, Car and Swissmetro\n",
        " SP data\n",
        "\"\"\"\n",
        "\n",
        "import pandas as pd\n",
        "import biogeme.database as db\n",
        "import biogeme.biogeme as bio\n",
        "import biogeme.models as models\n",
        "from biogeme.expressions import Beta, Derive\n",
        "\n",
        "# Read the data\n",
        "df = pd.read_csv('swissmetro.dat', '\\t')\n",
        "database = db.Database('swissmetro', df)\n",
        "\n",
        "# The Pandas data structure is available as database.data. Use all the\n",
        "# Pandas functions to investigate the database. For example:\n",
        "#print(database.data.describe())\n",
        "\n",
        "# The following statement allows you to use the names of the variable\n",
        "# as Python variable.\n",
        "globals().update(database.variables)\n",
        "\n",
        "# Removing some observations can be done directly using pandas.\n",
        "#remove = (((database.data.PURPOSE != 1) &\n",
        "#           (database.data.PURPOSE != 3)) |\n",
        "#          (database.data.CHOICE == 0))\n",
        "#database.data.drop(database.data[remove].index,inplace=True)\n",
        "\n",
        "# Here we use the \"biogeme\" way for backward compatibility\n",
        "exclude = ((PURPOSE != 1) * (PURPOSE != 3) + (CHOICE == 0)) > 0\n",
        "database.remove(exclude)\n",
        "\n",
        "# Parameters to be estimated\n",
        "ASC_CAR = Beta('ASC_CAR', 0, None, None, 0)\n",
        "ASC_TRAIN = Beta('ASC_TRAIN', 0, None, None, 0)\n",
        "ASC_SM = Beta('ASC_SM', 0, None, None, 1)\n",
        "B_TIME = Beta('B_TIME', 0, None, None, 0)\n",
        "B_COST = Beta('B_COST', 0, None, None, 0)\n",
        "\n",
        "# Definition of new variables\n",
        "SM_COST = SM_CO * (GA == 0)\n",
        "TRAIN_COST = TRAIN_CO * (GA == 0)\n",
        "\n",
        "# Definition of new variables: in simulation, do not use the DefineVariable operator,\n",
        "# as it hides the functional relationships. In particular, derivatives cannot be\n",
        "# calculated.\n",
        "CAR_AV_SP = CAR_AV * (SP != 0)\n",
        "TRAIN_AV_SP = TRAIN_AV * (SP != 0)\n",
        "TRAIN_TT_SCALED = TRAIN_TT / 100.0\n",
        "TRAIN_COST_SCALED = TRAIN_COST / 100\n",
        "SM_TT_SCALED = SM_TT / 100.0\n",
        "SM_COST_SCALED = SM_COST / 100\n",
        "CAR_TT_SCALED = CAR_TT / 100\n",
        "CAR_CO_SCALED = CAR_CO / 100\n",
        "\n",
        "# Definition of the utility functions\n",
        "V1 = ASC_TRAIN + \\\n",
        "     B_TIME * TRAIN_TT_SCALED + \\\n",
        "     B_COST * TRAIN_COST_SCALED\n",
        "V2 = ASC_SM + \\\n",
        "     B_TIME * SM_TT_SCALED + \\\n",
        "     B_COST * SM_COST_SCALED\n",
        "V3 = ASC_CAR + \\\n",
        "     B_TIME * CAR_TT_SCALED + \\\n",
        "     B_COST * CAR_CO_SCALED\n",
        "\n",
        "# Associate utility functions with the numbering of alternatives\n",
        "V = {1: V1,\n",
        "     2: V2,\n",
        "     3: V3}\n",
        "\n",
        "# Associate the availability conditions with the alternatives\n",
        "av = {1: TRAIN_AV_SP,\n",
        "      2: SM_AV,\n",
        "      3: CAR_AV_SP}\n",
        "\n",
        "# The choice model is a logit, with availability conditions\n",
        "prob1 = models.logit(V, av, 1)\n",
        "prob2 = models.logit(V, av, 2)\n",
        "prob3 = models.logit(V, av, 3)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "# Elasticities can be computed. We illustrate below two\n",
        "# formulas. Check in the output file that they produce the same\n",
        "# result.\n",
        "\n",
        "# First, the general definition of elasticities. This illustrates the\n",
        "# use of the Derive expression, and can be used with any model,\n",
        "# however complicated it is. Note the quotes in the Derive opertor.\n",
        "genelas1 = Derive(prob1, 'TRAIN_TT') * TRAIN_TT / prob1\n",
        "genelas2 = Derive(prob2, 'SM_TT') * SM_TT / prob2\n",
        "genelas3 = Derive(prob3, 'CAR_TT') * CAR_TT / prob3\n",
        "\n",
        "# Second, the elasticity of logit models. See Ben-Akiva and Lerman for\n",
        "# the formula\n",
        "\n",
        "logitelas1 = TRAIN_AV_SP * (1.0 - prob1) * TRAIN_TT_SCALED * B_TIME\n",
        "logitelas2 = SM_AV * (1.0 - prob2) * SM_TT_SCALED * B_TIME\n",
        "logitelas3 = CAR_AV_SP * (1.0 - prob3) * CAR_TT_SCALED * B_TIME\n",
        "\n",
        "simulate = {'Prob. train': prob1,\n",
        "            'Prob. Swissmetro': prob2,\n",
        "            'Prob. car': prob3,\n",
        "            'logit elas. 1': logitelas1,\n",
        "            'generic elas. 1': genelas1,\n",
        "            'logit elas. 2': logitelas2,\n",
        "            'generic elas. 2': genelas2,\n",
        "            'logit elas. 3': logitelas3,\n",
        "            'generic elas. 3': genelas3}\n",
        "\n",
        "\n",
        "biogeme = bio.BIOGEME(database, simulate)\n",
        "biogeme.modelName = '01logit_simul'\n",
        "betas = {'ASC_TRAIN': -0.701188,\n",
        "         'B_TIME': -1.27786,\n",
        "         'B_COST': -1.08379,\n",
        "         'ASC_SM': 0,\n",
        "         'ASC_CAR': -0.154633}\n",
        "\n",
        "\n",
        "results = biogeme.simulate(theBetaValues=betas)\n",
        "print(results.describe())\n"
      ],
      "outputs": [],
      "execution_count": null
    }
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