Week 1-2 - general intro to exploratory modelling/assignment 3 - multimodel_assignment.ipynb

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    "# EPA1361 - Model-Based Decision Making\n",
    "\n",
    "## Multi-model analysis\n",
    "\n",
    "This exercise uses a simple version of the [Lotka-Volterra predator-prey equations](https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations) to show how the EMA Workbench can be used for a\n",
    "multi-model analysis, in addition to typical parametric/structural uncertainties. This will let you test the connectors provided in the Workbench for Excel, NetLogo, and Vensim / PySD; we'll also use the models for the sensitivity analysis exercise in week 3.\n",
    "\n",
    "**Assignment**\n",
    "Using the three model files provided and the Python function below, define model objects for each implementation (Excel, NetLogo, Vensim/PySD, and Python), and test them using a single ensemble. Use 50 experiments sampled from the parameters below (so that each experiment will be executed for the 4 models, for a total of 200), and retrieve outputs for the _TIME_, _predators_, and _prey_ variables.\n",
    "   * Excel and Vensim are only supported on Windows\n",
    "   * Vensim requires the DSS version of Vensim\n",
    "   * Netlogo supoprt depends on [jpype](http://jpype.readthedocs.io/en/latest/install.html) and [pynetlogo](https://pynetlogo.readthedocs.io/en/latest/). Also, if you don't have NetLogo installed, please get [NetLogo 6.3.0](https://ccl.northwestern.edu/netlogo/download.shtml)\n",
    "   * for pysd, see [its documentation](http://pysd.readthedocs.io/en/master/installation.html)\n",
    "   * If possible try to work with all model versions, but even 2 or 3 (pure python and something else should be sufficient).\n",
    "\n",
    "\n",
    "|Parameter\t|Range or value\t        |\n",
    "|-----------|--------------:|\n",
    "|prey_birth_rate    \t|0.015 – 0.035\t|\n",
    "|predation_rate|0.0005 – 0.003 \t|\n",
    "|predator_efficiency     \t|0.001 – 0.004\t    |\n",
    "|predator_loss_rate\t    |0.04 – 0.08\t    |\n",
    "|Final time\t    |365\t    |\n",
    "|dt\t    |0.25\t    |\n",
    "\n",
    "* Note that your EMA Workbench installation includes [example scripts](https://github.com/quaquel/EMAworkbench/tree/master/ema_workbench/examples) for the different connectors. The different model objects follow a similar syntax but will need to be slightly adjusted depending on the software (e.g. to specify the NetLogo run length or the sheet name in Excel).\n",
    "  * This [tutorial](https://emaworkbench.readthedocs.io/en/latest/basic_tutorial.html) also shows a simple model in Python, Vensim and Excel connected to the workbench.\n",
    "\n",
    "* These model objects can be used with a replication functionality (for instance to test the effect of stochastic uncertainty in a NetLogo model), which repeats a given experiment over multiple replications. You can use a single replication in this exercise as the models are not stochastic. By default, each outcome array will then have a shape of (# experiments, # replications, # time steps). Try adapting the outcome arrays so that they can be used with the _lines_ plotting function of the Workbench, and plot the results grouped by model.\n",
    "\n",
    "* To check the graphical results, find the maximum absolute error of the time series you obtained for the _prey_ variable in the Excel, NetLogo, and Vensim/PySD models, relative to the Python function."
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      "C:\\Users\\Ewout\\AppData\\Local\\Programs\\Python\\Python311\\Lib\\site-packages\\ema_workbench\\connectors\\__init__.py:19: ImportWarning: vensim connector not available\n",
      "  warnings.warn(\"vensim connector not available\", ImportWarning)\n",
      "C:\\Users\\Ewout\\AppData\\Local\\Programs\\Python\\Python311\\Lib\\site-packages\\ema_workbench\\connectors\\__init__.py:34: ImportWarning: simio connector not available\n",
      "  warnings.warn(\"simio connector not available\", ImportWarning)\n",
      "C:\\Users\\Ewout\\AppData\\Local\\Programs\\Python\\Python311\\Lib\\site-packages\\ema_workbench\\analysis\\prim.py:30: ImportWarning: altair based interactive inspection not available\n",
      "  warnings.warn((\"altair based interactive \" \"inspection not available\"), ImportWarning)\n"
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   "source": [
    "# Some imports you may need\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from ema_workbench import (Model, RealParameter, TimeSeriesOutcome, perform_experiments, ema_logging)\n",
    "\n",
    "from ema_workbench.connectors.netlogo import NetLogoModel\n",
    "from ema_workbench.connectors.excel import ExcelModel\n",
    "from ema_workbench.connectors.pysd_connector import PysdModel\n",
    "\n",
    "from ema_workbench.em_framework.samplers import LHSSampler\n",
    "from ema_workbench.em_framework.salib_samplers import MorrisSampler, SobolSampler\n",
    "\n",
    "from ema_workbench.analysis.plotting import lines, Density"
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    "# Import the Python function\n",
    "from model.pred_prey import PredPrey"
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   "source": [
    "# Define uncertainties and outcomes\n",
    "\n",
    "\n",
    "# Define model objects for the different implementations\n"
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