<SYSTEM_TASK:>
Given the following text description, write Python code to implement the functionality described below step by step
<END_TASK>
<USER_TASK:>
Description:
 The Solow growth model
This post provides an example of the Solow growth model in the Black Rhino package. It will first cover the Solow model itself and how it is implemented in Black Rhino. Then, it will cover how to use Black Rhino to actually run the model and analyse the results.
Configuring the model
In the Black Rhino framework, parameters are stored in xml files. Using this notebook, you can set change them. First, you need to import the elementree from the xml Python module.
Step1:  Below you will find the parameter inputs for this model.
Step2:  To translate this to an xml document, which the framework can read, we first need create an ET element.
Step3:  And create parameter elements and give them the values seen below to add to the tree object.
Step4:  This object can now be transformed to a string and written to an xml file using the code below.
Step5:  Now, the parameter xml file has been generated and the model can be run. Before, running the model, you need to import a couple of extra modules. These are the Python logging module, the Black Rhino environment class, and the Black Rhino runner class.
Step6:  Then, before running the model, the logger needs to be initialized.
Step7:  First, the environment will be initialized. It contains the model parameters and variables. The environment also contains a list of agents. In the Solow model, the environment contains one bank, one firm, and one household. Finally, it also contains initialized transactions for these agents.
Step8:  Next up, the runner object is created. As the name suggests, the runner object handles the running of the model. But that is not all, it also initializes the updater.
Step9:  Now you can actually run the model. Since the agent-based model is simulated using Monte Carlo methods. This means that the model will be run multiple times (num_simulations). For every simulation run, the environment and runner will be (re-)initialized. Then, the runner will run the Solow model. During the run, the runner will write data about capital to a csv file specified within the Measurement class and print out all the transactions happening and the books of firm and household at the end of each sweep.
Step10:  So, now the model has been run, you will be able to analyse its outputs. If you are running the Ipython notebook to run the model. The following command will set the notebook to depict the output inside the noteobok.
Step11:  Futhermore, you should import the modules to create graphs (matplotlib) and dataframes (pandas).
Step12:  Running the model has generated a csv file that contains its output. We can use pandas to read the csv.
Step13:  The datafame looks as follows
Step14:  The Solow growth model is expected to produce an increase in total wealth that slows over time. In this version of the model, this means that there is deposit growth untill the equilibrium is reached. This is exactly what we observe.
<ASSISTANT_TASK:>
Python Code:
import xml.etree.ElementTree as ET
Explanation: The Solow growth model
This post provides an example of the Solow growth model in the Black Rhino package. It will first cover the Solow model itself and how it is implemented in Black Rhino. Then, it will cover how to use Black Rhino to actually run the model and analyse the results.
Configuring the model
In the Black Rhino framework, parameters are stored in xml files. Using this notebook, you can set change them. First, you need to import the elementree from the xml Python module.
End of explanation
parameter_values = (('num_sweeps', '30'),
                    ('num_simulations', '1'),
                    ('num_banks', '1'),
                    ('num_firms', '1'),
                    ('num_households', '1'),
                    ('bank_directory', 'agents/banks/'),
                    ('firm_directory', 'agents/firms/'),
                    ('household_directory', 'agents/households'),
                    ('measurement_config', 'measurements/test_output.xml')
                   )
Explanation: Below you will find the parameter inputs for this model.
End of explanation
environment = ET.Element('environment')
Explanation: To translate this to an xml document, which the framework can read, we first need create an ET element.
End of explanation
parameters = []
for x in range(len(parameter_values)):
    parameters.append(ET.SubElement(environment, 'parameter'))
    
for idx, p in enumerate(parameters):
    p.set('type', 'static')
    p.set('name', parameter_values[idx][0])
    p.set('value', parameter_values[idx][1])
Explanation: And create parameter elements and give them the values seen below to add to the tree object.
End of explanation
xml_params = ET.tostring(environment, encoding="unicode")
myfile = open("environments/solow_parameters.xml", "w")
myfile.write(xml_params)
myfile.close()
Explanation: This object can now be transformed to a string and written to an xml file using the code below.
End of explanation
import logging
import os
from src.environment import Environment
from src.runner import Runner
Explanation: Now, the parameter xml file has been generated and the model can be run. Before, running the model, you need to import a couple of extra modules. These are the Python logging module, the Black Rhino environment class, and the Black Rhino runner class.
End of explanation
log_directory = "log/"
identifier = "test_all_methods"
environment_directory = "environments/"
if not os.path.exists('log'):
    os.makedirs('log')
logging.basicConfig(format='%(asctime)s %(message)s', datefmt='%m/%d/%Y %H:%M:%S',
                    filename=log_directory + identifier + ".log", level=logging.INFO)
logging.info('START logging for run: %s',  environment_directory + identifier + ".xml")
Explanation: Then, before running the model, the logger needs to be initialized.
End of explanation
environment = Environment(environment_directory, identifier)
Explanation: First, the environment will be initialized. It contains the model parameters and variables. The environment also contains a list of agents. In the Solow model, the environment contains one bank, one firm, and one household. Finally, it also contains initialized transactions for these agents.
End of explanation
runner = Runner(environment)
Explanation: Next up, the runner object is created. As the name suggests, the runner object handles the running of the model. But that is not all, it also initializes the updater.
End of explanation
for i in range(int(environment.num_simulations)):
    logging.info('  STARTED with run %s',  str(i))
    environment.initialize(environment_directory,  identifier)
    runner.initialize(environment)
    
    runner.do_run(environment)
    logging.info('  DONE')
Explanation: Now you can actually run the model. Since the agent-based model is simulated using Monte Carlo methods. This means that the model will be run multiple times (num_simulations). For every simulation run, the environment and runner will be (re-)initialized. Then, the runner will run the Solow model. During the run, the runner will write data about capital to a csv file specified within the Measurement class and print out all the transactions happening and the books of firm and household at the end of each sweep.
End of explanation
%matplotlib inline
Explanation: So, now the model has been run, you will be able to analyse its outputs. If you are running the Ipython notebook to run the model. The following command will set the notebook to depict the output inside the noteobok.
End of explanation
import pandas as pd
#import numpy as np
import matplotlib.pyplot as plt
Explanation: Futhermore, you should import the modules to create graphs (matplotlib) and dataframes (pandas).
End of explanation
solow_data = pd.read_csv('measurements/TestMeasurement.csv', index_col=0) 
Explanation: Running the model has generated a csv file that contains its output. We can use pandas to read the csv.
End of explanation
solow_data.head(3)
Explanation: The datafame looks as follows:
End of explanation
fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(10,6))
ax.plot(solow_data.index, solow_data)
ax.set_xlabel('Time', fontsize='14')
ax.set_ylabel('Capital', fontsize='14')
fig.savefig('solow_capital.png')
Explanation: The Solow growth model is expected to produce an increase in total wealth that slows over time. In this version of the model, this means that there is deposit growth untill the equilibrium is reached. This is exactly what we observe.
End of explanation
<END_TASK>