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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Open Traffic Reporter
Map-Matching Optimization
The Open Traffic Reporter map-matching service is based on the Hidden Markov Model (HMM) design of Newton and Krumm (2009). Skipping over 99% of the innerworkings of how HMMs work (for more detail see here) there are two principal parameters in the HMM algorithm that must be estimated from data.
$$ p(z_t|r_i) = \frac{1}{\sqrt{2 \pi \sigma_z}} e^{-0.5(\frac{||z_t - x_{t,i}||_{\text{great circle}}}{\sigma_z})^2}$$
Step1:  1. Generate Random Routes
Generate routes from Google Maps POIs or Mapzen Venues
Step2:  Save or load a specific set of routes
Step3:  2. Grid Search for Optimal Parameter Values
Step4:  3. Plot the Curves
Step5:  5. Visualize Routes
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Python Code:
from __future__ import division
from matplotlib import pyplot as plt
import numpy as np
import os
import urllib
import json
import pandas as pd
from random import shuffle, choice
import pickle
import sys; sys.path.insert(0, os.path.abspath('..'));
import validator.validator as val
%matplotlib inline
mapzenKey = os.environ.get('MAPZEN_API')
gmapsKey = os.environ.get('GOOGLE_MAPS')
Explanation: Open Traffic Reporter
Map-Matching Optimization
The Open Traffic Reporter map-matching service is based on the Hidden Markov Model (HMM) design of Newton and Krumm (2009). Skipping over 99% of the innerworkings of how HMMs work (for more detail see here) there are two principal parameters in the HMM algorithm that must be estimated from data.
$$ p(z_t|r_i) = \frac{1}{\sqrt{2 \pi \sigma_z}} e^{-0.5(\frac{||z_t - x_{t,i}||_{\text{great circle}}}{\sigma_z})^2}$$
End of explanation
# routeList = val.get_POI_routes_by_length('Paris', 1, 5, 20, gmapsKey)
routeList = val.get_routes_by_length('San Francisco', 1, 5, 20, mapzenKey)
Explanation: 1. Generate Random Routes
Generate routes from Google Maps POIs or Mapzen Venues
End of explanation
# routeList = pickle.load(open('sf_routes.pkl','rb'))
# pickle.dump(routeList, open('saf_routes.pkl','wb'))
Explanation: Save or load a specific set of routes
End of explanation
df = pd.DataFrame(columns=['beta', 'sigma_z', 'score'])
outDfRow = -1
saveResults = False
noiseLevels = np.linspace(0, 100, 21)
noiseLevels = [5]
sampleRates = [1, 5, 10, 20, 30]
sampleRates = [5]
betas = np.linspace(1,10,19)
sigmaZs = np.linspace(1,10,19)
for i, rteCoords in enumerate(routeList):
    print("Processig route {0} of {1}".format(i, len(routeList)))
    shape, routeUrl = val.get_route_shape(rteCoords)
    
    for beta in betas:
        
        for sigmaZ in sigmaZs:
            print("Computing score for sigma_z: {0}, beta: {1}".format(
                        sigmaZ, beta))
            edges, shapeCoords, traceAttrUrl = val.get_trace_attrs(
                shape, beta=beta, sigmaZ=sigmaZ)
            edges = val.get_coords_per_second(shapeCoords, edges, '2768')
            for noise in noiseLevels:
                noise = round(noise,3)
                for sampleRate in sampleRates:
                    outDfRow += 1
                    df.loc[outDfRow, ['beta','sigma_z']] = [beta, sigmaZ]
                    dfEdges = val.format_edge_df(edges)
                    dfEdges, jsonDict, geojson = val.synthesize_gps(
                        dfEdges, shapeCoords, '2768', noise=noise, sampleRate=sampleRate, 
                        beta=beta, sigmaZ=sigmaZ)
                    segments, reportUrl = val.get_reporter_segments(jsonDict)
                    matches, score = val.get_matches(segments, dfEdges)
                    df.loc[outDfRow, 'score'] = score
                    if saveResults:
                        matches.to_csv(
                            '../data/matches_{0}_to_{1}_w_{2}_m_noise_at_{3}_Hz.csv'.format(
                                stName, endName, str(noise), str(Hz)), index=False)
                        with open('../data/trace_{0}_to_{1}_w_{2}_m_noise_at_{3}_Hz.geojson'.format(
                            stName, endName, str(noise), str(Hz)), 'w+') as fp:
                            json.dump(geojson, fp)
Explanation: 2. Grid Search for Optimal Parameter Values
End of explanation
df['score'] = df['score'].astype(float)
df['beta'] = df['beta'].astype(float)
df['sigma_z'] = df['sigma_z'].astype(float)
df.groupby('beta').agg('mean').reset_index().plot('beta','score', figsize=(12,8))
df.groupby('sigma_z').agg('mean').reset_index().plot('sigma_z','score', figsize=(12,8))
Explanation: 3. Plot the Curves
End of explanation
geojsonList = [trace for trace in os.listdir('../data/') if trace.endswith('json')]
fname = '../data/' + choice(geojsonList)
val.generate_route_map(fname, 14)
fname
Explanation: 5. Visualize Routes
End of explanation
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