code: import matplotlib.pyplot as plt
  import numpy as np
  import os
  import pandas as pd
  
  # Find path for cases
  curr_dir_path = os.path.dirname(os.path.realpath(__file__))
  # print(curr_dir_path)
  # cases = os.listdir(curr_dir_path + '/Cases')
  # pop = cases.index('baseCase')
  # cases.pop(pop)
  
  # Label graph with bold characters
  font_axis_publish = {
        'color':  'black',
        'weight': 'bold',
        'size': 22,
        }
  
  # Read in digitized data
  digi_n = pd.read_csv(
      curr_dir_path + '/n_nstar_radius.dat',
      header = 0,
      sep = '\t',
      names = ['r', 'n_nstar']
      )
  
  digi_T = pd.read_csv(
      curr_dir_path + '/T_Tstar_radius_DAC.dat',
      header = 0,
      sep = '\t',
      names = ['r', 'T_Tstar']
      )
  
  # Read in simulated data. 
  sim = pd.read_csv(
      curr_dir_path + '/postProcessing/sampleDict/0.3/horizontalLine_Ttra_Ar_rhoN_Ar.csv'
      )
  
  # Used to see what the values trend to. 
  print(sim['Ttra_Ar'])
  
  sim = sim[['x', 'rhoN_Ar', 'Ttra_Ar']].dropna()
  sim['rhoN_Ar'] = sim['rhoN_Ar'] / 8.377e20
  sim['Ttra_Ar'] = sim['Ttra_Ar'] / 1000.0
      
  
  # Producde Analytical Data
  def TTt_Ma(Ma, ga = 1.4):
      return (ga + 1) / (2 + (ga - 1) * Ma ** 2)
  
  def rrt_Ma(Ma, ga = 1.4):
    rrt = (1 / TTt_Ma(Ma, ga)) ** ((ga + 1) / (ga - 1))
    rrt = np.sqrt(np.sqrt(rrt) / Ma)
    return rrt
  
  def nnt_Ma(Ma, ga = 1.4):
    return TTt_Ma(Ma, ga) ** (1 / (ga - 1))
  
  def a(T, ga = 1.4, R = 287):
      return np.sqrt(ga * R * T)
  
  Ma_domain = np.linspace(1, 25, 100) 
  ga = 1.67
  TTt = TTt_Ma(Ma_domain, ga = ga)
  rrt = rrt_Ma(Ma_domain, ga = ga)
  nnt = nnt_Ma(Ma_domain, ga = ga)
  
  print("Printing rrt")
  print(rrt)
  
  # Graph Results
  plt.title('OpenFOAM vs DAC', fontdict = font_axis_publish)
  plt.ylabel('n/n*', fontdict = font_axis_publish)
  plt.xlabel('Radial distance, r (m)', fontdict = font_axis_publish)
  
  plt.plot(sim['x'], sim['rhoN_Ar'], label = 'OpenFOAM (Torres, Pitt, Kinzel)')
  plt.plot(digi_n['r'], digi_n['n_nstar'], label = 'DAC (Lumpkin, Stewart)')
  plt.plot(rrt, nnt, label = 'Analytical Solution')
  plt.legend()
  plt.yscale('log')
  plt.ylim(bottom = 1e-4, top = 1)
  plt.savefig(curr_dir_path + '/digitized_vs_analytical_n.png')
  plt.close()
  
  plt.title('OpenFOAM vs DAC', fontdict = font_axis_publish)
  plt.ylabel('T/T*', fontdict = font_axis_publish)
  plt.xlabel('Radial distance, r (m)', fontdict = font_axis_publish)
  
  plt.plot(sim['x'], sim['Ttra_Ar'], label = 'OpenFOAM (Torres, Pitt, Kinzel)')
  plt.plot(digi_T['r'], digi_T['T_Tstar'], label = 'DAC (Lumpkin, Stewart)')
  plt.plot(rrt, TTt, label = 'Analytical Solution')
  plt.legend()
  plt.yscale('log')
  plt.ylim(bottom = 1e-3, top = 1)
  plt.savefig(curr_dir_path + '/digitized_vs_analytical_T.png')
  plt.close()
  
apis: matplotlib.pyplot.legend pandas.read_csv matplotlib.pyplot.savefig matplotlib.pyplot.yscale matplotlib.pyplot.title matplotlib.pyplot.ylabel matplotlib.pyplot.ylim matplotlib.pyplot.close numpy.sqrt matplotlib.pyplot.plot numpy.linspace matplotlib.pyplot.xlabel