Merge pull request #5 from VlachosGroup/development

Provided examples and updated documentation

Examples/Python Script Examples/App_Ea-Example.py

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+# -*- coding: utf-8 -*-
+"""
+Created on Sun Jun 28 13:18:21 2020
+
+@author: Jane
+"""
+
+import arviz
+from ckbit import app_ea
+
+#Import data
+file = './App_Ea_Data.xlsx'
+
+#Run MAP estimation with standard priors
+map1 = app_ea.MAP(filename=file)
+
+#Run MCMC estimation with standard priors
+m1, m2 = app_ea.MCMC(filename=file,control={'adapt_delta':0.99999999, 'max_treedepth':100}, 
+                      iters=1000, chains=2)
+
+#Generate pairplot
+arviz.plot_pair(m1)
+
+#Run VI estimation with standard priors
+v1, v2 = app_ea.VI(filename=file)
+
+#Process data
+data_dict={'intercept':v1['sampler_params'][0], 
+           'Ea':v1['sampler_params'][1], 
+           'sigma':v1['sampler_params'][2]} 
+
+#Generate pairplot
+arviz.plot_pair(data_dict)
+
+#Run MCMC estimation with specified priors
+p1, p2 = app_ea.MCMC(filename=file,control={'adapt_delta':0.99999999,
+                           'max_treedepth':100}, iters=1000,
+                            priors = ['app_ea ~ normal(90,5)'])

Examples/Python Script Examples/CSTR-Example.py

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+# -*- coding: utf-8 -*-
+"""
+Created on Sun Jun 28 16:15:20 2020
+
+@author: Jane
+"""
+
+import arviz
+from ckbit import cstr
+
+#Import data
+file = './CSTR_Data.xlsx'
+
+#Run MAP estimation with standard priors
+map1 = cstr.MAP(filename=file, pH=True, seed=7)
+
+#Run MCMC estimation with standard priors
+m1, m2 = cstr.MCMC(filename=file, pH=True)
+
+#Generate pairplot
+arviz.plot_pair(m1)
+
+#Run VI estimation with standard priors
+v1, v2 = cstr.VI(filename=file, pH=True,
+                priors = ['A0[1] ~ normal(11,4)',
+                          'Ea[1] ~ normal(95,5)',
+                          'A0[2] ~ normal(17,4)',
+                          'Ea[2] ~ normal(140,5)'])

Examples/Python Script Examples/PFR_Batch-Example.py

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+# -*- coding: utf-8 -*-
+"""
+Created on Sun Jun 28 15:42:04 2020
+
+@author: Jane
+"""
+
+import arviz
+from ckbit import pfr
+
+#Import data
+file = './PFR_Data.xlsx'
+
+#Run MAP estimation with standard priors
+map1 = pfr.MAP(filename=file, pH=True, rel_tol=5E-6, abs_tol=5E-6, max_num_steps=1000)
+
+#Run MCMC estimation with standard priors
+m1, m2 = pfr.MCMC(filename=file, pH=True)
+
+#Generate pairplot
+arviz.plot_pair(m1)
+
+#Run MCMC estimation with specified priors
+p1, p2 = pfr.MCMC(filename=file, pH=True,
+                            priors = ['A0[1] ~ normal(10,5)',
+                                      'Ea[1] ~ normal(100,5)'])

Examples/Python Script Examples/README-for_test_files.txt

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+First, we should say we recommend using the Jupyter notebook named
+Test File - CSTR Example to test CKBIT since it is better displayed 
+and all functions are within a single file. However, we recognize some
+users will be more comfortable with standard Python scripts, so the 
+test files have been provided in this format as well:
+
+Test_file-generate_data.py - File used to generate the simulated data used for testing
+Test_file-MAP.py - file used to test the MAP functionality of CKBIT
+Test_file-MCMC.py - file used to test the MCMC functionality of CKBIT
+Test_file-VI.py - file used to test the VI functionality of CKBIT
+
+Please reference the Word document in this folder named Test File - Outputs Comparison
+to find the examples of the outputs this software should generate when running
+properly. 

Examples/Python Script Examples/Rxn_Ord-Example.py

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+# -*- coding: utf-8 -*-
+"""
+Created on Sun Jun 28 14:23:57 2020
+
+@author: Jane
+"""
+
+import arviz
+from ckbit import rxn_ord
+
+#Import data
+file = './RO_data.xlsx'
+
+#Run MAP estimation with standard priors
+map1 = rxn_ord.MAP(filename=file)
+
+#Run MCMC estimation with standard priors
+m1, m2 = rxn_ord.MCMC(filename=file,control={'adapt_delta':0.99999999, 
+                            'max_treedepth':100}, iters=1000, chains=2)
+
+#Generate pairplot
+arviz.plot_pair(m1)
+
+#Run VI estimation with standard priors
+v1, v2 = rxn_ord.VI(filename=file)
+
+#Process data
+data_dict={'intercept':v1['sampler_params'][0], 
+           'rxn_ord':v1['sampler_params'][1], 
+           'sigma':v1['sampler_params'][2]} 
+
+#Generate pairplot
+arviz.plot_pair(data_dict)
+
+#Run MCMC estimation with specified priors
+p1, p2 = rxn_ord.MCMC(filename=file,control={'adapt_delta':0.99999999,
+                           'max_treedepth':100}, iters=1000,
+                            priors = ['rxn_ord ~ normal(1,0.05)'])

Examples/Python Script Examples/Test_file-MAP.py

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+# -*- coding: utf-8 -*-
+"""
+Created on Sun Jun 28 12:07:40 2020
+
+@author: Jane
+"""
+
+# The MAP estimation. This yields point estimates of the modes of the posterior.    
+# These estimates are the values that fit the model best given the data and priors.
+
+#These output values can be compared against the values provided in the attached Word document   
+#named "Test File - Outputs Comparison" in the same folder as this script.
+
+from ckbit import cstr
+
+#Import data
+file = './CSTR_Data.xlsx'
+
+#Run MAP estimation with standard priors
+map_vals = cstr.MAP(filename=file, pH=True, seed=3)

Examples/Python Script Examples/Test_file-MCMC.py

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+# -*- coding: utf-8 -*-
+"""
+Created on Sun Jun 28 12:07:40 2020
+
+@author: Jane
+"""
+
+# The MCMC estimation. This yields estimates of the posterior distributions of   
+# each parameter being estimated.
+
+#These output values can be compared against the values provided in the attached Word document   
+#named "Test File - Outputs Comparison" in the same folder as this script.
+
+from ckbit import cstr
+import arviz 
+
+#Import data
+file = './CSTR_Data.xlsx'
+
+#Run MCMC estimation with standard priors
+m1, m2 = cstr.MCMC(filename=file, pH=True, seed=3, iters=10000)
+
+# There are convergence checks to ensure that these samples can be relied upon.   
+# These checks are discussed in detail in the published article. This run passes all    
+# those checks, and offers a successful inference we can trust.
+
+# It is important to visualize the correlation that exists between the samples of    
+# the parameters, which we can accomplish with a pair plot.
+
+#Generate pairplot
+arviz.plot_pair(m1)

Examples/Python Script Examples/Test_file-VI.py

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+# -*- coding: utf-8 -*-
+"""
+Created on Sun Jun 28 12:07:40 2020
+
+@author: Jane
+"""
+
+# The VI estimation. This yields estimates of the posterior distributions of   
+# each parameter being estimated, but using the VI technique instead of the MCMC.     
+# VI is better than MCMC at generating a large number of samples, but is a less      
+# robust technique. It is still in its experimental implementation phase.   
+# We demonstrate VI estimation below.  
+
+# We can also specify prior distributions and run inference with them. The following   
+# example shows the implementation of the follow prior distributions:   
+# For the A0 term of rxn 1, a normal distribution with a mean of 11 and standard deviation of 4.   
+# For the Ea term of rxn 1, a normal distribution with a mean of 95 and standard deviation of 5.   
+# For the Ea term of rxn 1, a normal distribution with a mean of 0.5 and standard deviation of 0.1.   
+# For the Ea term of rxn 2, a normal distribution with a mean of 140 and standard deviation of 5.   
+# All prior distribution specification must follow Stan's implementation forms:     
+# https://mc-stan.org/docs/2_23/functions-reference/unbounded-continuous-distributions.html
+
+#These output values can be compared against the values provided in the attached Word document   
+#named "Test File - Outputs Comparison" in the same folder as this script.
+
+from ckbit import cstr
+
+#Import data
+file = './CSTR_Data.xlsx'
+
+#Run VI estimation with standard priors
+v1, v2 = cstr.VI(filename=file, pH=True, seed=3, output_samples=10000,
+                priors = ['A0[1] ~ normal(11,4)',
+                          'Ea[1] ~ normal(95,5)',
+                          'A0[2] ~ normal(17,4)',
+                          'Ea[2] ~ normal(140,5)'])

Examples/Python Script Examples/Test_file-generate_data.py

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+# -*- coding: utf-8 -*-
+"""
+Created on Sun Jun 28 12:07:40 2020
+
+@author: Jane
+"""
+
+#First, we generate the CSTR data with experimental noise added to the concentrations.   
+#The smooth lines are the unperturbed data, and the data points are the noisy    
+#measurements we use as our data points.
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+np.random.seed(40)
+HMFinit = 100
+LFinit = 50
+Huinit = 50
+taus = np.linspace (0,20,11)
+Hconc = 0.1
+T = [423,448]
+R = 8.31446261815324*(1/1000) #units of kJ/(mol*K)
+
+#True params
+sigma = 5
+A0HLF = 11.31
+A0HHu = 16.69
+EaHLF = 94.72
+EaHHu = 141.94
+
+try:
+    del cHMF0,cHMF1,cLF0,cLF1,cHu0,cHu1
+except:
+    pass
+
+size0 = len(taus)
+cHMF0 = np.linspace(10,20,size0)
+cHMF1 = np.linspace(10,20,size0)
+cLF0 = np.linspace(10,20,size0)
+cLF1 = np.linspace(10,20,size0)
+cHu0 = np.linspace(10,20,size0)
+cHu1 = np.linspace(10,20,size0)
+total0 = np.linspace(10,20,size0)
+total1 = np.linspace(10,20,size0)
+kHLF0 = (10**A0HLF)*np.exp(-EaHLF/(R*T[0]))
+kHLF1 = (10**A0HLF)*np.exp(-EaHLF/(R*T[1]))
+kHHu0 = (10**A0HHu)*np.exp(-EaHHu/(R*T[0]))
+kHHu1 = (10**A0HHu)*np.exp(-EaHHu/(R*T[1]))
+#clean data
+for i in range(size0):
+    kHLF0 = (10**A0HLF)*np.exp(-EaHLF/(R*T[0]))
+    kHLF1 = (10**A0HLF)*np.exp(-EaHLF/(R*T[1]))
+    kHHu0 = (10**A0HHu)*np.exp(-EaHHu/(R*T[0]))
+    kHHu1 = (10**A0HHu)*np.exp(-EaHHu/(R*T[1]))
+    cHMF0[i] = HMFinit/(1+(Hconc*taus[i]*(kHLF0+kHHu0)))
+    cHMF1[i] = HMFinit/(1+(Hconc*taus[i]*(kHLF1+kHHu1)))
+    cLF0[i] = LFinit+(Hconc*taus[i]*kHLF0*cHMF0[i])
+    cLF1[i] = LFinit+(Hconc*taus[i]*kHLF1*cHMF1[i])
+    cHu0[i] = Huinit+(Hconc*taus[i]*kHHu0*cHMF0[i])
+    cHu1[i] = Huinit+(Hconc*taus[i]*kHHu1*cHMF1[i])
+
+f, ax = plt.subplots(1)
+ax.plot(taus,cHMF0, label='HMF, 150C')
+ax.plot(taus,cHMF1, label='HMF, 175C')
+ax.plot(taus,cLF0, label='LA+FA, 150C')
+ax.plot(taus,cLF1, label='LA+FA, 175C')
+ax.plot(taus,cHu0, label='Humins, 150C')
+ax.plot(taus,cHu1, label='Humins, 175C')
+
+
+for i in range(size0):
+    cHMF0[i] = cHMF0[i]+np.random.normal(0,sigma,1)
+    cHMF1[i] = cHMF1[i]+np.random.normal(0,sigma,1)
+    cLF0[i] = cLF0[i]+np.random.normal(0,sigma,1)
+    cLF1[i] = cLF1[i]+np.random.normal(0,sigma,1)
+    cHu0[i] = cHu0[i]+np.random.normal(0,sigma,1)
+    cHu1[i] = cHu1[i]+np.random.normal(0,sigma,1)
+
+cHMF0[0] = HMFinit
+cHMF1[0] = HMFinit
+cLF0[0] = LFinit
+cLF1[0] = LFinit
+cHu0[0] = Huinit
+cHu1[0] = Huinit
+
+for i in range (len(cHMF0)): 
+    cHMF0[i] = max(0,cHMF0[i])
+    cHMF1[i] = max(0,cHMF1[i])
+    cLF0[i] = max(0,cLF0[i])
+    cLF1[i] = max(0,cLF1[i])
+    cHu0[i] = max(0,cHu0[i])
+    cHu1[i] = max(0,cHu1[i])
+
+
+ax.scatter(taus,cHMF0)
+ax.scatter(taus,cHMF1)
+ax.scatter(taus,cLF0)
+ax.scatter(taus,cLF1)
+ax.scatter(taus,cHu0)
+ax.scatter(taus,cHu1)
+ax.set_xlabel('Residence Time (min)')
+ax.set_ylabel('Noisy CSTR Outlet Concs')
+ax.set_title('Noisy CSTR Outlet Concs vs. Residence Time')
+ax.legend()
+plt.show()