simple A->B->C data fitting

abc.csv

+time,A,C
+0.0,10.024835707650562,0.032384426905034625
+0.5,7.8641593252292585,0.09967474037287323
+1.0,6.144267227527182,0.37455145447449706
+1.5,4.750793515765054,0.7788535105553938
+2.0,3.69089252050547,1.194282946202239
+2.5,2.836933589827485,1.8169000160323985
+3.0,2.1859003968205224,2.4139562376543857
+3.5,1.726450627679802,2.8108338229529912
+4.0,1.3261337109664588,3.3558694842264747
+4.5,1.0727771647059234,3.9119158262286278
+5.0,0.7907646738172374,4.415234455686307
+5.5,0.5863930839496632,4.81729217625314
+6.0,0.5083138804799728,5.245600966261565
+6.5,0.39758515566859043,5.724866592805669
+7.0,0.2961914367338923,6.0174404020417755
+7.5,0.19918526328384978,6.490805091295746
+8.0,0.20033731725936038,6.773366500374303
+8.5,0.12338823735800432,7.080953314425451
+9.0,0.16263995229871547,7.277117637520087
+9.5,0.07105634500037562,7.613644911719786
+10.0,0.04342076809551818,7.734014850536418

fit_abc_data.py

+import matplotlib.pyplot as plt
+import numpy as np
+import pandas as pd
+
+from scipy.optimize import least_squares
+
+import kinetic as kn
+
+#%%
+df = pd.read_csv('abc.csv')
+
+#%%
+plt.plot(df.time, df.A, '.-', label='A')
+plt.plot(df.time, df.C, '.-', label='C')
+
+plt.grid()
+plt.legend()
+plt.show()
+
+#%%
+def residuals(p):
+    global df
+    
+    k1, k2 = p
+    
+    rxns = [kn.reaction('A -> B ; k1'),
+            kn.reaction('B -> C ; k2')]    
+    
+    c0 = {'A': 10.0}
+    kin = {'k1': k1, 'k2': k2}
+    ts = np.array(df.time)
+    
+    spcs, ct = kn.concentration(rxns, c0, kin, ts)
+    
+    rA = df.A - ct[:, spcs['A']]
+    rC = df.C - ct[:, spcs['C']]
+    
+    return np.concatenate([rA, rC])
+
+#%%
+p0 = [1.0, 1.0] # k1, k2
+
+print(residuals(p0))
+
+#%%
+res = least_squares(residuals, p0)
+
+p_opt = res.x
+

generate_abc_data.py

+import matplotlib.pyplot as plt
+import numpy as np
+import pandas as pd
+
+import kinetic as kn
+
+#%%
+rxns = [kn.reaction('A -> B ; k1'),
+        kn.reaction('B -> C ; k2')]
+
+c0 = {'A': 10.0}
+kin = {'k1': 0.5, 'k2': 0.2}
+ts = np.linspace(0.0, 10, 21)
+
+#%%
+spcs, ct = kn.concentration(rxns, c0, kin, ts)
+
+#%% randomize
+np.random.seed(42)
+
+sigma = 0.05
+ct += sigma*np.random.randn(*ct.shape)
+
+#%%
+df = pd.DataFrame({'time': ts,
+                   'A': ct[:, spcs['A']],
+                   'C': ct[:, spcs['C']]})
+
+df.to_csv('abc.csv', index=None)
+
+#%%
+print(spcs)
+for spc in spcs:
+    plt.plot(ts, ct[:, spcs[spc]], '.-', label=spc)
+
+#%%
+
+plt.grid()
+plt.legend()
+plt.show()
+
+# for i in range(len(ts)):
+#    print('%8.3f %12.6e' % (ts[i], ct[i, spcs['S']]))
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