In [15]:

    

%matplotlib notebook


    

In [16]:

    

import os, sys
sys.path.append(os.path.abspath('../../main/python'))


    

In [17]:

    

import collections as col

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd

from thalesians.tsa.distrs import NormalDistr as N
import thalesians.tsa.evaluation as evaluation
import thalesians.tsa.filtering as filtering
import thalesians.tsa.filtering.kalman as kalman
import thalesians.tsa.filtering.visual as visual
import thalesians.tsa.numpyutils as npu
import thalesians.tsa.optimization as optimization
import thalesians.tsa.optimization.visual as optvisual
import thalesians.tsa.processes as proc
import thalesians.tsa.randomness as rnd
import thalesians.tsa.simulation as sim

import importlib
importlib.reload(optvisual)
importlib.reload(npu)
importlib.reload(optimization)
importlib.reload(filtering)


    

    
Out[17]:





<module 'thalesians.tsa.filtering' from 'S:\\dev\\tsa\\src\\main\\python\\thalesians\\tsa\\filtering\\__init__.py'>

In [18]:

    

npu.init_warnings()


    

In [19]:

    

rnd.random_state(np.random.RandomState(seed=42), force=True);


    

In [20]:

    

X = proc.OrnsteinUhlenbeckProcess.create_multiscale_from_vol(transition_vector=[10., 10.], mean=15., vol=[[10., .0], [.0, 1.]])


    

In [21]:

    

X.transition


    

    
Out[21]:





array([[ 10.,   0.],
       [-10.,  10.]])

In [22]:

    

em = sim.EulerMaruyama(process=X, times=sim.xtimes(start=0., stop=5., step=.002))
df = sim.run(em)
plt.plot(df);


    

In [9]:

    

filtr = filtering.kalman.KalmanFilter(time=df.index[0], state_distr=N(mean=npu.col(0., 0.), cov=1000. * np.eye(2)), process=X)
state_observable = filtr.create_identity_observable(X)
first_observable = filtr.create_observable(kalman.KalmanFilterObsModel.create([[1., 0.]]), X)
last_observable = filtr.create_observable(kalman.KalmanFilterObsModel.create([[0., 1.]]), X)


    

In [10]:

    

run_df = filtering.run(observable=last_observable, obss=1, df=df, return_df=True)


    

In [11]:

    

run_df.df


    

    
Out[11]:







  

    

      

      
time
      
filter_name
      
filter_type
      
observable_name
      
accepted
      
obs_mean
      
obs_cov
      
predicted_obs_mean
      
predicted_obs_cov
      
cross_cov
      
innov_mean
      
innov_cov
      
prior_state_mean
      
prior_state_cov
      
posterior_state_mean
      
posterior_state_cov
      
true_value
      
log_likelihood
      
gain
    
  
  

    

      
0
      
0.000
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
None
      
None
      
NaN
      
NaN
      
NaN
      
NaN
      
None
      
NaN
      
NaN
      
[[0.0], [0.0]]
      
[[1000.0, 0.0], [0.0, 1000.0]]
      
[[0.0], [0.0]]
      
[[1000.0, 0.0], [0.0, 1000.0]]
      
None
      
NaN
      
None
    
    

      
1
      
0.000
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.000000
      
0.0
      
0.000000
      
1000.000000
      
[[0.0, 1000.0]]
      
0.000000
      
1000.000000
      
[[0.0], [0.0]]
      
[[1000.0, 0.0], [0.0, 1000.0]]
      
[[0.0], [0.0]]
      
[[1000.0, 0.0], [0.0, 1000.0]]
      
None
      
-4.372816
      
[[0.0], [1.0]]
    
    

      
2
      
0.002
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
-0.018550
      
0.0
      
0.005881
      
1.524274
      
[[38.0536803019, 1.52427428591]]
      
-0.024431
      
1.524274
      
[[0.297019900399], [0.00588138808219]]
      
[[960.985491957, 38.0536803019], [38.053680301...
      
[[0.297019900399], [0.00588138808219]]
      
[[960.985491957, 38.0536803019], [38.053680301...
      
None
      
-1.129894
      
[[24.9651133353], [1.0]]
    
    

      
3
      
0.004
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.207413
      
0.0
      
-0.024088
      
0.033933
      
[[0.421315561188, 0.0339327889712]]
      
0.231502
      
0.033933
      
[[-0.00969899966277], [-0.024088236855]]
      
[[10.7369221599, 0.421315561188], [0.421315561...
      
[[-0.00969899966277], [-0.024088236855]]
      
[[10.7369221599, 0.421315561188], [0.421315561...
      
None
      
-0.016945
      
[[12.4161783915], [1.0]]
    
    

      
4
      
0.006
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.211758
      
0.0
      
0.316364
      
0.025697
      
[[0.213363549245, 0.0256973375212]]
      
-0.104606
      
0.025697
      
[[3.10496100611], [0.31636380678]]
      
[[5.4859605661, 0.213363549245], [0.2133635492...
      
[[3.10496100611], [0.31636380678]]
      
[[5.4859605661, 0.213363549245], [0.2133635492...
      
None
      
0.698837
      
[[8.30294379986], [1.0]]
    
    

      
5
      
0.008
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.357234
      
0.0
      
0.296151
      
0.022998
      
[[0.145201955233, 0.0229979575393]]
      
0.061083
      
0.022998
      
[[2.48916042052], [0.296150799066]]
      
[[3.76482351635, 0.145201955233], [0.145201955...
      
[[2.48916042052], [0.296150799066]]
      
[[3.76482351635, 0.145201955233], [0.145201955...
      
None
      
0.886117
      
[[6.31368916064], [1.0]]
    
    

      
6
      
0.010
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.505951
      
0.0
      
0.460704
      
0.021692
      
[[0.112237444193, 0.0216924754345]]
      
0.045247
      
0.021692
      
[[3.11491588387], [0.460704275713]]
      
[[2.93244214235, 0.112237444193], [0.112237444...
      
[[3.11491588387], [0.460704275713]]
      
[[2.93244214235, 0.112237444193], [0.112237444...
      
None
      
0.949268
      
[[5.17402656657], [1.0]]
    
    

      
7
      
0.012
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.515241
      
0.0
      
0.621998
      
0.020945
      
[[0.0933517674056, 0.0209445525227]]
      
-0.106757
      
0.020945
      
[[3.57972924533], [0.621997921064]]
      
[[2.45556306551, 0.0933517674056], [0.09335176...
      
[[3.57972924533], [0.621997921064]]
      
[[2.45556306551, 0.0933517674056], [0.09335176...
      
None
      
0.741922
      
[[4.45709056349], [1.0]]
    
    

      
8
      
0.014
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.331819
      
0.0
      
0.621408
      
0.020474
      
[[0.0814712145983, 0.0204740511079]]
      
-0.289589
      
0.020474
      
[[3.33946154134], [0.621408058448]]
      
[[2.15556920673, 0.0814712145983], [0.08147121...
      
[[3.33946154134], [0.621408058448]]
      
[[2.15556920673, 0.0814712145983], [0.08147121...
      
None
      
-1.022636
      
[[3.9792425138], [1.0]]
    
    

      
9
      
0.016
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.351440
      
0.0
      
0.409591
      
0.020160
      
[[0.073552657065, 0.0201604552186]]
      
-0.058150
      
0.020160
      
[[2.44083028939], [0.409590589302]]
      
[[1.95561903027, 0.073552657065], [0.073552657...
      
[[2.44083028939], [0.409590589302]]
      
[[1.95561903027, 0.073552657065], [0.073552657...
      
None
      
0.949214
      
[[3.64836290984], [1.0]]
    
    

      
10
      
0.018
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.466853
      
0.0
      
0.430055
      
0.019943
      
[[0.0680695559363, 0.0199433098651]]
      
0.036798
      
0.019943
      
[[2.4815663255], [0.430055420045]]
      
[[1.81716615755, 0.0680695559363], [0.06806955...
      
[[2.4815663255], [0.430055420045]]
      
[[1.81716615755, 0.0680695559363], [0.06806955...
      
None
      
1.004544
      
[[3.41315240032], [1.0]]
    
    

      
11
      
0.020
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.338144
      
0.0
      
0.555635
      
0.019789
      
[[0.0641718149005, 0.0197889489779]]
      
-0.217491
      
0.019789
      
[[2.85255681121], [0.555634892748]]
      
[[1.7187449483, 0.0641718149005], [0.064171814...
      
[[2.85255681121], [0.555634892748]]
      
[[1.7187449483, 0.0641718149005], [0.064171814...
      
None
      
-0.152794
      
[[3.24281067036], [1.0]]
    
    

      
12
      
0.022
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.367940
      
0.0
      
0.414120
      
0.019677
      
[[0.061349033077, 0.0196771593277]]
      
-0.046180
      
0.019677
      
[[2.40177536587], [0.414120272713]]
      
[[1.64746735495, 0.061349033077], [0.061349033...
      
[[2.40177536587], [0.414120272713]]
      
[[1.64746735495, 0.061349033077], [0.061349033...
      
None
      
0.991020
      
[[3.11777894641], [1.0]]
    
    

      
13
      
0.024
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.272432
      
0.0
      
0.447039
      
0.019595
      
[[0.0592770964012, 0.0195951051377]]
      
-0.174607
      
0.019595
      
[[2.51010847078], [0.447038569864]]
      
[[1.59514922728, 0.0592770964012], [0.05927709...
      
[[2.51010847078], [0.447038569864]]
      
[[1.59514922728, 0.0592770964012], [0.05927709...
      
None
      
0.269361
      
[[3.02509713445], [1.0]]
    
    

      
14
      
0.026
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.397776
      
0.0
      
0.344565
      
0.019534
      
[[0.0577412394258, 0.0195342811263]]
      
0.053211
      
0.019534
      
[[2.23968138022], [0.344565474353]]
      
[[1.55636755878, 0.0577412394258], [0.05774123...
      
[[2.23968138022], [0.344565474353]]
      
[[1.55636755878, 0.0577412394258], [0.05774123...
      
None
      
0.976381
      
[[2.95589272278], [1.0]]
    
    

      
15
      
0.028
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.553465
      
0.0
      
0.481107
      
0.019489
      
[[0.0565944332063, 0.019488864557]]
      
0.072358
      
0.019489
      
[[2.64652371426], [0.481107263145]]
      
[[1.52740974607, 0.0565944332063], [0.05659443...
      
[[2.64652371426], [0.481107263145]]
      
[[1.52740974607, 0.0565944332063], [0.05659443...
      
None
      
0.915693
      
[[2.90393691437], [1.0]]
    
    

      
16
      
0.030
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.602373
      
0.0
      
0.648535
      
0.019455
      
[[0.0557334585548, 0.0194547676763]]
      
-0.046163
      
0.019455
      
[[3.09710070807], [0.648535402541]]
      
[[1.50566941865, 0.0557334585548], [0.05573345...
      
[[3.09710070807], [0.648535402541]]
      
[[1.50566941865, 0.0557334585548], [0.05573345...
      
None
      
0.996125
      
[[2.86477122122], [1.0]]
    
    

      
17
      
0.032
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.936020
      
0.0
      
0.699726
      
0.019429
      
[[0.0550844325836, 0.0194290645258]]
      
0.236294
      
0.019429
      
[[3.20316711718], [0.699725910763]]
      
[[1.48928097203, 0.0550844325836], [0.05508443...
      
[[3.20316711718], [0.699725910763]]
      
[[1.48928097203, 0.0550844325836], [0.05508443...
      
None
      
-0.385337
      
[[2.83515619141], [1.0]]
    
    

      
18
      
0.034
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.864957
      
0.0
      
1.055547
      
0.019410
      
[[0.0545936734028, 0.01940962916]]
      
-0.190590
      
0.019410
      
[[4.09342516], [1.05554722896]]
      
[[1.47688889375, 0.0545936734028], [0.05459367...
      
[[4.09342516], [1.05554722896]]
      
[[1.47688889375, 0.0545936734028], [0.05459367...
      
None
      
0.116317
      
[[2.81271079178], [1.0]]
    
    

      
19
      
0.036
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.784443
      
0.0
      
0.975014
      
0.019395
      
[[0.0542217242267, 0.0193948989857]]
      
-0.190571
      
0.019395
      
[[3.78392964241], [0.975013825497]]
      
[[1.4674968671, 0.0542217242267], [0.054221724...
      
[[3.78392964241], [0.975013825497]]
      
[[1.4674968671, 0.0542217242267], [0.054221724...
      
None
      
0.116175
      
[[2.79566932865], [1.0]]
    
    

      
20
      
0.038
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.632382
      
0.0
      
0.885771
      
0.019384
      
[[0.0539393252376, 0.0193837152365]]
      
-0.253389
      
0.019384
      
[[3.48379893151], [0.885770708519]]
      
[[1.46036605729, 0.0539393252376], [0.05393932...
      
[[3.48379893151], [0.885770708519]]
      
[[1.46036605729, 0.0539393252376], [0.05393932...
      
None
      
-0.603459
      
[[2.78271345712], [1.0]]
    
    

      
21
      
0.040
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.788624
      
0.0
      
0.721332
      
0.019375
      
[[0.0537246297624, 0.019375212726]]
      
0.067292
      
0.019375
      
[[3.02068858216], [0.721331730238]]
      
[[1.45494481763, 0.0537246297624], [0.05372462...
      
[[3.02068858216], [0.721331730238]]
      
[[1.45494481763, 0.0537246297624], [0.05372462...
      
None
      
0.936085
      
[[2.77285367249], [1.0]]
    
    

      
22
      
0.042
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
0.920334
      
0.0
      
0.888085
      
0.019369
      
[[0.053561240434, 0.019368742075]]
      
0.032250
      
0.019369
      
[[3.44079162627], [0.888084675771]]
      
[[1.45081910093, 0.053561240434], [0.053561240...
      
[[3.44079162627], [0.888084675771]]
      
[[1.45081910093, 0.053561240434], [0.053561240...
      
None
      
1.026260
      
[[2.76534429683], [1.0]]
    
    

      
23
      
0.044
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
1.005792
      
0.0
      
1.027157
      
0.019364
      
[[0.0534368004091, 0.0193638139199]]
      
-0.021365
      
0.019364
      
[[3.75709473269], [1.02715702211]]
      
[[1.4476768866, 0.0534368004091], [0.053436800...
      
[[3.75709473269], [1.02715702211]]
      
[[1.4476768866, 0.0534368004091], [0.053436800...
      
None
      
1.041450
      
[[2.75962166494], [1.0]]
    
    

      
24
      
0.046
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
1.038330
      
0.0
      
1.115792
      
0.019360
      
[[0.0533419690294, 0.0193600583456]]
      
-0.077462
      
0.019360
      
[[3.92192805016], [1.11579197819]]
      
[[1.44528231524, 0.0533419690294], [0.05334196...
      
[[3.92192805016], [1.11579197819]]
      
[[1.44528231524, 0.0533419690294], [0.05334196...
      
None
      
0.898365
      
[[2.75525869175], [1.0]]
    
    

      
25
      
0.048
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
1.290135
      
0.0
      
1.147456
      
0.019357
      
[[0.0532696689451, 0.0193571950704]]
      
0.142679
      
0.019357
      
[[3.93208655019], [1.14745603351]]
      
[[1.44345667786, 0.0532696689451], [0.05326966...
      
[[3.93208655019], [1.14745603351]]
      
[[1.44345667786, 0.0532696689451], [0.05326966...
      
None
      
0.527571
      
[[2.75193119413], [1.0]]
    
    

      
26
      
0.050
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
1.154234
      
0.0
      
1.413309
      
0.019355
      
[[0.0532145280246, 0.0193550113437]]
      
-0.259075
      
0.019355
      
[[4.53611499018], [1.4133093184]]
      
[[1.44206432367, 0.0532145280246], [0.05321452...
      
[[4.53611499018], [1.4133093184]]
      
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27
      
0.052
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[4.04511836098], [1.26329182999]]
      
[[1.44100214355, 0.0531724628737], [0.05317246...
      
None
      
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28
      
0.054
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[4.15553245322], [1.33444806752]]
      
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None
      
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29
      
0.056
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[4.65074138251], [1.56054138261]]
      
[[1.43957318948, 0.0531158725008], [0.05311587...
      
None
      
0.659112
      
[[2.74484967958], [1.0]]
    
    

      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
    
    

      
2472
      
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KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[14.2801601752], [13.9351631172]]
      
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None
      
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[[2.74121009734], [1.0]]
    
    

      
2473
      
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KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[14.327989042], [13.9623082902]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
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[[2.74121009734], [1.0]]
    
    

      
2474
      
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KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[14.2090045747], [13.9243667239]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
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[[2.74121009734], [1.0]]
    
    

      
2475
      
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KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[14.7453924319], [14.1426600391]]
      
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None
      
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[[2.74121009734], [1.0]]
    
    

      
2476
      
4.950
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[14.4404409647], [14.0432698535]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
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[[2.74121009734], [1.0]]
    
    

      
2477
      
4.952
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[14.7735168692], [14.1869533579]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
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[[2.74121009734], [1.0]]
    
    

      
2478
      
4.954
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[15.3387619072], [14.4327652754]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
0.458429
      
[[2.74121009734], [1.0]]
    
    

      
2479
      
4.956
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[15.7398344849], [14.6301199506]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
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[[2.74121009734], [1.0]]
    
    

      
2480
      
4.958
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[15.2756466781], [14.4947941901]]
      
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None
      
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[[2.74121009734], [1.0]]
    
    

      
2481
      
4.960
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[15.7664092911], [14.7223934771]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
0.863473
      
[[2.74121009734], [1.0]]
    
    

      
2482
      
4.962
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[15.9817287518], [14.8545779146]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
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[[2.74121009734], [1.0]]
    
    

      
2483
      
4.964
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[0.0530368656447, 0.019347975442]]
      
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[[15.6119276455], [14.759232076]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
0.968762
      
[[2.74121009734], [1.0]]
    
    

      
2484
      
4.966
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[0.0530368656447, 0.019347975442]]
      
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[[15.7538030361], [14.8535897317]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
1.038170
      
[[2.74121009734], [1.0]]
    
    

      
2485
      
4.968
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[15.673125632], [14.8624769193]]
      
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None
      
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[[2.74121009734], [1.0]]
    
    

      
2486
      
4.970
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
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[[16.0575547946], [15.0519810686]]
      
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None
      
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[[2.74121009734], [1.0]]
    
    

      
2487
      
4.972
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
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[[16.4668406535], [15.2618736521]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
0.936109
      
[[2.74121009734], [1.0]]
    
    

      
2488
      
4.974
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
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[[16.2565884533], [15.2365739592]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
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[[2.74121009734], [1.0]]
    
    

      
2489
      
4.976
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[15.4235704518], [14.9550999995]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
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[[2.74121009734], [1.0]]
    
    

      
2490
      
4.978
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
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[[0.0530368656447, 0.019347975442]]
      
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[[14.9028982412], [14.7698328169]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
1.053344
      
[[2.74121009734], [1.0]]
    
    

      
2491
      
4.980
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
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[[0.0530368656447, 0.019347975442]]
      
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[[14.9139987527], [14.7787336991]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
-1.052623
      
[[2.74121009734], [1.0]]
    
    

      
2492
      
4.982
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
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[[14.1486121234], [14.4793974729]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
0.317730
      
[[2.74121009734], [1.0]]
    
    

      
2493
      
4.984
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
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[[14.618893258], [14.6468520435]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
1.050795
      
[[2.74121009734], [1.0]]
    
    

      
2494
      
4.986
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
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[[14.5982222881], [14.6346977688]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
-0.371001
      
[[2.74121009734], [1.0]]
    
    

      
2495
      
4.988
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
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[[15.2370521344], [14.8839965894]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
1.051423
      
[[2.74121009734], [1.0]]
    
    

      
2496
      
4.990
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
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[[0.0530368656447, 0.019347975442]]
      
0.315943
      
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[[15.2572752911], [14.9076437608]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
-1.525950
      
[[2.74121009734], [1.0]]
    
    

      
2497
      
4.992
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
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[[0.0530368656447, 0.019347975442]]
      
0.056336
      
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[[16.1010974524], [15.2584260614]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
None
      
0.971627
      
[[2.74121009734], [1.0]]
    
    

      
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KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
KalmanObservable_2145234409120
      
True
      
15.348944
      
0.0
      
15.351158
      
0.019348
      
[[0.0530368656447, 0.019347975442]]
      
-0.002214
      
0.019348
      
[[16.2306661216], [15.3511580454]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
[[16.2306661216], [15.3511580454]]
      
[[1.43757820052, 0.0530368656447], [0.05303686...
      
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1.053519
      
[[2.74121009734], [1.0]]
    
    

      
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4.996
      
KalmanFilter_2145234408672
      
<class 'thalesians.tsa.filtering.kalman.Kalman...
      
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<class 'thalesians.tsa.filtering.kalman.Kalman...
      
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2502 rows × 19 columns

In [12]:

    

sp = visual.StatePlot(plot_obs_results=False)
sp.process_run_df(run_df.df)
sp.ax.set_ylim((-5, 25));


    

In [15]:

    

op = visual.ObsPlot();
op.process_run_df(run_df.df[1:])


    

In [16]:

    

ep = visual.InnovPlot()
ep.process_run_df(run_df.df[1:])
ep.ax.set_ylim((-1, 1));


    

In [19]:

    

llp = visual.ErrorPlot();
llp.process_run_df(run_df.df[1:])


    

In [18]:

    

llp = visual.LogLikelihoodPlot(cumulative=True);
llp.process_run_df(run_df.df)


    

In [20]:

    

llp = visual.LogLikelihoodPlot(cumulative=False)
llp.process_run_df(run_df.df)


    

In [21]:

    

cp = visual.CUSUMPlot()
cp.process_run_df(run_df.df)


    

In [22]:

    

gp = visual.GainPlot(matrix_norm=False)
gp.process_run_df(run_df.df)


    

In [23]:

    

gp = visual.GainPlot(matrix_norm=True)
gp.process_run_df(run_df.df)


    

In [21]:

    

filtr = filtering.kalman.KalmanFilter(time=df.index[0], state_distr=N(mean=npu.col(0., 0.), cov=1000. * np.eye(2)), process=X)
state_observable = filtr.create_identity_observable(X)
first_observable = filtr.create_observable(kalman.KalmanFilterObsModel.create([[1., 0.]]), X)
last_observable = filtr.create_observable(kalman.KalmanFilterObsModel.create([[0., 1.]]), X)


    

In [22]:

    

ts, priors, posteriors, prior_values, posterior_values = [], [], [], [], []
for i, t in enumerate(df.index):
    ts.append(t)
    priors.append(state_observable.predict(t))
    prior_values.append(priors[-1].distr.mean.flatten())
    process_value = df.iloc[i].values
    last_observable.observe(N(process_value[-1], 0.), t)
    posteriors.append(state_observable.predict(t))
    posterior_values.append(posteriors[-1].distr.mean.flatten())
priors_df = pd.DataFrame(data=priors, index=ts)
posteriors_df = pd.DataFrame(data=posteriors, index=ts)
prior_values_df = pd.DataFrame(data=prior_values, index=ts)
posterior_values_df = pd.DataFrame(data=posterior_values, index=ts)


    

In [23]:

    

plt.figure()
plt.plot(posterior_values_df);


    

In [24]:

    

plt.figure()
plt.plot(df);


    

In [30]:

    

len(posterior_values_df[0].values)


    

    
Out[30]:





2501

In [34]:

    

len(df[0].values)


    

    
Out[34]:





2501

In [40]:

    

plt.plot(df[0].values, posterior_values_df[0].values, 'x')


    

    
Out[40]:





[<matplotlib.lines.Line2D at 0x1f3009ce438>]






    

In [9]:

    

def filter_run(mu, sigma1, sigma2, theta1, theta2):
    X = proc.OrnsteinUhlenbeckProcess.create_multiscale_from_vol(transition_vector=[theta1, theta2], mean=mu, vol=[[sigma1, .0], [.0, sigma2]])
    filtr = filtering.kalman.KalmanFilter(time=df.index[0], state_distr=N(mean=npu.col(0., 0.), cov=1000. * np.eye(2)), process=X)
    state_observable = filtr.create_identity_observable(X)
    first_observable = filtr.create_observable(kalman.KalmanFilterObsModel.create([[1., 0.]]), X)
    last_observable = filtr.create_observable(kalman.KalmanFilterObsModel.create([[0., 1.]]), X)
    filter_run_result = filtering.run(observable=last_observable, obss=1, df=df)
    return npu.to_scalar(filter_run_result.cumulative_log_likelihood if filter_run_result.cumulative_log_likelihood is not None else np.nan)


    

In [10]:

    

filter_run(mu=20., sigma1=10., sigma2=3., theta1=20., theta2=20.)


    

    
Out[10]:





2186.0014159249545

In [11]:

    

param_ranges = col.OrderedDict((
        ('mu', np.linspace(0., 40., 5)),
        ('sigma1', np.linspace(1., 20., 5)),
        ('sigma2', np.linspace(1., 20., 5)),
        ('theta1', np.linspace(.1, 30., 5)),
        ('theta2', np.linspace(.1, 30., 5))))


    

In [12]:

    

result = optimization.grid_search(
        filter_run, param_ranges,
        evaluator=evaluation.IPyParallelEvaluator(),
        optimization_id='OU process calibration: Kalman filter maximum likelihood')


    

In [13]:

    

result.evaluation_statuses[10]


    

    
Out[13]:





Status(ready=True, work=Work(work_id=11, func=<function filter_run at 0x000001D14DE21620>, args=[], kwargs=OrderedDict([('mu', 0.0), ('sigma1', 1.0), ('sigma2', 1.0), ('theta1', 15.049999999999999), ('theta2', 0.10000000000000001)]), call_count=1, repeat_count=1, info={'param_ranges': OrderedDict([('mu', array([  0.,  10.,  20.,  30.,  40.])), ('sigma1', array([  1.  ,   5.75,  10.5 ,  15.25,  20.  ])), ('sigma2', array([  1.  ,   5.75,  10.5 ,  15.25,  20.  ])), ('theta1', array([  0.1  ,   7.575,  15.05 ,  22.525,  30.   ])), ('theta2', array([  0.1  ,   7.575,  15.05 ,  22.525,  30.   ]))]), 'param_names': ['mu', 'sigma1', 'sigma2', 'theta1', 'theta2'], 'param_value_indices': [0, 0, 0, 2, 0], 'optimization_id': 'OU process calibration: Kalman filter maximum likelihood', 'work_id': 11}), result=Result(work_id=11, func=<function filter_run at 0x000001D14F994730>, args=[], kwargs=OrderedDict([('mu', 0.0), ('sigma1', 1.0), ('sigma2', 1.0), ('theta1', 15.049999999999999), ('theta2', 0.10000000000000001)]), call_count=1, repeat_count=1, info={'param_ranges': OrderedDict([('mu', array([  0.,  10.,  20.,  30.,  40.])), ('sigma1', array([  1.  ,   5.75,  10.5 ,  15.25,  20.  ])), ('sigma2', array([  1.  ,   5.75,  10.5 ,  15.25,  20.  ])), ('theta1', array([  0.1  ,   7.575,  15.05 ,  22.525,  30.   ])), ('theta2', array([  0.1  ,   7.575,  15.05 ,  22.525,  30.   ]))]), 'param_names': ['mu', 'sigma1', 'sigma2', 'theta1', 'theta2'], 'param_value_indices': [0, 0, 0, 2, 0], 'optimization_id': 'OU process calibration: Kalman filter maximum likelihood', 'work_id': 11}, evaluation_id="c8052c87895248a4b3be0c02cf82a185", result=3220.2841131338223, exception=None, start_datetime=2018-04-26 23:23:45.362055, seconds_per_call=[5.097369587871493], hostname="DESKTOP-EFQ7TT8", pid=10656, thread_id=10656))

In [14]:

    

optvisual.visualize_grid_search(result, refresh_until_ready=True, aggregate_func=np.nanmax, empty_aggregate=np.nan);


    

    















    












    




---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
<ipython-input-14-c82eb26a56cd> in <module>()
----> 1 optvisual.visualize_grid_search(result, refresh_until_ready=True, aggregate_func=np.nanmax, empty_aggregate=np.nan);

S:\dev\tsa\src\main\python\thalesians\tsa\optimization\visual.py in visualize_grid_search(grid_search_result, aggregate_func, empty_aggregate, fig, title, refresh_until_ready)
     80         for i1 in range(len(param_names)):
     81             for i2 in range(i1):
---> 82                 new_data = _aggregate(aggregate_func, datas[(i1, i2)], empty_aggregate)
     83                 heatmaps[(i1, i2)].set_data(new_data)
     84                 heatmaps[(i1, i2)].autoscale()

S:\dev\tsa\src\main\python\thalesians\tsa\optimization\visual.py in _aggregate(aggregate_func, data, empty_aggregate)
     13 def _aggregate(aggregate_func, data, empty_aggregate):
     14     if empty_aggregate != 'none':
---> 15         return npu.apply(lambda x: empty_aggregate if len(x) == 0 else aggregate_func(x), data)
     16     else:
     17         return npu.apply(aggregate_func, data)

S:\dev\tsa\src\main\python\thalesians\tsa\numpyutils.py in apply(func, arg, dtype)
     14 def apply(func, arg, dtype=np.dtype('float64')):
     15     result = np.empty(np.shape(arg), dtype=dtype)
---> 16     result.flat[:] = [func(x) for x in arg.flat[:]]
     17     return result
     18 

S:\dev\tsa\src\main\python\thalesians\tsa\numpyutils.py in <listcomp>(.0)
     14 def apply(func, arg, dtype=np.dtype('float64')):
     15     result = np.empty(np.shape(arg), dtype=dtype)
---> 16     result.flat[:] = [func(x) for x in arg.flat[:]]
     17     return result
     18 

S:\dev\tsa\src\main\python\thalesians\tsa\optimization\visual.py in <lambda>(x)
     13 def _aggregate(aggregate_func, data, empty_aggregate):
     14     if empty_aggregate != 'none':
---> 15         return npu.apply(lambda x: empty_aggregate if len(x) == 0 else aggregate_func(x), data)
     16     else:
     17         return npu.apply(aggregate_func, data)

C:\Programs\Win64\Anaconda\V4.4.0_3.6\lib\site-packages\numpy\lib\nanfunctions.py in nanmax(a, axis, out, keepdims)
    351     else:
    352         # Slow, but safe for subclasses of ndarray
--> 353         a, mask = _replace_nan(a, -np.inf)
    354         res = np.amax(a, axis=axis, out=out, **kwargs)
    355         if mask is None:

C:\Programs\Win64\Anaconda\V4.4.0_3.6\lib\site-packages\numpy\lib\nanfunctions.py in _replace_nan(a, val)
     68         mask = a != a
     69     elif issubclass(a.dtype.type, np.inexact):
---> 70         mask = np.isnan(a)
     71     else:
     72         mask = None

KeyboardInterrupt: 

In [ ]: