` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_timeseries_manipulation.py: Manipulate a time series ======================== .. GENERATED FROM PYTHON SOURCE LINES 7-22 The objective here is to create and manipulate a time series. A time series is a particular field where the mesh :math:`\mathcal{M}` 1-d and regular, eg a time grid :math:`(t_0, \dots, t_{N-1})`. It is possible to draw a time series, using interpolation between the values: see the use case on the Field. A time series can be obtained as a realization of a multivariate stochastic process :math:`X: \Omega \times [0,T] \rightarrow \mathbb{R}^d` of dimension :math:`d` where :math:`[0,T]` is discretized according to the regular grid :math:`(t_0, \dots, t_{N-1})`. The values :math:`(\vect{x}_0, \dots, \vect{x}_{N-1})` of the time series are defined by: .. math:: \forall i \in [0, N-1],\quad \vect{x}_i= X(\omega)(t_i) A time series is stored in the :class:`~openturns.TimeSeries` object that stores the regular time grid and the associated values. .. GENERATED FROM PYTHON SOURCE LINES 24-30 .. code-block:: Python import openturns as ot import openturns.viewer as viewer from matplotlib import pylab as plt ot.Log.Show(ot.Log.NONE) .. GENERATED FROM PYTHON SOURCE LINES 31-32 Create the RegularGrid .. GENERATED FROM PYTHON SOURCE LINES 32-37 .. code-block:: Python tMin = 0.0 timeStep = 0.1 N = 100 myTimeGrid = ot.RegularGrid(tMin, timeStep, N) .. GENERATED FROM PYTHON SOURCE LINES 38-40 Case 1: Create a time series from a time grid and values. Be careful that the number of steps of the time grid must correspond to the size of the values .. GENERATED FROM PYTHON SOURCE LINES 40-44 .. code-block:: Python myValues = ot.Normal(3).getSample(myTimeGrid.getVertices().getSize()) myTimeSeries = ot.TimeSeries(myTimeGrid, myValues) myTimeSeries .. raw:: html

class=TimeSeries name=Unnamed derived from=class=FieldImplementation name=Unnamed mesh=class=Mesh name=Unnamed dimension=1 vertices=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=100 dimension=1 description=[t] data=[[0],[0.1],[0.2],[0.3],[0.4],[0.5],[0.6],[0.7],[0.8],[0.9],[1],[1.1],[1.2],[1.3],[1.4],[1.5],[1.6],[1.7],[1.8],[1.9],[2],[2.1],[2.2],[2.3],[2.4],[2.5],[2.6],[2.7],[2.8],[2.9],[3],[3.1],[3.2],[3.3],[3.4],[3.5],[3.6],[3.7],[3.8],[3.9],[4],[4.1],[4.2],[4.3],[4.4],[4.5],[4.6],[4.7],[4.8],[4.9],[5],[5.1],[5.2],[5.3],[5.4],[5.5],[5.6],[5.7],[5.8],[5.9],[6],[6.1],[6.2],[6.3],[6.4],[6.5],[6.6],[6.7],[6.8],[6.9],[7],[7.1],[7.2],[7.3],[7.4],[7.5],[7.6],[7.7],[7.8],[7.9],[8],[8.1],[8.2],[8.3],[8.4],[8.5],[8.6],[8.7],[8.8],[8.9],[9],[9.1],[9.2],[9.3],[9.4],[9.5],[9.6],[9.7],[9.8],[9.9]] simplices=[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23],[23,24],[24,25],[25,26],[26,27],[27,28],[28,29],[29,30],[30,31],[31,32],[32,33],[33,34],[34,35],[35,36],[36,37],[37,38],[38,39],[39,40],[40,41],[41,42],[42,43],[43,44],[44,45],[45,46],[46,47],[47,48],[48,49],[49,50],[50,51],[51,52],[52,53],[53,54],[54,55],[55,56],[56,57],[57,58],[58,59],[59,60],[60,61],[61,62],[62,63],[63,64],[64,65],[65,66],[66,67],[67,68],[68,69],[69,70],[70,71],[71,72],[72,73],[73,74],[74,75],[75,76],[76,77],[77,78],[78,79],[79,80],[80,81],[81,82],[82,83],[83,84],[84,85],[85,86],[86,87],[87,88],[88,89],[89,90],[90,91],[91,92],[92,93],[93,94],[94,95],[95,96],[96,97],[97,98],[98,99]] values=class=Sample name=Normal implementation=class=SampleImplementation name=Normal size=100 dimension=3 description=[X0,X1,X2] data=[[0.52378,0.12611,0.393794],[-0.248139,-0.16677,0.214858],[0.0247934,0.138394,0.430279],[-1.61823,0.558478,-1.30886],[-0.139764,-0.546122,-0.567461],[0.205057,0.904138,0.547278],[0.788237,1.49744,-1.41748],[0.47696,-1.43288,2.02109],[1.23468,0.157697,0.940324],[0.117709,-1.14723,-1.32423],[0.498823,0.801346,0.900951],[-1.34579,-0.466627,0.246984],[-0.588016,0.250813,-0.859715],[-0.431791,-1.73008,-1.10509],[-1.22603,-0.70203,1.08883],[-0.700387,-1.66383,1.73256],[0.865208,0.270015,-0.27368],[-0.733251,0.521748,0.362264],[-0.123077,0.573721,-0.328373],[-0.10364,-0.52281,-1.68534],[0.195637,-0.0788806,-1.94656],[1.32949,-1.26065,-0.137471],[-0.349241,0.927261,1.02351],[-0.528963,1.2413,0.273859],[0.207583,1.16668,1.04363],[-2.38573,-1.65012,-0.416396],[2.13326,-0.43238,-0.483701],[-0.923412,-0.325859,-1.19977],[0.803572,0.524339,-0.0630568],[-0.835405,0.0402377,-0.452565],[0.0257213,0.368049,-0.841262],[-1.01146,-2.18025,-1.58033],[-0.449535,0.890842,0.0743256],[1.8438,-0.300223,-1.13582],[0.603846,-1.57444,-0.95201],[0.620044,-0.831148,0.179603],[-0.444416,0.959874,0.393199],[0.607432,-0.442113,0.170379],[0.296909,0.291782,0.977481],[-0.190001,0.250078,0.434109],[0.323441,1.75839,-0.023602],[-0.967543,-0.400737,-1.29578],[-0.312378,-0.944492,1.75581],[1.04865,-0.830397,-0.892176],[0.433775,-0.825645,-0.537977],[-0.102559,0.84464,-1.91496],[0.406466,0.321913,-0.305269],[0.488492,0.122734,0.305202],[-0.386326,0.0689214,0.313803],[0.677903,0.495358,-0.490069],[0.315441,-0.379322,0.785857],[-0.35019,0.264677,1.1554],[-0.455589,-0.559667,-0.662289],[-0.84981,-1.48909,-0.438836],[0.545473,-0.369104,0.962339],[0.770285,0.5617,-0.0453834],[-0.548109,-1.08238,0.471951],[0.50024,-1.40894,0.656795],[-1.05172,0.263069,-0.418894],[0.30767,-0.416239,1.35256],[-0.02062,1.30727,0.445701],[-0.428967,-2.15109,1.10333],[1.20183,-0.65679,-0.0034805],[-1.53118,1.56066,0.317831],[0.206523,1.45024,-1.4915],[-2.71262,-1.60122,-1.73553],[0.315804,-0.389312,-0.835347],[0.915355,-1.11271,0.586068],[0.57727,0.0729422,-0.441155],[-0.145206,1.00515,-1.07333],[1.89198,-0.216602,0.214305],[-0.503722,-0.345728,-1.40113],[0.921629,0.229499,0.777413],[-1.17868,0.132514,0.400826],[0.79873,0.175534,0.6878],[1.1929,1.95488,-0.475165],[-0.434939,-0.563952,2.23404],[-0.139733,-0.897931,0.198825],[-1.95284,-0.125675,1.59678],[1.05037,0.207933,-0.607134],[-0.652396,-0.666132,-1.07025],[0.225309,-1.13645,0.0128528],[0.681485,-0.0589669,0.62219],[-0.784616,-0.500505,-0.497468],[-0.59515,-0.597179,1.28317],[1.98506,0.0321232,0.469106],[0.0181719,-1.12972,0.70832],[0.309358,-0.161451,-0.0337435],[0.242744,-0.720621,0.605114],[-0.0771294,0.22276,-1.78651],[-0.52325,0.174664,-0.704638],[-0.988056,-0.361028,-1.76169],[0.313168,0.825269,0.432011],[1.20499,0.884502,0.117486],[-0.0337554,-0.092368,0.437182],[-0.0595837,-0.637973,-0.887564],[-0.337387,-0.0849012,-0.399771],[0.344743,-1.22959,0.656478],[-0.21913,-0.018154,0.365455],[0.793991,-1.21411,-1.73067]] start=0 timeStep=0.1 n=100

.. GENERATED FROM PYTHON SOURCE LINES 45-46 Case 2: Get a time series from a Process .. GENERATED FROM PYTHON SOURCE LINES 46-50 .. code-block:: Python myProcess = ot.WhiteNoise(ot.Normal(3), myTimeGrid) myTimeSeries2 = myProcess.getRealization() myTimeSeries2 .. raw:: html

	t	X0	X1	X2
0	0	-1.670492	-1.138823	1.317518
1	0.1	0.004916539	0.207453	0.5854116
2	0.2	0.6318718	0.3769744	1.288444
3	0.3	-1.815059	-1.064866	-0.5376213
4	0.4	1.100027	-1.608281	0.2590714
5	0.5	0.2505065	-1.76158	0.6998717
6	0.6	0.9417183	-0.488464	-0.08899449
7	0.7	1.739529	-0.8246544	-0.0005616102
8	0.8	0.6088398	0.2800388	1.456377
9	0.9	-0.2445882	-0.9281551	-0.8752327
10	1	-0.9090887	0.09793622	0.5108138
11	1.1	-0.2333036	2.977989	-0.9998576
12	1.2	-1.182387	1.048563	1.703911
13	1.3	0.8708819	-1.284252	1.036737
14	1.4	-0.5798028	-1.859145	0.9250127
15	1.5	0.1757063	1.531778	0.5817077
16	1.6	1.024101	0.09670833	0.6195517
17	1.7	1.139809	-0.4087134	-0.2550477
18	1.8	0.5224197	0.3861234	-2.075111
19	1.9	0.6156748	1.977506	0.06924619
20	2	-1.367441	-1.178709	1.05263
21	2.1	2.36118	-1.022332	0.2285195
22	2.2	-0.9436299	0.05570427	0.8479874
23	2.3	1.947942	-1.768569	0.313241
24	2.4	1.393382	-0.5917899	-1.283321
25	2.5	-0.4261665	-2.275057	-1.122716
26	2.6	-0.9587	0.8365301	-0.2694569
27	2.7	0.8057302	1.089693	-0.6405182
28	2.8	-2.792036	-0.2587426	-0.3865208
29	2.9	0.3161664	0.7604701	-1.217716
30	3	-0.1682398	0.5425786	-1.366357
31	3.1	1.074819	0.01435018	0.1129411
32	3.2	-0.755817	-0.2352335	-0.3526476
33	3.3	1.031261	0.1387743	-0.1019698
34	3.4	0.1148558	1.307602	0.2750357
35	3.5	0.8908154	-0.6283213	0.03249425
36	3.6	0.8022597	-0.7750893	1.622367
37	3.7	-0.8908726	0.1450516	1.288845
38	3.8	0.7490533	-1.660132	-0.2574172
39	3.9	-0.6333344	-0.01390061	-0.5187067
40	4	-0.7641469	-0.8802884	-1.04384
41	4.1	1.624155	-0.08771599	-0.2191296
42	4.2	1.651487	0.1178754	-1.152759
43	4.3	-0.6219183	-1.12608	1.060989
44	4.4	1.310402	-1.324693	2.232301
45	4.5	-0.9766673	-0.5351095	-0.4692117
46	4.6	0.8752487	-0.6614909	0.4248837
47	4.7	0.9250794	0.1116855	-1.69762
48	4.8	-1.71699	0.5622419	-0.7709706
49	4.9	-0.2774593	-1.896383	2.738704
50	5	0.2583176	1.411942	0.5341219
51	5.1	0.813716	0.5418584	-0.7792782
52	5.2	-0.2821132	1.738024	-0.3488722
53	5.3	0.5248662	-0.4167478	-0.4363704
54	5.4	1.231982	-1.329614	0.4294014
55	5.5	-0.1988925	-0.5305423	0.1479477
56	5.6	1.087853	-0.1887557	0.8494047
57	5.7	0.9088333	0.7830113	0.6364255
58	5.8	0.3660167	0.2228301	0.7101552
59	5.9	0.2647587	-0.6881035	-1.005743
60	6	0.2375102	-1.817178	-0.7518762
61	6.1	-0.6579323	0.9981225	-0.07624542
62	6.2	-0.7847343	-0.1382298	-0.9096015
63	6.3	-0.6038747	-1.507997	1.923131
64	6.4	-0.8878048	-0.5890475	0.4536556
65	6.5	1.112655	-0.9013951	0.7350295
66	6.6	0.1578329	-1.229718	-0.7125437
67	6.7	0.3872097	-0.221006	-0.6366688
68	6.8	0.1411499	-1.382219	-0.9600347
69	6.9	-0.673238	1.35691	-1.472505
70	7	0.290016	-0.3173095	1.594927
71	7.1	0.427398	0.06673495	0.1377921
72	7.2	0.3715888	-0.409588	0.4125253
73	7.3	-0.7911313	-0.3134569	0.683661
74	7.4	0.2432084	1.35115	-1.572174
75	7.5	0.7591635	-0.5428189	0.894484
76	7.6	1.496315	1.494005	0.07607672
77	7.7	3.032252	-0.0697185	0.9362872
78	7.8	0.09534806	0.5547554	-0.1597999
79	7.9	-0.117537	0.8516132	-2.280891
80	8	0.4156774	0.1686187	-0.4769556
81	8.1	-1.248859	0.5411939	-2.166777
82	8.2	1.047143	0.4078612	-1.554764
83	8.3	-0.04557226	1.203224	0.9711234
84	8.4	-0.9533762	-0.5502569	0.7774226
85	8.5	0.4831444	-0.1721776	1.008082
86	8.6	1.217844	-0.4041445	1.793038
87	8.7	-0.8329919	1.636185	0.6188379
88	8.8	0.9314921	0.3700222	1.658918
89	8.9	-0.7589742	-0.1231373	-1.700695
90	9	-0.8901343	-0.8929079	0.1463011
91	9.1	-0.01782797	0.1991584	-1.521287
92	9.2	1.876469	-1.655881	0.08516664
93	9.3	0.4022144	-1.748718	0.5559068
94	9.4	-1.22224	1.493979	1.512701
95	9.5	-0.07158338	0.5902772	1.96161
96	9.6	0.1669381	-1.754113	1.140951
97	9.7	0.6632621	1.00617	-0.2992668
98	9.8	-0.7329082	-0.5431353	0.4164685
99	9.9	0.7069276	0.3009473	0.534359

.. GENERATED FROM PYTHON SOURCE LINES 51-52 Get the number of values of the time series .. GENERATED FROM PYTHON SOURCE LINES 52-54 .. code-block:: Python myTimeSeries.getSize() .. rst-class:: sphx-glr-script-out .. code-block:: none 100 .. GENERATED FROM PYTHON SOURCE LINES 55-56 Get the dimension of the values observed at each time .. GENERATED FROM PYTHON SOURCE LINES 56-58 .. code-block:: Python myTimeSeries.getMesh().getDimension() .. rst-class:: sphx-glr-script-out .. code-block:: none 1 .. GENERATED FROM PYTHON SOURCE LINES 59-60 Get the value :math:`X_i` at index :math:`i` .. GENERATED FROM PYTHON SOURCE LINES 60-63 .. code-block:: Python i = 37 print("Xi = ", myTimeSeries.getValueAtIndex(i)) .. rst-class:: sphx-glr-script-out .. code-block:: none Xi = [0.607432,-0.442113,0.170379] .. GENERATED FROM PYTHON SOURCE LINES 64-65 Get the time series at index :math:`i` : :math:`X_i` .. GENERATED FROM PYTHON SOURCE LINES 65-68 .. code-block:: Python i = 37 print("Xi = ", myTimeSeries[i]) .. rst-class:: sphx-glr-script-out .. code-block:: none Xi = [0.607432,-0.442113,0.170379] .. GENERATED FROM PYTHON SOURCE LINES 69-70 Get a the marginal value at index :math:`i` of the time series .. GENERATED FROM PYTHON SOURCE LINES 70-76 .. code-block:: Python i = 37 # get the time stamp: print("ti = ", myTimeSeries.getTimeGrid().getValue(i)) # get the first component of the corresponding value : print("Xi1 = ", myTimeSeries[i, 0]) .. rst-class:: sphx-glr-script-out .. code-block:: none ti = 3.7 Xi1 = 0.6074317802523269 .. GENERATED FROM PYTHON SOURCE LINES 77-78 Get all the values :math:`(X_1, \dots, X_n)` of the time series .. GENERATED FROM PYTHON SOURCE LINES 78-80 .. code-block:: Python myTimeSeries.getValues() .. raw:: html

	X0	X1	X2
0	0.5237798	0.12611	0.3937941
1	-0.2481388	-0.1667702	0.2148585
2	0.02479338	0.1383943	0.430279
3	-1.618226	0.5584776	-1.30886
4	-0.139764	-0.5461219	-0.5674607
5	0.2050574	0.9041375	0.5472782
6	0.7882369	1.49744	-1.417477
7	0.4769603	-1.432882	2.021089
8	1.23468	0.1576975	0.9403244
9	0.117709	-1.147233	-1.324232
10	0.4988229	0.801346	0.9009509
11	-1.34579	-0.466627	0.2469844
12	-0.5880163	0.2508129	-0.8597147
13	-0.4317908	-1.730083	-1.105085
14	-1.226028	-0.7020297	1.088834
15	-0.7003868	-1.663834	1.732557
16	0.865208	0.2700146	-0.2736801
17	-0.7332508	0.5217478	0.3622642
18	-0.1230767	0.5737211	-0.3283734
19	-0.1036404	-0.5228103	-1.685336
20	0.1956371	-0.07888063	-1.946558
21	1.329493	-1.260652	-0.1374706
22	-0.3492414	0.9272612	1.023511
23	-0.5289635	1.241303	0.2738588
24	0.2075833	1.166677	1.043628
25	-2.385726	-1.650125	-0.4163961
26	2.133258	-0.4323803	-0.4837005
27	-0.9234119	-0.3258593	-1.199766
28	0.8035719	0.5243393	-0.06305676
29	-0.835405	0.04023769	-0.4525647
30	0.0257213	0.3680492	-0.8412618
31	-1.011461	-2.180247	-1.580328
32	-0.4495348	0.8908425	0.07432561
33	1.843799	-0.3002226	-1.135818
34	0.6038459	-1.574439	-0.9520099
35	0.6200444	-0.8311482	0.1796026
36	-0.4444155	0.9598739	0.3931992
37	0.6074318	-0.4421131	0.1703794
38	0.2969089	0.2917823	0.9774806
39	-0.1900015	0.2500776	0.4341087
40	0.3234411	1.758392	-0.02360201
41	-0.9675434	-0.4007368	-1.295784
42	-0.3123782	-0.9444916	1.755809
43	1.048647	-0.8303966	-0.8921762
44	0.4337751	-0.825645	-0.5379767
45	-0.1025594	0.8446397	-1.914963
46	0.4064664	0.321913	-0.3052688
47	0.4884916	0.1227336	0.3052021
48	-0.3863256	0.06892144	0.3138032
49	0.6779029	0.4953577	-0.490069
50	0.3154414	-0.3793216	0.7858567
51	-0.3501902	0.2646774	1.155399
52	-0.4555892	-0.5596673	-0.6622893
53	-0.8498098	-1.489086	-0.4388359
54	0.5454725	-0.369104	0.9623389
55	0.7702848	0.5617002	-0.04538344
56	-0.5481091	-1.082383	0.4719511
57	0.5002396	-1.408936	0.6567949
58	-1.051715	0.2630691	-0.4188936
59	0.3076702	-0.416239	1.352556
60	-0.02062003	1.307273	0.4457012
61	-0.4289673	-2.151095	1.103334
62	1.201832	-0.65679	-0.003480504
63	-1.531184	1.560664	0.3178313
64	0.2065234	1.45024	-1.491504
65	-2.712616	-1.601219	-1.735534
66	0.3158041	-0.3893124	-0.8353471
67	0.9153545	-1.112714	0.5860682
68	0.5772697	0.07294216	-0.4411553
69	-0.1452064	1.005149	-1.073327
70	1.891982	-0.2166016	0.2143049
71	-0.5037216	-0.345728	-1.401125
72	0.9216287	0.2294988	0.7774133
73	-1.178678	0.1325139	0.4008258
74	0.7987302	0.1755338	0.6877997
75	1.1929	1.954883	-0.4751648
76	-0.434939	-0.5639525	2.234044
77	-0.1397326	-0.8979314	0.1988251
78	-1.952842	-0.1256751	1.596785
79	1.050368	0.2079334	-0.6071344
80	-0.6523957	-0.6661315	-1.07025
81	0.2253092	-1.136449	0.01285282
82	0.681485	-0.05896693	0.62219
83	-0.784616	-0.5005054	-0.4974685
84	-0.5951495	-0.5971793	1.283174
85	1.985056	0.03212315	0.4691064
86	0.01817188	-1.129723	0.7083197
87	0.3093576	-0.1614505	-0.03374345
88	0.2427443	-0.7206208	0.6051135
89	-0.07712943	0.2227604	-1.786512
90	-0.5232505	0.1746638	-0.7046384
91	-0.9880562	-0.3610281	-1.761685
92	0.3131678	0.8252694	0.4320112
93	1.204991	0.8845017	0.1174865
94	-0.03375537	-0.09236796	0.4371824
95	-0.05958368	-0.6379726	-0.8875642
96	-0.3373875	-0.08490124	-0.3997714
97	0.3447429	-1.229588	0.6564776
98	-0.2191304	-0.01815395	0.3654549
99	0.7939912	-1.214108	-1.730674

.. GENERATED FROM PYTHON SOURCE LINES 81-83 Compute the temporal Mean It corresponds to the mean of the values of the time series .. GENERATED FROM PYTHON SOURCE LINES 83-85 .. code-block:: Python myTimeSeries.getInputMean() .. raw:: html

class=Point name=Unnamed dimension=3 values=[0.00695924,-0.100262,-0.0396681]

.. GENERATED FROM PYTHON SOURCE LINES 86-87 Draw the marginal :math:`i` of the time series using linear interpolation .. GENERATED FROM PYTHON SOURCE LINES 87-90 .. code-block:: Python graph = myTimeSeries.drawMarginal(0) view = viewer.View(graph) .. image-sg:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_timeseries_manipulation_001.png :alt: Unnamed - 0 marginal :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_timeseries_manipulation_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 91-92 With no interpolation .. GENERATED FROM PYTHON SOURCE LINES 92-95 .. code-block:: Python graph = myTimeSeries.drawMarginal(0, False) view = viewer.View(graph) plt.show() .. image-sg:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_timeseries_manipulation_002.png :alt: Unnamed - 0 marginal :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_timeseries_manipulation_002.png :class: sphx-glr-single-img .. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_timeseries_manipulation.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_timeseries_manipulation.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_timeseries_manipulation.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_timeseries_manipulation.zip `