` 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 24-29 .. code-block:: Python import openturns as ot import openturns.viewer as viewer from matplotlib import pyplot as plt .. GENERATED FROM PYTHON SOURCE LINES 30-31 Create the RegularGrid .. GENERATED FROM PYTHON SOURCE LINES 31-36 .. code-block:: Python tMin = 0.0 timeStep = 0.1 N = 100 myTimeGrid = ot.RegularGrid(tMin, timeStep, N) .. GENERATED FROM PYTHON SOURCE LINES 37-39 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 39-43 .. 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=[[0.608202,-1.26617,-0.438266],[1.20548,-2.18139,0.350042],[-0.355007,1.43725,0.810668],[0.793156,-0.470526,0.261018],[-2.29006,-1.28289,-1.31178],[-0.0907838,0.995793,-0.139453],[-0.560206,0.44549,0.322925],[0.445785,-1.03808,-0.856712],[0.473617,-0.125498,0.351418],[1.78236,0.0702074,-0.781366],[-0.721533,-0.241223,-1.78796],[0.40136,1.36783,1.00434],[0.741548,-0.0436123,0.539345],[0.29995,0.407717,-0.485112],[-0.382992,-0.752817,0.257926],[1.96876,-0.671291,1.85579],[0.0521593,0.790446,0.716353],[-0.743622,0.184356,-1.53073],[0.655027,0.538071,1.73821],[-0.958722,0.377922,-0.181004],[1.67297,-1.03896,-0.353552],[1.21381,-0.777033,-1.36853],[0.103474,-0.89182,0.905602],[0.334794,-0.483642,0.677958],[1.70938,1.07062,-0.506925],[-1.66086,2.24623,0.759602],[-0.510764,-0.633066,-0.957072],[0.544047,0.814561,-0.734708],[-0.111461,0.994482,-0.160625],[-0.938771,-1.96869,-0.657603],[0.338751,1.01556,0.637167],[-0.0899071,-0.855886,1.27128],[-0.238253,1.3263,2.11968],[-0.901581,-1.51696,-1.29938],[0.230372,-3.09737,0.01323],[-1.25743,1.02776,-0.766431],[0.217512,1.04533,0.331569],[-0.488205,-0.465482,0.332084],[-0.167726,3.01263,0.94204],[0.61189,0.611715,-1.5375],[-2.4067,0.662936,-0.65616],[-0.751611,0.438177,-0.455335],[1.86038,0.219721,1.72546],[-0.543405,-0.736749,-0.508206],[-2.25867,-0.5964,-0.31468],[-1.78274,-0.684734,0.0611157],[0.87372,-1.46295,-0.318786],[1.26314,-0.426726,-1.89234],[-0.514391,0.647229,0.00370249],[0.729688,-0.247234,0.479191],[-0.0336098,-0.0367271,0.110256],[-0.37687,-0.0955894,0.109122],[-0.198754,0.47362,0.161637],[0.384483,0.116468,-0.10008],[1.49156,1.22301,0.526646],[-0.656923,-0.131228,-1.45347],[1.17414,0.929395,-0.337113],[0.578688,-0.582459,-1.38886],[-0.499748,-1.55516,0.483083],[0.205004,-0.0972525,0.592563],[-0.602044,-1.21009,-0.886698],[-0.141114,0.441983,0.519162],[-1.51455,-0.676917,0.667678],[-1.40585,-0.0295335,-0.631829],[-0.342157,2.05339,1.1587],[-1.45717,-0.844367,-0.28861],[0.419271,-0.836064,0.858269],[-0.906566,-0.91681,1.16322],[0.301918,0.490331,0.475425],[-0.788704,-0.669449,-0.137928],[-0.971531,-1.18784,1.4282],[-0.58923,-1.73218,0.824993],[3.02799,1.6948,-1.64827],[-0.996469,0.773121,-0.519476],[-0.0351973,-0.439866,-0.259332],[-0.875419,-2.53986,-0.0566709],[-0.0217279,0.59922,0.146868],[-0.74536,-0.521596,0.59202],[-0.470039,-2.17211,-0.432617],[0.26775,-0.36799,1.14842],[-0.0343283,0.461082,-0.622424],[-1.62506,-0.543099,-0.269535],[0.0208818,0.623854,0.767137],[0.888798,1.48031,0.661002],[1.40895,0.576125,1.89326],[0.858611,-0.907348,-0.537503],[-0.638434,1.34856,-2.26608],[0.423232,-0.996141,-1.08751],[0.11108,0.677663,-1.05502],[-0.00409659,0.562833,-0.029616],[0.0702065,-0.23527,-1.29031],[-1.01864,-1.71131,0.943326],[-0.542319,-0.999111,-1.40457],[1.94606,0.779572,1.13848],[0.711148,-0.453386,0.618319],[0.722044,0.660021,0.465919],[-0.40773,1.45919,-0.411565],[0.549439,1.45019,-0.327249],[-1.39796,1.30115,-0.485259],[-0.272407,-0.338823,-0.790757]] start=0 timeStep=0.1 n=100

.. GENERATED FROM PYTHON SOURCE LINES 44-45 Case 2: Get a time series from a Process .. GENERATED FROM PYTHON SOURCE LINES 45-49 .. code-block:: Python myProcess = ot.WhiteNoise(ot.Normal(3), myTimeGrid) myTimeSeries2 = myProcess.getRealization() myTimeSeries2 .. raw:: html

	t	X0	X1	X2
0	0	1.739449	0.9359392	1.275114
1	0.1	-0.5950037	-0.0230083	1.853373
2	0.2	0.3561882	-1.317651	-1.194996
3	0.3	-0.4436842	-0.8262043	-0.7488164
4	0.4	0.4340344	-0.6442085	-0.559902
5	0.5	0.05466818	-0.05647917	0.7575347
6	0.6	-0.6631575	0.6836458	0.5910434
7	0.7	-2.208718	-0.7790315	-0.7030859
8	0.8	-0.05669555	0.5881009	0.7388395
9	0.9	0.7271276	-1.183102	0.8531994
10	1	1.031982	0.1044672	0.5155103
11	1.1	-1.732508	0.3692314	0.6671036
12	1.2	-0.5128099	-0.4777539	1.262641
13	1.3	1.578458	1.890055	0.3902966
14	1.4	0.2357594	0.2449476	0.5716903
15	1.5	-0.4205421	0.5532545	-2.19382
16	1.6	0.4212794	0.7537578	-0.5124193
17	1.7	-0.3062254	-1.211032	0.01748019
18	1.8	-1.165014	0.06438942	0.7176094
19	1.9	-0.3042681	-0.3913752	0.2582147
20	2	-1.490777	1.061818	0.3749687
21	2.1	-0.1654673	0.3578707	0.8851181
22	2.2	1.737898	-0.7131956	1.706424
23	2.3	0.4286364	-0.2775952	0.4112949
24	2.4	0.3704449	0.1878542	1.432656
25	2.5	-0.4161282	-0.1228684	0.950488
26	2.6	-0.4111282	-0.9804902	0.564196
27	2.7	-1.556663	0.6248883	1.057974
28	2.8	-0.7695287	1.542366	0.3748018
29	2.9	0.5061052	0.4197679	1.58128
30	3	0.009563751	-0.3830202	0.1636987
31	3.1	1.256104	0.006203967	0.2720044
32	3.2	-0.1537841	-0.404166	2.092243
33	3.3	0.6750433	-0.3832085	-0.3552394
34	3.4	-1.305296	-1.515767	0.172158
35	3.5	0.5776802	-0.1730494	0.6621723
36	3.6	0.6978382	0.7895777	0.4793068
37	3.7	-0.4494332	1.765705	0.281658
38	3.8	0.1279809	-0.7479662	0.5128914
39	3.9	1.08613	-0.5519517	1.578906
40	4	-0.2223936	0.2055034	1.338509
41	4.1	0.04525299	2.156495	1.009849
42	4.2	1.188981	1.287652	-0.2798472
43	4.3	-0.5673421	0.07894311	-0.3740983
44	4.4	0.36891	-0.2162491	-0.9644931
45	4.5	1.142547	0.2719525	-0.6267599
46	4.6	-1.245543	-0.7938689	0.8086521
47	4.7	0.551898	1.262139	-0.3987307
48	4.8	-2.13505	0.4206717	-0.1649563
49	4.9	-1.277891	-0.748335	0.447628
50	5	1.606495	-1.238318	-0.8571127
51	5.1	-0.7960124	2.555329	-1.409656
52	5.2	0.1617572	1.071526	-0.07561517
53	5.3	-0.3858102	-0.6958986	-0.2401711
54	5.4	0.01403395	-1.327828	-0.4218051
55	5.5	-1.31457	-0.314242	0.8700968
56	5.6	-1.050287	-0.6617487	-0.3989571
57	5.7	-0.3068693	2.240972	-1.842254
58	5.8	-1.126287	-0.343091	1.357067
59	5.9	-1.141444	0.7199106	0.6912884
60	6	0.01574154	0.8978544	-0.02689165
61	6.1	-1.172528	-1.223227	1.337288
62	6.2	-0.4120875	1.405077	0.8399413
63	6.3	-0.1718261	-0.6121364	0.4331895
64	6.4	1.259888	-2.151353	0.6383845
65	6.5	1.198597	0.5760515	-2.721058
66	6.6	-0.4566343	0.8344516	0.1897228
67	6.7	-1.559897	0.141706	-0.3128766
68	6.8	-1.096692	1.306282	-0.6035431
69	6.9	0.08447148	-1.011566	-0.4541302
70	7	0.184323	1.111031	0.03326554
71	7.1	-0.4027267	0.8121354	0.1379583
72	7.2	-0.5523964	0.7122982	0.6577979
73	7.3	-0.2971004	0.2881424	-0.843501
74	7.4	1.481402	0.9048591	0.9005403
75	7.5	0.2113785	0.408217	-0.2907085
76	7.6	-1.037685	0.4036742	-0.03612466
77	7.7	-0.04399572	1.578567	1.445033
78	7.8	-0.9083433	-1.329003	-0.4762143
79	7.9	1.022384	-1.197875	2.596026
80	8	0.1498547	-0.390626	-0.3116555
81	8.1	-0.4514491	0.2370956	0.6243862
82	8.2	-0.5553002	0.7656447	0.5092548
83	8.3	0.4161323	-1.428256	-0.1552423
84	8.4	1.198645	-0.1898108	-1.099809
85	8.5	0.7271951	0.5664686	-1.437003
86	8.6	-0.2535926	0.8982354	0.7326738
87	8.7	-0.1095485	-0.4859692	-0.3567203
88	8.8	-1.259387	0.03497645	-0.4096377
89	8.9	0.7955166	-2.108143	-0.9148845
90	9	1.095021	-0.06328519	2.003632
91	9.1	-0.1248814	0.06040856	-0.4496756
92	9.2	0.15909	-2.043173	1.061442
93	9.3	-1.444155	0.7511011	0.8440584
94	9.4	-1.239076	0.743606	1.434637
95	9.5	0.07700021	-2.187386	0.2376129
96	9.6	0.8050322	0.7841974	1.021327
97	9.7	-0.3590296	-1.166527	1.017866
98	9.8	0.2758391	0.907344	0.359928
99	9.9	1.178278	1.578528	2.0749

.. GENERATED FROM PYTHON SOURCE LINES 50-51 Get the number of values of the time series .. GENERATED FROM PYTHON SOURCE LINES 51-53 .. code-block:: Python myTimeSeries.getSize() .. rst-class:: sphx-glr-script-out .. code-block:: none 100 .. GENERATED FROM PYTHON SOURCE LINES 54-55 Get the dimension of the values observed at each time .. GENERATED FROM PYTHON SOURCE LINES 55-57 .. code-block:: Python myTimeSeries.getMesh().getDimension() .. rst-class:: sphx-glr-script-out .. code-block:: none 1 .. GENERATED FROM PYTHON SOURCE LINES 58-59 Get the value :math:`X_i` at index :math:`i` .. GENERATED FROM PYTHON SOURCE LINES 59-62 .. code-block:: Python i = 37 print("Xi = ", myTimeSeries.getValueAtIndex(i)) .. rst-class:: sphx-glr-script-out .. code-block:: none Xi = [-0.488205,-0.465482,0.332084] .. GENERATED FROM PYTHON SOURCE LINES 63-64 Get the time series at index :math:`i` : :math:`X_i` .. GENERATED FROM PYTHON SOURCE LINES 64-67 .. code-block:: Python i = 37 print("Xi = ", myTimeSeries[i]) .. rst-class:: sphx-glr-script-out .. code-block:: none Xi = [-0.488205,-0.465482,0.332084] .. GENERATED FROM PYTHON SOURCE LINES 68-69 Get a the marginal value at index :math:`i` of the time series .. GENERATED FROM PYTHON SOURCE LINES 69-75 .. 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 = -0.4882047479037244 .. GENERATED FROM PYTHON SOURCE LINES 76-77 Get all the values :math:`(X_1, \dots, X_n)` of the time series .. GENERATED FROM PYTHON SOURCE LINES 77-79 .. code-block:: Python myTimeSeries.getValues() .. raw:: html

	X0	X1	X2
0	0.6082017	-1.266173	-0.4382656
1	1.205478	-2.181385	0.3500421
2	-0.355007	1.437249	0.810668
3	0.793156	-0.4705256	0.2610179
4	-2.290062	-1.282885	-1.311781
5	-0.09078383	0.9957932	-0.1394528
6	-0.5602056	0.4454897	0.322925
7	0.4457853	-1.038077	-0.8567123
8	0.4736169	-0.1254977	0.3514178
9	1.782359	0.07020736	-0.7813665
10	-0.7215334	-0.2412235	-1.787964
11	0.4013597	1.367826	1.004343
12	0.7415484	-0.04361234	0.5393447
13	0.2999504	0.4077172	-0.485112
14	-0.382992	-0.7528166	0.2579264
15	1.96876	-0.6712905	1.855792
16	0.05215933	0.7904458	0.7163526
17	-0.743622	0.184356	-1.530734
18	0.6550275	0.5380715	1.738213
19	-0.9587223	0.3779221	-0.1810042
20	1.672965	-1.038958	-0.3535524
21	1.213814	-0.7770331	-1.368531
22	0.1034744	-0.8918195	0.9056017
23	0.3347945	-0.4836416	0.6779583
24	1.709379	1.07062	-0.5069247
25	-1.660864	2.246229	0.7596015
26	-0.5107638	-0.6330662	-0.9570722
27	0.5440466	0.8145607	-0.7347084
28	-0.1114608	0.9944819	-0.1606253
29	-0.9387706	-1.968692	-0.6576035
30	0.3387511	1.015558	0.6371672
31	-0.08990712	-0.8558864	1.271283
32	-0.2382526	1.326299	2.119676
33	-0.9015814	-1.516965	-1.29938
34	0.2303724	-3.097374	0.01323
35	-1.25743	1.02776	-0.7664307
36	0.2175121	1.045333	0.3315688
37	-0.4882047	-0.4654821	0.3320839
38	-0.1677258	3.012627	0.9420405
39	0.6118901	0.6117152	-1.537497
40	-2.406702	0.662936	-0.6561602
41	-0.7516115	0.438177	-0.4553346
42	1.860378	0.2197212	1.725463
43	-0.5434055	-0.7367488	-0.5082064
44	-2.258672	-0.5963998	-0.31468
45	-1.782738	-0.6847338	0.06111571
46	0.8737197	-1.462953	-0.3187856
47	1.263142	-0.4267256	-1.892343
48	-0.5143905	0.6472294	0.003702486
49	0.7296878	-0.2472338	0.479191
50	-0.03360983	-0.03672706	0.1102562
51	-0.3768704	-0.09558941	0.1091224
52	-0.1987541	0.4736195	0.1616373
53	0.3844829	0.1164676	-0.1000805
54	1.491564	1.223005	0.5266463
55	-0.6569234	-0.1312282	-1.453471
56	1.174145	0.9293947	-0.3371135
57	0.5786883	-0.5824589	-1.388861
58	-0.4997483	-1.555158	0.483083
59	0.2050042	-0.09725248	0.5925631
60	-0.6020445	-1.210086	-0.8866979
61	-0.1411137	0.4419834	0.519162
62	-1.514551	-0.6769174	0.6676776
63	-1.405845	-0.02953347	-0.6318287
64	-0.3421569	2.053386	1.158703
65	-1.45717	-0.8443667	-0.2886103
66	0.4192711	-0.8360644	0.8582686
67	-0.9065659	-0.9168099	1.163221
68	0.3019183	0.4903313	0.4754246
69	-0.7887043	-0.6694492	-0.137928
70	-0.9715312	-1.187838	1.428203
71	-0.5892299	-1.732176	0.8249934
72	3.02799	1.694797	-1.648267
73	-0.9964693	0.7731214	-0.5194758
74	-0.03519734	-0.4398656	-0.2593322
75	-0.875419	-2.539863	-0.05667093
76	-0.02172791	0.5992195	0.1468679
77	-0.7453604	-0.521596	0.5920202
78	-0.4700387	-2.172109	-0.4326173
79	0.2677502	-0.3679897	1.148417
80	-0.0343283	0.4610818	-0.6224244
81	-1.625056	-0.5430992	-0.2695349
82	0.0208818	0.6238537	0.7671373
83	0.8887984	1.480306	0.6610018
84	1.408952	0.5761247	1.893265
85	0.8586112	-0.9073479	-0.5375027
86	-0.6384336	1.348564	-2.266083
87	0.4232324	-0.9961412	-1.087506
88	0.11108	0.6776631	-1.055018
89	-0.004096592	0.5628333	-0.02961597
90	0.07020646	-0.2352699	-1.290308
91	-1.01864	-1.711309	0.943326
92	-0.5423195	-0.9991113	-1.40457
93	1.946062	0.7795719	1.138475
94	0.7111476	-0.4533858	0.6183194
95	0.7220435	0.6600207	0.4659188
96	-0.4077298	1.45919	-0.4115654
97	0.5494387	1.450193	-0.3272495
98	-1.397957	1.301151	-0.4852593
99	-0.2724066	-0.3388229	-0.7907566

.. GENERATED FROM PYTHON SOURCE LINES 80-82 Compute the temporal Mean It corresponds to the mean of the values of the time series .. GENERATED FROM PYTHON SOURCE LINES 82-84 .. code-block:: Python myTimeSeries.getInputMean() .. raw:: html

class=Point name=Unnamed dimension=3 values=[-0.025392,-0.027327,-0.0146978]

.. GENERATED FROM PYTHON SOURCE LINES 85-86 Draw the marginal :math:`i` of the time series using linear interpolation .. GENERATED FROM PYTHON SOURCE LINES 86-89 .. 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.svg :alt: Unnamed - 0 marginal :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_timeseries_manipulation_001.svg :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 90-91 With no interpolation .. GENERATED FROM PYTHON SOURCE LINES 91-94 .. 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.svg :alt: Unnamed - 0 marginal :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_timeseries_manipulation_002.svg :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 `