` 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 6-21 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:`(\underline{x}_0, \dots, \underline{x}_{N-1})` of the time series are defined by: .. math:: \forall i \in [0, N-1],\quad \underline{x}_i= X(\omega)(t_i) A time series is stored in the **TimeSeries** object that stores the regular time grid and the associated values. .. GENERATED FROM PYTHON SOURCE LINES 23-29 .. 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 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 Care! 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=[[1.01189,-0.608942,0.259667],[0.324782,0.541045,0.124925],[0.63389,0.71797,0.204209],[-0.230565,-0.441029,0.218173],[0.358047,0.389048,0.0223299],[1.65473,0.718066,1.20039],[-0.0428541,0.299168,-1.95814],[0.342204,-0.822006,0.414328],[-0.336382,1.84368,-0.637582],[0.411799,-0.176888,-1.10384],[-0.414421,0.266101,-0.340295],[0.716981,-0.624488,1.48763],[-0.235484,0.22803,-0.8464],[-0.0506129,0.963482,-0.266606],[0.718303,-1.35427,-0.399967],[0.827442,-1.60123,-0.789026],[-0.470555,-1.17375,-1.17225],[1.44633,-0.0109896,-0.392194],[0.423681,-0.215168,-1.36186],[0.653895,1.87561,-0.402469],[0.623307,-0.207295,1.17231],[0.2915,-2.07544,-0.229841],[0.93204,-2.89787,-0.485802],[-0.315465,0.563317,-1.54763],[1.74913,-0.711751,0.120468],[0.85627,0.591214,-1.07519],[-0.751024,-0.550295,-1.29029],[0.776951,0.556825,-0.989392],[2.2382,-0.015504,0.87992],[1.10091,-1.08794,1.28143],[0.770213,-1.11943,0.361488],[-1.43777,0.192138,-1.69362],[1.48814,-0.979175,-1.66438],[2.75891,-0.0568873,-0.517364],[0.0644103,-0.497525,-1.67019],[-0.527852,1.15265,0.156536],[-0.790078,0.119299,-1.69795],[-0.4429,-0.541246,-1.35629],[-0.549982,-1.22042,-0.177045],[1.70917,-0.636661,0.218454],[0.448041,1.22407,-0.239304],[-0.437019,-0.533459,0.430689],[-0.549999,-0.920782,-2.35124],[-0.956058,0.943051,0.725423],[0.103282,0.516111,2.00502],[1.63507,-1.43977,0.529791],[1.03687,-0.444105,-0.753347],[0.100154,-0.550234,1.41372],[0.464214,0.447407,-1.05761],[1.35995,-0.710775,-0.164241],[-1.28354,0.556653,0.548566],[1.68737,0.79344,-0.540027],[-0.848387,-0.103264,0.958601],[-1.02522,-0.354939,-0.869302],[0.266897,0.296524,-2.24114],[-1.5607,-2.272,0.722451],[-2.16128,-0.32861,1.06975],[-1.77994,-0.832708,-0.245372],[-0.0205006,-0.170101,0.529296],[-0.725104,-1.16247,0.199523],[0.727148,-0.260688,-0.136772],[0.52023,-0.659133,-0.180673],[-1.04885,0.512371,0.20648],[-0.960832,0.414682,-1.22871],[2.57497,-0.00804901,-1.8859],[0.830757,-0.378346,0.479046],[1.60938,-0.570841,0.269096],[0.803503,0.583218,0.449756],[-0.693556,1.89666,0.0270818],[-0.258272,-0.37012,0.0456596],[-0.343048,-0.392484,-2.41093],[1.93921,-0.590044,0.22705],[-0.141765,0.855507,0.286761],[0.564812,-0.509701,1.40334],[-1.37852,0.434035,0.0342518],[0.896116,-0.870577,1.36995],[0.272597,0.579223,-1.5321],[0.957065,0.427663,-0.36668],[0.648699,-0.00464944,0.171548],[-0.0795761,0.455389,-2.14009],[0.933245,0.818686,-1.54826],[0.370246,-0.773089,-0.0129833],[0.187309,-2.13145,-1.19768],[-0.00500185,-0.125673,-1.89201],[3.40565,-0.103576,0.415448],[0.727255,0.978855,1.15808],[0.295275,0.283934,1.29426],[0.200773,0.342265,0.164085],[-0.608383,0.144346,0.537733],[0.696557,1.18791,2.18097],[-0.194809,0.628316,0.230866],[-0.648071,-0.0280203,0.871005],[1.24473,-0.106358,-0.234489],[-2.0102,0.121701,-1.33163],[-0.825457,-1.21658,-1.02579],[-1.22486,-0.735057,0.267431],[-0.313967,0.328403,-1.18542],[0.272577,-0.537997,-0.154628],[0.0348939,0.357208,0.87381],[-1.4897,-1.60323,0.276884]] 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	-0.2052791	0.3135911	1.520626
1	0.1	2.127892	0.1574096	0.05643199
2	0.2	1.05201	-1.069286	0.03896958
3	0.3	0.1088619	1.560223	0.8978581
4	0.4	0.07131786	0.3290581	0.7683447
5	0.5	-0.2017215	0.1483074	0.4988259
6	0.6	-0.5406089	0.202215	1.52964
7	0.7	-1.192179	0.5249542	-0.1271758
8	0.8	1.001217	0.2995675	-0.07324792
9	0.9	-0.5928008	0.509773	1.568079
10	1	0.3693428	0.6873462	0.2602205
11	1.1	1.560101	0.6838802	-0.2604079
12	1.2	0.1696515	-1.016573	0.8102853
13	1.3	-0.9345477	0.4402335	0.1026545
14	1.4	0.1625502	0.9776058	-0.6851276
15	1.5	-0.04119683	-0.1615313	0.009488993
16	1.6	-0.6992373	0.8356431	0.9612086
17	1.7	-0.3953424	0.2505092	-1.712787
18	1.8	-0.3033722	1.713433	0.2879968
19	1.9	-0.3462038	-1.243077	-0.6619336
20	2	-0.5396257	0.7891796	0.525199
21	2.1	0.2655049	-0.6153533	0.6677281
22	2.2	-0.3206562	-0.00603524	-1.440427
23	2.3	0.07065125	0.4005165	-0.5370034
24	2.4	-2.130432	0.1862285	-1.326288
25	2.5	0.2426011	-0.8973327	-0.9573643
26	2.6	1.588237	-0.2380769	-0.6543979
27	2.7	1.498919	-0.7131357	-1.335157
28	2.8	0.5676285	0.640198	-0.259729
29	2.9	0.1922855	-1.402221	0.5600177
30	3	-1.356244	1.034522	-0.3787931
31	3.1	-0.1257271	-0.5878356	1.078941
32	3.2	-1.669386	1.708344	-0.8459409
33	3.3	-0.1786205	-0.1958844	1.811325
34	3.4	0.4000363	1.108118	-0.4552358
35	3.5	-0.7934174	2.283829	0.351885
36	3.6	-0.06082214	1.182574	2.057236
37	3.7	2.083603	-1.109457	0.6461174
38	3.8	0.3140881	-1.259195	2.51347
39	3.9	1.106768	-1.237082	-0.4050629
40	4	1.244775	0.2588656	-0.1137998
41	4.1	0.3814998	0.1557911	0.4024124
42	4.2	1.332716	-0.8056192	0.3854209
43	4.3	-1.61086	-0.6874292	-0.02107395
44	4.4	-1.405266	-0.6029087	-0.07453712
45	4.5	-0.287633	-0.4026233	-0.4894317
46	4.6	-0.5803388	1.196489	1.004556
47	4.7	0.5372572	-0.08770909	1.423935
48	4.8	0.6820146	2.884055	0.2796988
49	4.9	-1.178997	-0.143892	0.6813079
50	5	0.01437919	0.5099701	-1.060234
51	5.1	0.04483657	0.2499197	1.24773
52	5.2	-0.3856004	-0.2880728	-0.5890517
53	5.3	0.4995753	1.132313	-0.8437811
54	5.4	1.43619	-0.1876503	0.940522
55	5.5	0.7151117	-1.439318	-0.1429401
56	5.6	-0.1765888	0.9054335	0.6688361
57	5.7	-0.1848348	-0.2056171	0.8539061
58	5.8	1.082717	0.7860448	-1.839514
59	5.9	-0.4807376	-0.7431111	0.2583894
60	6	0.06498678	0.8220976	-0.2202976
61	6.1	-1.267407	0.06548754	-2.506485
62	6.2	0.2182682	-0.3734256	-0.3483342
63	6.3	-1.020392	-0.9373684	0.793814
64	6.4	-0.983334	-0.4151898	0.1049272
65	6.5	-0.4991656	0.3643877	-0.1627931
66	6.6	0.4925782	0.3548167	-0.8811936
67	6.7	-0.819895	-2.106536	0.1773956
68	6.8	-0.04881701	-0.9867962	-0.8862132
69	6.9	1.219161	0.266691	0.188304
70	7	0.8090514	1.619885	-0.5646788
71	7.1	-0.9921044	0.7245245	0.3057475
72	7.2	-0.4119946	2.759856	0.4088039
73	7.3	1.121707	-0.6501654	-1.034288
74	7.4	1.150379	0.5587453	1.332409
75	7.5	-0.3225148	0.4750779	-0.1536095
76	7.6	1.035535	1.381175	1.225896
77	7.7	-0.1056646	0.3069166	0.4924758
78	7.8	0.4262604	-0.5698308	-0.4156163
79	7.9	-2.609303	-2.173168	-1.324497
80	8	-1.45585	0.1801837	1.421198
81	8.1	1.866039	-0.1742316	-1.55547
82	8.2	1.4884	1.303924	-1.061323
83	8.3	-1.305955	-1.629615	-0.2962869
84	8.4	0.8739792	0.1051378	-0.02998592
85	8.5	-1.516032	1.474471	-1.03669
86	8.6	-1.534651	0.8259901	0.457382
87	8.7	-0.3865615	1.28411	-0.3259461
88	8.8	1.637177	-0.8420178	-0.2924097
89	8.9	0.3615991	0.4570965	0.237978
90	9	1.020826	1.699262	-0.5438809
91	9.1	0.4973056	-1.469904	-2.294773
92	9.2	-0.2623551	-1.554523	-2.82731
93	9.3	0.5825531	0.4139608	-0.9302437
94	9.4	0.549059	-0.69065	-0.6021352
95	9.5	-0.7677184	1.285077	-0.22259
96	9.6	1.221741	0.4439343	-0.7078664
97	9.7	-1.056912	0.5648551	0.2980986
98	9.8	1.342418	1.085837	0.8239627
99	9.9	-0.6283856	-0.8834576	0.8607533

.. 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 Xi at index 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 = [-0.4429,-0.541246,-1.35629] .. GENERATED FROM PYTHON SOURCE LINES 63-64 Get the time series at index i : Xi .. 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 = [-0.4429,-0.541246,-1.35629] .. GENERATED FROM PYTHON SOURCE LINES 68-69 Get a the marginal value at index 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 = -0.44290028916853585 .. GENERATED FROM PYTHON SOURCE LINES 76-77 Get all the values (X1, .., Xn) of the time series .. GENERATED FROM PYTHON SOURCE LINES 77-79 .. code-block:: Python myTimeSeries.getValues() .. raw:: html

	X0	X1	X2
0	1.011887	-0.6089418	0.259667
1	0.3247816	0.5410446	0.124925
2	0.6338902	0.7179695	0.2042093
3	-0.2305653	-0.4410291	0.2181727
4	0.3580472	0.3890482	0.02232993
5	1.654732	0.7180658	1.200392
6	-0.04285412	0.2991685	-1.958143
7	0.3422039	-0.8220064	0.4143278
8	-0.3363815	1.84368	-0.637582
9	0.4117993	-0.1768882	-1.10384
10	-0.4144207	0.2661011	-0.3402945
11	0.7169809	-0.6244882	1.487634
12	-0.2354843	0.2280304	-0.8464
13	-0.05061286	0.9634821	-0.2666059
14	0.7183027	-1.35427	-0.3999666
15	0.8274424	-1.601233	-0.7890261
16	-0.470555	-1.173748	-1.172249
17	1.446331	-0.01098964	-0.3921936
18	0.4236814	-0.2151677	-1.361857
19	0.6538955	1.875609	-0.4024692
20	0.6233072	-0.2072951	1.17231
21	0.2915004	-2.075439	-0.2298406
22	0.9320396	-2.897866	-0.485802
23	-0.3154649	0.5633166	-1.547632
24	1.749131	-0.7117512	0.1204685
25	0.8562701	0.5912137	-1.075188
26	-0.751024	-0.5502947	-1.290288
27	0.7769506	0.5568254	-0.9893918
28	2.238198	-0.01550398	0.87992
29	1.100906	-1.087936	1.281433
30	0.7702127	-1.119431	0.3614885
31	-1.437774	0.1921378	-1.693616
32	1.488139	-0.9791753	-1.664384
33	2.758905	-0.05688733	-0.5173643
34	0.06441027	-0.4975254	-1.670192
35	-0.5278518	1.152648	0.1565362
36	-0.790078	0.1192994	-1.69795
37	-0.4429003	-0.5412464	-1.356292
38	-0.5499819	-1.220419	-0.1770449
39	1.709167	-0.6366608	0.2184536
40	0.4480405	1.224067	-0.2393039
41	-0.4370185	-0.5334587	0.4306893
42	-0.5499989	-0.9207816	-2.351244
43	-0.9560584	0.943051	0.7254229
44	0.1032824	0.5161109	2.005021
45	1.635069	-1.439767	0.5297914
46	1.036868	-0.4441049	-0.7533471
47	0.1001542	-0.5502341	1.41372
48	0.464214	0.4474071	-1.057613
49	1.359945	-0.710775	-0.1642414
50	-1.283544	0.5566532	0.5485656
51	1.687374	0.7934399	-0.5400267
52	-0.848387	-0.1032642	0.9586013
53	-1.025222	-0.3549386	-0.8693017
54	0.266897	0.296524	-2.241144
55	-1.560704	-2.271998	0.7224505
56	-2.161275	-0.3286104	1.069747
57	-1.779941	-0.8327076	-0.2453716
58	-0.0205006	-0.1701006	0.5292955
59	-0.7251038	-1.162473	0.1995235
60	0.7271477	-0.2606875	-0.1367718
61	0.5202298	-0.6591333	-0.1806734
62	-1.048847	0.5123711	0.2064803
63	-0.960832	0.4146824	-1.228714
64	2.57497	-0.008049008	-1.885899
65	0.830757	-0.3783459	0.4790463
66	1.609382	-0.5708413	0.2690964
67	0.8035033	0.5832181	0.4497564
68	-0.6935559	1.896662	0.02708176
69	-0.258272	-0.37012	0.04565963
70	-0.3430478	-0.3924844	-2.410929
71	1.939206	-0.5900438	0.2270499
72	-0.1417654	0.8555065	0.286761
73	0.5648119	-0.5097008	1.403344
74	-1.378522	0.4340351	0.03425181
75	0.8961165	-0.8705775	1.369953
76	0.2725969	0.5792226	-1.532103
77	0.957065	0.4276634	-0.3666802
78	0.6486989	-0.004649441	0.1715484
79	-0.07957611	0.4553892	-2.140093
80	0.9332446	0.8186856	-1.548256
81	0.370246	-0.773089	-0.01298333
82	0.1873089	-2.131449	-1.197682
83	-0.005001849	-0.1256726	-1.892007
84	3.40565	-0.1035762	0.4154477
85	0.7272545	0.9788553	1.158081
86	0.2952752	0.2839339	1.294258
87	0.2007735	0.342265	0.1640854
88	-0.6083832	0.1443463	0.5377329
89	0.6965567	1.187906	2.180975
90	-0.1948093	0.6283156	0.2308662
91	-0.6480712	-0.02802031	0.8710046
92	1.244731	-0.1063582	-0.2344887
93	-2.010204	0.1217012	-1.331632
94	-0.8254575	-1.216578	-1.025789
95	-1.224865	-0.7350567	0.2674311
96	-0.3139666	0.3284034	-1.185418
97	0.2725766	-0.5379969	-0.1546276
98	0.03489387	0.3572081	0.8738098
99	-1.489697	-1.603233	0.2768838

.. 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=[0.153322,-0.0887119,-0.139828]

.. GENERATED FROM PYTHON SOURCE LINES 85-86 Draw the marginal 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.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 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.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 `