` 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=[[-1.40973,0.711103,-1.75418],[-1.33661,0.269893,1.41368],[0.499241,1.15854,-0.098967],[-0.650467,1.46114,0.61372],[2.14201,-1.66772,-0.151473],[2.4158,0.137289,-0.969704],[-0.292688,-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,-0.205279,0.313591],[1.52063,2.12789,0.15741],[0.056432,1.05201,-1.06929],[0.0389696,0.108862,1.56022],[0.897858,0.0713179,0.329058],[0.768345,-0.201722,0.148307],[0.498826,-0.540609,0.202215],[1.52964,-1.19218,0.524954],[-0.127176,1.00122,0.299567],[-0.0732479,-0.592801,0.509773],[1.56808,0.369343,0.687346],[0.26022,1.5601,0.68388],[-0.260408,0.169652,-1.01657],[0.810285,-0.934548,0.440233],[0.102655,0.16255,0.977606],[-0.685128,-0.0411968,-0.161531],[0.00948899,-0.699237,0.835643],[0.961209,-0.395342,0.250509],[-1.71279,-0.303372,1.71343],[0.287997,-0.346204,-1.24308],[-0.661934,-0.539626,0.78918],[0.525199,0.265505,-0.615353],[0.667728,-0.320656,-0.00603524],[-1.44043,0.0706512,0.400517],[-0.537003,-2.13043,0.186229],[-1.32629,0.242601,-0.897333],[-0.957364,1.58824,-0.238077],[-0.654398,1.49892,-0.713136],[-1.33516,0.567629,0.640198],[-0.259729,0.192286,-1.40222],[0.560018,-1.35624,1.03452],[-0.378793,-0.125727,-0.587836],[1.07894,-1.66939,1.70834],[-0.845941,-0.178621,-0.195884],[1.81133,0.400036,1.10812],[-0.455236,-0.793417,2.28383],[0.351885,-0.0608221,1.18257],[2.05724,2.0836,-1.10946],[0.646117,0.314088,-1.25919],[2.51347,1.10677,-1.23708],[-0.405063,1.24478,0.258866],[-0.1138,0.3815,0.155791],[0.402412,1.33272,-0.805619],[0.385421,-1.61086,-0.687429],[-0.021074,-1.40527,-0.602909],[-0.0745371,-0.287633,-0.402623],[-0.489432,-0.580339,1.19649]] 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	1.004556	0.5372572	-0.08770909
1	0.1	1.423935	0.6820146	2.884055
2	0.2	0.2796988	-1.178997	-0.143892
3	0.3	0.6813079	0.01437919	0.5099701
4	0.4	-1.060234	0.04483657	0.2499197
5	0.5	1.24773	-0.3856004	-0.2880728
6	0.6	-0.5890517	0.4995753	1.132313
7	0.7	-0.8437811	1.43619	-0.1876503
8	0.8	0.940522	0.7151117	-1.439318
9	0.9	-0.1429401	-0.1765888	0.9054335
10	1	0.6688361	-0.1848348	-0.2056171
11	1.1	0.8539061	1.082717	0.7860448
12	1.2	-1.839514	-0.4807376	-0.7431111
13	1.3	0.2583894	0.06498678	0.8220976
14	1.4	-0.2202976	-1.267407	0.06548754
15	1.5	-2.506485	0.2182682	-0.3734256
16	1.6	-0.3483342	-1.020392	-0.9373684
17	1.7	0.793814	-0.983334	-0.4151898
18	1.8	0.1049272	-0.4991656	0.3643877
19	1.9	-0.1627931	0.4925782	0.3548167
20	2	-0.8811936	-0.819895	-2.106536
21	2.1	0.1773956	-0.04881701	-0.9867962
22	2.2	-0.8862132	1.219161	0.266691
23	2.3	0.188304	0.8090514	1.619885
24	2.4	-0.5646788	-0.9921044	0.7245245
25	2.5	0.3057475	-0.4119946	2.759856
26	2.6	0.4088039	1.121707	-0.6501654
27	2.7	-1.034288	1.150379	0.5587453
28	2.8	1.332409	-0.3225148	0.4750779
29	2.9	-0.1536095	1.035535	1.381175
30	3	1.225896	-0.1056646	0.3069166
31	3.1	0.4924758	0.4262604	-0.5698308
32	3.2	-0.4156163	-2.609303	-2.173168
33	3.3	-1.324497	-1.45585	0.1801837
34	3.4	1.421198	1.866039	-0.1742316
35	3.5	-1.55547	1.4884	1.303924
36	3.6	-1.061323	-1.305955	-1.629615
37	3.7	-0.2962869	0.8739792	0.1051378
38	3.8	-0.02998592	-1.516032	1.474471
39	3.9	-1.03669	-1.534651	0.8259901
40	4	0.457382	-0.3865615	1.28411
41	4.1	-0.3259461	1.637177	-0.8420178
42	4.2	-0.2924097	0.3615991	0.4570965
43	4.3	0.237978	1.020826	1.699262
44	4.4	-0.5438809	0.4973056	-1.469904
45	4.5	-2.294773	-0.2623551	-1.554523
46	4.6	-2.82731	0.5825531	0.4139608
47	4.7	-0.9302437	0.549059	-0.69065
48	4.8	-0.6021352	-0.7677184	1.285077
49	4.9	-0.22259	1.221741	0.4439343
50	5	-0.7078664	-1.056912	0.5648551
51	5.1	0.2980986	1.342418	1.085837
52	5.2	0.8239627	-0.6283856	-0.8834576
53	5.3	0.8607533	1.456264	0.1421699
54	5.4	-0.3323323	0.8952978	0.1655028
55	5.5	0.02714461	0.1645807	0.2626963
56	5.6	1.638611	0.1818056	-0.1240066
57	5.7	1.56386	-0.5471615	0.4136208
58	5.8	-0.5009097	-1.561814	-2.157897
59	5.9	-0.8845609	-0.03278067	-0.4371368
60	6	0.9263022	0.3640217	1.127778
61	6.1	-0.2958129	0.521623	-0.5048369
62	6.2	-1.126024	-0.1538759	0.9138794
63	6.3	-2.058274	1.093646	0.353957
64	6.4	-0.5708488	1.521397	0.2852253
65	6.5	-1.835236	-0.3044852	0.9165636
66	6.6	0.9140664	0.1075705	0.06927429
67	6.7	-0.6650488	1.951216	0.7997068
68	6.8	-0.8125796	-0.5797791	0.1117721
69	6.9	-0.2133026	-1.116885	-0.872058
70	7	1.629164	3.399959	-0.9405087
71	7.1	0.8080016	-0.5450092	1.626903
72	7.2	-0.06128802	0.308256	-0.9618253
73	7.3	-1.255094	0.4358796	-0.7273887
74	7.4	-0.3513546	-1.318261	-0.47417
75	7.5	-0.1005602	1.643525	-0.4139103
76	7.6	0.8686027	-0.4322521	1.012874
77	7.7	-1.114927	0.469528	0.9161205
78	7.8	-0.356955	1.022334	-2.00257
79	7.9	-1.71516	0.6274581	-1.352094
80	8	-0.03491598	-0.03793251	0.05596954
81	8.1	-0.2810947	0.144073	-2.171863
82	8.2	-0.3389453	0.5843859	-0.8390798
83	8.3	-1.04138	0.3519497	1.069267
84	8.4	-2.866462	1.182504	0.2067203
85	8.5	-0.6907754	-0.7425984	1.164752
86	8.6	-0.09003073	-1.209451	0.7730654
87	8.7	-0.8069562	-1.046643	0.1396704
88	8.8	1.067365	0.1232827	-0.776005
89	8.9	-0.882326	-0.0145659	0.2200673
90	9	0.4727389	-0.3159074	1.723677
91	9.1	0.5338985	0.4875888	-0.5419431
92	9.2	0.7959215	-0.9714537	-0.3666259
93	9.3	0.1363355	1.229809	-0.4606246
94	9.4	0.5330227	-0.9875807	0.2573491
95	9.5	0.415046	-0.7534109	0.07963906
96	9.6	0.5442014	-1.354907	-0.03364811
97	9.7	-0.7464795	-0.6355808	0.7484256
98	9.8	-1.11568	0.1287166	0.8080038
99	9.9	-0.5232872	-0.02984434	0.04724269

.. 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 = [-1.89201,3.40565,-0.103576] .. 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 = [-1.89201,3.40565,-0.103576] .. 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 = -1.892006989486264 .. 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	-1.409734	0.7111029	-1.754176
1	-1.336608	0.2698927	1.413675
2	0.4992414	1.158536	-0.09896703
3	-0.6504669	1.461145	0.6137203
4	2.142012	-1.667722	-0.1514732
5	2.4158	0.1372886	-0.9697043
6	-0.292688	-1.025222	-0.3549386
7	-0.8693017	0.266897	0.296524
8	-2.241144	-1.560704	-2.271998
9	0.7224505	-2.161275	-0.3286104
10	1.069747	-1.779941	-0.8327076
11	-0.2453716	-0.0205006	-0.1701006
12	0.5292955	-0.7251038	-1.162473
13	0.1995235	0.7271477	-0.2606875
14	-0.1367718	0.5202298	-0.6591333
15	-0.1806734	-1.048847	0.5123711
16	0.2064803	-0.960832	0.4146824
17	-1.228714	2.57497	-0.008049008
18	-1.885899	0.830757	-0.3783459
19	0.4790463	1.609382	-0.5708413
20	0.2690964	0.8035033	0.5832181
21	0.4497564	-0.6935559	1.896662
22	0.02708176	-0.258272	-0.37012
23	0.04565963	-0.3430478	-0.3924844
24	-2.410929	1.939206	-0.5900438
25	0.2270499	-0.1417654	0.8555065
26	0.286761	0.5648119	-0.5097008
27	1.403344	-1.378522	0.4340351
28	0.03425181	0.8961165	-0.8705775
29	1.369953	0.2725969	0.5792226
30	-1.532103	0.957065	0.4276634
31	-0.3666802	0.6486989	-0.004649441
32	0.1715484	-0.07957611	0.4553892
33	-2.140093	0.9332446	0.8186856
34	-1.548256	0.370246	-0.773089
35	-0.01298333	0.1873089	-2.131449
36	-1.197682	-0.005001849	-0.1256726
37	-1.892007	3.40565	-0.1035762
38	0.4154477	0.7272545	0.9788553
39	1.158081	0.2952752	0.2839339
40	1.294258	0.2007735	0.342265
41	0.1640854	-0.6083832	0.1443463
42	0.5377329	0.6965567	1.187906
43	2.180975	-0.1948093	0.6283156
44	0.2308662	-0.6480712	-0.02802031
45	0.8710046	1.244731	-0.1063582
46	-0.2344887	-2.010204	0.1217012
47	-1.331632	-0.8254575	-1.216578
48	-1.025789	-1.224865	-0.7350567
49	0.2674311	-0.3139666	0.3284034
50	-1.185418	0.2725766	-0.5379969
51	-0.1546276	0.03489387	0.3572081
52	0.8738098	-1.489697	-1.603233
53	0.2768838	-0.2052791	0.3135911
54	1.520626	2.127892	0.1574096
55	0.05643199	1.05201	-1.069286
56	0.03896958	0.1088619	1.560223
57	0.8978581	0.07131786	0.3290581
58	0.7683447	-0.2017215	0.1483074
59	0.4988259	-0.5406089	0.202215
60	1.52964	-1.192179	0.5249542
61	-0.1271758	1.001217	0.2995675
62	-0.07324792	-0.5928008	0.509773
63	1.568079	0.3693428	0.6873462
64	0.2602205	1.560101	0.6838802
65	-0.2604079	0.1696515	-1.016573
66	0.8102853	-0.9345477	0.4402335
67	0.1026545	0.1625502	0.9776058
68	-0.6851276	-0.04119683	-0.1615313
69	0.009488993	-0.6992373	0.8356431
70	0.9612086	-0.3953424	0.2505092
71	-1.712787	-0.3033722	1.713433
72	0.2879968	-0.3462038	-1.243077
73	-0.6619336	-0.5396257	0.7891796
74	0.525199	0.2655049	-0.6153533
75	0.6677281	-0.3206562	-0.00603524
76	-1.440427	0.07065125	0.4005165
77	-0.5370034	-2.130432	0.1862285
78	-1.326288	0.2426011	-0.8973327
79	-0.9573643	1.588237	-0.2380769
80	-0.6543979	1.498919	-0.7131357
81	-1.335157	0.5676285	0.640198
82	-0.259729	0.1922855	-1.402221
83	0.5600177	-1.356244	1.034522
84	-0.3787931	-0.1257271	-0.5878356
85	1.078941	-1.669386	1.708344
86	-0.8459409	-0.1786205	-0.1958844
87	1.811325	0.4000363	1.108118
88	-0.4552358	-0.7934174	2.283829
89	0.351885	-0.06082214	1.182574
90	2.057236	2.083603	-1.109457
91	0.6461174	0.3140881	-1.259195
92	2.51347	1.106768	-1.237082
93	-0.4050629	1.244775	0.2588656
94	-0.1137998	0.3814998	0.1557911
95	0.4024124	1.332716	-0.8056192
96	0.3854209	-1.61086	-0.6874292
97	-0.02107395	-1.405266	-0.6029087
98	-0.07453712	-0.287633	-0.4026233
99	-0.4894317	-0.5803388	1.196489

.. 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=[0.0252771,0.032915,0.00141464]

.. 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 `