Ähnlichkeitsmaß/Distanzmaß für Verteilungsfunktion
- R Paket für DTW (Dynamic Time Warp) http://dtw.r-forge.r-project.org/
- Distanzwerte in alignment<-dtw(query,template,keep=TRUE);
- distance: alignment$distance
- normalizedDistance: alignment$normalizedDistance (0 ist maximale Ähnlichkeit!)
Example
library(dtw)
# test data:
# simulation time:
testtmpa <- c(2.4091387755102036,3.735209863945578,3.948852933673469,6.550112925170068,7.58168537414966,9.083768536433803,9.424487224091765,9.736785734224984,10.954984278017502,11.629491250806614,11.72087390386784,14.181778212350645,16.366718783969873,16.63714360164278,16.962133440078155,24.309420189037144,25.538810814489448,34.693466870664786,43.416086576525025,47.34122444545807,52.98907486267503,81.2861152309902,85.05494216309314,86.2987600860957,87.83377940461791,88.07211525818586,93.47182001390095,94.97391334551114,104.04375896075167,104.09042112424925,107.20509701635206,112.04074645055361,120.98244006744503,121.43304521686338,126.10250615510621,126.87794871129609,133.49389635720223,137.19751458173712,147.46015195502295,149.3533375193588,157.32285721720925,167.3166985576902,171.12136992096134,177.2937409258128,181.1254945938556,184.61281319480395,185.3646757412304,189.43123777665681,191.45741146894485,198.27032842930612,200.60810157060854,206.26849816196759,215.30122209962528,218.74926081983804,219.02462884214697,219.68991557965506,219.72359928595387,224.92122136351898,225.54230085710262,227.70400768972632,242.85156352138097,243.2530242038226,243.49924005805397,254.50274303241844,276.92720335975326,282.4435829498703,284.5828176312921,292.15454380944715,296.11726144012647,300.5078485055279,302.3088187820531,325.04282946570646,334.7751250015979,338.35769797337605,339.41273129879556,340.61140434492467,342.44109846334266,342.66365024793043,349.2012929009292,349.85370468722033,350.3420535888438,350.9583436326143,361.90983554321116,367.8696177822645,378.49200653364625,388.41915299122974,397.7415192402082,400.52782378771957,402.1610290143724,406.19676377568305,413.8663785637998,420.51533361408303,421.5743008763778,424.3528394503143,424.42417050252317,428.26192449477685,428.59912589078755,433.4852470198678,436.4155414394412,437.29977828024147,439.6893841714604,442.22785590751226,444.96740456768663,445.97542814884673,455.8904278853569,462.2064859341175,467.2693229968791,472.682975409358,476.39843181843077,477.2123040458117,480.739490756152,482.00374811021925,490.1047888897667,491.3587669333578,493.38446365220085,498.0984330599476,508.66418209096986,509.007646767261,516.8080255896812,517.7572203724468,520.2966935472562,525.5169515981514,526.0078615254931,528.6492242306501,532.2541651205217,532.7414601396173,534.9023529557643,541.8676105888582,544.4230061949849,555.5212239431239,557.5627734944874,558.1026253592622,560.9064600599824,563.0980361055333,568.0248835423488,568.0374257004798,570.3335896433209,574.1667048797834,574.2727156431392,575.4056843551804,590.6124141936896,596.7775509588297,599.8252365903422,599.8311154297928,617.3642885178408,618.649135890108,633.0543595829848,634.7691063685523,638.3150067397149,640.6060655332868,640.949307467042,642.420915495763,643.3469610883574,644.1065020808906,644.1680931750711,647.5499655071826,682.3029198354028,708.9682997636696,716.4809628397823,720.2243705422629,720.9485987693154,725.1593679137902,725.2445418040128,730.1076321897569,730.1938927070927,731.0748549174234,733.2257605173744,742.8069555833303,743.4013797451761,767.4453755715432,773.3940864047105,779.429187048392,779.6000805707155,782.5274639419952,787.8929618957807,789.3215200003827,799.0550970520519,800.6268837277028,819.0496224827874,824.356347570268,825.5744678653059,838.0005692157686,838.1179506573035,847.2039340275047,849.4317619979978,854.5127935201241,857.3685480274908,859.8072189576321,862.2018521187025,862.8614947771644,864.2213730024555,868.1274995550185,876.8346319303857,892.0187271748964,895.1542480864748,898.5278974150169,906.3759938820219,914.7839155281255,923.7930595967578,924.2451044584541,926.1851880462467,934.8578574853021,935.8797176490923,937.0847862126545,938.2534660371754,942.7369103989926,943.5474445308023,947.1186880946149,949.8823151469596,971.7155091142331,975.0940673681007,975.6341305176145,976.6632461121281,978.6419967436417,984.1276907842712,985.1500868830732,985.7040908196963,987.6744226840093,989.0864654969643,992.8627340806551,1001.385525383829,1003.8827607689204,1004.4396761372485,1014.4235320074617,1018.8875179945475,1020.2522335304319,1020.5693521409129,1022.2160892692473,1028.2326280107445,1029.301970751265,1035.2256205214196,1045.7885661483335,1046.7605540418908,1050.438288669589,1056.4057368967726,1056.6940978088357,1057.655986788299,1065.4920328853989,1068.3476121047995,1071.6786364341358,1077.2368876432258,1078.8085032948304,1084.0649165967193,1084.6861600263267,1086.5221598480841,1092.6585057822415,1103.0767078424415,1107.7274559939785,1115.7549841580028,1132.4668097097097,1143.3753096563817,1150.9570099901907,1154.009946849218,1155.9995401764966,1156.3076440611665,1158.8983393848648,1172.2313538548442,1194.9027696425933,1202.9984884883252,1203.901335997493,1204.5983415025119,1208.0971961240848,1209.6848846252467,1215.9340314964775,1221.1088909262337,1224.9282567380747,1241.8763744913545,1254.3313282009233,1261.9807415000269,1262.8044037335246,1264.0129918750933,1277.5730651211722,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# similar to a; but last values deviate:
testtmpb <- c(6.243788350340135,6.341125170068026,6.502772406462585,7.880092397108845,8.386400233772674,3.027649551799888,10.285771254676868,12.126825797193876,12.948880320153062,5.863425425170066,8.407439935870183,9.28228756561817,3.935668004150777,5.3646795950376,5.006771922239693,9.870134742879856,1.402080967045947,6.542482715943365,12.3572923548045,6.205462018183013,3.8351579910334124,1.5875471663538292,4.756927552058713,7.210897451856127,9.835502484953992,7.1192194490059535,6.325137709859419,2.4625050842586518,10.8635539364886,12.313454801147273,4.984939116059891,3.9013276242831125,8.42379094333532,4.046803187606585,5.717845090865609,6.947183648773432,6.030585436203694,10.122898707901044,8.385070574256304,2.1375895463064296,11.834442257988059,9.139453652545882,4.229598937074826,10.877319632750158,4.520269215250295,6.804491122613513,5.531833857746022,7.781930089512343,5.030878300836406,11.206180304910305,5.439803459146276,7.768645535662387,7.441714255084008,5.4267711207862135,3.829252682968871,3.547453751728767,10.930167922136633,4.374534821428568,12.075195671647975,7.637453320168419,4.1741404908146365,10.977579947356531,3.031609197870978,11.066941067487562,10.403427693469581,8.331763348475135,4.582032017333802,10.400562789448884,8.722258186179317,9.000072416115245,4.748426072279244,8.44743486284358,4.449722349609942,12.086333255189345,3.861176955782298,2.9069674319727596,11.836903331364908,9.240650091601196,2.121856509072245,11.421431221231387,8.84406273427345,5.030239864310033,10.723730033162155,10.118930841906376,10.717594549648425,8.70167640493753,10.69901147513059,9.939320625280004,1.6025056755846094,6.401457618509312,1.6789768541744365,4.577035774160549,12.38410721745953,6.711106264438513,8.086729845150614,7.140151526458965,2.4021877660968016,8.727306647456999,12.346161756450783,9.592874855353898,12.076234837039124,5.9465888593499585,10.126205032617293,8.10337226369137,8.97866743197278,8.012520620748319,4.475626526349004,9.96076896334148,6.49819203421788,8.199450528056161,12.212143367346982,3.622218774540329,2.156898167624263,3.0738734872572877,4.246412455850589,8.77142726154517,2.471958869646528,5.9827843758530435,4.525148393499194,7.618684175016256,4.499148143341699,10.081538825260395,10.396918455008176,3.0114774151707024,11.810946925997087,6.375399852167334,10.775057563228984,2.2514308195188732,10.408395442953633,5.831283616358633,3.462779539525286,9.842606717279637,3.3482394254391465,4.244759413721454,2.0172453016713234,8.205505482181138,10.393019754228021,7.66133077353561,6.868803357852698,9.57046415723596,6.082593384737038,8.487643887757486,4.012288957833221,8.955914757917412,12.197418321762484,9.190189343153406,6.4806596555192755,7.108459850041413,5.026527333392551,4.69138053907534,10.588777892130793,11.213176514075144,5.3832875626488885,10.701407140185324,1.3576232799368881,6.774817220695127,5.044870461600112,7.988050501144926,4.726562077232529,4.965945088196349,6.176120053771001,5.202926844415401,9.79162669976381,12.28464677787872,2.1838391218680044,11.714283889411831,9.160922479677424,11.69494614787402,8.383363530664155,7.800923808729976,5.865196378864766,3.20499185173594,2.382174377365004,3.525873249212964,5.255547022081714,4.606554787864411,1.9143245241858722,5.0144313598833605,2.7566480867346854,7.2545216646764175,6.646254432579326,8.909535717620088,11.60658506520349,10.876648889981311,2.5115760204081425,5.2092770877209205,2.754389710884311,9.84083009336348,10.116986892471914,6.2646554400146215,1.5854030278352411,1.214515222974569,5.429137880600933,7.382142307531808,7.643737162974048,1.7341380952381087,8.33001439228235,4.182224522995853,5.8644117818522545,10.841909057938665,5.479520999399938,5.6314234364366484,8.250863515466676,8.944256991899692,7.063211834609888,10.64704854044362,5.105450877308613,5.279266251240756,11.975338668374661,6.3645203561537755,8.658756751049282,6.208680819088613,4.288185759799603,7.962261899317923,9.838141235937087,9.755117971207596,6.934459555667786,6.482487765588189,11.716389296200418,5.7811574367711955,1.4921653811856004,7.996940096628123,9.065739490127953,4.879048574596368,3.739408340283944,11.210047092295554,5.34146249371463,6.974061010405194,8.509204399817918,3.5295596097887483,4.593718875061768,3.9525420593981835,8.935056836200602,9.636282729057712,1.4300620066792362,11.025008451732447,4.259548427005484,7.779555095679825,1.9641723639456359,7.710546776124829,8.91487065379306,8.706745601890589,7.887514707788114,5.164177202224664,8.179517393310107,10.242185074349436,8.423089864697886,10.530392058007465,8.23536591130437,7.014632652151022,5.721738415863683,8.720745746596776,6.2166695327694015,6.579302709058538,1.9045158807939515,3.8121716845782885,5.646450198138837,11.709838087707112,4.121675409650834,9.855177164700535,1.7523317219547607,6.555544599807035,5.041131440901381,3.3348143881964916,4.337449241261311,11.30707785550544,8.516930416081777,3.16721440109427,6.655035351774131,4.755995074958719,12.236769942156798,7.254165867516576,11.357624207483695,5.72889055625546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# 1. execution of a simulation run
a <- c(6.243788350340135,6.341125170068026,6.502772406462585,7.880092397108845,8.386400233772674,3.027649551799888,10.285771254676868,12.126825797193876,12.948880320153062,5.863425425170066,8.407439935870183,9.28228756561817,3.935668004150777,5.3646795950376,5.006771922239693,9.870134742879856,1.402080967045947,6.542482715943365,12.3572923548045,6.205462018183013,3.8351579910334124,1.5875471663538292,4.756927552058713,7.210897451856127,9.835502484953992,7.1192194490059535,6.325137709859419,2.4625050842586518,10.8635539364886,12.313454801147273,4.984939116059891,3.9013276242831125,8.42379094333532,4.046803187606585,5.717845090865609,6.947183648773432,6.030585436203694,10.122898707901044,8.385070574256304,2.1375895463064296,11.834442257988059,9.139453652545882,4.229598937074826,10.877319632750158,4.520269215250295,6.804491122613513,5.531833857746022,7.781930089512343,5.030878300836406,11.206180304910305,5.439803459146276,7.768645535662387,7.441714255084008,5.4267711207862135,3.829252682968871,3.547453751728767,10.930167922136633,4.374534821428568,12.075195671647975,7.637453320168419,4.1741404908146365,10.977579947356531,3.031609197870978,11.066941067487562,10.403427693469581,8.331763348475135,4.582032017333802,10.400562789448884,8.722258186179317,9.000072416115245,4.748426072279244,8.44743486284358,4.449722349609942,12.086333255189345,3.861176955782298,2.9069674319727596,11.836903331364908,9.240650091601196,2.121856509072245,11.421431221231387,8.84406273427345,5.030239864310033,10.723730033162155,10.118930841906376,10.717594549648425,8.70167640493753,10.69901147513059,9.939320625280004,1.6025056755846094,6.401457618509312,1.6789768541744365,4.577035774160549,12.38410721745953,6.711106264438513,8.086729845150614,7.140151526458965,2.4021877660968016,8.727306647456999,12.346161756450783,9.592874855353898,12.076234837039124,5.9465888593499585,10.126205032617293,8.10337226369137,8.97866743197278,8.012520620748319,4.475626526349004,9.96076896334148,6.49819203421788,8.199450528056161,12.212143367346982,3.622218774540329,2.156898167624263,3.0738734872572877,4.246412455850589,8.77142726154517,2.471958869646528,5.9827843758530435,4.525148393499194,7.618684175016256,4.499148143341699,10.081538825260395,10.396918455008176,3.0114774151707024,11.810946925997087,6.375399852167334,10.775057563228984,2.2514308195188732,10.408395442953633,5.831283616358633,3.462779539525286,9.842606717279637,3.3482394254391465,4.244759413721454,2.0172453016713234,8.205505482181138,10.393019754228021,7.66133077353561,6.868803357852698,9.57046415723596,6.082593384737038,8.487643887757486,4.012288957833221,8.955914757917412,12.197418321762484,9.190189343153406,6.4806596555192755,7.108459850041413,5.026527333392551,4.69138053907534,10.588777892130793,11.213176514075144,5.3832875626488885,10.701407140185324,1.3576232799368881,6.774817220695127,5.044870461600112,7.988050501144926,4.726562077232529,4.965945088196349,6.176120053771001,5.202926844415401,9.79162669976381,12.28464677787872,2.1838391218680044,11.714283889411831,9.160922479677424,11.69494614787402,8.383363530664155,7.800923808729976,5.865196378864766,3.20499185173594,2.382174377365004,3.525873249212964,5.255547022081714,4.606554787864411,1.9143245241858722,5.0144313598833605,2.7566480867346854,7.2545216646764175,6.646254432579326,8.909535717620088,11.60658506520349,10.876648889981311,2.5115760204081425,5.2092770877209205,2.754389710884311,9.84083009336348,10.116986892471914,6.2646554400146215,1.5854030278352411,1.214515222974569,5.429137880600933,7.382142307531808,7.643737162974048,1.7341380952381087,8.33001439228235,4.182224522995853,5.8644117818522545,10.841909057938665,5.479520999399938,5.6314234364366484,8.250863515466676,8.944256991899692,7.063211834609888,10.64704854044362,5.105450877308613,5.279266251240756,11.975338668374661,6.3645203561537755,8.658756751049282,6.208680819088613,4.288185759799603,7.962261899317923,9.838141235937087,9.755117971207596,6.934459555667786,6.482487765588189,11.716389296200418,5.7811574367711955,1.4921653811856004,7.996940096628123,9.065739490127953,4.879048574596368,3.739408340283944,11.210047092295554,5.34146249371463,6.974061010405194,8.509204399817918,3.5295596097887483,4.593718875061768,3.9525420593981835,8.935056836200602,9.636282729057712,1.4300620066792362,11.025008451732447,4.259548427005484,7.779555095679825,1.9641723639456359,7.710546776124829,8.91487065379306,8.706745601890589,7.887514707788114,5.164177202224664,8.179517393310107,10.242185074349436,8.423089864697886,10.530392058007465,8.23536591130437,7.014632652151022,5.721738415863683,8.720745746596776,6.2166695327694015,6.579302709058538,1.9045158807939515,3.8121716845782885,5.646450198138837,11.709838087707112,4.121675409650834,9.855177164700535,1.7523317219547607,6.555544599807035,5.041131440901381,3.3348143881964916,4.337449241261311,11.30707785550544,8.516930416081777,3.16721440109427,6.655035351774131,4.755995074958719,12.236769942156798,7.254165867516576,11.357624207483695,5.72889055625546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# 2. execution of a simulation run
b <- c(2.4091387755102036,3.735209863945578,3.948852933673469,6.550112925170068,7.58168537414966,9.083768536433803,9.424487224091765,9.736785734224984,10.954984278017502,11.629491250806614,11.72087390386784,4.915972223993762,6.942231559878108,6.900357867417796,10.412020514908086,10.1276419766865,11.154070378047042,10.384046681627641,5.331135034013599,3.9251378689330423,11.885016379262247,10.352409012594308,2.492995178317358,9.24148206698922,7.337532212569798,6.786000027195655,5.638040609283038,8.328360942362636,6.520909728096754,7.029808786214801,5.337892767038369,7.505869926929947,8.24116675456446,2.950495287807101,2.5802963286196245,9.109406224289458,7.005404143164768,3.5562296415678816,3.9890279797803885,11.57447194513125,7.969519697850444,9.993841340480941,3.6606572566724083,3.7548797289941547,8.991844242492647,7.319072268991135,12.36944021268522,7.140874698884403,2.0261736922880402,10.572547399477997,5.577219259070574,4.854402763605435,8.187723937657722,4.883262598352729,6.129381515141176,11.471520173821602,8.257377224811137,5.231305783863917,6.51767201495565,6.716782564831419,10.668040785747252,3.145014741798974,8.51454725533452,9.766698528244035,7.69612403350277,7.335851779140455,12.18128195727428,5.95552324157768,2.61807920840846,4.390587065401405,2.7397393214509975,1.9532344063690061,10.737646990177609,11.773597436769364,7.681548250123342,1.821871256395184,2.7005079931972773,10.115857892563099,8.589888556004553,7.412606223877674,7.6784033409133485,4.503578968464524,2.937198953865959,8.44031179050421,4.397302364176085,9.725270569846487,5.320015896491043,10.298982866426798,11.978713264586418,8.455244535474833,10.492273690195134,2.539984991306426,6.6881374856224625,6.373245757483858,10.930180447876637,1.0905752428143387,4.1749553882643795,11.30732262918167,2.9302944195733858,6.5997395021393,11.427459676683554,5.812314468071065,11.746694900086538,6.286043977386328,10.9230233176703,7.150768169815706,3.6147776687382134,7.344298690803669,4.879113863544774,10.054340052624696,8.529465500771096,8.317677147022891,8.708465735333107,8.206575613730877,4.503712937924206,4.713969407746731,10.565749031022278,5.106613079691499,10.12209460722687,9.871030944713084,2.638056854287697,5.220258050895268,4.63233003480525,3.1322726324987116,8.772572334301685,6.733598614124162,8.705579139569295,9.126150449240868,5.630821062513519,7.7576955321605965,5.654207828610424,7.191971196629652,5.754696152787801,4.320650808327741,10.462110047861415,4.939389594946533,6.441306838631249,3.833115236462504,5.726584631310288,8.337449934668712,2.632028718734773,6.270706294841034,3.047685631512536,8.469628500778299,11.804801881735557,11.551650703679456,7.33899844226255,4.73850760966036,9.718795077765435,8.653724812322594,4.843934428709531,4.604276625233069,5.031954348642444,9.337395712338207,10.077067897352435,4.2030044188252305,4.922227770162976,5.611531450515145,12.336758373067937,11.256070778593312,4.539402677797511,11.226090153704376,7.740068670493088,8.538379192189723,5.343278814412088,5.830313113410625,11.83265051517401,2.8261825626210566,10.17561922780169,4.272396312129558,4.511973888731404,4.858794964510253,9.78957658525178,12.247781038388325,6.336568812827522,6.243204268419277,11.162135156271233,6.240114158126744,6.531999243837845,3.6692931066194205,6.651592346736379,8.417001150620877,4.250451344162229,1.1127221107034302,5.600903812369779,1.9889683574093624,1.4668572533790893,10.375456959634334,5.155538463462108,4.554449499220254,2.902729448861578,6.795125323193815,9.920306170417689,11.473536914495867,8.699008067490581,7.214778115923082,10.157372974780856,1.1116618197278285,5.404397758732443,5.821050700954061,5.126304897813611,10.942841461090552,9.15076005409469,7.615427927344967,8.633301669112143,5.652124186338028,4.5744939428414,9.447151474107955,3.542563222789113,6.114653257891746,10.671839323646282,11.392752759020482,5.949669431556231,6.926487629408598,7.464444672143031,6.0081186737206735,5.249457472174072,4.648904377698614,1.1196429051394716,3.5966162318563875,7.690444112653154,3.933713265306096,5.788433375850332,8.800196083161381,2.560076658163325,1.7909979591836418,12.128662327547886,1.9638557388153686,6.016538741497243,8.732618610352006,5.492313716283434,10.562945626913915,12.121384071611828,3.778643551753703,12.23871614399286,5.232724740844333,7.883735647546018,7.836046097099825,8.661815082181647,2.613089043880109,7.137871334884039,5.701361748894669,1.10165857673951,4.628903414828756,2.946312933740046,11.335191862961437,10.418202060199974,10.366748918851727,6.193074642593274,6.416791882776579,10.973421273051827,7.832673196709038,8.160087934628109,2.9860976989052688,4.4223882416745255,9.560701587952053,9.102767401864412,8.393149664599378,2.878327243341573,6.398405209727116,11.946067731241328,6.417240193925863,11.204056115886942,7.4967538048988445,11.424006300987003,8.994225241597178,7.18329300219898,3.885403574736074,4.874524447850945,6.437322463299324,4.677554892069111,1.1139951530612962,11.757362134534787,4.1795433120630605,7.574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# calculate
alignment<-dtw(a,b,keep=TRUE);
# normalized result:
alignment$normalizedDistance
