Lets suppose I have the following two sets of data, where y is a not a proper function of x:
x1 = [-200,-195,-190,-185,-180,-175,-170,-165,-160,-155,-150,-145,-140,-135,-130,-125,-120,-115,-110,-105,-100,-98.75,-97.5,-96.25,-95,-93.75,-92.5,-91.25,-90,-88.75,-87.5,-86.25,-85,-83.75,-82.5,-81.25,-80,-78.75,-77.5,-76.25,-75,-73.75,-72.5,-71.25,-70,-68.75,-67.5,-66.25,-65,-63.75,-62.5,-61.25,-60,-58.75,-57.5,-56.25,-55,-53.75,-52.5,-51.25,-50,-48.75,-47.5,-46.25,-45,-43.75,-42.5,-41.25,-40,-38.75,-37.5,-36.25,-35,-33.75,-32.5,-31.25,-30,-28.75,-27.5,-26.25,-25,-23.75,-22.5,-21.25,-20,-18.75,-17.5,-16.25,-15,-13.75,-12.5,-11.25,-10,-8.75,-7.5,-6.25,-5,-3.75,-2.5,-1.25,0,1.25,2.5,3.75,5,6.25,7.5,8.75,10,11.25,12.5,13.75,15,16.25,17.5,18.75,20,21.25,22.5,23.75,25,26.25,27.5,28.75,30,31.25,32.5,33.75,35,36.25,37.5,38.75,40,41.25,42.5,43.75,45,46.25,47.5,48.75,50,51.25,52.5,53.75,55,56.25,57.5,58.75,60,61.25,62.5,63.75,65,66.25,67.5,68.75,70,71.25,72.5,73.75,75,76.25,77.5,78.75,80,81.25,82.5,83.75,85,86.25,87.5,88.75,90,91.25,92.5,93.75,95,96.25,97.5,98.75,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180,185,190,195,200,200,195,190,185,180,175,170,165,160,155,150,145,140,135,130,125,120,115,110,105,100,98.75,97.5,96.25,95,93.75,92.5,91.25,90,88.75,87.5,86.25,85,83.75,82.5,81.25,80,78.75,77.5,76.25,75,73.75,72.5,71.25,70,68.75,67.5,66.25,65,63.75,62.5,61.25,60,58.75,57.5,56.25,55,53.75,52.5,51.25,50,48.75,47.5,46.25,45,43.75,42.5,41.25,40,38.75,37.5,36.25,35,33.75,32.5,31.25,30,28.75,27.5,26.25,25,23.75,22.5,21.25,20,18.75,17.5,16.25,15,13.75,12.5,11.25,10,8.75,7.5,6.25,5,3.75,2.5,1.25,0,-1.25,-2.5,-3.75,-5,-6.25,-7.5,-8.75,-10,-11.25,-12.5,-13.75,-15,-16.25,-17.5,-18.75,-20,-21.25,-22.5,-23.75,-25,-26.25,-27.5,-28.75,-30,-31.25,-32.5,-33.75,-35,-36.25,-37.5,-38.75,-40,-41.25,-42.5,-43.75,-45,-46.25,-47.5,-48.75,-50,-51.25,-52.5,-53.75,-55,-56.25,-57.5,-58.75,-60,-61.25,-62.5,-63.75,-65,-66.25,-67.5,-68.75,-70,-71.25,-72.5,-73.75,-75,-76.25,-77.5,-78.75,-80,-81.25,-82.5,-83.75,-85,-86.25,-87.5,-88.75,-90,-91.25,-92.5,-93.75,-95,-96.25,-97.5,-98.75,-100,-105,-110,-115,-120,-125,-130,-135,-140,-145,-150,-155,-160,-165,-170,-175,-180,-185,-190,-195,-200];y1 = [-0.998164595,-0.998078365,-0.997986113,-0.997887339,-0.997781497,-0.997667995,-0.997546191,-0.997415382,-0.997274804,-0.997123618,-0.996960906,-0.996785654,-0.996596749,-0.996392948,-0.996172861,-0.995934932,-0.9956774,-0.99539826,-0.99509522,-0.994765636,-0.994406441,-0.994311705,-0.994214737,-0.99411558,-0.994014157,-0.993910397,-0.993804234,-0.993695584,-0.993584373,-0.993470516,-0.993353924,-0.993234501,-0.993112141,-0.992986783,-0.992858315,-0.992726605,-0.992591565,-0.992453059,-0.992310959,-0.99216513,-0.99190296,-0.9917469,-0.991586658,-0.991422063,-0.991252944,-0.991079118,-0.990900393,-0.990716565,-0.990527421,-0.990332733,-0.990132259,-0.989925745,-0.989712921,-0.989493497,-0.989267171,-0.989033615,-0.988792483,-0.988543405,-0.988285987,-0.988019807,-0.987744414,-0.987459322,-0.987164013,-0.986857927,-0.986540465,-0.986210976,-0.985868761,-0.985513058,-0.985143054,-0.984757846,-0.984356469,-0.983937869,-0.983500875,-0.983044211,-0.982566505,-0.982066184,-0.98154156,-0.980990653,-0.980411354,-0.979801307,-0.979157756,-0.978477618,-0.977757243,-0.976992368,-0.976177837,-0.975307221,-0.97437204,-0.973360408,-0.97225378,-0.9710193,-0.969586882,-0.967751822,-0.96504007,-0.961099005,-0.95486125,-0.942362109,-0.918761451,-0.891813695,-0.730557262,-0.670544475,-0.608495977,-0.544449362,-0.478272201,-0.409966632,-0.339177458,-0.265166123,0.414538615,0.479074024,0.533638997,0.5842766,0.620066944,0.658075109,0.690081822,0.721732218,0.748082282,0.777318797,0.798508123,0.870643811,0.878835187,0.891094754,0.900880759,0.907494578,0.914513834,0.92288014,0.928661143,0.981759598,0.982282358,0.982782685,0.983263306,0.983731727,0.984356368,0.984757709,0.985142934,0.985512957,0.985868672,0.986210898,0.986540397,0.986857866,0.987163956,0.987459268,0.987744362,0.988019756,0.988285937,0.988543354,0.988792432,0.989033564,0.989267121,0.989493446,0.98971287,0.989925694,0.99013221,0.990332683,0.990527374,0.99071652,0.990900347,0.991079074,0.991252901,0.991422022,0.991586618,0.991746861,0.991902916,0.99205494,0.992203077,0.992347471,0.992488255,0.992625555,0.992759494,0.992890186,0.993017741,0.993142267,0.993263863,0.993382625,0.993498643,0.993612009,0.993722803,0.993831109,0.993936999,0.994040552,0.994141838,0.994240923,0.994337871,0.994705532,0.99504362,0.995355254,0.995643117,0.995909537,0.996156539,0.996385879,0.99659673,0.996785649,0.996960904,0.997123613,0.997274797,0.997415377,0.997546184,0.99766799,0.997781493,0.997887335,0.997986111,0.998078364,0.998164596,0.998164595,0.998078365,0.997986113,0.997887339,0.997781497,0.997667995,0.997546191,0.997415382,0.997274804,0.997123618,0.996960906,0.996785654,0.996596749,0.996392948,0.996172861,0.995934932,0.9956774,0.99539826,0.99509522,0.994765636,0.994406441,0.994311705,0.994214737,0.99411558,0.994014157,0.993910397,0.993804234,0.993695584,0.993584373,0.993470516,0.993353924,0.993234501,0.993112141,0.992986783,0.992858315,0.992726605,0.992591565,0.992453059,0.992310959,0.99216513,0.99190296,0.9917469,0.991586658,0.991422063,0.991252944,0.991079118,0.990900393,0.990716565,0.990527421,0.990332733,0.990132259,0.989925745,0.989712921,0.989493497,0.989267171,0.989033615,0.988792483,0.988543405,0.988285987,0.988019807,0.987744414,0.987459322,0.987164013,0.986857927,0.986540465,0.986210976,0.985868761,0.985513058,0.985143054,0.984757846,0.984356469,0.983937869,0.983500875,0.983044211,0.982566505,0.982066184,0.98154156,0.980990653,0.980411354,0.979801307,0.979157756,0.978477618,0.977757243,0.976992368,0.976177837,0.975307221,0.97437204,0.973360408,0.97225378,0.9710193,0.969586882,0.967751822,0.96504007,0.961099005,0.95486125,0.942362109,0.918761451,0.891813695,0.730557262,0.670544475,0.608495977,0.544449362,0.478272201,0.409966632,0.339177458,0.265166123,-0.414538615,-0.479074024,-0.533638997,-0.5842766,-0.620066944,-0.658075109,-0.690081822,-0.721732218,-0.748082282,-0.777318797,-0.798508123,-0.870643811,-0.878835187,-0.891094754,-0.900880759,-0.907494578,-0.914513834,-0.92288014,-0.928661143,-0.981759598,-0.982282358,-0.982782685,-0.983263306,-0.983731727,-0.984356368,-0.984757709,-0.985142934,-0.985512957,-0.985868672,-0.986210898,-0.986540397,-0.986857866,-0.987163956,-0.987459268,-0.987744362,-0.988019756,-0.988285937,-0.988543354,-0.988792432,-0.989033564,-0.989267121,-0.989493446,-0.98971287,-0.989925694,-0.99013221,-0.990332683,-0.990527374,-0.99071652,-0.990900347,-0.991079074,-0.991252901,-0.991422022,-0.991586618,-0.991746861,-0.991902916,-0.99205494,-0.992203077,-0.992347471,-0.992488255,-0.992625555,-0.992759494,-0.992890186,-0.993017741,-0.993142267,-0.993263863,-0.993382625,-0.993498643,-0.993612009,-0.993722803,-0.993831109,-0.993936999,-0.994040552,-0.994141838,-0.994240923,-0.994337871,-0.994705532,-0.99504362,-0.995355254,-0.995643117,-0.995909537,-0.996156539,-0.996385879,-0.99659673,-0.996785649,-0.996960904,-0.997123613,-0.997274797,-0.997415377,-0.997546184,-0.99766799,-0.997781493,-0.997887335,-0.997986111,-0.998078364,-0.998164596];x2 = [200,197.5,195,192.5,190,187.5,185,182.5,180,177.5,175,172.5,170,167.5,165,162.5,160,157.5,155,152.5,150,147.5,145,142.5,140,137.5,135,132.5,130,127.5,125,122.5,120,117.5,115,112.5,110,107.5,105,102.5,100,50,49.28571429,48.57142857,47.85714286,47.14285714,46.42857143,45.71428571,45,44.28571429,43.57142857,42.85714286,42.14285714,41.42857143,40.71428571,40,39.28571429,38.57142857,37.85714286,37.14285714,36.42857143,35.71428571,35,34.28571429,33.57142857,32.85714286,32.14285714,31.42857143,30.71428571,30,29.28571429,28.57142857,27.85714286,27.14285714,26.42857143,25.71428571,25,24.28571429,23.57142857,22.85714286,22.14285714,21.42857143,20.71428571,20,19.28571429,18.57142857,17.85714286,17.14285714,16.42857143,15.71428571,15,14.28571429,13.57142857,12.85714286,12.14285714,11.42857143,10.71428571,10,9.285714286,8.571428571,7.857142857,7.142857143,6.428571429,5.714285714,5,4.285714286,3.571428571,2.857142857,2.142857143,1.428571429,0.714285714,0,-0.714285714,-1.428571429,-2.142857143,-2.857142857,-3.571428571,-4.285714286,-5,-5.714285714,-6.428571429,-7.142857143,-7.857142857,-8.571428571,-9.285714286,-10,-10.71428571,-11.42857143,-12.14285714,-12.85714286,-13.57142857,-14.28571429,-15,-15.71428571,-16.42857143,-17.14285714,-17.85714286,-18.57142857,-19.28571429,-20,-20.71428571,-21.42857143,-22.14285714,-22.85714286,-23.57142857,-24.28571429,-25,-25.71428571,-26.42857143,-27.14285714,-27.85714286,-28.57142857,-29.28571429,-30,-30.71428571,-31.42857143,-32.14285714,-32.85714286,-33.57142857,-34.28571429,-35,-35.71428571,-36.42857143,-37.14285714,-37.85714286,-38.57142857,-39.28571429,-40,-40.71428571,-41.42857143,-42.14285714,-42.85714286,-43.57142857,-44.28571429,-45,-45.71428571,-46.42857143,-47.14285714,-47.85714286,-48.57142857,-49.28571429,-50,-53.75,-57.5,-61.25,-65,-68.75,-72.5,-76.25,-80,-83.75,-87.5,-91.25,-95,-98.75,-102.5,-106.25,-110,-113.75,-117.5,-121.25,-125,-128.75,-132.5,-136.25,-140,-143.75,-147.5,-151.25,-155,-158.75,-162.5,-166.25,-170,-173.75,-177.5,-181.25,-185,-188.75,-192.5,-196.25,-200,-197.5,-195,-192.5,-190,-187.5,-185,-182.5,-180,-177.5,-175,-172.5,-170,-167.5,-165,-162.5,-160,-157.5,-155,-152.5,-150,-147.5,-145,-142.5,-140,-137.5,-135,-132.5,-130,-127.5,-125,-122.5,-120,-117.5,-115,-112.5,-110,-107.5,-105,-102.5,-100,-50,-49.28571429,-48.57142857,-47.85714286,-47.14285714,-46.42857143,-45.71428571,-45,-44.28571429,-43.57142857,-42.85714286,-42.14285714,-41.42857143,-40.71428571,-40,-39.28571429,-38.57142857,-37.85714286,-37.14285714,-36.42857143,-35.71428571,-35,-34.28571429,-33.57142857,-32.85714286,-32.14285714,-31.42857143,-30.71428571,-30,-29.28571429,-28.57142857,-27.85714286,-27.14285714,-26.42857143,-25.71428571,-25,-24.28571429,-23.57142857,-22.85714286,-22.14285714,-21.42857143,-20.71428571,-20,-19.28571429,-18.57142857,-17.85714286,-17.14285714,-16.42857143,-15.71428571,-15,-14.28571429,-13.57142857,-12.85714286,-12.14285714,-11.42857143,-10.71428571,-10,-9.285714286,-8.571428571,-7.857142857,-7.142857143,-6.428571429,-5.714285714,-5,-4.285714286,-3.571428571,-2.857142857,-2.142857143,-1.428571429,-0.714285714,0,0.714285714,1.428571429,2.142857143,2.857142857,3.571428571,4.285714286,5,5.714285714,6.428571429,7.142857143,7.857142857,8.571428571,9.285714286,10,10.71428571,11.42857143,12.14285714,12.85714286,13.57142857,14.28571429,15,15.71428571,16.42857143,17.14285714,17.85714286,18.57142857,19.28571429,20,20.71428571,21.42857143,22.14285714,22.85714286,23.57142857,24.28571429,25,25.71428571,26.42857143,27.14285714,27.85714286,28.57142857,29.28571429,30,30.71428571,31.42857143,32.14285714,32.85714286,33.57142857,34.28571429,35,35.71428571,36.42857143,37.14285714,37.85714286,38.57142857,39.28571429,40,40.71428571,41.42857143,42.14285714,42.85714286,43.57142857,44.28571429,45,45.71428571,46.42857143,47.14285714,47.85714286,48.57142857,49.28571429,50,53.75,57.5,61.25,65,68.75,72.5,76.25,80,83.75,87.5,91.25,95,98.75,102.5,106.25,110,113.75,117.5,121.25,125,128.75,132.5,136.25,140,143.75,147.5,151.25,155,158.75,162.5,166.25,170,173.75,177.5,181.25,185,188.75,192.5,196.25,20-];y2 = [0.997146363,0.99708675,0.997025361,0.996962134,0.996897004,0.996829904,0.996760766,0.996689516,0.996616079,0.996540377,0.996462326,0.996381842,0.996298836,0.996213214,0.996124878,0.996033726,0.995939649,0.995842538,0.995742273,0.995638729,0.995531778,0.995421281,0.995307095,0.995189066,0.995067033,0.994940826,0.994810266,0.994675161,0.994535309,0.994390494,0.994240491,0.994085054,0.993923926,0.993756831,0.993583474,0.99340354,0.993216693,0.993022572,0.992731781,0.992517773,0.992295203,0.984838992,0.984663413,0.984484496,0.984302226,0.984116507,0.983927237,0.983734306,0.983537599,0.983336983,0.983132341,0.982923526,0.98271042,0.982492851,0.982270671,0.982043702,0.981811767,0.981574654,0.981332181,0.981084091,0.980830152,0.980570071,0.980303566,0.980030289,0.979749857,0.979461845,0.979165745,0.97886099,0.978546882,0.978222598,0.977887159,0.97753931,0.977177546,0.976799966,0.976404246,0.975987524,0.975546431,0.975077197,0.974575598,0.974037122,0.97345635,0.972827384,0.972144151,0.971399509,0.97058671,0.969698626,0.968727494,0.96766162,0.966482429,0.965160634,0.963655517,0.961921782,0.959916204,0.957571092,0.954701078,0.950902769,0.945879628,0.939786039,0.932788555,0.922068417,0.879552425,0.861986051,0.844707961,0.827076942,0.808916164,0.783376445,0.760860309,0.738601393,0.696489554,0.561909966,0.06598797,0.008646147,-0.047904486,-0.091419305,-0.128018286,-0.165218319,-0.195875322,-0.226573705,-0.249872295,-0.290316146,-0.312049377,-0.335098655,-0.375971146,-0.398221925,-0.429215406,-0.451017313,-0.47271821,-0.502919473,-0.749931153,-0.781972439,-0.809132394,-0.820311643,-0.833036737,-0.845148011,-0.887040911,-0.894259084,-0.898348184,-0.90449425,-0.910835452,-0.915962824,-0.918640837,-0.923153948,-0.925590813,-0.93168999,-0.940176579,-0.941797032,-0.94483286,-0.967948246,-0.968642973,-0.969332265,-0.973445746,-0.973939863,-0.974415163,-0.974872362,-0.975312559,-0.975737149,-0.976147535,-0.976545136,-0.97693126,-0.977307241,-0.977674557,-0.978034995,-0.978391451,-0.978751444,-0.980482889,-0.980758424,-0.981029683,-0.981298828,-0.981579942,-0.982127018,-0.982356723,-0.98258198,-0.982802684,-0.983019037,-0.983231226,-0.983439443,-0.983643897,-0.983844811,-0.984042476,-0.984237277,-0.984429903,-0.984622323,-0.985711384,-0.986508047,-0.987238678,-0.987911105,-0.988532003,-0.989107017,-0.989640961,-0.990138,-0.99060172,-0.991035255,-0.991441355,-0.991822436,-0.992180618,-0.992517816,-0.992835702,-0.9931358,-0.993419465,-0.993687916,-0.993942245,-0.994183443,-0.994412413,-0.994629974,-0.994836872,-0.995033792,-0.995221352,-0.995400127,-0.995570641,-0.99573337,-0.995888723,-0.996033719,-0.996169389,-0.99629884,-0.996422396,-0.996540379,-0.996653078,-0.996760768,-0.996863707,-0.996962137,-0.997056285,-0.997146363,-0.99708675,-0.997025361,-0.996962134,-0.996897004,-0.996829904,-0.996760766,-0.996689516,-0.996616079,-0.996540377,-0.996462326,-0.996381842,-0.996298836,-0.996213214,-0.996124878,-0.996033726,-0.995939649,-0.995842538,-0.995742273,-0.995638729,-0.995531778,-0.995421281,-0.995307095,-0.995189066,-0.995067033,-0.994940826,-0.994810266,-0.994675161,-0.994535309,-0.994390494,-0.994240491,-0.994085054,-0.993923926,-0.993756831,-0.993583474,-0.99340354,-0.993216693,-0.993022572,-0.992731781,-0.992517773,-0.992295203,-0.984838992,-0.984663413,-0.984484496,-0.984302226,-0.984116507,-0.983927237,-0.983734306,-0.983537599,-0.983336983,-0.983132341,-0.982923526,-0.98271042,-0.982492851,-0.982270671,-0.982043702,-0.981811767,-0.981574654,-0.981332181,-0.981084091,-0.980830152,-0.980570071,-0.980303566,-0.980030289,-0.979749857,-0.979461845,-0.979165745,-0.97886099,-0.978546882,-0.978222598,-0.977887159,-0.97753931,-0.977177546,-0.976799966,-0.976404246,-0.975987524,-0.975546431,-0.975077197,-0.974575598,-0.974037122,-0.97345635,-0.972827384,-0.972144151,-0.971399509,-0.97058671,-0.969698626,-0.968727494,-0.96766162,-0.966482429,-0.965160634,-0.963655517,-0.961921782,-0.959916204,-0.957571092,-0.954701078,-0.950902769,-0.945879628,-0.939786039,-0.932788555,-0.922068417,-0.879552425,-0.861986051,-0.844707961,-0.827076942,-0.808916164,-0.783376445,-0.760860309,-0.738601393,-0.696489554,-0.561909966,-0.06598797,-0.008646147,0.047904486,0.091419305,0.128018286,0.165218319,0.195875322,0.226573705,0.249872295,0.290316146,0.312049377,0.335098655,0.375971146,0.398221925,0.429215406,0.451017313,0.47271821,0.502919473,0.749931153,0.781972439,0.809132394,0.820311643,0.833036737,0.845148011,0.887040911,0.894259084,0.898348184,0.90449425,0.910835452,0.915962824,0.918640837,0.923153948,0.925590813,0.93168999,0.940176579,0.941797032,0.94483286,0.967948246,0.968642973,0.969332265,0.973445746,0.973939863,0.974415163,0.974872362,0.975312559,0.975737149,0.976147535,0.976545136,0.97693126,0.977307241,0.977674557,0.978034995,0.978391451,0.978751444,0.980482889,0.980758424,0.981029683,0.981298828,0.981579942,0.982127018,0.982356723,0.98258198,0.982802684,0.983019037,0.983231226,0.983439443,0.983643897,0.983844811,0.984042476,0.984237277,0.984429903,0.984622323,0.985711384,0.986508047,0.987238678,0.987911105,0.988532003,0.989107017,0.989640961,0.990138,0.99060172,0.991035255,0.991441355,0.991822436,0.992180618,0.992517816,0.992835702,0.9931358,0.993419465,0.993687916,0.993942245,0.994183443,0.994412413,0.994629974,0.994836872,0.995033792,0.995221352,0.995400127,0.995570641,0.99573337,0.995888723,0.996033719,0.996169389,0.99629884,0.996422396,0.996540379,0.996653078,0.996760768,0.996863707,0.996962137,0.997056285,0.997146367];Which when plotted looks like:
and
You may have noticed that the vectors x1 and y1 are not of the same length as x2 and y2, and the step size in the y's is not consistant.
I would like to add a*x1 to b* x2 and map them onto the same y values, where a and b are constants. Since x1 and x2 are not of the same length, simply adding them does not work. I've attempted to use interpolation in the following:
x2New = interp1(x2, y2, x1);However I get the following error:
The grid vectors must contain unique points.Could someone please help me out on how I could achive adding x1 to x2?
Best Answer