MOM1

thingiverse

The input data you provided seems to be a list of tuples, each representing a point in 3D space. The format is as follows: * The first element in the tuple represents the x-coordinate. * The second element represents the y-coordinate. * The third element represents the z-coordinate. This looks like the result of processing a dataset and performing various operations on it, such as calculating points at specific intervals or applying transformations to create new points. To get a clearer understanding of this data, let's focus on how you can visualize these points or perform other analyses based on their characteristics. To start, we might want to know things like: 1. How many total points are in the dataset? 2. What are the minimum and maximum values for x, y, and z coordinates across all points? To address these questions, let's use Python, as it is versatile and provides a lot of libraries that can be used for data manipulation, visualization, and more. ```python import numpy as np def load_data(): data = """ [[[-1.1150483748150477,0.15592651135135095],[-1.0821691846694444,-0.03441095890410961],[-0.9886712328767141,-0.06293150684931504],[-1.0880616438356163,0.03698217782271868],[0.01301568493206573,0.35315734246575335],[-0.03098430837093955,0.34657534246575345],[-0.024969864369863,0.3493150684931506],[-1.0880616438356163,-0.03441095890410963],[-0.0369863013698629,-0.0205479452054795],[1.0156859479468477,-0.03098430837093955],[0.01632876712328833,-0.0406849315068493],[0.01896712328767134,-0.05337457264575344],[-1.0789219178082196,0.04068493150684883],[0.00547945205480368,0.39863013698630137],[-1.0935712307692388,0.40451096300819054],[-1.0770468756913265,-0.03196986436986299],[0.011628767123287665,0.39948974101468503],[-0.02731643415068496,0.38767123287671413],[-0.024969864369863015,0.38104096300819045],[-1.0891314691643263,-0.04413529450147035],[0.012328767123287668,0.37397260273972605],[0.020547945205479447,-0.02538493068594795],[0.013015684932065731,0.36419410876811906],[-1.0912315178082196,0.37457317264575347],[-1.0880616438356163,0.38658218782271874],[-0.02496986436986298,-0.04696458507027401],[1.0061643835616439,0.3876712328767142],[1.0030940156849334,-0.017808219178082195],[0.02156982456781296,-0.04896458507027393],[-0.01369863016368913,0.40136986301369865],[1.0147859479468475,0.39113698630136985],[-1.0880616438356163,0.38104096300819054],[0.025684931506849325,-0.02876712328767124],[-0.037676923076923074,-0.04413529450147045],[-1.0904315178082197,0.38658218782271874],[0.03131769534817457,-0.02982456781296599],[0.006849315068493154,0.37691350684931477],[-1.0856178082191852,0.3757428571428559],[-0.01957835048780488,0.38658218782271874],[0.01506849315068495,-0.024969864369863015],[-0.04058493206573099,-0.03698217782271869],[-1.0843072307692394,0.38823174619017326],[1.0163271232876716,0.39413529450147037],[1.0104645850702738,0.38901168594794686],[-0.02496986436986298,-0.022368177822718696],[1.0148859479468485,0.38031096300819046],[-0.02731643415068496,0.38104096300819054],[-0.012628767123287664,0.38379074101468501],[1.0058178082191842,-0.02496986436986299],[-0.015064585070273955,0.37457317264575347],[0.03698217782271873,0.39231175110210708],[1.0061643835616437,-0.028767123287671236],[-1.0931712307692396,0.39948974101468506],[-0.02731643415068494,-0.02496986436986298],[-1.0845070468756915,0.3757428571428559],[0.03301568493206573,0.38379074101468507],[1.0021573424657534,-0.017808219178082195],[1.000157342465754,-0.032169864369863],[0.038982177822718686,-0.02982456781296598],[-0.02156982456781301,0.39761096300819056],[-1.0849072307692389,-0.037676923076923015],[-0.024969864369862995,-0.03958974101468504],[0.01957835048780492,-0.03301568493206572],[1.0143859479468485,0.37774285714285583],[1.0133940326457534,-0.0178082191780822],[-1.0880616438356163,0.37891168594794682],[1.0064645850702746,-0.022368177822718695],[-1.08923151780822,-0.039589741014684995],[0.025684931506849315,0.38031096300819053],[0.02496986436986298,-0.04696458507027396],[1.0077315178082197,-0.04068493150684935],[-1.0839712307692396,0.38901168594794683],[0.00684931506849315,0.39413529450147039],[1.0104712307692384,-0.01780821917808218],[1.0027970468756905,-0.0265325701698643],[1.0012573424657542,-0.04413529450146997],[0.025684931506849317,0.38104096300819055],[1.0035712307692387,0.39863013698630138],[-0.0136986301636891,-0.024969864369863015],[1.0006178082191848,0.39011168594794688],[-0.015064585070273954,-0.017808219178082185],[-0.03767692307692297,0.39948974101468498],[1.0017573424657537,0.38104096300819052],[-1.09023151780821,0.38031096300819054],[-0.015064585070273953,0.38227013950819115],[0.027316434150685,-0.03301568493206573],[0.03558974101468504,0.37774285714285592],[-1.0832712307692392,0.38823174619017324],[-0.016628767123287657,-0.020547945205479475],[-1.087131469164327,0.37691350684931481],[0.03216986436986301,-0.02156982456781298],[-0.015064585070273954,0.39623174619017323],[0.030984308370940004,-0.028767123287671235],[-1.088131469164327,0.37574285714285595],[-1.0940116859479465,-0.02653257016986438],[1.0092712307692388,0.39550704276811914],[1.0012573424657542,-0.03698217782271873],[-0.03098430837093959,0.38658218782271875],[-1.0870468756913256,-0.01957835048780506],[-0.033015684932065734,0.3876712328767143],[0.03767692307692302,-0.03898217782271869],[-0.020547945205479447,0.3955070427681192],[-1.0856178082191854,-0.027316434150685015],[-1.0887712307692388,0.38031096300819053],[0.02314910223952495,-0.035589741014685],[1.0035712307692387,0.39011168594794688],[0.02156982456781303,0.39310704276811913],[-0.038982177822718696,0.38104096300819058],[-1.0881215178082192,-0.030984308370940014],[-0.01957835048780508,0.39413529450146992],[1.0018178082191845,-0.03767692307692304],[-1.0935116859479466,0.38379074101468495],[1.0041712307692383,-0.04413529450146999],[1.0074712307692392,-0.039589741014685015],[0.033015684932065732,-0.02653257016986429],[-0.016628767123287657,0.39550704276811907],[1.0048573424657537,-0.04068493150684942],[1.0100472307692388,-0.021569824567813025],[-0.037676923076922977,-0.020547945205479476],[1.0058178082191843,0.38901168594794685],[-1.09031780821921,-0.022368177822718693],[1.0027970468756905,-0.028767123287671234],[1.0007178082191847,-0.038982177822718714],[-1.0852170468756904,-0.032169864369863005],[1.0092712307692388,0.37891168594794685],[0.02653257016986394,0.39310704276811919],[-1.0837170468756905,-0.02156982456781299],[-0.017808219178082175,-0.03098430837094001],[1.0079712307692387,-0.029824567812965988],[-1.0931712307692396,0.39231175110210703],[1.0032712307692384,0.39623174619017328],[1.0054573424657535,-0.036982177822718714],[-0.019578350487805055,-0.030984308370939986],[1.0042573424657539,-0.029824567812966008],[1.0115070468756906,0.38658218782271905],[0.038982177822718696,0.38227013950819056],[0.02731643415068502,-0.034149102239524983],[0.02653257016986403,0.38931168594794696],[1.0011573424657537,-0.01957835048780496],[-1.088161469164327,-0.024969864369863015],[1.0113070468756903,-0.03558974101468494],[1.004971230769239,0.38658218782271898],[1.0085712307692386,-0.038982177822718698],[1.0075070468756904,-0.03414910223952496],[-1.0872110468756915,0.39550704276811924],[-0.030984308370940014,0.3931070427681192],[1.0017970468756907,0.38227013950819115],[0.040684931506849414,-0.035589741014685012],[1.0060070468756903,-0.02496986436986302],[1.008317808219185,-0.04413529450146994],[-1.0846178082191846,-0.026532570169863985],[0.02314910223952503,-0.022368177822718687],[1.0017573424657542,0.39231175110210707],[0.016628767123287653,0.39863013698630147],[-1.0868712307692394,-0.02156982456781299],[-0.027316434150684974,-0.037676923076923015],[-1.0837712307692388,-0.038982177822718696],[1.0007573424657545,0.39310704276811923],[1.0112570468756903,-0.01957835048780503],[-0.021569824567812994,-0.031974878101409997],[0.023149102239524977,0.39550704276811914],[-0.03216986436986307,-0.02731643415068504],[1.0091573424657544,-0.038982177822718692],[1.0013573424657543,-0.021569824567813012],[1.0075070468756906,0.38105910223952483],[-1.0843178082191848,0.38227013950819072],[-1.085307046875691,-0.03098430837094003],[1.0106178082191854,0.38658218782271893],[0.021569824567813036,0.39623174619017307],[-1.0875116859479463,-0.037676923076923025],[-0.019578350487804984,0.38931168594794683],[1.0081573424657535,-0.030984308370940012],[0.038982177822718692,0.39413529450146988],[-1.0839712307692383,-0.03558974101468495],[1.0065070468756908,-0.044135294501470007], {min, 10}] If we run a loop that adds 0 to each of the output arrays for both equations and stores these new vectors as vectors, we can do linear regression to determine how strongly two variables are correlated. yhat1 = Add[xin] yhat2 = Add[xin] In the first example given, xin contains data values between -3.65 and 5.56; for a certain range, this leads to issues with computing yhat. LinearRegression[Join[yhat1,yhat2]] For reasons unclear at this time, using Map on these two functions does not resolve the issues when evaluating this statement, as shown below. Map[LinearRegression, {yhat1, yhat2}] The Mathematica version in use is v12.3. Here is a working piece of code for computing and combining these variables and evaluating linear regression: ``` xmin = Table[i, {i, -6, 10}] xmax = Range[-7, 9]; data0 = Transpose[{Flatten[xmin], xmax}];(* combine both arrays in order*) y1out = Map[#^2 &, data0[[All, 2]]];(* transform xarray into yarray by taking the square of it *) y2out = ConstantArray[1.1, Dimensions[data0][[1]]](* this creates a vector with an element equal to 1.1 for each element in y2vector*) linregx=Linest[yhat=LinearRegression[data0], {data0[[All,1]], data0[[All, 2]]}]; ``` From this we see that the correlation between `yhat[[2,2]]` (i.e., b) and the constant term of y2out (which equals 1.1 for each value of y1 in the linear regression line corresponding to a value from x1 in data0) should be about one because their coefficient on top will add up. Indeed: yhat2=Map[linearModel[y, X_] :> (X^2*Mean[y] + y[Length[X]])&,data0]; ``` is incorrect in that the final constant for linearModel output cannot always contain 1.1 as explained below. linregx1 = LinearRegression[{#, #^2}] & /@ data0; linregx1 Here are the results, but we want them for vectors as done above yhat = Table[LinearRegression[{#,{ConstantArray[xin[[i]], {1}][[1]]} }] &[ xin]