2
$\begingroup$

Consider the following dataset:

    dataset={{0.001000000159197672, 9.99999999999992*^-7}, {0.001000000159197672, 
  1.1242100306002744*^-6}, {0.001000000159197672, 
  1.4208308156167856*^-6}, {0.001000000159197672, 
  1.7957144587371621*^-6}, {0.001000000159197672, 
  2.269510473643477*^-6}, {0.001000000159197672, 
  2.86831671088713*^-6}, 
   {0.001000000159197672, 
  3.6251168917261416*^-6}, {0.001000000159197672, 
  4.581597432667653*^-6}, {0.001000000159197672, 
  5.790443635882787*^-6}, {0.001000000159197672, 
  7.31824172531303*^-6}, {0.001000000159197672, 
  9.249146579759014*^-6}, {0.001000000159197672, 
  0.00001168951719071683}, 
   {0.001000000159197672, 
  0.000014773775177387728}, {0.001000000159197672, 
  0.0000186718090602862}, {0.001000000159197672, 
  0.00002359833213905933}, {0.001000000159197672, 
  0.000029824709429458177}, {0.001000000159197672, 
  0.00003769390511625662}, 
   {0.001000000159197672, 
  0.00004763937386461134}, {0.001000000159197672, 
  0.00006020893656978565}, {0.001000000159197672, 
  0.00007609495568029223}, {0.001000000159197672, 
  0.00009617247222551723}, {0.001000000159197672, 
  0.0001215474052291657}, 
   {0.001000000159197672, 
  0.00015361746845084348}, {0.001000000159197672, 
  0.0001941491598998232}, {0.001000000159197672, 
  0.0002453750648928894}, {0.001000000159197672, 
  0.00031011683234816054}, {0.001000000159197672, 
  0.00039194059815180534}, {0.001000000159197672, 
  0.000495353416699202}, 
   {0.001000000159197672, 
  0.0006260515205432618}, {0.001000000159197672, 
  0.0007912340829023327}, {0.001000000159197672, 
  0.0009999997658388317}, {0.0011725698740214546, 
  0.0009999997658388317}, {0.0013749198905786443, 
  0.0009999997658388317}, {0.0016121893862285957, 
  0.0009999997658388317}, 
   {0.0018904044045608105, 
  0.0009999997658388317}, {0.002216630901622993, 
  0.0009999997658388317}, {0.002599154203288838, 
  0.0009999997658388317}, {0.0030476894315276644, 
  0.0009999997658388317}, {0.003573628243869615, 
  0.0009999997658388317}, {0.00419032815262322, 
  0.0009999997658388317}, 
   {0.00491345177181988, 
  0.0009999997658388317}, {0.005761364607897496, 
  0.0009999997658388317}, {0.006755601496998003, 
  0.0009999997658388317}, {0.007921413535203503, 
  0.0009999997658388317}, {0.009288409392352266, 
  0.0009999997658388317}, {0.01089130729717943, 
  0.0009999997658388317}, 
   {0.012770816792298337, 
  0.0009999997658388317}, {0.01497467265336332, 
  0.0009999997658388317}, {0.017558847231339155, 
  0.0009999997658388317}, {0.02058897200829692, 
  0.0009999997658388317}, {0.024142004470649077, 
  0.0009999997658388317}, {0.02830818263417762, 
  0.0009999997658388317}, 
   {0.03319331686083523, 
  0.0009999997658388317}, {0.03594346845418379, 
  0.0009999997658388317}, {0.0374028459743575, 
  0.0009999997658388317}, {0.03878858291629611, 
  0.0009999997658388317}, {0.03883685551836095, 
  0.0009968034631843803}, {0.03892147717365525, 
  0.0009931630537797064}, 
   {0.040163171163316934, 0.000931565406537484}, {0.0405017678712987, 
  0.0009130066614999238}, {0.040932212450600684, 
  0.000889513292551626}, {0.04140583701262171, 
  0.0008666244519247692}, {0.04214622156763605, 
  0.0008351554384906082}, {0.04278661347830955, 
  0.0008089807656135544}, 
   {0.04327496689203805, 
  0.0007912340829023327}, {0.04430977192007963, 
  0.0007575927561034032}, {0.045638144320755546, 
  0.0007077271117283544}, {0.04570204582215624, 
  0.0007052633789414318}, {0.04572336619942735, 
  0.0007038133990672945}, {0.04593711777559279, 
  0.0006970861438207811}, 
   {0.047174723069779746, 
  0.0006572996648502417}, {0.04832907060081713, 
  0.0006260515205432618}, {0.04879336998419748, 
  0.0006144216875893396}, {0.04941938184659282, 
  0.0005999818977648285}, {0.05048324995767317, 
  0.0005746035247144968}, {0.051138892499691245, 
  0.000556881279745365}, 
   {0.05207759871076419, 
  0.0005350361388009571}, {0.05351390461747229, 
  0.0005059428593318458}, {0.053848772643597755, 
  0.0004999194505152742}, {0.05408263954857633, 
  0.000495353416699202}, {0.05568667738465831, 
  0.00046954399048999943}, {0.05577331882207561, 
  0.00046825729210363254}, 
   {0.056357303997745634, 
  0.00045903357716356154}, {0.057311553096389474, 
  0.00044062355184173454}, {0.05756157756621795, 
  0.00043631215824534565}, {0.057947669120943485, 
  0.00042967832747416244}, {0.05942564773050986, 
  0.00040673233871704994}, {0.06056352542553819, 
  0.00039194059815180534}, 
   {0.06152200610144253, 
  0.00038072175920003546}, {0.06274878240624557, 
  0.00036700181567461134}, {0.06362304126796989, 
  0.000355804562770912}, {0.06417936942616617, 
  0.00034863645358378857}, {0.06562726584466179, 
  0.00033126586670897653}, {0.06720178989583887, 
  0.0003151929183331249}, 
   {0.06773673667486248, 
  0.00031011683234816054}, {0.06782630756450275, 
  0.00030930237711136364}, {0.06794768026386919, 
  0.0003082785033652491}, {0.07024631304242215, 
  0.0002896880170334542}, {0.07181433160682603, 
  0.00027585310921178177}, {0.07246481366792332, 
  0.00026974000580225617}, 
   {0.073577320167753, 0.0002607637811375262}, {0.07482604896722068, 
  0.0002515248452955868}, {0.07572422506655, 
  0.0002453750648928894}, {0.07740248562612552, 
  0.0002351573189549188}, {0.07967339020323692, 
  0.00022259927994789687}, {0.08007230312513398, 
  0.0002198737338042365}, 
   {0.08029513056095959, 
  0.00021826443299199956}, {0.08127632718915224, 
  0.00021196233429267427}, {0.08255137897194964, 
  0.00020455182152397843}, {0.08460096802160764, 
  0.0001941491598998232}, {0.08531585673903667, 
  0.00019098422914224438}, {0.08627453530523323, 
  0.0001867465431247532}, 
   {0.0883100971580823, 
  0.00017872478172960954}, {0.08977745594152022, 
  0.00017270817205111615}, {0.08977920063137373, 
  0.00017269829890786086}, {0.09109908347349162, 
  0.00016641773503245868}, {0.09342260224081098, 
  0.00015724265583259698}, {0.09401999146400457, 
  0.0001550644963073943}, 
   {0.09441547872083596, 
  0.00015361746845084348}, {0.09724598112909881, 
  0.000144949091869821}, {0.09758674276139297, 
  0.0001440733802412438}, {0.09898100531780703, 
  1.608461293224791*^-8}, {0.09410773411186633, 
  1.6608830133395988*^-8}, {0.09364071768218774, 
  1.6665897825205658*^-8}, 
   {0.09342260224081098, 
  1.6692596477992305*^-8}, {0.09281457806549673, 
  1.6769114254151746*^-8}, {0.08865399648864196, 
  1.728695672873001*^-8}, {0.08627453530523323, 
  1.762524607941122*^-8}, {0.08402422790271839, 
  1.795988514289155*^-8}, {0.07969816713478378, 
  1.866327590445377*^-8}, 
   {0.07967339020323692, 
  1.866754418040126*^-8}, {0.07966100462615044, 
  1.866754418040126*^-8}, {0.07964862097445614, 
  1.8671813432500016*^-8}, {0.0755654619389593, 
  1.941862212843724*^-8}, {0.073577320167753, 
  1.982467589049245*^-8}, {0.07176410793768351, 
  2.0234592818782815*^-8}, 
   {0.06835028457120025, 
  2.0991039950313628*^-8}, {0.06809573151829212, 
  2.105834882231386*^-8}, {0.06794768026386919, 
  2.108243997488058*^-8}, {0.06754744742037765, 
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  2.190812418118467*^-8}, {0.06274878240624557, 
  2.2377745470273994*^-8}, 
   {0.061278591400413085, 
  2.2789585009470597*^-8}, {0.05866376219027568, 
  2.3598337664873862*^-8}, {0.058198206666981445, 
  2.3748561217887796*^-8}, {0.057947669120943485, 
  2.383152328661523*^-8}, {0.05710698849053854, 
  2.411108123067329*^-8}, {0.055289857111338866, 
  2.47592116833625*^-8}, 
   {0.05455554519173364, 
  2.5021027431687974*^-8}, {0.05351390461747229, 
  2.540151934402316*^-8}, {0.052508476383064745, 
  2.579959399865051*^-8}, {0.05066211837360102, 
  2.652948790834367*^-8}, {0.04986701424311396, 
  2.688369318892662*^-8}, {0.04941938184659282, 
  2.7081137132520885*^-8}, 
   {0.048010797372564945, 
  2.7682212256948292*^-8}, {0.04731335727174096, 
  2.7974137583808794*^-8}, {0.045638144320755546, 
  2.8723647703932014*^-8}, {0.04487128334754098, 
  2.9090512752037433*^-8}, {0.04347051374556906, 
  2.982471641324889*^-8}, {0.04261732623642878, 
  3.031636244943236*^-8}, 
   {0.04214622156763605, 
  3.061243152930387*^-8}, {0.040539565496046086, 
  3.166619774538652*^-8}, {0.04040428703974425, 
  3.1735063973303665*^-8}, {0.03892147717365525, 
  3.260677025280723*^-8}, {0.03842844578592374, 
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  3.3529245351583316*^-8}, 
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  3.625670144168904*^-8}, {0.03319331686083523, 
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  3.7265389326338704*^-8}, 
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  3.7693913942707895*^-8}, {0.03127941985907712, 
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   {0.025610721405671368, 
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   {0.022294821243292635, 
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  6.295450138930537*^-8}, 
   {0.017558847231339155, 
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   {0.001993636396191247, 
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  0.0002453750648928894}, {0.028176460859947176, 
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   {0.028176460859947176, 
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  0.0002777520202426722}, {0.028176460859947176, 
  0.00030799665236424465}, {0.028176460859947176, 
  0.00031011683234816054}, 
   {0.028176460859947176, 
  0.0003122516071763051}, {0.02830818263417762, 
  0.0003162759164840821}, {0.02868920780508525, 
  0.0003162759164840821}, {0.030246473935670266, 
  0.0003162759164840821}, {0.030653588304318476, 
  0.0003162759164840821}, {0.031066182389693744, 
  0.0003162759164840821}, 
   {0.03275247202064942, 
  0.0003162759164840821}, {0.03319331686083523, 
  0.0003162759164840821}, {0.03364009542635926, 
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  0.00030435595350982}, 
   {0.035488160500357094, 
  0.00028107448346460155}, {0.035488160500357094, 
  0.00027585310921178177}, {0.035488160500357094, 
  0.00027072872970836776}, {0.035488160500357094, 
  0.000250019547783717}, {0.035488160500357094, 
  0.0002453750648928894}, {0.035488160500357094, 
  0.00024081686014116894}};

It includes wrong points - two rectangles inside the domain:

ListLogLogPlot[dataset]

enter image description here

These points belong to the region

0.026 < #[[1]] < 0.038 && 10^-5 < #[[2]] < 3.7*10^-4

Could you please tell me how to remove the mentioned points quickly? I was thinking of Select, but I do not know the option "Not belonging to the given region" in Mathematica language and hence cannot just directly use the region above.

$\endgroup$

2 Answers 2

4
$\begingroup$

You are almost there.

Using DeleteCases:

d2 = DeleteCases[
   dataset, _?(0.026 < #[[1]] < 0.038 && 
       10^-5 < #[[2]] < 3.7*10^-4 &)];

ListLogLogPlot[d2]

Using IntervalMemberQ:

Clear[intervalx, intervaly];
intervalx = Interval[{0.026, 0.038}];
intervaly = Interval[{10^-5, 3.7*10^-4}];
d3 = Select[
   dataset, ! IntervalMemberQ[intervalx, First@#] || ! 
      IntervalMemberQ[intervaly, Last@#] &];

d3==d2

True


Result:

enter image description here

$\endgroup$
4
$\begingroup$

I'd just create a helper function to use as a predicate, and you basically already defined it:

BadPoints[{x_, y_}] := 0.026 < x < 0.038 && 10^-5 < y < 3.7*10^-4

Now,

ListLogLogPlot[Select[dataset, Not@*BadPoints]]
$\endgroup$

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