sailsim.RdA dataset containing simulated data used in the accompanying paper to this package
sailsim
A list with 7 elements:
a matrix of dimension
100 x 20 where rows are observations and columns are
predictors
a numeric response vector of length 100
a numeric exposure vector of length 100
the true functions
The code used to simulate the data is available at
https://github.com/sahirbhatnagar/sail/blob/master/data-raw/SIMULATED_data.R.
See gendata for more details. The true model is given by
$$Y = f1(X1) + f2(X2) + f3(X3) + f4(X4) + E * (2 + f3(X3) +
f4(X4))$$ where
f2(t)=3(2t - 1)^2
f3(t)= 4sin(2pi*t) / (2-sin(2pi*t)
f4(t)=6(0.1sin(2pi*t) + 0.2cos(2pi*t) + 0.3sin(2pi*t)^2 + 0.4cos(2pi*t)^3 + 0.5sin(2pi*t)^3)
Lin, Y., & Zhang, H. H. (2006). Component selection and smoothing in multivariate nonparametric regression. The Annals of Statistics, 34(5), 2272-2297.
Huang J, Horowitz JL, Wei F. Variable selection in nonparametric additive models (2010). Annals of statistics. Aug 1;38(4):2282.
Bhatnagar SR, Yang Y, Greenwood CMT. Sparse additive interaction models with the strong heredity property (2018+). Preprint.
sailsim#> $x #> X1 X2 X3 X4 X5 X6 #> [1,] 0.918269079 0.558447814 0.093077163 0.402654149 0.513329960 0.108696877 #> [2,] 0.410693559 0.141769885 0.787817827 0.006500182 0.026438628 0.977739160 #> [3,] 0.031466635 0.078718231 0.768249805 0.850392241 0.767466367 0.051661229 #> [4,] 0.139289037 0.235001856 0.571775141 0.075654456 0.690776185 0.376860922 #> [5,] 0.043225337 0.473602177 0.796429249 0.686278469 0.277182099 0.825344038 #> [6,] 0.541450880 0.149062061 0.649435041 0.693991740 0.483847484 0.701358107 #> [7,] 0.804297888 0.364338255 0.539137510 0.243328579 0.144458811 0.316207919 #> [8,] 0.919484263 0.005697682 0.223786583 0.546938408 0.670017587 0.718059951 #> [9,] 0.250728327 0.993247639 0.397984891 0.399510205 0.618896582 0.025442871 #> [10,] 0.907571222 0.220336673 0.290059658 0.456858369 0.904414072 0.009690499 #> [11,] 0.349457752 0.333680904 0.116905655 0.613235970 0.942974040 0.349506491 #> [12,] 0.537413983 0.725525791 0.086629451 0.150518012 0.157165192 0.477145310 #> [13,] 0.737063563 0.819859477 0.146866767 0.259164873 0.246693158 0.627589751 #> [14,] 0.290884012 0.417723272 0.231230645 0.681784781 0.288159012 0.203849256 #> [15,] 0.160384690 0.541995476 0.191287199 0.162567490 0.005485648 0.389565845 #> [16,] 0.577349542 0.027588344 0.326394256 0.867198404 0.032309966 0.418046734 #> [17,] 0.259170652 0.278588474 0.599024196 0.614619324 0.111773070 0.433453151 #> [18,] 0.511335388 0.972919439 0.170091753 0.731547860 0.590604357 0.891433475 #> [19,] 0.482714009 0.638631678 0.533267865 0.462121789 0.056429218 0.329247452 #> [20,] 0.289148305 0.912464221 0.661843865 0.272505555 0.745270712 0.307622275 #> [21,] 0.092544849 0.404640990 0.566313418 0.190793676 0.923130517 0.311147721 #> [22,] 0.295560639 0.845001844 0.651135013 0.039814066 0.637823154 0.424831189 #> [23,] 0.055727404 0.504693865 0.603942817 0.955560014 0.431130010 0.239310450 #> [24,] 0.995092802 0.028319959 0.134100311 0.269587249 0.243254295 0.344532467 #> [25,] 0.980426212 0.668513181 0.699965235 0.527050356 0.541846638 0.355681637 #> [26,] 0.579623078 0.111907076 0.407037264 0.186452534 0.075655303 0.791223413 #> [27,] 0.842065119 0.547666735 0.256610427 0.202209257 0.099172842 0.935521836 #> [28,] 0.643489873 0.284608032 0.727608676 0.663979909 0.199200688 0.544091445 #> [29,] 0.559368738 0.260679788 0.467046066 0.258613658 0.028652255 0.926350324 #> [30,] 0.385571765 0.220144983 0.142050270 0.308194516 0.361999650 0.449998267 #> [31,] 0.387070375 0.760740802 0.272220036 0.874574474 0.787015017 0.810402758 #> [32,] 0.235415933 0.272880020 0.555234163 0.989568571 0.819821968 0.828716257 #> [33,] 0.712535433 0.077349979 0.366052995 0.072075998 0.449988666 0.819770810 #> [34,] 0.615262844 0.022543827 0.976080917 0.462774031 0.340412029 0.189685963 #> [35,] 0.403406707 0.859161389 0.328070697 0.127863202 0.482436555 0.799225194 #> [36,] 0.258537860 0.478214060 0.512818700 0.465370459 0.098102531 0.585084590 #> [37,] 0.046793783 0.609890997 0.259384452 0.896023224 0.181922966 0.081666230 #> [38,] 0.474801444 0.510414007 0.523892158 0.572144479 0.266449734 0.304159877 #> [39,] 0.025472944 0.395811494 0.322014237 0.800299945 0.366658207 0.346785525 #> [40,] 0.255168821 0.537315284 0.169593521 0.922191335 0.537305671 0.581217286 #> [41,] 0.854805695 0.438797273 0.973417659 0.846566127 0.337148180 0.619988889 #> [42,] 0.191822105 0.720291457 0.670376878 0.775789222 0.713104505 0.016332273 #> [43,] 0.353357093 0.031101877 0.266653169 0.490891914 0.001002802 0.519009865 #> [44,] 0.016159547 0.810021117 0.277189713 0.219021406 0.296395551 0.189877041 #> [45,] 0.595484344 0.143388595 0.636277534 0.838474641 0.442690343 0.020126043 #> [46,] 0.519982670 0.399730126 0.678278664 0.942553181 0.062797634 0.626396426 #> [47,] 0.774889001 0.503619910 0.291910523 0.520133443 0.313984717 0.859582365 #> [48,] 0.951050141 0.074852764 0.139031575 0.131735145 0.494498092 0.316031892 #> [49,] 0.223979242 0.300682204 0.042987005 0.764386855 0.799322373 0.566930006 #> [50,] 0.506514526 0.304581977 0.788620976 0.347267838 0.717229215 0.197590932 #> [51,] 0.976415853 0.516145747 0.884457446 0.097769594 0.101188256 0.513643197 #> [52,] 0.196528801 0.377375676 0.838223068 0.394454320 0.398465788 0.441964680 #> [53,] 0.110837307 0.822319338 0.341352799 0.907802003 0.670462441 0.547003601 #> [54,] 0.533423107 0.014165551 0.247067037 0.951938565 0.636656032 0.351583839 #> [55,] 0.139622942 0.512377216 0.733675575 0.378356625 0.424767569 0.320289093 #> [56,] 0.438220554 0.916262580 0.619261510 0.540243495 0.059905778 0.853969702 #> [57,] 0.002419612 0.041166625 0.146992574 0.610074901 0.457120124 0.440121267 #> [58,] 0.902678325 0.066588636 0.130082085 0.873095056 0.778547351 0.862884514 #> [59,] 0.176727775 0.073346010 0.324467469 0.289609017 0.827072870 0.036059189 #> [60,] 0.078368968 0.400896524 0.528824968 0.435979542 0.554796444 0.708748515 #> [61,] 0.344214699 0.037072053 0.822074730 0.364078004 0.312676736 0.973003031 #> [62,] 0.110902997 0.898239583 0.827229639 0.756482603 0.915829229 0.708642759 #> [63,] 0.431381719 0.996676240 0.508035749 0.063930179 0.265461242 0.717598652 #> [64,] 0.027512266 0.126031120 0.652914108 0.433821107 0.339932892 0.938884038 #> [65,] 0.061979635 0.196399820 0.409304228 0.572162173 0.554877705 0.220763184 #> [66,] 0.156336126 0.448661022 0.093934239 0.307743124 0.155744052 0.200854301 #> [67,] 0.546510532 0.627865088 0.965411797 0.328880145 0.461418653 0.569631652 #> [68,] 0.831944724 0.437273697 0.516606085 0.273495131 0.094969925 0.716679775 #> [69,] 0.903424153 0.212427269 0.133783087 0.885008100 0.887842488 0.402276749 #> [70,] 0.167994321 0.009537142 0.436890686 0.111041002 0.810975616 0.234409705 #> [71,] 0.387023457 0.392003975 0.042622711 0.939922748 0.270081474 0.154003220 #> [72,] 0.453640668 0.327829084 0.772879307 0.824748147 0.676052027 0.838116247 #> [73,] 0.832437994 0.903311718 0.026848910 0.378516500 0.672563684 0.369178864 #> [74,] 0.914951958 0.162691106 0.150931782 0.089930808 0.100228976 0.012316891 #> [75,] 0.491276706 0.963524260 0.632210241 0.708524133 0.267204202 0.667464091 #> [76,] 0.011130042 0.200038061 0.582199646 0.440668041 0.441853744 0.761430913 #> [77,] 0.643601380 0.198199827 0.812412135 0.556818929 0.611241488 0.859337094 #> [78,] 0.890314281 0.088830528 0.760676860 0.019640554 0.413553276 0.303462965 #> [79,] 0.841329425 0.276542830 0.891727017 0.051693353 0.340798181 0.504035697 #> [80,] 0.563878688 0.789441475 0.786084124 0.004508346 0.407000764 0.429401340 #> [81,] 0.124701626 0.403946611 0.545458282 0.331979740 0.256463366 0.009377800 #> [82,] 0.474716450 0.831135477 0.332906649 0.355467940 0.503864266 0.427490406 #> [83,] 0.118958933 0.123790459 0.376520006 0.579657652 0.285904203 0.284488700 #> [84,] 0.822722090 0.508466700 0.439359511 0.184103871 0.169473461 0.568854957 #> [85,] 0.068665220 0.680388429 0.952029936 0.248018465 0.514889192 0.217321144 #> [86,] 0.584579721 0.030161421 0.682410259 0.625827871 0.281114624 0.221791084 #> [87,] 0.792840975 0.734655632 0.573565088 0.781446611 0.044247418 0.480627770 #> [88,] 0.699162430 0.682543678 0.004940897 0.612126804 0.768278913 0.268783335 #> [89,] 0.940467187 0.043293049 0.857166413 0.418124462 0.356610466 0.445065073 #> [90,] 0.988289991 0.642071936 0.960639883 0.474036853 0.713793294 0.982232013 #> [91,] 0.973152647 0.119379754 0.337078044 0.591690438 0.385764441 0.491041785 #> [92,] 0.069346865 0.170730710 0.419147852 0.164868720 0.299630684 0.396881002 #> [93,] 0.432433760 0.213072861 0.360881179 0.473872739 0.853195648 0.200957361 #> [94,] 0.802309286 0.042694838 0.290104616 0.301069390 0.266727379 0.556157547 #> [95,] 0.702119869 0.823214378 0.204643525 0.642891227 0.174350634 0.433420980 #> [96,] 0.755529146 0.626706493 0.880058714 0.491344710 0.614452287 0.061617158 #> [97,] 0.713333455 0.021435094 0.497460861 0.924244193 0.029308480 0.524218775 #> [98,] 0.400548182 0.062377964 0.165192778 0.720243294 0.864840602 0.797919753 #> [99,] 0.384375111 0.930333338 0.023370353 0.752071470 0.540496156 0.691052151 #> [100,] 0.489202927 0.212487728 0.166479208 0.373844606 0.353293943 0.615138526 #> X7 X8 X9 X10 X11 X12 #> [1,] 0.051250849 0.5957425488 0.26509781 0.52452295 0.349708573 0.369411233 #> [2,] 0.300626530 0.7314908972 0.42865124 0.59275715 0.038592480 0.015125651 #> [3,] 0.484540881 0.8368777081 0.50204370 0.68557182 0.291898028 0.160063417 #> [4,] 0.033936431 0.2916696800 0.57977329 0.38991155 0.899261829 0.628670894 #> [5,] 0.914297574 0.4375823478 0.48816427 0.28332536 0.527337488 0.670555037 #> [6,] 0.862538750 0.7453307656 0.82317723 0.48634809 0.589780780 0.263520854 #> [7,] 0.039838086 0.3891682967 0.56132528 0.25058347 0.319265400 0.191405967 #> [8,] 0.632053483 0.8715615608 0.35344362 0.36664116 0.588647229 0.732180534 #> [9,] 0.098899216 0.5133802902 0.53093717 0.32341713 0.721693232 0.351439335 #> [10,] 0.843670109 0.8088676850 0.46304995 0.57522039 0.974604385 0.662468216 #> [11,] 0.401227074 0.1465984324 0.36181369 0.04591417 0.605644482 0.728334280 #> [12,] 0.413576920 0.2002980963 0.11702495 0.50803857 0.248692958 0.900331389 #> [13,] 0.936378039 0.1515782760 0.03293680 0.20396032 0.165225696 0.158129339 #> [14,] 0.742613880 0.5797804033 0.02511214 0.70524525 0.780200699 0.084834663 #> [15,] 0.473772413 0.2834316902 0.13378354 0.70642343 0.115716574 0.067480715 #> [16,] 0.769874048 0.0651748427 0.07687078 0.57244564 0.082224241 0.302947630 #> [17,] 0.219289307 0.4066697375 0.76824991 0.90305939 0.328320395 0.155874907 #> [18,] 0.954580692 0.6957603698 0.52033888 0.35510641 0.844091072 0.830850207 #> [19,] 0.628902683 0.6296993257 0.45004974 0.74340204 0.910610619 0.340222195 #> [20,] 0.825846039 0.2123513843 0.30363760 0.27271448 0.719536948 0.753632589 #> [21,] 0.109928537 0.1169954059 0.74527695 0.08327421 0.040895763 0.399558151 #> [22,] 0.542555873 0.2849802880 0.13738126 0.86776080 0.210936374 0.492976930 #> [23,] 0.579532464 0.9074938260 0.39839066 0.28092556 0.636384573 0.253023881 #> [24,] 0.580564987 0.8527146454 0.05161284 0.34899637 0.085034045 0.707789566 #> [25,] 0.165809945 0.2054445802 0.38243044 0.48415766 0.782511678 0.476574886 #> [26,] 0.905160652 0.0539713274 0.43349983 0.12481553 0.886873778 0.546778013 #> [27,] 0.011966763 0.5814372306 0.83648525 0.89540412 0.627567684 0.507070857 #> [28,] 0.906282802 0.8817938215 0.04599801 0.38385115 0.354849321 0.589575083 #> [29,] 0.850448683 0.1529690197 0.53372766 0.33406307 0.466775220 0.499598382 #> [30,] 0.028329807 0.9648464934 0.89060369 0.58887559 0.810480417 0.774576466 #> [31,] 0.567252356 0.3970254660 0.24473394 0.20135943 0.658813146 0.575818556 #> [32,] 0.386724862 0.0562249057 0.79948629 0.37569514 0.276053655 0.335148320 #> [33,] 0.412717713 0.2698397739 0.98854733 0.62488803 0.323073623 0.844989780 #> [34,] 0.577926494 0.0001215118 0.02389191 0.08748498 0.868277377 0.487440545 #> [35,] 0.332108641 0.8786905240 0.01174771 0.32240835 0.490113497 0.376095920 #> [36,] 0.527235373 0.4877088461 0.62995197 0.87579879 0.830073687 0.551435495 #> [37,] 0.312400921 0.5261569594 0.45413302 0.28363945 0.107767334 0.078346761 #> [38,] 0.804247237 0.6915988124 0.62992304 0.96041071 0.373100822 0.813407619 #> [39,] 0.544797445 0.3376643339 0.47115453 0.49639428 0.448245066 0.120225705 #> [40,] 0.968749521 0.0453832506 0.07148714 0.90779420 0.605233564 0.847833287 #> [41,] 0.381697190 0.5008840268 0.21558394 0.88000774 0.667164954 0.857044800 #> [42,] 0.437371198 0.3106835377 0.24776380 0.17796975 0.476180397 0.851258274 #> [43,] 0.023380000 0.1705267651 0.09986972 0.51540259 0.309054144 0.948425551 #> [44,] 0.938584714 0.1972948874 0.37033483 0.70721566 0.044888581 0.118115195 #> [45,] 0.305506194 0.8346836441 0.69301682 0.42291535 0.536501576 0.923144253 #> [46,] 0.871997487 0.7092315503 0.54217170 0.01331532 0.512236837 0.545280965 #> [47,] 0.034045131 0.8871208834 0.65955701 0.49274382 0.276408578 0.638219755 #> [48,] 0.165968426 0.6720145545 0.36518163 0.04846610 0.592745907 0.575564258 #> [49,] 0.234500438 0.0995969628 0.08918600 0.43738711 0.084261131 0.395674204 #> [50,] 0.495495090 0.3151181436 0.79227361 0.37390139 0.028167106 0.774721188 #> [51,] 0.539430498 0.1728193234 0.02359644 0.54598066 0.351432004 0.355007345 #> [52,] 0.044242854 0.8354712778 0.28403389 0.47040541 0.427161450 0.059828859 #> [53,] 0.777686922 0.5065454387 0.08220816 0.53711506 0.331276976 0.723660255 #> [54,] 0.090485287 0.3866296655 0.89833232 0.61480575 0.268096578 0.968205380 #> [55,] 0.485698828 0.0628014163 0.24372231 0.45314216 0.960310944 0.825416530 #> [56,] 0.927735974 0.0667823781 0.13792549 0.46044201 0.599371140 0.717120813 #> [57,] 0.215333645 0.1165844759 0.18076601 0.77764903 0.289057790 0.157416687 #> [58,] 0.152649746 0.1578864101 0.27334588 0.60766863 0.839783213 0.895878548 #> [59,] 0.006087820 0.1513687610 0.45428098 0.56849599 0.112000271 0.383232586 #> [60,] 0.616379163 0.9222628975 0.34883083 0.51984145 0.752788310 0.540333078 #> [61,] 0.580209429 0.8725872433 0.20559531 0.18073305 0.083514236 0.326415988 #> [62,] 0.348851353 0.7559573480 0.82112883 0.11742475 0.898598405 0.781340331 #> [63,] 0.584581874 0.8445693187 0.75096711 0.94434581 0.665176412 0.274197805 #> [64,] 0.840761270 0.9187786346 0.57079683 0.90301165 0.713882138 0.159909864 #> [65,] 0.655512605 0.0174823969 0.03801290 0.28274764 0.568139676 0.873807005 #> [66,] 0.661289958 0.9057632172 0.72347927 0.18013607 0.753439316 0.358272681 #> [67,] 0.352256053 0.2404843864 0.80064447 0.53688951 0.549350068 0.428158886 #> [68,] 0.872682411 0.9878275576 0.46133760 0.49391835 0.440369058 0.010057402 #> [69,] 0.749796630 0.1924670711 0.24656680 0.85395846 0.322932110 0.325435224 #> [70,] 0.326974686 0.4500787714 0.34988938 0.01028343 0.264143605 0.544209020 #> [71,] 0.123765346 0.9808052627 0.40150753 0.36466646 0.267829475 0.304109624 #> [72,] 0.807249954 0.1660895073 0.80365081 0.35983865 0.737797627 0.450125968 #> [73,] 0.240639150 0.4391523944 0.36756995 0.51947366 0.326266326 0.737691169 #> [74,] 0.910565859 0.8386189409 0.53822855 0.65595096 0.999204152 0.419486589 #> [75,] 0.131669420 0.8127739490 0.30445009 0.10926099 0.292216122 0.329265428 #> [76,] 0.932171619 0.9491764542 0.30436694 0.29681370 0.757826575 0.983948960 #> [77,] 0.694469087 0.8053596513 0.10047684 0.71063439 0.302114654 0.804358248 #> [78,] 0.859019333 0.4640268511 0.24146090 0.14370809 0.095215284 0.244199022 #> [79,] 0.416549545 0.4702145006 0.23877431 0.41233849 0.239307726 0.523577426 #> [80,] 0.324157798 0.1484315293 0.70644799 0.52820459 0.129029072 0.998082974 #> [81,] 0.720716821 0.5112213746 0.14185019 0.85311482 0.560758006 0.085949145 #> [82,] 0.013682514 0.2443848336 0.41293163 0.18218791 0.383148760 0.542022555 #> [83,] 0.282866625 0.3326649244 0.27214637 0.66433782 0.274244078 0.907544211 #> [84,] 0.643113525 0.7364541725 0.14108889 0.18626127 0.591024777 0.918112600 #> [85,] 0.459054344 0.2779763634 0.81390022 0.37681008 0.777753179 0.777671839 #> [86,] 0.971069103 0.8146307415 0.70035744 0.68302568 0.229597993 0.238469133 #> [87,] 0.517061466 0.4256697302 0.14795514 0.43581421 0.558074702 0.141902916 #> [88,] 0.126252175 0.0658713724 0.30857534 0.31514394 0.828848425 0.002788955 #> [89,] 0.351539544 0.6739544130 0.63096603 0.60220411 0.499293189 0.186825749 #> [90,] 0.700608476 0.0370469745 0.72616052 0.79409330 0.515084817 0.942472696 #> [91,] 0.157343564 0.1913293151 0.92427005 0.93508311 0.778548252 0.490282284 #> [92,] 0.267330989 0.0052216304 0.38154241 0.41673551 0.658837383 0.532869165 #> [93,] 0.965627941 0.4031937318 0.54505225 0.52254336 0.993112781 0.220324067 #> [94,] 0.226237028 0.4845074771 0.90893308 0.08574552 0.272600627 0.225540050 #> [95,] 0.866385565 0.3260656712 0.01495559 0.60247847 0.947428681 0.654834588 #> [96,] 0.007217147 0.1310635384 0.63569273 0.79911950 0.831636348 0.111621266 #> [97,] 0.218898789 0.7677468795 0.60510203 0.37699196 0.003861378 0.658005348 #> [98,] 0.385844760 0.1539296200 0.60919889 0.93662241 0.590495935 0.932408870 #> [99,] 0.271102833 0.6778194795 0.34655422 0.45840849 0.642785594 0.333341864 #> [100,] 0.926284179 0.7062709520 0.05390803 0.07129375 0.880876372 0.134567201 #> X13 X14 X15 X16 X17 X18 #> [1,] 0.024199279 0.939985754 0.050952427 0.920357616 0.81047731 0.35781537 #> [2,] 0.739010666 0.551293217 0.166065088 0.481766801 0.22701586 0.25051520 #> [3,] 0.476295705 0.065616481 0.793197343 0.306548994 0.71214655 0.24431060 #> [4,] 0.568885727 0.826624048 0.666762468 0.158245282 0.42217234 0.18979738 #> [5,] 0.247936813 0.602093439 0.140022141 0.026358857 0.61339972 0.48098631 #> [6,] 0.528323212 0.239066765 0.690651701 0.035480533 0.45451557 0.43469831 #> [7,] 0.511807900 0.468903573 0.022106569 0.524446410 0.79884815 0.26636901 #> [8,] 0.760540257 0.512505026 0.670483330 0.479230838 0.46031622 0.43892228 #> [9,] 0.277064109 0.824339381 0.657686269 0.560292587 0.90337852 0.08969454 #> [10,] 0.214449165 0.328801775 0.211869506 0.008375495 0.57925904 0.16764799 #> [11,] 0.283369033 0.440126390 0.764198587 0.826453380 0.46664201 0.69151006 #> [12,] 0.102769196 0.402092807 0.787946705 0.644694323 0.27332759 0.45536543 #> [13,] 0.098681611 0.106277970 0.872010108 0.445905291 0.71214762 0.07568710 #> [14,] 0.102066732 0.707817795 0.161470991 0.178842996 0.15398451 0.29399577 #> [15,] 0.570834562 0.961833559 0.300647212 0.055869623 0.14117071 0.74263045 #> [16,] 0.274367876 0.657155989 0.454352858 0.081850790 0.72342938 0.65598308 #> [17,] 0.344667414 0.877605306 0.383663955 0.154449057 0.72127114 0.59188395 #> [18,] 0.052849809 0.626645339 0.293650825 0.073078520 0.55915568 0.38276311 #> [19,] 0.502455293 0.605641056 0.080272312 0.735606654 0.09150990 0.08193191 #> [20,] 0.012098661 0.969547066 0.765080196 0.497920701 0.40246831 0.43979384 #> [21,] 0.267072157 0.847277067 0.075724479 0.294634596 0.41353206 0.17239624 #> [22,] 0.274574167 0.737894434 0.700850532 0.768800075 0.36888853 0.42196598 #> [23,] 0.741514030 0.372651792 0.839743035 0.100719568 0.92021685 0.78835271 #> [24,] 0.621631034 0.003212775 0.693736281 0.599445805 0.29902050 0.36322365 #> [25,] 0.462566932 0.680447986 0.009596745 0.132010981 0.23483914 0.96928034 #> [26,] 0.252903595 0.032017939 0.580335994 0.924670432 0.43028939 0.44052671 #> [27,] 0.782272017 0.417841700 0.337980897 0.156340748 0.83763796 0.77396504 #> [28,] 0.096650909 0.561834418 0.677265212 0.165489307 0.86777754 0.76302474 #> [29,] 0.869775673 0.595059473 0.709411990 0.332962039 0.13912051 0.25653965 #> [30,] 0.696626219 0.388694002 0.118053270 0.682848772 0.77918472 0.83008716 #> [31,] 0.386769633 0.083397886 0.883182328 0.158581917 0.75581160 0.66585469 #> [32,] 0.452431357 0.143306390 0.855776970 0.736478803 0.22612597 0.81994216 #> [33,] 0.580057597 0.961758373 0.937834050 0.676479256 0.26668475 0.76274462 #> [34,] 0.437164479 0.315962560 0.932182220 0.034093186 0.83035259 0.58890245 #> [35,] 0.320951395 0.586159811 0.326229965 0.258337923 0.27878669 0.93958369 #> [36,] 0.607485648 0.908382888 0.690128237 0.022666451 0.36323780 0.04028590 #> [37,] 0.073646204 0.314921908 0.160594769 0.155148273 0.45054320 0.70859337 #> [38,] 0.798823850 0.819127199 0.511837869 0.296870015 0.03296280 0.03064708 #> [39,] 0.974653284 0.273585572 0.151887508 0.172459827 0.03774186 0.45828322 #> [40,] 0.989218190 0.413194772 0.349677839 0.321708640 0.19747541 0.19312492 #> [41,] 0.138367370 0.709884819 0.423532716 0.911335027 0.97736241 0.84889880 #> [42,] 0.335369900 0.754377073 0.780900159 0.738997408 0.72504024 0.09510751 #> [43,] 0.357174248 0.609885308 0.355405470 0.045447003 0.43255322 0.89959562 #> [44,] 0.813316548 0.252174418 0.080471691 0.523033540 0.27999045 0.65905891 #> [45,] 0.217859757 0.066413892 0.249207186 0.820063872 0.24259218 0.64700904 #> [46,] 0.324243617 0.479474704 0.025694568 0.878537262 0.81005983 0.71183388 #> [47,] 0.134407841 0.334764203 0.371766501 0.558413671 0.12478627 0.66852502 #> [48,] 0.156441789 0.057055550 0.365378057 0.410529766 0.31489179 0.72721408 #> [49,] 0.134528509 0.643832332 0.384766091 0.043921584 0.34503892 0.06186440 #> [50,] 0.023168908 0.515543546 0.708108566 0.869379519 0.86772011 0.21702012 #> [51,] 0.132683312 0.091792385 0.531177880 0.193939599 0.24045673 0.40625907 #> [52,] 0.322198506 0.912802517 0.720245807 0.593183281 0.06624062 0.24787155 #> [53,] 0.068020272 0.168420194 0.053571911 0.994840134 0.70361040 0.41036669 #> [54,] 0.300104515 0.695714814 0.394497395 0.963499170 0.74567084 0.06662904 #> [55,] 0.471481774 0.315808436 0.005248397 0.145381655 0.13650517 0.85042788 #> [56,] 0.541549504 0.141237027 0.277250929 0.100646042 0.54343460 0.76085674 #> [57,] 0.592807244 0.067277145 0.674214954 0.308464153 0.64322339 0.05046847 #> [58,] 0.311207264 0.265782468 0.236041147 0.813806968 0.31684176 0.56038824 #> [59,] 0.023716222 0.178563702 0.562378017 0.278562333 0.46022727 0.33796491 #> [60,] 0.448954924 0.733219243 0.513015572 0.980906009 0.78159292 0.70742773 #> [61,] 0.086798228 0.562190852 0.063356605 0.273176553 0.76507000 0.98209667 #> [62,] 0.539736887 0.387290403 0.496727285 0.450855178 0.19424479 0.32524144 #> [63,] 0.017948614 0.469254803 0.972279326 0.292354539 0.38758882 0.10506643 #> [64,] 0.108469758 0.225713741 0.875946500 0.394642972 0.68066188 0.73670760 #> [65,] 0.824347021 0.332708934 0.176746421 0.020987231 0.43222627 0.72969225 #> [66,] 0.152460170 0.403016458 0.604542293 0.210876980 0.30529665 0.19997518 #> [67,] 0.922748362 0.101341207 0.729823518 0.072810312 0.79709663 0.55695430 #> [68,] 0.905766397 0.673253935 0.096110511 0.778456384 0.40590189 0.35460059 #> [69,] 0.059741637 0.461672124 0.614181560 0.872112688 0.34807350 0.60638022 #> [70,] 0.261339135 0.165669600 0.364745622 0.392409558 0.13216524 0.32509612 #> [71,] 0.184473351 0.922920644 0.707564817 0.139370172 0.76704809 0.43246011 #> [72,] 0.770016806 0.084545061 0.689500412 0.829428753 0.64583391 0.52757426 #> [73,] 0.708368328 0.129269761 0.555359930 0.089548296 0.38223859 0.39365952 #> [74,] 0.858482486 0.774512431 0.211766708 0.916099153 0.45750457 0.23518374 #> [75,] 0.902432794 0.127917842 0.539377177 0.364430541 0.23930105 0.56390388 #> [76,] 0.280097844 0.420478459 0.608567175 0.905744889 0.50443783 0.01120071 #> [77,] 0.224922758 0.431881476 0.293028510 0.028952668 0.07894625 0.22615804 #> [78,] 0.694532221 0.332778141 0.934059724 0.473574324 0.02471611 0.86526377 #> [79,] 0.092126579 0.622664365 0.231969391 0.291703859 0.48948824 0.33446295 #> [80,] 0.855764009 0.382954349 0.151565749 0.016736526 0.06624884 0.33478130 #> [81,] 0.444856383 0.856118420 0.994622131 0.349058545 0.22150436 0.21715946 #> [82,] 0.322996937 0.431661625 0.432201526 0.072877337 0.55885284 0.27247768 #> [83,] 0.903894214 0.151958320 0.794854700 0.321597263 0.28416371 0.24501640 #> [84,] 0.774772740 0.139145806 0.328189018 0.025666208 0.49310804 0.26776145 #> [85,] 0.820749959 0.665646566 0.940701707 0.794004100 0.47904923 0.49657720 #> [86,] 0.773370078 0.508192473 0.502854940 0.410681716 0.80298168 0.02334600 #> [87,] 0.802256230 0.393001517 0.075589457 0.815080853 0.31299080 0.49994914 #> [88,] 0.970527292 0.744799136 0.600088335 0.066746941 0.46123098 0.30553271 #> [89,] 0.894667754 0.531022261 0.291565002 0.582434383 0.30079932 0.86361600 #> [90,] 0.490863920 0.222387988 0.456604044 0.605246356 0.08525159 0.77132515 #> [91,] 0.039564040 0.785082851 0.394311282 0.919838686 0.97872860 0.55596413 #> [92,] 0.254544809 0.378015508 0.875721058 0.136153754 0.95946043 0.23910189 #> [93,] 0.277974521 0.026022919 0.835034176 0.711464465 0.63431581 0.99325969 #> [94,] 0.658659923 0.232063391 0.520363447 0.307791704 0.87101480 0.10675358 #> [95,] 0.282956393 0.162380780 0.051277444 0.708080926 0.12591008 0.42769397 #> [96,] 0.460884104 0.901555473 0.065264998 0.345277901 0.02306850 0.17515386 #> [97,] 0.007345145 0.120420029 0.113982938 0.468734543 0.51996378 0.98505899 #> [98,] 0.344656466 0.666237830 0.958786549 0.232827508 0.09634926 0.71853681 #> [99,] 0.864690330 0.203793515 0.250646451 0.290854400 0.16248663 0.85818103 #> [100,] 0.569788400 0.938931024 0.210830781 0.292389079 0.59916307 0.27862373 #> X19 X20 #> [1,] 0.24140422 0.53508413 #> [2,] 0.89406624 0.03375841 #> [3,] 0.81890864 0.41248497 #> [4,] 0.13613675 0.23577136 #> [5,] 0.81310768 0.90595767 #> [6,] 0.20197644 0.31753686 #> [7,] 0.12728306 0.60115974 #> [8,] 0.02500543 0.02539099 #> [9,] 0.50583613 0.67545368 #> [10,] 0.42238214 0.75117191 #> [11,] 0.42531677 0.08183596 #> [12,] 0.14836002 0.10786269 #> [13,] 0.37882117 0.33051960 #> [14,] 0.32298506 0.70729565 #> [15,] 0.50596994 0.53955629 #> [16,] 0.10602984 0.36939439 #> [17,] 0.38537332 0.03845316 #> [18,] 0.14617422 0.57676590 #> [19,] 0.38904630 0.95277371 #> [20,] 0.61764377 0.87168801 #> [21,] 0.30391222 0.45166008 #> [22,] 0.46369767 0.98355831 #> [23,] 0.58995048 0.84712579 #> [24,] 0.35267555 0.90788451 #> [25,] 0.02913312 0.72115625 #> [26,] 0.93257014 0.60812449 #> [27,] 0.60271061 0.97367934 #> [28,] 0.11767273 0.74099449 #> [29,] 0.03549462 0.04948158 #> [30,] 0.90268298 0.95058775 #> [31,] 0.71057068 0.19273520 #> [32,] 0.17420392 0.14196982 #> [33,] 0.81003014 0.90945326 #> [34,] 0.34139851 0.05540302 #> [35,] 0.52808135 0.08698340 #> [36,] 0.20118982 0.52030824 #> [37,] 0.78352154 0.26771381 #> [38,] 0.11162081 0.36257094 #> [39,] 0.55803956 0.63267987 #> [40,] 0.58148543 0.62640101 #> [41,] 0.25102662 0.05927219 #> [42,] 0.99443282 0.81840348 #> [43,] 0.50212810 0.87570941 #> [44,] 0.36755249 0.49213823 #> [45,] 0.92125209 0.68708039 #> [46,] 0.69740044 0.01465982 #> [47,] 0.14216640 0.09797399 #> [48,] 0.14057286 0.71894777 #> [49,] 0.80188385 0.28952820 #> [50,] 0.42337938 0.32651857 #> [51,] 0.24970298 0.76738532 #> [52,] 0.98004315 0.95502095 #> [53,] 0.00842069 0.22748521 #> [54,] 0.50922818 0.80710536 #> [55,] 0.77712169 0.99691547 #> [56,] 0.08434836 0.94169053 #> [57,] 0.11495872 0.96618797 #> [58,] 0.42306962 0.12745155 #> [59,] 0.09793884 0.97696637 #> [60,] 0.70642608 0.05796030 #> [61,] 0.39519601 0.93895101 #> [62,] 0.79854273 0.78519529 #> [63,] 0.05296383 0.34941599 #> [64,] 0.23328058 0.86933318 #> [65,] 0.16656617 0.86935406 #> [66,] 0.84294441 0.50309620 #> [67,] 0.36737425 0.30491925 #> [68,] 0.24289295 0.10255846 #> [69,] 0.35856621 0.03814178 #> [70,] 0.98947354 0.70679144 #> [71,] 0.86760476 0.92929863 #> [72,] 0.06335751 0.19333452 #> [73,] 0.06151930 0.77160055 #> [74,] 0.66183488 0.15791686 #> [75,] 0.16305224 0.21784860 #> [76,] 0.59506375 0.62403476 #> [77,] 0.04815618 0.61070779 #> [78,] 0.28663152 0.70210580 #> [79,] 0.44341967 0.58481985 #> [80,] 0.11610151 0.85125172 #> [81,] 0.47343442 0.68777651 #> [82,] 0.60916294 0.06297770 #> [83,] 0.60446113 0.51198446 #> [84,] 0.06603141 0.60019643 #> [85,] 0.27306099 0.25691559 #> [86,] 0.68658600 0.80801338 #> [87,] 0.35188371 0.25013432 #> [88,] 0.95658085 0.45069492 #> [89,] 0.08900851 0.18521541 #> [90,] 0.31031309 0.41083672 #> [91,] 0.47889176 0.32214733 #> [92,] 0.43024737 0.03462926 #> [93,] 0.30462492 0.33477118 #> [94,] 0.09907522 0.02977788 #> [95,] 0.42324896 0.09638374 #> [96,] 0.33362797 0.56298137 #> [97,] 0.17463600 0.92795370 #> [98,] 0.55074979 0.04594482 #> [99,] 0.24002467 0.58809356 #> [100,] 0.34855339 0.09753863 #> #> $y #> [1] 2.64141457 3.34198672 -0.99708005 11.57701632 2.05980232 0.87725068 #> [7] 13.56115922 6.75263454 2.89234437 6.34970822 -1.22583843 5.51990846 #> [13] 15.27338881 -0.10695644 14.52034121 5.27746011 -3.25336570 -0.08164529 #> [19] 4.81438702 5.64072574 6.68143531 4.64535810 -4.61737702 11.95052404 #> [25] -0.81581696 12.41343609 12.12549113 -4.51566961 15.83846154 3.69111986 #> [31] 10.18844098 5.92020936 8.98576653 2.99608490 18.42487710 -4.35441745 #> [37] 7.99801164 4.67816626 3.02564342 1.39517373 5.73465410 0.86785469 #> [43] 6.13171992 17.18997401 2.94863113 2.01555631 1.55037684 16.77056844 #> [49] -0.11702998 13.88029075 6.42392020 0.08355090 8.88906145 11.96028432 #> [55] -0.38008844 -0.26299205 3.88787808 10.98340494 16.33013288 -0.22818879 #> [61] 0.98704051 -3.44673097 8.20566834 -2.74137768 0.96055157 6.82822925 #> [67] 2.72674730 6.78568034 10.50415134 10.24596515 3.54129355 -2.16198714 #> [73] 5.08556058 5.88395022 9.01467603 -1.98489007 -1.32222991 15.73021556 #> [79] 3.61229961 1.84877582 3.93934834 6.81528703 2.63548134 6.39349046 #> [85] 3.42975024 1.45098754 4.43356537 -4.65730630 6.26751915 5.59972200 #> [91] 8.87100591 10.41157676 3.73894043 6.10533276 3.38444628 3.59204636 #> [97] 8.26104031 13.13957549 7.06421131 3.94976416 #> #> $e #> [1] -0.75707185 -0.58976189 0.49544908 0.84670712 -0.59139575 -0.08563390 #> [7] 0.68861145 -0.52229842 0.63289130 -0.55385135 -0.13351657 0.04421288 #> [13] 0.11910019 -0.69940746 0.59781626 -0.73439497 0.75952534 -0.88917111 #> [19] -0.32326132 -0.48912581 0.13938597 -0.55932054 -0.54320582 -0.24559684 #> [25] 0.36764859 -0.15537878 -0.49157144 0.35456267 0.52248952 -0.98525765 #> [31] -0.27553513 0.35918773 -0.41589947 0.47015301 0.74891693 0.95889122 #> [37] -0.35452898 -0.20560735 -0.21122506 -0.22574737 0.13435908 -0.09540532 #> [43] -0.20195152 0.68823367 0.55917770 0.17996861 0.17241897 0.37793950 #> [49] 0.19430209 0.93415348 -0.54292847 -0.20287084 0.58591979 -0.20967543 #> [55] -0.74667100 0.44337950 -0.12011884 0.12018609 -0.15115786 -0.12499030 #> [61] -0.77088480 -0.38944971 0.11352771 -0.40960795 -0.55034136 -0.54824575 #> [67] -0.17980185 -0.44602451 0.30829878 -0.25990996 -0.73977685 -0.08474036 #> [73] -0.14943082 -0.80337628 -0.49754434 -0.61223951 -0.51105481 0.68400578 #> [79] -0.25709837 -0.90320971 -0.24561208 -0.94365159 0.11303964 -0.62108243 #> [85] -0.09250825 -0.05721819 -0.06182550 0.04827889 -0.53050289 -0.97899863 #> [91] 0.88219455 0.01178292 -0.03335050 -0.56237866 -0.63036433 -0.47674469 #> [97] 0.35020749 0.55624489 -0.93339467 -0.59468344 #> #> $f1 #> function(x) 5 * x #> <bytecode: 0x55c6d2cf2de0> #> <environment: 0x55c6d23e0728> #> #> $f2 #> function(x) 3 * (2 * x - 1)^2 #> <bytecode: 0x55c6d2cf1de8> #> <environment: 0x55c6d23e0728> #> #> $f3 #> function(x) 4 * sin(2 * pi * x) / (2 - sin(2 * pi * x)) #> <bytecode: 0x55c6d2cf49b8> #> <environment: 0x55c6d23e0728> #> #> $f4 #> function(x) 6 * (0.1 * sin(2 * pi * x) + 0.2 * cos(2 * pi * x) + #> 0.3 * sin(2 * pi * x)^2 + 0.4 * cos(2 * pi * x)^3 + #> 0.5 * sin(2 * pi * x)^3) #> <bytecode: 0x55c6d2cf72b0> #> <environment: 0x55c6d23e0728> #> #> $f3.inter #> function(x, e) e * f3(x) #> <bytecode: 0x55c6d2cf8fa0> #> <environment: 0x55c6d23e0728> #> #> $f4.inter #> function(x, e) e * f4(x) #> <bytecode: 0x55c6d2cfb7b8> #> <environment: 0x55c6d23e0728> #>