Often, researchers will conduct a few high-resolution time course experiments (or densely sample points along a spatial axis), but then they must select a subset of points to sample in follow-up experiments due to financial constraints. NITPicker is a tool to select the best points to subsample. We present three different definitions of what constitutes a `good’ set of time points:
Please note that this is not a very fast value to compute– it may take a few hours to complete on a large dataset. The precise definition and motivation for these three criteria can be found at: https://doi.org/10.1101/301796
Please note that this package relies heavily on the fdasrvf package, which is used to generate probability distributions of curves, based on a set of example functions.
Please cite the following if you use this R package:
Ezer, D. and Keir J.C. Selection of time points for costly experiments: a comparison between human intuition and computer-aided experimental design. bioarxiv, :10.1101/301796 (2018).
It might also be advisable to cite this paper, which presents the fdasrvf package which is an important part of this project:
Tucker, J. D., Wu, W., Srivastava, A., Generative Models for Function Data using Phase and Amplitude Separation, Computational Statistics and Data Analysis (2012), 10.1016/j.csda.2012.12.001.
For more background on why it might be useful to minimise the L2-error for finding optimal time points to sample, please see:
Michael Kleyman, Emre Sefer, Teodora Nicola, Celia Espinoza, Divya Chhabra, James S Hagood, Naftali Kaminski, Namasivayam Ambalavanan, Ziv Bar-Joseph. Selecting the most appropriate time points to profile in high-throughput studies. eLife 2017;6:e18541 (2017).
In this example, we try to find 4 months to subsample that will let us estimate the shape of the curves as accurately as possible (minimise L2-error). In this case, we sample only 3 example curves from the distribution of curves when estimating the integral– this should be much higher (100 curves is usually suitable), but we make it 3 here to speed up loading the vignette.
Note that the tables that are printed as the evaluation are the optimisation tables that are used as part of the NITPicker algorithm’s dynamic programming algorithm.
library(fda)
#> Loading required package: splines
#> Loading required package: Matrix
#>
#> Attaching package: 'fda'
#> The following object is masked from 'package:graphics':
#>
#> matplot
library(NITPicker)
#> Loading required package: fdasrvf
#> Loading required package: fda.usc
#> Loading required package: MASS
#> Loading required package: mgcv
#> Loading required package: nlme
#> This is mgcv 1.8-23. For overview type 'help("mgcv-package")'.
#> Loading required package: rpart
mat=CanadianWeather$monthlyTemp #load data - a matrix with 12 rows, representing months (time); and 35 columns, representing cities (experiments)
a=findPathF1(c(1:12), mat, 4, numPerts=500) #find a set of points that help predict the shape of the curve
#> lambda = 0.0
#>
#> Initializing...
#> Computing Karcher mean of 35 functions in SRSF space...
#> updating step: r=1
#> updating step: r=2
#> updating step: r=3
#> updating step: r=4
#> updating step: r=5
#> updating step: r=6
#> updating step: r=7
#> updating step: r=8
#> updating step: r=9
#> updating step: r=10
#> updating step: r=11
#> updating step: r=12
#> updating step: r=13
#> updating step: r=14
#> updating step: r=15
#> updating step: r=16
#> updating step: r=17
#> updating step: r=18
#> [,1]
#> [1,] 0
#> [2,] Inf
#> [3,] Inf
#> [4,] Inf
#> [5,] Inf
#> [,1] [,2]
#> [1,] 405386.3 Inf
#> [2,] Inf 0
#> [3,] Inf Inf
#> [4,] Inf Inf
#> [5,] Inf Inf
#> [,1] [,2] [,3]
#> [1,] 12754641 Inf Inf
#> [2,] Inf 402987.9 405386.3
#> [3,] Inf Inf 0.0
#> [4,] Inf Inf Inf
#> [5,] Inf Inf Inf
#> [,1] [,2] [,3] [,4]
#> [1,] 76710128 Inf Inf Inf
#> [2,] Inf 2691586 566219.1 12754640.8
#> [3,] Inf Inf 160832.8 402987.9
#> [4,] Inf Inf Inf 0.0
#> [5,] Inf Inf Inf Inf
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 209951996 Inf Inf Inf Inf
#> [2,] Inf 5204859 698771.0 12761361.222 76710127.9
#> [3,] Inf Inf 293384.7 409708.318 566219.1
#> [4,] Inf Inf Inf 6720.452 160832.8
#> [5,] Inf Inf Inf Inf 0.0
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 382507122 Inf Inf Inf Inf Inf
#> [2,] Inf 5264874 646543.1 13106225.8 76793763.00 2.099520e+08
#> [3,] Inf Inf 241156.8 754572.9 649854.16 6.987710e+05
#> [4,] Inf Inf Inf 351585.0 244467.88 2.933847e+05
#> [5,] Inf Inf Inf Inf 83635.07 6.720452e+03
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 514207138 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 4327509 3736712 16528427 78183000 210179365.1 382507122.0
#> [3,] Inf Inf 3331326 4176774 2039091 926140.2 646543.1
#> [4,] Inf Inf Inf 3773786 1633705 520753.9 241156.8
#> [5,] Inf Inf Inf Inf 1472872 234089.7 244467.9
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 473815404 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 22257196 29448384 37850239 89419317 214180641 383180660.8
#> [3,] Inf Inf 29042997 25498586 13275408 4927416 1320081.9
#> [4,] Inf Inf Inf 25095598 12870022 4522030 914695.6
#> [5,] Inf Inf Inf Inf 12709189 4235366 918006.7
#> [,8]
#> [1,] Inf
#> [2,] 514207138.3
#> [3,] 3736712.2
#> [4,] 646543.1
#> [5,] 241156.8
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 301568981 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 113501857 122664213 110684752 132584847 234160346 389372771
#> [3,] Inf Inf 122258827 98333099 56440938 24907121 7512192
#> [4,] Inf Inf Inf 97930111 56035552 24501735 7106806
#> [5,] Inf Inf Inf Inf 55874719 24215071 7110117
#> [,8] [,9]
#> [1,] Inf Inf
#> [2,] 514906845.6 473815403.8
#> [3,] 4436419.5 22257195.9
#> [4,] 1346250.4 1320081.9
#> [5,] 940864.1 646543.1
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 227383372 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 295326609 291690105 239624085 211446143 273324356 403428583
#> [3,] Inf Inf 291284719 227272432 135302234 64071132 21568004
#> [4,] Inf Inf Inf 226869444 134896848 63665745 21162618
#> [5,] Inf Inf Inf Inf 134736015 63379081 21165929
#> [,8] [,9] [,10]
#> [1,] Inf Inf Inf
#> [2,] 517438201 473900449.3 301568981
#> [3,] 6967775 22342241.4 110684752
#> [4,] 3877605 1405127.4 4436419
#> [5,] 3472219 731588.5 1320082
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 383414673 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 580963702 546264276 431871174 331410271 335681857 428133989
#> [3,] Inf Inf 545858890 419519521 255266362 126428632 46273410
#> [4,] Inf Inf Inf 419116533 254860975 126023246 45868023
#> [5,] Inf Inf Inf Inf 254700143 125736582 45871334
#> [,8] [,9] [,10] [,11]
#> [1,] Inf Inf Inf Inf
#> [2,] 523362361 474572008 301635771 227383372
#> [3,] 12891935 23013800 110751541 211446143
#> [4,] 9801765 2076686 4503209 6967775
#> [5,] 9396379 1403147 1386871 1405127
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 795952515 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 906415161 828832215 641404449 460231248 401394221 453421513
#> [3,] Inf Inf 828426829 629052796 384087340 192140996 71560934
#> [4,] Inf Inf Inf 628649808 383681953 191735610 71155548
#> [5,] Inf Inf Inf Inf 383521121 191448946 71158859
#> [,8] [,9] [,10] [,11] [,12]
#> [1,] Inf Inf Inf Inf Inf
#> [2,] 529088074 475106411 301651203 227393966 383414673
#> [3,] 18617648 23548203 110766973 211456737 227383372
#> [4,] 15527478 2611089 4518641 6978369 12891935
#> [5,] 15122092 1937551 1402303 1415722 2076686
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 0 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 1058711071 865705906 510500721 276180996 322618020 544844386
#> [3,] Inf Inf 865300520 498149068 200037087 113364795 162983807
#> [4,] Inf Inf Inf 497746081 199631701 112959409 162578421
#> [5,] Inf Inf Inf Inf 199470868 112672745 162581732
#> [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] Inf Inf Inf Inf Inf Inf
#> [2,] 745849265 682822544 411978766 265186735 387714474 795952515
#> [3,] 235378839 231264336 221094537 249249506 231683173 227393966
#> [4,] 232288670 210327222 114846204 44771138 17191735 18617648
#> [5,] 231883284 209653684 111729867 39208490 6376486 2611089
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 0 0 0 0
#> [2,] 0 1 0 0 0
#> [3,] 0 1 2 0 0
#> [4,] 0 2 2 3 0
#> [5,] 0 2 2 3 4
#> [6,] 0 2 2 4 5
#> [7,] 0 2 6 6 5
#> [8,] 0 1 6 7 7
#> [9,] 0 3 7 8 8
#> [10,] 0 4 7 8 8
#> [11,] 0 10 7 8 9
#> [12,] 0 10 7 8 9
#> [13,] 0 10 5 11 12
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0 Inf Inf Inf Inf
#> [2,] 405386.3 0.0 Inf Inf Inf
#> [3,] 12754640.8 402987.9 0.0 Inf Inf
#> [4,] 76710127.9 566219.1 160832.8 0.000 Inf
#> [5,] 209951995.9 698771.0 293384.7 6720.452 0.000
#> [6,] 382507122.0 646543.1 241156.8 244467.877 6720.452
#> [7,] 514207138.3 3736712.2 646543.1 241156.800 234089.687
#> [8,] 473815403.8 22257195.9 1320081.9 646543.082 241156.800
#> [9,] 301568981.4 110684751.7 4436419.5 1320081.921 646543.082
#> [10,] 227383372.2 211446142.7 6967774.6 1405127.355 731588.515
#> [11,] 383414673.3 227383372.2 12891934.6 2076685.594 1386871.264
#> [12,] 795952514.6 227393966.3 18617647.6 2611089.346 1402303.103
#> [13,] 0.0 265186735.3 113364795.3 17191735.022 2611089.346
print(a) #indices of months to select for follow-up experiments
#> [1] 2 6 8 12
print(rownames(CanadianWeather$monthlyTemp)[a]) #month names selected
#> [1] "Feb" "Jun" "Aug" "Dec"In this example, we consider Canadian cities to be different experimental conditions, and we consider Resolute, Canada to be the control condition. We want to find a set of points that will enable us to estimate the profile of the difference in temperature between Resolute and other cities in Canada. In this case, we sample only 3 example curves from the distribution of curves when estimating the integral– this should be much higher (100 curves is usually suitable), but we make it 3 here to speed up loading the vignette.
Note that the tables that are printed as the evaluation are the optimisation tables that are used as part of the NITPicker algorithm’s dynamic programming algorithm.
library(fda)
library(NITPicker)
mat=CanadianWeather$monthlyTemp #load data - a matrix with 12 rows, representing months (time); and 35 columns, representing cities (experiments)
y=CanadianWeather$monthlyTemp[,"Resolute"]
a=findPathF2(c(1:12), y, mat, 4, numPerts=500) #find a set of points that help predict the shape of the curve
#> lambda = 0.0
#>
#> Initializing...
#> Computing Karcher mean of 35 functions in SRSF space...
#> updating step: r=1
#> updating step: r=2
#> updating step: r=3
#> updating step: r=4
#> updating step: r=5
#> updating step: r=6
#> updating step: r=7
#> updating step: r=8
#> updating step: r=9
#> updating step: r=10
#> updating step: r=11
#> updating step: r=12
#> updating step: r=13
#> updating step: r=14
#> updating step: r=15
#> updating step: r=16
#> updating step: r=17
#> updating step: r=18
#> [,1]
#> [1,] 0
#> [2,] Inf
#> [3,] Inf
#> [4,] Inf
#> [5,] Inf
#> [,1] [,2]
#> [1,] 365301.9 Inf
#> [2,] Inf 0
#> [3,] Inf Inf
#> [4,] Inf Inf
#> [5,] Inf Inf
#> [,1] [,2] [,3]
#> [1,] 12548826 Inf Inf
#> [2,] Inf 431379.5 365301.9
#> [3,] Inf Inf 0.0
#> [4,] Inf Inf Inf
#> [5,] Inf Inf Inf
#> [,1] [,2] [,3] [,4]
#> [1,] 76245505 Inf Inf Inf
#> [2,] Inf 2810254 526415.0 12548826.2
#> [3,] Inf Inf 161113.1 365301.9
#> [4,] Inf Inf Inf 0.0
#> [5,] Inf Inf Inf Inf
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 208843455 Inf Inf Inf Inf
#> [2,] Inf 5398116 655270.1 12556017.19 76245505.1
#> [3,] Inf Inf 289968.2 372492.91 526415.0
#> [4,] Inf Inf Inf 7191.02 161113.1
#> [5,] Inf Inf Inf Inf 0.0
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 382591642 Inf Inf Inf Inf Inf
#> [2,] Inf 5570194 599109.8 12883180.7 76322515.06 208843455.47
#> [3,] Inf Inf 233807.9 699656.4 603424.98 655270.12
#> [4,] Inf Inf Inf 334354.5 238123.10 289968.23
#> [5,] Inf Inf Inf Inf 77009.99 7191.02
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 515803981 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 4487408 3595760 16234667 77682806 209072841.4 382591641.8
#> [3,] Inf Inf 3230458 4051143 1963716 884656.0 599109.8
#> [4,] Inf Inf Inf 3685841 1598414 519354.1 233807.9
#> [5,] Inf Inf Inf Inf 1437301 236576.9 238123.1
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 474631012 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 21965495 29297649 37595429 88975900 213148069 383280728.0
#> [3,] Inf Inf 28932347 25411905 13256810 4959884 1288196.0
#> [4,] Inf Inf Inf 25046603 12891508 4594582 922894.1
#> [5,] Inf Inf Inf Inf 12730395 4311805 927209.3
#> [,8]
#> [1,] Inf
#> [2,] 515803981.4
#> [3,] 3595759.9
#> [4,] 599109.8
#> [5,] 233807.9
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 302734286 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 112055517 122176732 110234863 132074679 233183130 389464846
#> [3,] Inf Inf 121811430 98051339 56355589 24994945 7472314
#> [4,] Inf Inf Inf 97686037 55990287 24629643 7107012
#> [5,] Inf Inf Inf Inf 55829174 24346866 7111328
#> [,8] [,9]
#> [1,] Inf Inf
#> [2,] 516489538.1 474631011.9
#> [3,] 4281316.7 21965494.7
#> [4,] 1284666.6 1288196.0
#> [5,] 919364.7 599109.8
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 227484274 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 292375521 290788428 238942146 210853677 272413913 403500945
#> [3,] Inf Inf 290423127 226758622 135134587 64225728 21508413
#> [4,] Inf Inf Inf 226393320 134769285 63860426 21143111
#> [5,] Inf Inf Inf Inf 134608172 63577648 21147427
#> [,8] [,9] [,10]
#> [1,] Inf Inf Inf
#> [2,] 518995041 474717060.6 302734286
#> [3,] 6786820 22051543.3 110234863
#> [4,] 3790169 1374244.7 4281317
#> [5,] 3424868 685158.4 1284667
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 378494828 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 573737294 542688208 429175879 329491420 334082514 427774958
#> [3,] Inf Inf 542322906 416992355 253772329 125894329 45782426
#> [4,] Inf Inf Inf 416627053 253407028 125529027 45417124
#> [5,] Inf Inf Inf Inf 253245915 125246250 45421440
#> [,8] [,9] [,10] [,11]
#> [1,] Inf Inf Inf Inf
#> [2,] 524727127 475355309 302794197 227484274
#> [3,] 12518906 22689791 110294775 210853677
#> [4,] 9522256 2012493 4341228 6786820
#> [5,] 9156954 1323406 1344578 1374245
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 790692602 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 900199197 827362190 640554158 459754086 400882270 453598670
#> [3,] Inf Inf 826996888 628370634 384034996 192694085 71606138
#> [4,] Inf Inf Inf 628005332 383669694 192328783 71240836
#> [5,] Inf Inf Inf Inf 383508581 192046006 71245151
#> [,8] [,9] [,10] [,11] [,12]
#> [1,] Inf Inf Inf Inf Inf
#> [2,] 530656498 475960172 302824015 227489772 378494828
#> [3,] 18448277 23294655 110324592 210859176 227484274
#> [4,] 15451627 2617356 4371046 6792318 12518906
#> [5,] 15086325 1928270 1374396 1379743 2012493
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 0 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 1051784935 868720034 512479240 276302970 320445911 542967197
#> [3,] Inf Inf 868354732 500295716 200583880 112257726 160974665
#> [4,] Inf Inf Inf 499930414 200218578 111892424 160609363
#> [5,] Inf Inf Inf Inf 200057465 111609646 160613678
#> [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] Inf Inf Inf Inf Inf Inf
#> [2,] 745774319 681665462 412151468 264878522 382862284 790692602
#> [3,] 233566097 228999945 219652045 248247925 231851730 227489772
#> [4,] 230569447 208322646 113698499 44181067 16886362 18448277
#> [5,] 230204145 207633560 110701849 38768492 6379949 2617356
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 0 0 0 0
#> [2,] 0 1 0 0 0
#> [3,] 0 2 2 0 0
#> [4,] 0 2 2 3 0
#> [5,] 0 2 2 3 4
#> [6,] 0 2 2 4 5
#> [7,] 0 2 6 6 5
#> [8,] 0 1 6 7 7
#> [9,] 0 3 7 7 8
#> [10,] 0 4 7 8 8
#> [11,] 0 10 7 8 8
#> [12,] 0 10 7 8 9
#> [13,] 0 10 5 11 12
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0 Inf Inf Inf Inf
#> [2,] 365301.9 0.0 Inf Inf Inf
#> [3,] 12548826.2 365301.9 0.0 Inf Inf
#> [4,] 76245505.1 526415.0 161113.1 0.00 Inf
#> [5,] 208843455.5 655270.1 289968.2 7191.02 0.00
#> [6,] 382591641.8 599109.8 233807.9 238123.10 7191.02
#> [7,] 515803981.4 3595759.9 599109.8 233807.90 236576.91
#> [8,] 474631011.9 21965494.7 1288196.0 599109.78 233807.90
#> [9,] 302734285.8 110234862.9 4281316.7 1284666.56 599109.78
#> [10,] 227484274.2 210853677.4 6786819.5 1374244.65 685158.43
#> [11,] 378494827.7 227484274.2 12518905.8 2012492.69 1323406.47
#> [12,] 790692602.2 227489772.3 18448276.8 2617356.28 1374395.56
#> [13,] 0.0 264878521.6 112257725.6 16886362.06 2617356.28
print(a) #indices of months to select for follow-up experiments
#> [1] 2 6 8 12
print(rownames(CanadianWeather$monthlyTemp)[a])
#> [1] "Feb" "Jun" "Aug" "Dec"In this example, we try to identify points that can predict the shape of the curve of the difference between the temperatures of Canadian cities that are along the Atlantic with those that are Continental– however, we don’t care too much about sampling time points where there is lots of noise, so we normalise this by the variance at each point.
In this case, we sample only 3 example curves from the distribution of curves when estimating the integral– this should be much higher (100 curves is usually suitable), but we make it 3 here to speed up loading the vignette.
Note that the tables that are printed as the evaluation are the optimisation tables that are used as part of the NITPicker algorithm’s dynamic programming algorithm.
library(fda)
library(NITPicker)
#Set up data:
atlanticCities=which(CanadianWeather$region[as.character(colnames(CanadianWeather$monthlyTemp))]=="Atlantic")
matAtlantic=CanadianWeather$monthlyTemp[, names(atlanticCities)]
continentalCities=which(CanadianWeather$region[as.character(colnames(CanadianWeather$monthlyTemp))]=="Continental")
matContinental=CanadianWeather$monthlyTemp[, names(continentalCities)]
#find a set of points that helps capture the difference between Atlantic and Continental cities, normalised by the variance
a=findPathF3(c(1:12), matAtlantic, matContinental, 4, numPerts=500) #find a set of points that help predict the shape of the curve
#> lambda = 0.0
#>
#> Initializing...
#> Computing Karcher mean of 15 functions in SRSF space...
#> updating step: r=1
#> updating step: r=2
#> updating step: r=3
#> updating step: r=4
#> updating step: r=5
#> updating step: r=6
#> updating step: r=7
#> updating step: r=8
#> updating step: r=9
#> updating step: r=10
#> updating step: r=11
#> lambda = 0.0
#>
#> Initializing...
#> Computing Karcher mean of 12 functions in SRSF space...
#> updating step: r=1
#> updating step: r=2
#> updating step: r=3
#> updating step: r=4
#> updating step: r=5
#> updating step: r=6
#> lambda = 0.0
#>
#> Initializing...
#> Computing Karcher mean of 500 functions in SRSF space...
#> updating step: r=1
#> updating step: r=2
#> updating step: r=3
#> updating step: r=4
#> updating step: r=5
#> updating step: r=6
#> updating step: r=7
#> updating step: r=8
#> updating step: r=9
#> updating step: r=10
#> updating step: r=11
#> updating step: r=12
#> updating step: r=13
#> updating step: r=14
#> updating step: r=15
#> updating step: r=16
#> updating step: r=17
#> updating step: r=18
#> updating step: r=19
#> updating step: r=20
#> maximal number of iterations is reached.
#> [,1]
#> [1,] 0
#> [2,] Inf
#> [3,] Inf
#> [4,] Inf
#> [5,] Inf
#> [,1] [,2]
#> [1,] 224.7612 Inf
#> [2,] Inf 0
#> [3,] Inf Inf
#> [4,] Inf Inf
#> [5,] Inf Inf
#> [,1] [,2] [,3]
#> [1,] 3384.579 Inf Inf
#> [2,] Inf 32.39191 224.7612
#> [3,] Inf Inf 0.0000
#> [4,] Inf Inf Inf
#> [5,] Inf Inf Inf
#> [,1] [,2] [,3] [,4]
#> [1,] 13371.38 Inf Inf Inf
#> [2,] Inf 101.9706 225.0703718 3384.57875
#> [3,] Inf Inf 0.3091552 32.39191
#> [4,] Inf Inf Inf 0.00000
#> [5,] Inf Inf Inf Inf
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 33895.8 Inf Inf Inf Inf
#> [2,] Inf 192.7369 226.235829 3.384621e+03 1.337138e+04
#> [3,] Inf Inf 1.474612 3.243463e+01 1.019706e+02
#> [4,] Inf Inf Inf 4.271714e-02 3.091552e-01
#> [5,] Inf Inf Inf Inf 0.000000e+00
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 66026.3 Inf Inf Inf Inf Inf
#> [2,] Inf 234.5203 225.999879 3386.246720 1.337231e+04 3.389580e+04
#> [3,] Inf Inf 1.238662 34.059882 1.029025e+02 1.927369e+02
#> [4,] Inf Inf Inf 1.667969 1.241093e+00 1.474612e+00
#> [5,] Inf Inf Inf Inf 9.319376e-01 4.271714e-02
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 105625.6 Inf Inf Inf Inf Inf
#> [2,] Inf 182.7482 286.03070 3437.07130 13399.53197 33901.418189
#> [3,] Inf Inf 61.26948 84.88447 130.12528 198.357741
#> [4,] Inf Inf Inf 52.49255 28.46387 7.095429
#> [5,] Inf Inf Inf Inf 28.15472 5.663534
#> [,7]
#> [1,] Inf
#> [2,] 66026.297408
#> [3,] 225.999879
#> [4,] 1.238662
#> [5,] 1.241093
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 150878.1 Inf Inf Inf Inf Inf
#> [2,] Inf 248.3435 576.7843 3653.9977 13520.6577 33939.87188
#> [3,] Inf Inf 352.0230 301.8109 251.2510 236.81143
#> [4,] Inf Inf Inf 269.4190 149.5896 45.54912
#> [5,] Inf Inf Inf Inf 149.2804 44.11722
#> [,7] [,8]
#> [1,] Inf Inf
#> [2,] 66029.630219 1.056256e+05
#> [3,] 229.332690 1.827482e+02
#> [4,] 4.571474 6.126948e+01
#> [5,] 4.573904 1.238662e+00
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 199354.6 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 711.947 1327.404 4201.6505 13842.0409 34068.0084 66056.46035
#> [3,] Inf Inf 1102.643 849.4636 572.6342 364.9480 256.16282
#> [4,] Inf Inf Inf 817.0717 470.9728 173.6857 31.40160
#> [5,] Inf Inf Inf Inf 470.6637 172.2538 31.40403
#> [,8] [,9]
#> [1,] Inf Inf
#> [2,] 1.056283e+05 1.508781e+05
#> [3,] 1.854628e+02 2.483435e+02
#> [4,] 6.398404e+01 1.827482e+02
#> [5,] 3.953226e+00 4.571474e+00
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 243212.1 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 2196.48 3120.178 5525.334 14674.066 34472.2769 66196.5210
#> [3,] Inf Inf 2895.417 2173.147 1404.659 769.2165 396.2235
#> [4,] Inf Inf Inf 2140.755 1302.998 577.9542 171.4623
#> [5,] Inf Inf Inf Inf 1302.689 576.5223 171.4647
#> [,8] [,9] [,10]
#> [1,] Inf Inf Inf
#> [2,] 105666.73651 150883.84613 199354.5620
#> [3,] 223.93149 254.13433 711.9470
#> [4,] 102.45277 188.53900 185.4628
#> [5,] 42.42196 10.36228 31.4016
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 269467.5 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 6355.351 7467.094 8822.732 16902.479 35745.660 66800.6827
#> [3,] Inf Inf 7242.333 5470.546 3633.072 2042.600 1000.3851
#> [4,] Inf Inf Inf 5438.154 3531.410 1851.337 775.6239
#> [5,] Inf Inf Inf Inf 3531.101 1849.905 775.6263
#> [,8] [,9] [,10] [,11]
#> [1,] Inf Inf Inf Inf
#> [2,] 105924.9984 150969.41830 199367.74310 243212.0976
#> [3,] 482.1933 339.70651 725.12815 2196.4796
#> [4,] 360.7146 274.11117 198.64390 223.9315
#> [5,] 300.6838 95.93445 44.58274 102.4528
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 236877.2 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 22085.5 22552.23 20797.49 25740.71 41674.652 70426.397
#> [3,] Inf Inf 22327.47 17445.30 12471.30 7971.592 4626.099
#> [4,] Inf Inf Inf 17412.91 12369.64 7780.329 4401.338
#> [5,] Inf Inf Inf Inf 12369.33 7778.898 4401.340
#> [,8] [,9] [,10] [,11] [,12]
#> [1,] Inf Inf Inf Inf Inf
#> [2,] 108030.098 152051.842 199791.6326 243302.4314 269467.4577
#> [3,] 2587.293 1422.130 1149.0177 2286.8135 6355.3509
#> [4,] 2465.814 1356.534 622.5334 314.2653 339.7065
#> [5,] 2405.783 1178.358 468.4723 192.7866 198.6439
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 0 Inf Inf Inf Inf Inf Inf Inf
#> [2,] Inf 484464 386310.7 264377.3 175135.5 122961.28 108937.46 123970.09
#> [3,] Inf Inf 386086.0 261025.1 161866.0 89258.22 43137.16 18527.29
#> [4,] Inf Inf Inf 260992.7 161764.4 89066.96 42912.40 18405.81
#> [5,] Inf Inf Inf Inf 161764.1 89065.53 42912.40 18345.78
#> [,9] [,10] [,11] [,12] [,13]
#> [1,] Inf Inf Inf Inf Inf
#> [2,] 157106.918 200623.769 243276.1628 269523.5473 236877.2431
#> [3,] 6477.206 1981.154 2260.5448 6411.4405 20797.4873
#> [4,] 6411.611 1454.670 287.9967 395.7961 1149.0177
#> [5,] 6233.434 1300.609 166.5180 254.7335 314.2653
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 0 0 0 0
#> [2,] 0 1 0 0 0
#> [3,] 0 1 2 0 0
#> [4,] 0 1 2 3 0
#> [5,] 0 1 2 3 4
#> [6,] 0 2 2 4 5
#> [7,] 0 1 2 6 6
#> [8,] 0 1 7 6 7
#> [9,] 0 1 7 6 7
#> [10,] 0 1 7 7 8
#> [11,] 0 1 8 9 9
#> [12,] 0 3 9 10 10
#> [13,] 0 6 9 10 10
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0000 Inf Inf Inf Inf
#> [2,] 224.7612 0.00000 Inf Inf Inf
#> [3,] 3384.5788 32.39191 0.0000000 Inf Inf
#> [4,] 13371.3773 101.97057 0.3091552 0.00000000 Inf
#> [5,] 33895.7974 192.73692 1.4746119 0.04271714 0.00000000
#> [6,] 66026.2974 225.99988 1.2386624 1.24109283 0.04271714
#> [7,] 105625.5532 182.74819 61.2694805 1.23866236 1.24109283
#> [8,] 150878.0553 248.34353 182.7481929 4.57147379 1.23866236
#> [9,] 199354.5620 711.94701 185.4627562 31.40160152 3.95322559
#> [10,] 243212.0976 2196.47963 223.9314864 102.45277395 10.36227636
#> [11,] 269467.4577 6355.35088 339.7065087 198.64389934 44.58274469
#> [12,] 236877.2431 20797.48733 1149.0176650 314.26533920 192.78662674
#> [13,] 0.0000 108937.45803 1981.1542206 287.99667069 166.51795823
print(a) #indices of months to select for follow-up experiments
#> [1] 1 2 7 10
print(rownames(CanadianWeather$monthlyTemp)[a]) #month names selected
#> [1] "Jan" "Feb" "Jul" "Oct"