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] 12 1
#> [,1]
#> [1,] 0
#> [2,] Inf
#> [3,] Inf
#> [4,] Inf
#> [5,] Inf
#> [,1] [,2]
#> [1,] 94119.21 Inf
#> [2,] Inf 0
#> [3,] Inf Inf
#> [4,] Inf Inf
#> [5,] Inf Inf
#> [,1] [,2] [,3]
#> [1,] 7227618 Inf Inf
#> [2,] Inf 395438.2 94119.21
#> [3,] Inf Inf 0.00
#> [4,] Inf Inf Inf
#> [5,] Inf Inf Inf
#> [,1] [,2] [,3] [,4]
#> [1,] 54302055 Inf Inf Inf
#> [2,] Inf 2759868 270921.9 7227618.08
#> [3,] Inf Inf 176802.6 94119.21
#> [4,] Inf Inf Inf 0.00
#> [5,] Inf Inf Inf Inf
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 162631616 Inf Inf Inf Inf
#> [2,] Inf 5511374 444956.9 7232202.59 54302054.87
#> [3,] Inf Inf 350837.7 98703.72 270921.86
#> [4,] Inf Inf Inf 4584.51 94119.21
#> [5,] Inf Inf Inf Inf 0.00
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 310482479 Inf Inf Inf Inf Inf
#> [2,] Inf 5752868 351909.8 7545230.9 54382889.07 162631616.49
#> [3,] Inf Inf 257790.6 411732.0 351756.05 444956.87
#> [4,] Inf Inf Inf 317612.8 174953.40 98703.72
#> [5,] Inf Inf Inf Inf 80834.19 4584.51
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 426724724 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 4555736 3155093 10879139 55772283 162862863.2 310482479.10
#> [3,] Inf Inf 3060974 3745641 1741150 676203.5 351909.84
#> [4,] Inf Inf Inf 3651521 1564347 329950.4 257790.63
#> [5,] Inf Inf Inf Inf 1470228 235831.2 98703.72
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 391589760 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 21653899 28434775 32224711 67200690 166965369 311175729.0
#> [3,] Inf Inf 28340656 25091213 13169557 4778709 1045159.7
#> [4,] Inf Inf Inf 24997093 12992755 4432456 951040.5
#> [5,] Inf Inf Inf Inf 12898635 4338337 791953.6
#> [,8]
#> [1,] Inf
#> [2,] 426724724.5
#> [3,] 3155093.1
#> [4,] 351909.8
#> [5,] 257790.6
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 244781356 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 112045310 121546437 105804433 111044479 187340235 317485475
#> [3,] Inf Inf 121452318 98670934 57013346 25153575 7354906
#> [4,] Inf Inf Inf 98576815 56836544 24807322 7260787
#> [5,] Inf Inf Inf Inf 56742424 24713203 7101700
#> [,8] [,9]
#> [1,] Inf Inf
#> [2,] 427432129.4 391589760.3
#> [3,] 3862498.0 21653899.0
#> [4,] 1059314.8 1045159.7
#> [5,] 965195.6 351909.8
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 197005323 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 294282876 291730500 236611435 191490147 227385872 331864344
#> [3,] Inf Inf 291636381 229477936 137459014 65199212 21733775
#> [4,] Inf Inf Inf 229383816 137282211 64852959 21639656
#> [5,] Inf Inf Inf Inf 137188092 64758840 21480569
#> [,8] [,9] [,10]
#> [1,] Inf Inf Inf
#> [2,] 430019521 391678775.7 244781356
#> [3,] 6449890 21742914.5 105804433
#> [4,] 3646706 1134175.2 3862498
#> [5,] 3552587 440925.3 1045160
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 372393353 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 577239411 544573843 428902219 311790819 289822504 356410748
#> [3,] Inf Inf 544479724 421768720 257759686 127635844 46280179
#> [4,] Inf Inf Inf 421674601 257582883 127289591 46186059
#> [5,] Inf Inf Inf Inf 257488764 127195472 46026972
#> [,8] [,9] [,10] [,11]
#> [1,] Inf Inf Inf Inf
#> [2,] 435808921 392307481 244837631 197005323
#> [3,] 12239290 22371619 105860708 191490147
#> [4,] 9436107 1762880 3918773 6449890
#> [5,] 9341987 1069630 1101434 1134175
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 790227866 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 900569372 826195050 638471938 440874878 355556661 381536894
#> [3,] Inf Inf 826100931 631338439 386843745 193370002 71406324
#> [4,] Inf Inf Inf 631244320 386666942 193023749 71312205
#> [5,] Inf Inf Inf Inf 386572823 192929629 71153118
#> [,8] [,9] [,10] [,11] [,12]
#> [1,] Inf Inf Inf Inf Inf
#> [2,] 441375516 392797147 244847819 197015173 372393353
#> [3,] 17805885 22861286 105870896 191499997 197005323
#> [4,] 15002702 2252546 3928961 6459739 12239290
#> [5,] 14908583 1559297 1111623 1144025 1762880
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 0 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 1050478970 866032049 511769682 247411261 245398925 419493658
#> [3,] Inf Inf 865937930 504636183 193380128 83212266 109363089
#> [4,] Inf Inf Inf 504542064 193203325 82866013 109268970
#> [5,] Inf Inf Inf Inf 193109206 82771893 109109883
#> [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] Inf Inf Inf Inf Inf Inf
#> [2,] 590258388 537181322 314503729 215989651 373458779 790227866
#> [3,] 166688756 167245461 175526806 210474475 198070750 197015173
#> [4,] 163885573 146636722 73584871 25434217 13304716 17805885
#> [5,] 163791454 145943472 70767533 20118503 2828306 2252546
#> [,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 3 3 0
#> [5,] 0 2 3 3 4
#> [6,] 0 2 2 5 5
#> [7,] 0 2 6 6 6
#> [8,] 0 1 6 7 7
#> [9,] 0 3 7 8 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,] 0.00 Inf Inf Inf Inf
#> [2,] 94119.21 0.00 Inf Inf Inf
#> [3,] 7227618.08 94119.21 0.00 Inf Inf
#> [4,] 54302054.87 270921.86 94119.21 0.00 Inf
#> [5,] 162631616.49 444956.87 98703.72 4584.51 0.00
#> [6,] 310482479.10 351909.84 257790.63 98703.72 4584.51
#> [7,] 426724724.48 3155093.06 351909.84 257790.63 98703.72
#> [8,] 391589760.30 21653899.02 1045159.73 351909.84 257790.63
#> [9,] 244781356.33 105804433.15 3862497.98 1045159.73 351909.84
#> [10,] 197005323.27 191490147.02 6449889.52 1134175.16 440925.28
#> [11,] 372393352.54 197005323.27 12239289.74 1762880.09 1069630.21
#> [12,] 790227865.58 197015172.78 17805885.06 2252546.49 1111622.65
#> [13,] 0.00 215989650.90 83212265.80 13304716.11 2252546.49
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] 12 1
#> [,1]
#> [1,] 0
#> [2,] Inf
#> [3,] Inf
#> [4,] Inf
#> [5,] Inf
#> [,1] [,2]
#> [1,] 166747.5 Inf
#> [2,] Inf 0
#> [3,] Inf Inf
#> [4,] Inf Inf
#> [5,] Inf Inf
#> [,1] [,2] [,3]
#> [1,] 3896413 Inf Inf
#> [2,] Inf 21803.31 166747.5
#> [3,] Inf Inf 0.0
#> [4,] Inf Inf Inf
#> [5,] Inf Inf Inf
#> [,1] [,2] [,3] [,4]
#> [1,] 3221102 Inf Inf Inf
#> [2,] Inf 1192634 797388.2 3896413.20
#> [3,] Inf Inf 630640.7 21803.31
#> [4,] Inf Inf Inf 0.00
#> [5,] Inf Inf Inf Inf
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 16516905 Inf Inf Inf Inf
#> [2,] Inf 17625001 9072491 5088276 3221102.24
#> [3,] Inf Inf 8905744 1213666 797388.18
#> [4,] Inf Inf Inf 1191863 21803.31
#> [5,] Inf Inf Inf Inf 0.00
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 74589747 Inf Inf Inf Inf Inf
#> [2,] Inf 40631572 19465838 6350294 3245040.22 16516904.61
#> [3,] Inf Inf 19299090 2475684 821326.16 3221102.24
#> [4,] Inf Inf Inf 2453881 45741.29 797388.18
#> [5,] Inf Inf Inf Inf 23937.97 21803.31
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 105552558 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 44530574 18845609 5633819 4981716 16970796 74589746.59
#> [3,] Inf Inf 18678862 1759209 2558002 3674994 3245040.22
#> [4,] Inf Inf Inf 1737406 1782418 1251280 821326.16
#> [5,] Inf Inf Inf Inf 1760614 475695 45741.29
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 79345757 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 35136073 15167245 11610343 14990762 20650357 74964333.5
#> [3,] Inf Inf 15000498 7735733 12567048 7354555 3619627.1
#> [4,] Inf Inf Inf 7713929 11791463 4930841 1195913.1
#> [5,] Inf Inf Inf Inf 11769659 4155256 420328.2
#> [,8]
#> [1,] Inf
#> [2,] 105552557.9
#> [3,] 4981716.4
#> [4,] 1759209.2
#> [5,] 821326.2
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 54139862 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 32412714 19716015 26930568 32096174 27180841 75873330
#> [3,] Inf Inf 19549268 23055958 29672460 13885038 4528624
#> [4,] Inf Inf Inf 23034155 28896875 11461324 2104910
#> [5,] Inf Inf Inf Inf 28875071 10685739 1329325
#> [,8] [,9]
#> [1,] Inf Inf
#> [2,] 105560987.1 79345757
#> [3,] 4990145.7 11610343
#> [4,] 1767638.5 3619627
#> [5,] 829755.4 1195913
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 42095449 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 43458597 41901618 63156561 66617657 42422099 79581544
#> [3,] Inf Inf 41734871 59281952 64193943 29126297 8236838
#> [4,] Inf Inf Inf 59260148 63418359 26702583 5813124
#> [5,] Inf Inf Inf Inf 63396555 25926998 5037539
#> [,8] [,9] [,10]
#> [1,] Inf Inf Inf
#> [2,] 106115193 79487773 54139862
#> [3,] 5544352 11752358 19716015
#> [4,] 2321844 3761642 4528624
#> [5,] 1383961 1337928 1767638
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 56439254 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 53563786 57971766 87985589 89138500 50322728 80349975
#> [3,] Inf Inf 57805018 84110979 86714786 37026925 9005268
#> [4,] Inf Inf Inf 84089176 85939201 34603211 6581554
#> [5,] Inf Inf Inf Inf 85917398 33827626 5805970
#> [,8] [,9] [,10] [,11]
#> [1,] Inf Inf Inf Inf
#> [2,] 105923550 79444393 54292435 42095449
#> [3,] 5352708 11708978 19868588 41901618
#> [4,] 2130201 3718263 4681197 5544352
#> [5,] 1192318 1294549 1920212 2321844
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 41358411 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 40943793 41199224 69947404 73657089 40562669 79723102
#> [3,] Inf Inf 41032477 66072795 71233375 27266866 8378395
#> [4,] Inf Inf Inf 66050991 70457791 24843152 5954681
#> [5,] Inf Inf Inf Inf 70435987 24067568 5179096
#> [,8] [,9] [,10] [,11] [,12]
#> [1,] Inf Inf Inf Inf Inf
#> [2,] 111019466 84557237 58233886 42874727 56439254
#> [3,] 10448625 16821823 23810039 42680897 42095449
#> [4,] 7226117 8831107 8622648 6323630 5352708
#> [5,] 6288234 6407393 5861663 3101123 2130201
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 0 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 41324407 62190171 146071608 135335338 41725175 93547814
#> [3,] Inf Inf 62023424 142196998 132911624 28429373 22203107
#> [4,] Inf Inf Inf 142175194 132136039 26005659 19779393
#> [5,] Inf Inf Inf Inf 132114236 25230074 19003808
#> [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] Inf Inf Inf Inf Inf Inf
#> [2,] 137789880 99656274 63743239 42561751 56577039 41358411
#> [3,] 37219038 31920859 29319392 42367920 42233234 40562669
#> [4,] 33996531 23930144 14132000 6010654 5490494 8378395
#> [5,] 33058648 21506430 11371015 2788147 2267986 5352708
#> [,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 3 3 0
#> [5,] 0 4 4 4 4
#> [6,] 0 4 4 4 5
#> [7,] 0 4 3 6 6
#> [8,] 0 3 6 6 6
#> [9,] 0 2 6 7 7
#> [10,] 0 2 7 7 8
#> [11,] 0 10 7 7 7
#> [12,] 0 5 6 11 11
#> [13,] 0 1 6 11 11
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0 Inf Inf Inf Inf
#> [2,] 166747.5 0.00 Inf Inf Inf
#> [3,] 3896413.2 21803.31 0.00 Inf Inf
#> [4,] 3221102.2 797388.18 21803.31 0.00 Inf
#> [5,] 16516904.6 3221102.24 797388.18 21803.31 0.00
#> [6,] 74589746.6 3245040.22 821326.16 45741.29 21803.31
#> [7,] 105552557.9 4981716.43 1759209.21 821326.16 45741.29
#> [8,] 79345757.5 11610342.60 3619627.14 1195913.09 420328.22
#> [9,] 54139861.9 19716015.11 4528623.74 1767638.46 829755.42
#> [10,] 42095448.9 41901618.24 5544351.58 2321844.35 1337928.32
#> [11,] 56439254.0 42095448.88 5352708.12 2130200.89 1192317.84
#> [12,] 41358411.3 40562668.84 8378395.29 5352708.12 2130200.89
#> [13,] 0.0 41324407.30 22203107.16 5490493.53 2267986.31
print(a) #indices of months to select for follow-up experiments
#> [1] 1 3 7 11
print(rownames(CanadianWeather$monthlyTemp)[a])
#> [1] "Jan" "Mar" "Jul" "Nov"In this example, we try to identify points that can predict the shape of the curve of the difference between the temperatures of Canadian cities that are along the Atlantic with those that are Continental– however, we don’t care too much about sampling time points where there is lots of noise, so we normalise this by the variance at each point.
In this case, we sample only 3 example curves from the distribution of curves when estimating the integral– this should be much higher (100 curves is usually suitable), but we make it 3 here to speed up loading the vignette.
Note that the tables that are printed as the evaluation are the optimisation tables that are used as part of the NITPicker algorithm’s dynamic programming algorithm.
library(fda)
library(NITPicker)
#Set up data:
atlanticCities=which(CanadianWeather$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
#> [1] 12 1
#> [,1]
#> [1,] 0
#> [2,] Inf
#> [3,] Inf
#> [4,] Inf
#> [5,] Inf
#> [,1] [,2]
#> [1,] 1805.35 Inf
#> [2,] Inf 0
#> [3,] Inf Inf
#> [4,] Inf Inf
#> [5,] Inf Inf
#> [,1] [,2] [,3]
#> [1,] 6055.183 Inf Inf
#> [2,] Inf 1692.906 1805.35
#> [3,] Inf Inf 0.00
#> [4,] Inf Inf Inf
#> [5,] Inf Inf Inf
#> [,1] [,2] [,3] [,4]
#> [1,] 93997.03 Inf Inf Inf
#> [2,] Inf 1922.912 4722.562 6055.183
#> [3,] Inf Inf 2917.212 1692.906
#> [4,] Inf Inf Inf 0.000
#> [5,] Inf Inf Inf Inf
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 209946.7 Inf Inf Inf Inf
#> [2,] Inf 1310.847 4181.313 7135.119 93997.028
#> [3,] Inf Inf 2375.963 2772.841 1922.912
#> [4,] Inf Inf Inf 1079.936 1692.906
#> [5,] Inf Inf Inf Inf 0.000
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 181418.1 Inf Inf Inf Inf Inf
#> [2,] Inf 21761.75 13726.70 22545.43 96325.788 209946.719
#> [3,] Inf Inf 11921.35 18183.15 4251.671 1310.847
#> [4,] Inf Inf Inf 16490.25 4021.665 1922.912
#> [5,] Inf Inf Inf Inf 2328.759 1079.936
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 104971.1 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 110548.1 65873.06 69141.66 107619.40 210587.939 181418.116
#> [3,] Inf Inf 64067.71 64779.38 15545.28 1952.067 13726.695
#> [4,] Inf Inf Inf 63086.48 15315.27 2564.131 1310.847
#> [5,] Inf Inf Inf Inf 13622.37 1721.155 1922.912
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 121147.4 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 278635.5 168293.1 149018.4 130623.23 213341.357 181546.937
#> [3,] Inf Inf 166487.7 144656.1 38549.11 4705.484 13855.517
#> [4,] Inf Inf Inf 142963.2 38319.11 5317.549 1439.669
#> [5,] Inf Inf Inf Inf 36626.20 4474.573 2051.733
#> [,8]
#> [1,] Inf
#> [2,] 104971.142
#> [3,] 65873.063
#> [4,] 1952.067
#> [5,] 1310.847
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 480461.1 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 616890.4 386154.4 312250.4 191397.61 228356.32 185097.684
#> [3,] Inf Inf 384349.1 307888.1 99323.50 19720.45 17406.264
#> [4,] Inf Inf Inf 306195.2 99093.49 20332.51 4990.416
#> [5,] Inf Inf Inf Inf 97400.58 19489.54 5602.480
#> [,8] [,9]
#> [1,] Inf Inf
#> [2,] 105689.731 121147.444
#> [3,] 66591.653 104971.142
#> [4,] 2670.656 4705.484
#> [5,] 2029.437 1439.669
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 578579.8 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 691096.5 411397.5 321843.8 177374.00 219736.63 184888.254
#> [3,] Inf Inf 409592.2 317481.5 85299.88 11100.75 17196.833
#> [4,] Inf Inf Inf 315788.6 85069.88 11712.82 4780.985
#> [5,] Inf Inf Inf Inf 83376.97 10869.84 5393.050
#> [,8] [,9] [,10]
#> [1,] Inf Inf Inf
#> [2,] 109045.224 124786.484 480461.076
#> [3,] 69947.146 108610.182 105689.731
#> [4,] 6026.149 8344.524 17406.264
#> [5,] 5384.930 5078.709 2670.656
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 2042185 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 1326369 833448.1 632931.4 309871.6 260889.56 197031.08
#> [3,] Inf Inf 831642.7 628569.1 217797.5 52253.69 29339.66
#> [4,] Inf Inf Inf 626876.2 217567.5 52865.75 16923.81
#> [5,] Inf Inf Inf Inf 215874.6 52022.78 17535.88
#> [,8] [,9] [,10] [,11]
#> [1,] Inf Inf Inf Inf
#> [2,] 112806.301 126913.321 488376.51 578579.778
#> [3,] 73708.223 110737.018 113605.17 109045.224
#> [4,] 9787.226 10471.361 25321.70 11100.755
#> [5,] 9146.007 7205.545 10586.09 4780.985
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 1331458 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 1019380 587255.2 436436.1 207423.4 241625.43 215532.80
#> [3,] Inf Inf 585449.9 432073.8 115349.3 32989.56 47841.38
#> [4,] Inf Inf Inf 430380.9 115119.3 33601.62 35425.54
#> [5,] Inf Inf Inf Inf 113426.4 32758.64 36037.60
#> [,8] [,9] [,10] [,11] [,12]
#> [1,] Inf Inf Inf Inf Inf
#> [2,] 141092.70 152294.15 495792.96 598250.69 2042184.691
#> [3,] 101994.63 136117.85 121021.62 128716.14 112806.301
#> [4,] 38073.63 35852.19 32738.15 30771.67 29339.659
#> [5,] 37432.41 32586.38 18002.54 24451.90 9787.226
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 0 Inf Inf Inf Inf Inf Inf Inf
#> [2,] Inf 839090.2 412346.1 369184.8 611792.2 1021578.5 922147.8 599818.4
#> [3,] Inf Inf 410540.8 364822.5 519718.1 812942.6 754456.4 560720.3
#> [4,] Inf Inf Inf 363129.6 519488.1 813554.7 742040.6 496799.3
#> [5,] Inf Inf Inf Inf 517795.2 812711.7 742652.6 496158.1
#> [,9] [,10] [,11] [,12] [,13]
#> [1,] Inf Inf Inf Inf Inf
#> [2,] 382343.3 543884.77 626678.77 2042983.32 1331458.35
#> [3,] 366167.0 169113.42 157144.22 113604.93 141092.70
#> [4,] 265901.4 80829.96 59199.75 30138.29 32989.56
#> [5,] 262635.6 66094.35 52879.98 10585.86 29339.66
#> [,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 3 3 0
#> [5,] 0 1 4 3 4
#> [6,] 0 2 5 5 5
#> [7,] 0 2 5 6 5
#> [8,] 0 7 5 6 7
#> [9,] 0 7 6 7 8
#> [10,] 0 7 5 6 9
#> [11,] 0 7 6 7 10
#> [12,] 0 7 5 11 11
#> [13,] 0 3 11 11 11
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.000 Inf Inf Inf Inf
#> [2,] 1805.350 0.000 Inf Inf Inf
#> [3,] 6055.183 1692.906 0.000 Inf Inf
#> [4,] 93997.028 1922.912 1692.906 0.000 Inf
#> [5,] 209946.719 1310.847 1922.912 1079.936 0.000
#> [6,] 181418.116 13726.695 1310.847 1922.912 1079.936
#> [7,] 104971.142 65873.063 1952.067 1310.847 1721.155
#> [8,] 121147.444 104971.142 4705.484 1439.669 1310.847
#> [9,] 480461.076 105689.731 17406.264 2670.656 1439.669
#> [10,] 578579.778 109045.224 11100.755 4780.985 2670.656
#> [11,] 2042184.691 112806.301 29339.659 9787.226 4780.985
#> [12,] 1331458.352 141092.705 32989.556 29339.659 9787.226
#> [13,] 0.000 369184.768 113604.931 30138.289 10585.856
print(a) #indices of months to select for follow-up experiments
#> [1] 1 5 7 11
print(rownames(CanadianWeather$monthlyTemp)[a]) #month names selected
#> [1] "Jan" "May" "Jul" "Nov"