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 1.8-26. 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,] 98161.66 Inf
#> [2,] Inf 0
#> [3,] Inf Inf
#> [4,] Inf Inf
#> [5,] Inf Inf
#> [,1] [,2] [,3]
#> [1,] 7263666 Inf Inf
#> [2,] Inf 385151.6 98161.66
#> [3,] Inf Inf 0.00
#> [4,] Inf Inf Inf
#> [5,] Inf Inf Inf
#> [,1] [,2] [,3] [,4]
#> [1,] 54351958 Inf Inf Inf
#> [2,] Inf 2707799 273577.4 7263665.59
#> [3,] Inf Inf 175415.8 98161.66
#> [4,] Inf Inf Inf 0.00
#> [5,] Inf Inf Inf Inf
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 162170011 Inf Inf Inf Inf
#> [2,] Inf 5371544 438565.6 7268892.746 54351958.17
#> [3,] Inf Inf 340403.9 103388.811 273577.44
#> [4,] Inf Inf Inf 5227.154 98161.66
#> [5,] Inf Inf Inf Inf 0.00
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 309452876 Inf Inf Inf Inf Inf
#> [2,] Inf 5584152 351380.0 7583666.7 54431132.86 1.621700e+08
#> [3,] Inf Inf 253218.3 418162.8 352752.13 4.385656e+05
#> [4,] Inf Inf Inf 320001.1 177336.34 1.033888e+05
#> [5,] Inf Inf Inf Inf 79174.69 5.227154e+03
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 425464491 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 4445679 3159110 10899951 55802960 162399221.5 309452876.3
#> [3,] Inf Inf 3060948 3734447 1724580 667775.7 351380.0
#> [4,] Inf Inf Inf 3636286 1549164 332599.0 253218.3
#> [5,] Inf Inf Inf Inf 1451002 234437.3 103388.8
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 390046785 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 21744173 28455413 32213724 67192090 166500909 310148826.8
#> [3,] Inf Inf 28357252 25048220 13113709 4769463 1047330.5
#> [4,] Inf Inf Inf 24950059 12938293 4434286 949168.8
#> [5,] Inf Inf Inf Inf 12840131 4336125 799339.3
#> [,8]
#> [1,] Inf
#> [2,] 425464491.3
#> [3,] 3159109.7
#> [4,] 351380.0
#> [5,] 253218.3
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 243566824 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 112491891 121562459 105710594 110949392 186870171 316464226
#> [3,] Inf Inf 121464298 98545090 56871011 25138726 7362730
#> [4,] Inf Inf Inf 98446928 56695595 24803549 7264568
#> [5,] Inf Inf Inf Inf 56597434 24705387 7114738
#> [,8] [,9]
#> [1,] Inf Inf
#> [2,] 426170851.1 390046785
#> [3,] 3865469.5 21744173
#> [4,] 1057739.8 1047330
#> [5,] 959578.1 351380
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 196615350 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 295502110 292027891 236646724 191448114 227008558 330899104
#> [3,] Inf Inf 291929729 229481220 137369734 65277112 21797608
#> [4,] Inf Inf Inf 229383058 137194318 64941935 21699446
#> [5,] Inf Inf Inf Inf 137096156 64843774 21549616
#> [,8] [,9] [,10]
#> [1,] Inf Inf Inf
#> [2,] 428771140 390137484.6 243566824
#> [3,] 6465759 21834871.8 105710594
#> [4,] 3658029 1138029.6 3865470
#> [5,] 3559867 442079.2 1047330
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 375170922 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 580373075 546078174 429784580 312304736 289868341 355679445
#> [3,] Inf Inf 545980013 422619076 258226355 128136895 46577949
#> [4,] Inf Inf Inf 422520914 258050939 127801718 46479787
#> [5,] Inf Inf Inf Inf 257952778 127703556 46329957
#> [,8] [,9] [,10] [,11]
#> [1,] Inf Inf Inf Inf
#> [2,] 434641059 390784722 243625352 196615350
#> [3,] 12335677 22482109 105769122 191448114
#> [4,] 9527948 1785267 3923997 6465759
#> [5,] 9429786 1089317 1105858 1138030
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 790524900 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 901052882 824818315 636915236 439588817 354516849 380219824
#> [3,] Inf Inf 824720153 629749732 385510437 192785404 71118327
#> [4,] Inf Inf Inf 629651571 385335021 192450227 71020166
#> [5,] Inf Inf Inf Inf 385236859 192352065 70870336
#> [,8] [,9] [,10] [,11] [,12]
#> [1,] Inf Inf Inf Inf Inf
#> [2,] 439958264 391209980 243624885 196630217 375170922
#> [3,] 17652882 22907367 105768655 191462981 196615350
#> [4,] 14845152 2210525 3923531 6480626 12335677
#> [5,] 14746991 1514575 1105391 1152897 1785267
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 0 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 1050901116 862698400 509151920 246398756 245298621 419238421
#> [3,] Inf Inf 862600238 501986416 192320375 83567175 110136924
#> [4,] Inf Inf Inf 501888255 192144960 83231999 110038763
#> [5,] Inf Inf Inf Inf 192046798 83133837 109888933
#> [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] Inf Inf Inf Inf Inf Inf
#> [2,] 589966923 536377763 313728277 215710765 376216045 790524900
#> [3,] 167661541 168075150 175872047 210543530 197660472 196630217
#> [4,] 164853812 147378308 74026922 25561174 13380800 17652882
#> [5,] 164755650 146682357 71208783 20233445 2830390 2210525
#> [,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,] 98161.66 0.00 Inf Inf Inf
#> [3,] 7263665.59 98161.66 0.00 Inf Inf
#> [4,] 54351958.17 273577.44 98161.66 0.000 Inf
#> [5,] 162170011.40 438565.59 103388.81 5227.154 0.000
#> [6,] 309452876.33 351380.00 253218.35 103388.811 5227.154
#> [7,] 425464491.34 3159109.74 351380.00 253218.348 103388.811
#> [8,] 390046785.46 21744172.64 1047330.48 351380.004 253218.348
#> [9,] 243566824.14 105710594.04 3865469.51 1047330.476 351380.004
#> [10,] 196615349.50 191448114.40 6465758.55 1138029.635 442079.164
#> [11,] 375170921.93 196615349.50 12335677.33 1785267.099 1089316.628
#> [12,] 790524899.57 196630216.52 17652881.94 2210525.201 1105391.498
#> [13,] 0.00 215710764.86 83567175.34 13380800.258 2210525.201
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,] 165439.2 Inf
#> [2,] Inf 0
#> [3,] Inf Inf
#> [4,] Inf Inf
#> [5,] Inf Inf
#> [,1] [,2] [,3]
#> [1,] 3796698 Inf Inf
#> [2,] Inf 19444.1 165439.2
#> [3,] Inf Inf 0.0
#> [4,] Inf Inf Inf
#> [5,] Inf Inf Inf
#> [,1] [,2] [,3] [,4]
#> [1,] 3014801 Inf Inf Inf
#> [2,] Inf 1227157 800669.5 3796698.2
#> [3,] Inf Inf 635230.4 19444.1
#> [4,] Inf Inf Inf 0.0
#> [5,] Inf Inf Inf Inf
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 16931803 Inf Inf Inf Inf
#> [2,] Inf 17618936 8991464 4964204 3014801.2
#> [3,] Inf Inf 8826025 1186950 800669.5
#> [4,] Inf Inf Inf 1167506 19444.1
#> [5,] Inf Inf Inf Inf 0.0
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 74946333 Inf Inf Inf Inf Inf
#> [2,] Inf 40185406 19087104 6153057 3041835.81 16931803.0
#> [3,] Inf Inf 18921665 2375803 827704.16 3014801.2
#> [4,] Inf Inf Inf 2356359 46478.71 800669.5
#> [5,] Inf Inf Inf Inf 27034.61 19444.1
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 104369013 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 43511206 18210985 5480594 4849486 17396617.1 74946332.70
#> [3,] Inf Inf 18045546 1703340 2635354 3479615.3 3041835.81
#> [4,] Inf Inf Inf 1683896 1854129 1265483.6 827704.16
#> [5,] Inf Inf Inf Inf 1834685 484258.2 46478.71
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 77610703 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 34213227 14784205 11767585 14977261 21076080 75313093.7
#> [3,] Inf Inf 14618766 7990331 12763130 7159078 3408596.8
#> [4,] Inf Inf Inf 7970887 11981904 4944946 1194465.2
#> [5,] Inf Inf Inf Inf 11962460 4163721 413239.7
#> [,8]
#> [1,] Inf
#> [2,] 104369013.0
#> [3,] 4849486.1
#> [4,] 1703340.0
#> [5,] 827704.2
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 53100196 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 31796602 19581006 27145890 31899955 27438858 76166185
#> [3,] Inf Inf 19415567 23368636 29685823 13521856 4261688
#> [4,] Inf Inf Inf 23349192 28904597 11307725 2047557
#> [5,] Inf Inf Inf Inf 28885153 10526499 1266331
#> [,8] [,9]
#> [1,] Inf Inf
#> [2,] 104375348.2 77610703
#> [3,] 4855821.4 11767585
#> [4,] 1709675.3 3408597
#> [5,] 834039.4 1194465
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 41697533 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 42913463 41639910 62879569 65661291 42144573 79655333
#> [3,] Inf Inf 41474471 59102315 63447160 28227571 7750836
#> [4,] Inf Inf Inf 59082871 62665934 26013440 5536705
#> [5,] Inf Inf Inf Inf 62646490 25232214 4755479
#> [,8] [,9] [,10]
#> [1,] Inf Inf Inf
#> [2,] 104883615 77746094 53100196
#> [3,] 5364088 11902977 19581006
#> [4,] 2217942 3543989 4261688
#> [5,] 1342307 1329857 1709675
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 55572869 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 52806959 57404754 87178887 87509618 49639726 80312414
#> [3,] Inf Inf 57239315 83401633 85295487 35722724 8407917
#> [4,] Inf Inf Inf 83382189 84514261 33508592 6193785
#> [5,] Inf Inf Inf Inf 84494817 32727367 5412560
#> [,8] [,9] [,10] [,11]
#> [1,] Inf Inf Inf Inf
#> [2,] 104695038 77706517 53249777 41697533
#> [3,] 5175511 11863399 19730587 41639910
#> [4,] 2029365 3504411 4411269 5364088
#> [5,] 1153729 1290279 1859256 2217942
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 40901786 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 40512624 41231535 70006672 72803118 40329745 79828813
#> [3,] Inf Inf 41066096 66229418 70588986 26412743 7924316
#> [4,] Inf Inf Inf 66209974 69807761 24198612 5710184
#> [5,] Inf Inf Inf Inf 69788316 23417386 4928959
#> [,8] [,9] [,10] [,11] [,12]
#> [1,] Inf Inf Inf Inf Inf
#> [2,] 109655375 82582137 56995725 42429667 55572869
#> [3,] 10135848 16739019 23476535 42372045 41697533
#> [4,] 6989702 8380031 8157217 6096223 5175511
#> [5,] 6114066 6165899 5605204 2950077 2029365
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 0 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 40914229 62437637 145466337 132727172 41148513 94148655
#> [3,] Inf Inf 62272198 141689083 130513040 27231511 22244158
#> [4,] Inf Inf Inf 141669639 129731815 25017380 20030027
#> [5,] Inf Inf Inf Inf 129712371 24236154 19248801
#> [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] Inf Inf Inf Inf Inf Inf
#> [2,] 136364068 97363603 62387919 42144360 55700845 40901786
#> [3,] 36844541 31520485 28868729 42086737 41825508 40329745
#> [4,] 33698395 23161497 13549411 5810915 5303486 7924316
#> [5,] 32822759 20947365 10997398 2664769 2157340 5175511
#> [,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 12 6 11 11
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0 Inf Inf Inf Inf
#> [2,] 165439.2 0.0 Inf Inf Inf
#> [3,] 3796698.2 19444.1 0.0 Inf Inf
#> [4,] 3014801.2 800669.5 19444.1 0.00 Inf
#> [5,] 16931803.0 3014801.2 800669.5 19444.10 0.00
#> [6,] 74946332.7 3041835.8 827704.2 46478.71 19444.10
#> [7,] 104369013.0 4849486.1 1703340.0 827704.16 46478.71
#> [8,] 77610702.6 11767585.1 3408596.8 1194465.15 413239.71
#> [9,] 53100196.0 19581006.0 4261688.3 1709675.27 834039.41
#> [10,] 41697532.6 41639910.2 5364088.5 2217942.37 1329856.88
#> [11,] 55572869.5 41697532.6 5175510.8 2029364.73 1153728.86
#> [12,] 40901786.3 40329745.0 7924315.8 5175510.83 2029364.73
#> [13,] 0.0 40901786.3 22244158.5 5303486.22 2157340.12
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,] 1885.478 Inf
#> [2,] Inf 0
#> [3,] Inf Inf
#> [4,] Inf Inf
#> [5,] Inf Inf
#> [,1] [,2] [,3]
#> [1,] 7385.792 Inf Inf
#> [2,] Inf 1523.843 1885.478
#> [3,] Inf Inf 0.000
#> [4,] Inf Inf Inf
#> [5,] Inf Inf Inf
#> [,1] [,2] [,3] [,4]
#> [1,] 109127.6 Inf Inf Inf
#> [2,] Inf 2156.638 4955.513 7385.792
#> [3,] Inf Inf 3070.035 1523.843
#> [4,] Inf Inf Inf 0.000
#> [5,] Inf Inf Inf Inf
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 227923.4 Inf Inf Inf Inf
#> [2,] Inf 1353.102 4058.134 8885.316 109127.639
#> [3,] Inf Inf 2172.655 3023.366 2156.638
#> [4,] Inf Inf Inf 1499.523 1523.843
#> [5,] Inf Inf Inf Inf 0.000
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 189005.6 Inf Inf Inf Inf Inf
#> [2,] Inf 26954.02 17266.13 27100.75 111630.840 227923.384
#> [3,] Inf Inf 15380.65 21238.80 4659.839 1353.102
#> [4,] Inf Inf Inf 19714.95 4027.043 2156.638
#> [5,] Inf Inf Inf Inf 2503.201 1499.523
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 105129.1 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 137594.8 84331.00 83667.08 125028.38 228796.254 189005.604
#> [3,] Inf Inf 82445.52 77805.13 18057.38 2225.972 17266.130
#> [4,] Inf Inf Inf 76281.29 17424.59 3029.508 1353.102
#> [5,] Inf Inf Inf Inf 15900.75 2372.393 2156.638
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 142963.6 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 321454.9 196918.9 167862.7 147243.03 231033.580 189032.240
#> [3,] Inf Inf 195033.4 162000.8 40272.03 4463.298 17292.766
#> [4,] Inf Inf Inf 160476.9 39639.24 5266.834 1379.738
#> [5,] Inf Inf Inf Inf 38115.39 4609.719 2183.274
#> [,8]
#> [1,] Inf
#> [2,] 105129.137
#> [3,] 83667.084
#> [4,] 2225.972
#> [5,] 1353.102
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 488317.5 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 643423.1 401429.0 315635.2 195987.97 240788.52 190617.664
#> [3,] Inf Inf 399543.5 309773.2 89016.97 14218.24 18878.190
#> [4,] Inf Inf Inf 308249.4 88384.17 15021.77 2965.162
#> [5,] Inf Inf Inf Inf 86860.33 14364.66 3768.698
#> [,8] [,9]
#> [1,] Inf Inf
#> [2,] 105526.905 142963.581
#> [3,] 84064.852 105129.137
#> [4,] 2623.740 4463.298
#> [5,] 1750.871 1379.738
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 510510.8 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 678121.5 399166.9 303863.9 174978.73 235047.171 195188.223
#> [3,] Inf Inf 397281.4 298002.0 68007.73 8476.889 23448.750
#> [4,] Inf Inf Inf 296478.1 67374.93 9280.425 7535.722
#> [5,] Inf Inf Inf Inf 65851.09 8623.310 8339.258
#> [,8] [,9] [,10]
#> [1,] Inf Inf Inf
#> [2,] 110898.862 146926.661 488317.48
#> [3,] 89436.809 109092.217 105526.91
#> [4,] 7995.697 8426.378 14218.24
#> [5,] 7122.828 5342.818 2623.74
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 1859442 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 1290872 800934.6 592293.9 285719.8 262578.55 199901.14
#> [3,] Inf Inf 799049.1 586432.0 178748.8 36008.27 28161.66
#> [4,] Inf Inf Inf 584908.1 178116.0 36811.80 12248.64
#> [5,] Inf Inf Inf Inf 176592.2 36154.69 13052.17
#> [,8] [,9] [,10] [,11]
#> [1,] Inf Inf Inf Inf
#> [2,] 113234.903 149920.566 497547.48 510510.757
#> [3,] 91772.850 112086.122 114756.91 110898.862
#> [4,] 10331.738 11420.284 23448.24 8476.889
#> [5,] 9458.868 8336.724 11853.74 7535.722
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 1327679 Inf Inf Inf Inf Inf Inf
#> [2,] Inf 1052485 602806.8 433297.8 204431.95 251122.11 217139.43
#> [3,] Inf Inf 600921.3 427435.9 97460.95 24551.83 45399.96
#> [4,] Inf Inf Inf 425912.0 96828.15 25355.37 29486.93
#> [5,] Inf Inf Inf Inf 95304.31 24698.25 30290.47
#> [,8] [,9] [,10] [,11] [,12]
#> [1,] Inf Inf Inf Inf Inf
#> [2,] 131232.98 163761.91 499580.60 527269.75 1859442.272
#> [3,] 109770.93 125927.46 116790.02 127657.85 113234.903
#> [4,] 28329.81 25261.63 25481.36 25235.88 28161.663
#> [5,] 27456.94 22178.07 13886.86 24294.71 8476.889
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 0 Inf Inf Inf Inf Inf Inf Inf
#> [2,] Inf 885238.6 412609.9 354759.7 628742.9 1044676.8 908972.4 535324.7
#> [3,] Inf Inf 410724.4 348897.8 521771.9 818106.5 737233.0 513862.6
#> [4,] Inf Inf Inf 347373.9 521139.1 818910.1 721319.9 432421.5
#> [5,] Inf Inf Inf Inf 519615.2 818252.9 722123.5 431548.6
#> [,9] [,10] [,11] [,12] [,13]
#> [1,] Inf Inf Inf Inf Inf
#> [2,] 354312.1 539702.45 558545.90 1859913.855 1327679.45
#> [3,] 316477.6 156911.87 158934.00 113706.486 131232.98
#> [4,] 215811.8 65603.20 56512.03 28633.247 24551.83
#> [5,] 212728.2 54008.71 55570.86 8948.472 25235.88
#> [,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 3 5 6 6
#> [8,] 0 7 5 6 7
#> [9,] 0 7 5 7 8
#> [10,] 0 7 5 6 9
#> [11,] 0 7 6 10 10
#> [12,] 0 7 5 10 11
#> [13,] 0 8 11 12 11
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.000 Inf Inf Inf Inf
#> [2,] 1885.478 0.000 Inf Inf Inf
#> [3,] 7385.792 1523.843 0.000 Inf Inf
#> [4,] 109127.639 2156.638 1523.843 0.000 Inf
#> [5,] 227923.384 1353.102 2156.638 1499.523 0.000
#> [6,] 189005.604 17266.130 1353.102 2156.638 1499.523
#> [7,] 105129.137 83667.084 2225.972 1353.102 2156.638
#> [8,] 142963.581 105129.137 4463.298 1379.738 1353.102
#> [9,] 488317.480 105526.905 14218.238 2623.740 1379.738
#> [10,] 510510.757 110898.862 8476.889 7535.722 2623.740
#> [11,] 1859442.272 113234.903 28161.663 8476.889 7535.722
#> [12,] 1327679.453 131232.979 24551.829 25235.880 8476.889
#> [13,] 0.000 354312.066 113706.486 24551.829 8948.472
print(a) #indices of months to select for follow-up experiments
#> [1] 1 5 10 11
print(rownames(CanadianWeather$monthlyTemp)[a]) #month names selected
#> [1] "Jan" "May" "Oct" "Nov"