Depth calculation

Description

Depth calculation

Usage

depth(u, X, method = "Projection", name = "X", threads = -1, ...)

Arguments

Details

Calculate depth functions.

Author(s)

Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.

References

Liu, R.Y., Parelius, J.M. and Singh, K. (1999), Multivariate analysis by data depth: Descriptive statistics, graphics and inference (with discussion), Ann. Statist., 27, 783-858.

Mosler K (2013). Depth statistics. In C Becker, R Fried, K S (eds.), Robustness and Complex Data Structures, Festschrift in Honour of Ursula Gather, pp. 17-34. Springer.

Rousseeuw, P.J. and Struyf, A. (1998), Computing location depth and regression depth in higher dimensions, Stat. Comput., 8, 193-203.

Zuo, Y. and Serfling, R. (2000), General Notions of Statistical Depth Functions, Ann. Statist., 28, no. 2, 461-482.

See Also

depthContour and depthPersp for depth graphics.

Examples

require(robustbase)

 ## Calculation of Projection depth
 data(starsCYG, package = "robustbase")
 depth(t(colMeans(starsCYG)), starsCYG)

 #Aslo for matrices
 depth(starsCYG, starsCYG)

 ## Projection depth applied to a large bivariate data set
 x = matrix(rnorm(9999), nc = 3)
 depth(x, x)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(DepthProc)
Loading required package: ggplot2
Loading required package: Rcpp
Loading required package: rrcov
Loading required package: robustbase
Scalable Robust Estimators with High Breakdown Point (version 1.3-11)

Loading required package: MASS
Loading required package: np
Nonparametric Kernel Methods for Mixed Datatypes (version 0.60-2)
[vignette("np_faq",package="np") provides answers to frequently asked questions]
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/DepthProc/depth.Rd_%03d_medium.png", width=480, height=480)
> ### Name: depth
> ### Title: Depth calculation
> ### Aliases: depth
> ### Keywords: depth function multivariate nonparametric robust
> 
> ### ** Examples
> 
> require(robustbase)
> 
>  ## Calculation of Projection depth
>  data(starsCYG, package = "robustbase")
>  depth(t(colMeans(starsCYG)), starsCYG)
Depth method:  Projection 
Set name: X 
[1] 0.3884428
> 
>  #Aslo for matrices
>  depth(starsCYG, starsCYG)
Depth method:  Projection 
Set name: X 
 [1] 0.44557144 0.32526002 0.31896413 0.32526002 0.31392709 0.45387534
 [7] 0.10838443 0.31440414 0.20229833 0.51806802 0.05778045 0.42341109
[13] 0.46072649 0.18193418 0.30163845 0.35181534 0.23549176 0.23487239
[19] 0.27420889 0.05659986 0.33162677 0.29281231 0.29338483 0.35638886
[25] 0.65595119 0.39072358 0.43179195 0.64837969 0.31804742 0.05484409
[31] 0.32832078 0.29509422 0.57658613 0.05316737 0.30796370 0.29672080
[37] 0.34405938 0.57658613 0.36591415 0.36531332 0.42768191 0.58575106
[43] 0.45099633 0.52444634 0.36193925 0.53168768 0.31995429
> 
>  ## Projection depth applied to a large bivariate data set
>  x = matrix(rnorm(9999), nc = 3)
>  depth(x, x)
Depth method:  Projection 
Set name: X 
   [1] 0.3164602 0.3177188 0.5244488 0.2222312 0.2902773 0.2788257 0.1613214
   [8] 0.3830985 0.3541705 0.4046002 0.2703734 0.3202917 0.4644404 0.2899090
  [15] 0.2507960 0.2568941 0.2515138 0.2665351 0.3729913 0.4489452 0.2364013
  [22] 0.3065561 0.2293735 0.2413349 0.2709162 0.1731899 0.2559807 0.3115733
  [29] 0.2880930 0.1851399 0.2585553 0.3625537 0.3009385 0.3697227 0.5577264
  [36] 0.4822098 0.2122783 0.3142005 0.3398655 0.2990645 0.4795530 0.2494926
  [43] 0.2497295 0.2277810 0.3803938 0.2656904 0.3891478 0.3157503 0.5429394
  [50] 0.4958212 0.2764137 0.4153980 0.4000401 0.4916502 0.2911952 0.4874447
  [57] 0.1822345 0.3242165 0.2607696 0.2414744 0.2325025 0.3726172 0.3859660
  [64] 0.2925085 0.2361683 0.2664266 0.2711880 0.2435617 0.4102478 0.1953509
  [71] 0.2077150 0.2902308 0.3683537 0.3574368 0.4094076 0.2865246 0.4013405
  [78] 0.3239810 0.3195920 0.2690203 0.2630827 0.3962952 0.1724557 0.3070656
  [85] 0.3164998 0.5122822 0.2563105 0.4463653 0.2885993 0.2595179 0.3555514
  [92] 0.2675772 0.3112900 0.4932578 0.3192989 0.2907064 0.4032599 0.3533912
  [99] 0.3702181 0.2342440 0.2805631 0.3349574 0.3685585 0.4163728 0.2187304
 [106] 0.5106784 0.5994707 0.2888332 0.2999630 0.3912059 0.2760891 0.2459325
 [113] 0.3142867 0.3095450 0.2477866 0.4431481 0.3944226 0.1913619 0.3924452
 [120] 0.3524858 0.2114490 0.4448983 0.5754500 0.2922956 0.3065292 0.2352488
 [127] 0.3325384 0.2851727 0.2820781 0.2448708 0.4038602 0.2449808 0.2883558
 [134] 0.2176557 0.4430513 0.3082377 0.2682937 0.2196982 0.3243052 0.4114514
 [141] 0.5551971 0.4463856 0.1973153 0.3418760 0.3967168 0.3237013 0.3889928
 [148] 0.2193754 0.5296869 0.4496043 0.4475323 0.3928805 0.2721606 0.4412743
 [155] 0.4274600 0.2914044 0.3038170 0.4267881 0.2622763 0.2421535 0.2144822
 [162] 0.3143176 0.3432536 0.2287408 0.4047567 0.2497208 0.2889337 0.2628279
 [169] 0.3358429 0.2761021 0.2438940 0.2265799 0.2484402 0.3017374 0.5736219
 [176] 0.2842602 0.5272867 0.3047804 0.1929862 0.2556321 0.3387579 0.5949707
 [183] 0.2886174 0.1828337 0.2824030 0.2383510 0.6969298 0.3701379 0.1910723
 [190] 0.2354236 0.3492448 0.3462005 0.4263585 0.3142470 0.2305104 0.2014871
 [197] 0.5898127 0.3816303 0.2448601 0.2280764 0.3086860 0.2418604 0.4609304
 [204] 0.2607823 0.3329390 0.2777567 0.3727413 0.2750460 0.3168794 0.4033451
 [211] 0.3342943 0.2300112 0.3176539 0.3185014 0.2371802 0.4886903 0.1924042
 [218] 0.2353965 0.2728992 0.2685158 0.3211973 0.2667155 0.4411290 0.3859006
 [225] 0.2367126 0.6841499 0.2800145 0.3155437 0.2719464 0.2459885 0.2161436
 [232] 0.3008010 0.2159803 0.5135738 0.2289696 0.3476103 0.3167582 0.3419076
 [239] 0.2434414 0.2971803 0.4424717 0.3106622 0.3754168 0.4415969 0.3459588
 [246] 0.3059265 0.3927230 0.4574404 0.4672019 0.1750546 0.5596742 0.2755226
 [253] 0.5727805 0.2373306 0.2888117 0.2614282 0.3057241 0.2625288 0.2773244
 [260] 0.4464804 0.1668699 0.2910066 0.2202623 0.2868537 0.2850794 0.3282877
 [267] 0.5146452 0.2414793 0.2972963 0.5183388 0.3059917 0.4859530 0.1676173
 [274] 0.2839752 0.2964916 0.2369502 0.2677481 0.3138694 0.2552581 0.2475093
 [281] 0.3962775 0.4338338 0.4892682 0.3066814 0.2502686 0.2236414 0.4857960
 [288] 0.2873059 0.1985202 0.3207338 0.2210143 0.5318421 0.2867576 0.2411747
 [295] 0.2282929 0.2154435 0.3796672 0.2288803 0.2755437 0.2515100 0.3382546
 [302] 0.2034096 0.3468120 0.3637453 0.3920506 0.2568463 0.3506922 0.4265298
 [309] 0.4002137 0.3611585 0.3853347 0.1626681 0.2150516 0.2783083 0.2396849
 [316] 0.2124812 0.2480020 0.3295695 0.3125126 0.3563818 0.3935472 0.2286405
 [323] 0.3212702 0.2616580 0.3647053 0.3573141 0.3345101 0.2444420 0.3178503
 [330] 0.3441148 0.4773770 0.2457424 0.3378449 0.2411508 0.2348241 0.1544345
 [337] 0.3474510 0.3107675 0.3032940 0.4100564 0.3756605 0.3927021 0.2836354
 [344] 0.4105341 0.2582225 0.4140376 0.2853689 0.3245882 0.2856474 0.2223532
 [351] 0.2660147 0.3578405 0.3745069 0.6628786 0.2094298 0.4756271 0.4104708
 [358] 0.2322517 0.4924378 0.2789313 0.2943625 0.3496191 0.3213656 0.2437755
 [365] 0.6183903 0.2588820 0.3592703 0.4623279 0.3440178 0.4629386 0.4542608
 [372] 0.3816224 0.3345079 0.6992160 0.5660480 0.3096991 0.1979665 0.4605970
 [379] 0.2735274 0.1745870 0.4103445 0.2584888 0.2347191 0.2353640 0.2649733
 [386] 0.3961311 0.2240572 0.4218546 0.2174945 0.2445400 0.2868368 0.2252582
 [393] 0.3130271 0.3075174 0.1958304 0.2277372 0.5213462 0.3818228 0.3583466
 [400] 0.2214412 0.1873298 0.4138428 0.2926087 0.3484149 0.3241125 0.1771997
 [407] 0.4312697 0.4359018 0.2991714 0.4287707 0.3172197 0.1506415 0.4038147
 [414] 0.3986044 0.3145013 0.2780226 0.5309263 0.3563372 0.3988912 0.3545191
 [421] 0.4821612 0.3984945 0.2375585 0.3682863 0.3513153 0.2709139 0.3257002
 [428] 0.4156657 0.6410935 0.3360737 0.3527242 0.6183383 0.2040673 0.3827625
 [435] 0.2346872 0.2160922 0.4602870 0.3830444 0.2413615 0.2595447 0.1944745
 [442] 0.3016750 0.5503884 0.2552551 0.2741506 0.2012013 0.2773529 0.2291974
 [449] 0.3286696 0.4016644 0.5015465 0.3318304 0.5295449 0.3138559 0.3563458
 [456] 0.3064014 0.2422207 0.3418121 0.3530251 0.3306700 0.2406458 0.5184167
 [463] 0.2047734 0.3539193 0.4011680 0.3424618 0.2426894 0.4714338 0.4219994
 [470] 0.2742073 0.2451007 0.2887156 0.2868392 0.3113814 0.2226351 0.2438961
 [477] 0.2800405 0.2781868 0.4114659 0.5263676 0.2362220 0.3083263 0.1961995
 [484] 0.2435109 0.2670246 0.3073109 0.4210418 0.4196779 0.6193657 0.2554279
 [491] 0.3432620 0.2756966 0.2870568 0.3264405 0.6054057 0.2877477 0.4522660
 [498] 0.3250667 0.3146214 0.2162379 0.3490384 0.2627209 0.4533970 0.3924847
 [505] 0.2966448 0.2734839 0.2612374 0.3778013 0.3106224 0.3031055 0.2726559
 [512] 0.3057886 0.2516328 0.5805421 0.2939300 0.3097451 0.4122447 0.2659890
 [519] 0.3799058 0.2080571 0.3003677 0.2550384 0.3649297 0.1813654 0.1944737
 [526] 0.2029434 0.2552234 0.3054042 0.3740448 0.4739176 0.4676361 0.2730267
 [533] 0.2514611 0.2343892 0.5123893 0.3794652 0.1904414 0.2455004 0.2932940
 [540] 0.2106155 0.3460369 0.2851095 0.3241654 0.2877065 0.1967636 0.4615018
 [547] 0.3890930 0.2728431 0.3063182 0.3910207 0.2093806 0.5039553 0.4580257
 [554] 0.3451310 0.2064316 0.1892421 0.3459956 0.4342623 0.1928213 0.3446621
 [561] 0.2909417 0.2693216 0.2520676 0.2333851 0.2138118 0.3347865 0.2868960
 [568] 0.3809069 0.2373856 0.4322567 0.3479724 0.1666021 0.5641799 0.5224477
 [575] 0.3848415 0.2698213 0.3332881 0.2066241 0.2783741 0.3334300 0.2305227
 [582] 0.4775269 0.7645455 0.3894488 0.4113624 0.2724757 0.3111667 0.2919169
 [589] 0.3198192 0.3591268 0.3264896 0.7102798 0.2268352 0.2089034 0.3189753
 [596] 0.3117989 0.2450921 0.3540597 0.3102649 0.5848402 0.3626534 0.2211197
 [603] 0.3583472 0.2350130 0.2708408 0.2621290 0.1683726 0.5672214 0.6253456
 [610] 0.5249452 0.2715599 0.3627409 0.3700073 0.2662768 0.4635462 0.1607550
 [617] 0.3801775 0.2359197 0.2769542 0.3453691 0.2601311 0.1859769 0.3244102
 [624] 0.2705061 0.2859641 0.2011284 0.2014471 0.2462854 0.1985124 0.2593404
 [631] 0.3373168 0.3595596 0.4423194 0.4649012 0.2100052 0.4901891 0.3023816
 [638] 0.2632326 0.4016649 0.2332612 0.2742889 0.2879827 0.1522960 0.3716121
 [645] 0.1541107 0.1880996 0.3406377 0.4879829 0.3412559 0.3529767 0.2790724
 [652] 0.2813767 0.2151204 0.3270566 0.2955603 0.2455202 0.2065187 0.1780675
 [659] 0.5900682 0.2476127 0.3168830 0.3153069 0.4068607 0.3621009 0.4391631
 [666] 0.5322823 0.2695950 0.2521398 0.3679064 0.2105913 0.4746724 0.2105111
 [673] 0.2035971 0.3691044 0.1755014 0.2877829 0.4344151 0.4342827 0.2861987
 [680] 0.1789839 0.3105879 0.4678487 0.3040836 0.4749527 0.4919631 0.3260238
 [687] 0.2992676 0.2764673 0.3185192 0.6760873 0.3974518 0.3226958 0.3214682
 [694] 0.3175252 0.2465551 0.2958935 0.1955038 0.7341168 0.2445805 0.4555649
 [701] 0.3075647 0.4997812 0.2929734 0.4778054 0.3536156 0.2858362 0.3361051
 [708] 0.5666038 0.2853732 0.1891841 0.1986621 0.2050387 0.3547798 0.3693619
 [715] 0.2418283 0.3913309 0.5351366 0.2762496 0.2847493 0.3692865 0.3154510
 [722] 0.4647380 0.3561691 0.2456094 0.3987781 0.3616418 0.4710685 0.3850617
 [729] 0.4338681 0.5122921 0.2721875 0.3576081 0.2957448 0.2237735 0.2127267
 [736] 0.2203461 0.2550577 0.5271260 0.2892976 0.6235063 0.3349138 0.2404099
 [743] 0.2937964 0.2406518 0.2861874 0.4447739 0.3046672 0.3907631 0.2506087
 [750] 0.2287661 0.2060009 0.2716046 0.3419820 0.3386651 0.2976531 0.3863928
 [757] 0.2023422 0.4977950 0.3182503 0.2615313 0.4943061 0.3199792 0.2263374
 [764] 0.1824296 0.4169089 0.2764365 0.2076575 0.4611543 0.5472144 0.4100241
 [771] 0.2453402 0.3075907 0.2816716 0.3416436 0.5117260 0.3074193 0.2000989
 [778] 0.3942680 0.4075863 0.3144036 0.2414713 0.4831858 0.2938618 0.3031246
 [785] 0.5562124 0.2596277 0.3150783 0.1734991 0.2370560 0.3152583 0.2569982
 [792] 0.3630850 0.3036413 0.4042656 0.3518835 0.4200794 0.2250010 0.2593963
 [799] 0.3237673 0.3414697 0.2537847 0.2471239 0.3322688 0.2192342 0.3761222
 [806] 0.2586588 0.2492098 0.3230357 0.3455719 0.1918991 0.2924598 0.2633212
 [813] 0.2795111 0.2519633 0.2813259 0.3711204 0.3019402 0.2488672 0.3539794
 [820] 0.2334440 0.2554754 0.3845460 0.4147635 0.3798251 0.5164630 0.3844523
 [827] 0.3765183 0.3875285 0.3474883 0.3611433 0.2219749 0.2812769 0.1708506
 [834] 0.3891737 0.2043457 0.2988016 0.3161820 0.2778063 0.3172004 0.1953167
 [841] 0.3939328 0.3196297 0.4060637 0.2973533 0.2787042 0.2043911 0.3232480
 [848] 0.1897248 0.3960891 0.3481364 0.2552773 0.2703040 0.4241089 0.3226319
 [855] 0.2431411 0.2400493 0.3438057 0.2598693 0.3851612 0.2958081 0.2236737
 [862] 0.3772126 0.3034420 0.3068236 0.2763307 0.3315172 0.2862399 0.1981895
 [869] 0.5372788 0.4674242 0.5062146 0.3405012 0.1739769 0.1673971 0.2321586
 [876] 0.2851939 0.3014580 0.2907008 0.2169033 0.3060818 0.2834390 0.3258496
 [883] 0.2613234 0.3164607 0.2898499 0.4922415 0.2298299 0.6860552 0.2637938
 [890] 0.2136787 0.4184037 0.2049513 0.4976650 0.4407242 0.2090343 0.2725172
 [897] 0.3431081 0.2389367 0.2445703 0.3583592 0.3657392 0.5344224 0.1984682
 [904] 0.2186058 0.2016151 0.4176253 0.4437863 0.2380688 0.5376520 0.4104597
 [911] 0.3198332 0.2917730 0.2639880 0.2983603 0.2642430 0.3612625 0.2456837
 [918] 0.2945485 0.3799448 0.2917247 0.2038371 0.4102931 0.2182780 0.4182243
 [925] 0.2121048 0.2856621 0.2825926 0.2003744 0.1955227 0.4000457 0.3608754
 [932] 0.2896669 0.4466804 0.3155721 0.2735664 0.3014933 0.1913267 0.5079809
 [939] 0.2153931 0.2564810 0.3082631 0.2397602 0.2944110 0.2370054 0.2772777
 [946] 0.2582699 0.3523722 0.3676929 0.2709351 0.3275997 0.4231816 0.1858695
 [953] 0.1926472 0.4101252 0.2664828 0.5698503 0.2889890 0.3501886 0.2853451
 [960] 0.2558099 0.2616298 0.1788725 0.3005919 0.2082708 0.1969546 0.2829949
 [967] 0.5278906 0.4003221 0.3662897 0.2288729 0.2423361 0.6396542 0.3980292
 [974] 0.3329863 0.2142721 0.3670142 0.1692712 0.2485876 0.3458802 0.3766130
 [981] 0.1993099 0.3163297 0.5237193 0.3098215 0.2154281 0.2589480 0.2317850
 [988] 0.2388288 0.2545183 0.2533413 0.3072073 0.2186861 0.3918769 0.5834205
 [995] 0.3550450 0.3663225 0.2990390 0.4235393 0.5653752 0.1846940 0.2843557
[1002] 0.1779204 0.6191356 0.3088765 0.3871202 0.3533823 0.2496733 0.2824628
[1009] 0.3518774 0.2083305 0.3032328 0.2693601 0.1756165 0.7349350 0.2712171
[1016] 0.2452237 0.4176262 0.2355660 0.3607135 0.5112670 0.2612631 0.2145513
[1023] 0.4758669 0.2641807 0.2024122 0.2862636 0.2039395 0.2943271 0.3077978
[1030] 0.2465637 0.3327904 0.2701461 0.3554993 0.3002728 0.1727835 0.2746368
[1037] 0.3145995 0.2569270 0.6372041 0.2792895 0.4287087 0.3581504 0.4209605
[1044] 0.2168122 0.3796370 0.5223485 0.4277533 0.2028293 0.4737876 0.2586816
[1051] 0.5731756 0.2722956 0.2467424 0.3576524 0.1931635 0.2944815 0.2151582
[1058] 0.2326031 0.3553610 0.2931954 0.2477141 0.5660451 0.3515261 0.2249675
[1065] 0.3148905 0.3285352 0.2794109 0.2488690 0.3941261 0.4777225 0.2211963
[1072] 0.2191870 0.2617823 0.2109033 0.3828376 0.1957254 0.2843746 0.2590338
[1079] 0.2654331 0.5120455 0.5164274 0.5753183 0.2302246 0.2561728 0.3245034
[1086] 0.2925901 0.2769316 0.1897434 0.3285162 0.2571270 0.2688974 0.3198331
[1093] 0.4257125 0.3393459 0.3209717 0.2598996 0.3292678 0.3038141 0.3493454
[1100] 0.2575633 0.2932726 0.4232675 0.2031213 0.3958882 0.2031419 0.1982654
[1107] 0.4689167 0.6470675 0.1914516 0.3327449 0.2475626 0.6308652 0.3151975
[1114] 0.4071275 0.4120746 0.2016648 0.2248230 0.3549261 0.4827126 0.2678030
[1121] 0.8572434 0.2973896 0.2663427 0.3036499 0.3150248 0.3832197 0.1829906
[1128] 0.1475574 0.5492846 0.2880891 0.2453251 0.2086604 0.4553775 0.3616356
[1135] 0.2404485 0.3529141 0.1994586 0.6331762 0.1678575 0.2967305 0.2056692
[1142] 0.4342514 0.2589658 0.3537203 0.2144520 0.3359545 0.2552967 0.3396786
[1149] 0.2954174 0.5053894 0.4807872 0.3431134 0.3572237 0.2376028 0.2375304
[1156] 0.1835005 0.3125298 0.2429450 0.7806278 0.1913421 0.4779040 0.2533564
[1163] 0.3123900 0.3492373 0.2227170 0.2825548 0.4266893 0.3341514 0.2712362
[1170] 0.2704566 0.3772392 0.2454276 0.2677179 0.2926492 0.2386991 0.2584509
[1177] 0.2060638 0.3470381 0.2347889 0.1928977 0.4741588 0.2622517 0.3133846
[1184] 0.3565317 0.6092636 0.2912477 0.1824218 0.4078464 0.2727717 0.1810787
[1191] 0.3479615 0.3118513 0.2836054 0.3717443 0.5131570 0.3435050 0.4034917
[1198] 0.3199172 0.2802647 0.2793002 0.3015897 0.1865790 0.2465643 0.2739075
[1205] 0.3743577 0.2753682 0.1995505 0.5743358 0.2680701 0.5306256 0.2622879
[1212] 0.5359951 0.3619949 0.2019823 0.3307758 0.4090370 0.2286812 0.2311054
[1219] 0.3554178 0.3795314 0.2195072 0.5182751 0.4032574 0.2303103 0.1983729
[1226] 0.5404503 0.2661290 0.2117790 0.4286693 0.2488323 0.4644119 0.3350482
[1233] 0.2202964 0.4989687 0.3057689 0.3805706 0.3523014 0.2088745 0.2987528
[1240] 0.4502088 0.3590994 0.7738771 0.2180578 0.3077886 0.2726936 0.2999598
[1247] 0.4568022 0.2704213 0.3072385 0.2803982 0.2824208 0.2394710 0.3875530
[1254] 0.3017178 0.3025321 0.3353293 0.5318542 0.2246754 0.3611240 0.2990064
[1261] 0.2127936 0.3143077 0.2847930 0.3848053 0.2269090 0.7931446 0.5029265
[1268] 0.2690315 0.2919433 0.2547490 0.2872581 0.2250223 0.2400489 0.1903208
[1275] 0.2742324 0.3126859 0.3027935 0.4040763 0.5379337 0.4581771 0.3030068
[1282] 0.3849586 0.2582318 0.2843691 0.2223691 0.4292609 0.2521588 0.2337706
[1289] 0.2367061 0.3024807 0.2638161 0.3117492 0.4020308 0.2954693 0.3580057
[1296] 0.4015815 0.2003471 0.3379844 0.1925488 0.3544952 0.2852162 0.3523932
[1303] 0.2295883 0.3707684 0.2787729 0.3542725 0.2770774 0.3160016 0.4224830
[1310] 0.2786299 0.2646833 0.3868025 0.2854944 0.2090665 0.3154242 0.3009599
[1317] 0.4648017 0.5029602 0.4140346 0.2847893 0.2156340 0.4699193 0.2610413
[1324] 0.3599299 0.3675440 0.3364599 0.3781148 0.3434014 0.7292204 0.2177502
[1331] 0.2858470 0.3619778 0.3668495 0.3362802 0.3258806 0.4999553 0.1575978
[1338] 0.3814538 0.3169428 0.3428600 0.2349013 0.3171090 0.2494493 0.3087725
[1345] 0.3037404 0.1701784 0.2998757 0.3048929 0.2190499 0.6032009 0.3723345
[1352] 0.3088141 0.1853470 0.2555341 0.5565616 0.2146921 0.5568733 0.3366489
[1359] 0.2965724 0.2185398 0.2901171 0.6310013 0.2047804 0.3197605 0.1814538
[1366] 0.2451270 0.2365181 0.3695419 0.3123177 0.2592114 0.1610265 0.2610261
[1373] 0.3059841 0.3088018 0.2804722 0.5362501 0.3944514 0.4073453 0.5505188
[1380] 0.2413050 0.4417814 0.3614442 0.2963801 0.2197486 0.4332687 0.4588667
[1387] 0.2630151 0.3591203 0.2311659 0.4754744 0.2513449 0.4511676 0.3901167
[1394] 0.1669193 0.4646432 0.2073482 0.3444709 0.4940829 0.5376454 0.2193507
[1401] 0.3566977 0.3117627 0.3818047 0.2249561 0.2314993 0.6341939 0.1831911
[1408] 0.2505314 0.4829294 0.3745715 0.4971075 0.3962243 0.4111231 0.4846049
[1415] 0.2705970 0.2812143 0.2066877 0.3851404 0.2634827 0.3554703 0.3563656
[1422] 0.2852537 0.4934253 0.3179400 0.3555619 0.2149467 0.2683494 0.2746524
[1429] 0.3013668 0.2696620 0.4862956 0.3848235 0.3862911 0.3084425 0.2804673
[1436] 0.2513433 0.3924860 0.2160519 0.3019522 0.3087910 0.2401152 0.2658343
[1443] 0.2485817 0.3013937 0.3061368 0.2932066 0.3327160 0.2740397 0.2470110
[1450] 0.4651523 0.4288606 0.3575207 0.6081991 0.1776681 0.3720442 0.2672985
[1457] 0.2031179 0.3688650 0.3245582 0.2766728 0.3537786 0.3086506 0.3327242
[1464] 0.5695890 0.2832886 0.2101727 0.4576676 0.3675158 0.2528559 0.2769570
[1471] 0.4810298 0.2621174 0.2964380 0.2044039 0.1531319 0.3049558 0.2648580
[1478] 0.3345489 0.3921870 0.2453308 0.2837128 0.2338667 0.3944524 0.2935481
[1485] 0.1949500 0.3142623 0.3668150 0.1963563 0.3859364 0.3354628 0.2994911
[1492] 0.4348927 0.4260101 0.3576019 0.3895060 0.3144018 0.2061320 0.4018590
[1499] 0.7205567 0.2742899 0.2399930 0.3688525 0.2902123 0.2664977 0.2326702
[1506] 0.3033594 0.2065917 0.2318019 0.2568868 0.3412873 0.2385879 0.5461123
[1513] 0.3349541 0.3559960 0.2520688 0.2188540 0.3179929 0.2621468 0.2101507
[1520] 0.2949333 0.2236692 0.2824363 0.2822914 0.2100502 0.3679244 0.3028766
[1527] 0.5231939 0.2263192 0.4577351 0.2830375 0.2412324 0.7893386 0.2563904
[1534] 0.2629401 0.2191978 0.4456537 0.2015211 0.1599672 0.2873968 0.2545325
[1541] 0.4017769 0.2293302 0.3644594 0.3144609 0.2351457 0.3153148 0.2170056
[1548] 0.2101658 0.2252606 0.2357026 0.3625598 0.4257006 0.3715542 0.2215838
[1555] 0.4904458 0.2313912 0.3199800 0.4401654 0.2238150 0.2517043 0.3467810
[1562] 0.2510462 0.2640286 0.2306606 0.2294369 0.3819002 0.1865237 0.2208101
[1569] 0.3593110 0.2676055 0.2528189 0.3356610 0.4351998 0.1881374 0.2697454
[1576] 0.3109623 0.5671246 0.6989405 0.2973438 0.4211442 0.2869736 0.2079839
[1583] 0.5276486 0.3385632 0.3776209 0.2740728 0.4289621 0.5895176 0.3972543
[1590] 0.2133317 0.2773589 0.2646847 0.3092460 0.6157873 0.2773524 0.3883290
[1597] 0.3256787 0.2618548 0.3078699 0.4632989 0.3728772 0.5908290 0.2654390
[1604] 0.3187013 0.2708426 0.2802353 0.4133783 0.2152070 0.3427596 0.2514024
[1611] 0.2438602 0.2322884 0.3095512 0.3175443 0.1754975 0.1583287 0.4414474
[1618] 0.1980638 0.2844491 0.3317386 0.2310158 0.4422082 0.2096852 0.2965096
[1625] 0.2480605 0.3139724 0.4195379 0.2350615 0.2392041 0.4172483 0.3426369
[1632] 0.7109617 0.5627402 0.4803763 0.2544651 0.5038088 0.2675781 0.3046031
[1639] 0.2507106 0.2713160 0.3378620 0.2864227 0.3202886 0.3633674 0.2849119
[1646] 0.2145053 0.2378572 0.2758164 0.2773802 0.2281157 0.4483360 0.3538979
[1653] 0.2422637 0.3744803 0.4154269 0.2371651 0.2906430 0.4128841 0.3671091
[1660] 0.2772039 0.2840046 0.4114528 0.2869454 0.2747541 0.1621119 0.4823367
[1667] 0.3734069 0.3096027 0.3815415 0.4025958 0.3065849 0.2623946 0.3167680
[1674] 0.4038209 0.1703948 0.2765031 0.2934860 0.2196819 0.2848306 0.3598758
[1681] 0.2552708 0.2356888 0.3202815 0.2878481 0.4247568 0.2954593 0.2093856
[1688] 0.2881693 0.3168216 0.3440139 0.5603300 0.3962921 0.3714862 0.3846374
[1695] 0.2672602 0.6602261 0.4475265 0.3315886 0.3331015 0.2616329 0.3371173
[1702] 0.3702712 0.3243744 0.4109977 0.3360531 0.2112738 0.2856500 0.5365923
[1709] 0.2916403 0.4407257 0.4844354 0.3296490 0.4198889 0.2649131 0.2342455
[1716] 0.3373768 0.2793461 0.3750997 0.2876176 0.2824814 0.3103475 0.3375606
[1723] 0.2683498 0.3579817 0.6488574 0.3392387 0.1916167 0.4045835 0.3126003
[1730] 0.2518822 0.3983181 0.2364331 0.3156957 0.3486757 0.2025431 0.5667625
[1737] 0.2036066 0.3081688 0.3187494 0.3480257 0.2437478 0.3434000 0.3401626
[1744] 0.3491366 0.2777288 0.2168948 0.2600506 0.4366480 0.3317245 0.3657191
[1751] 0.1938675 0.2831690 0.3123203 0.4052564 0.2491639 0.2766250 0.1775160
[1758] 0.2938673 0.3961664 0.2440972 0.2327730 0.5045797 0.2544008 0.3807611
[1765] 0.2882125 0.5046608 0.2439490 0.2589411 0.3753107 0.2322949 0.4129931
[1772] 0.2912214 0.2738703 0.5042514 0.2858008 0.2115145 0.2664686 0.2633971
[1779] 0.2849410 0.2957238 0.3298013 0.3131267 0.2678709 0.1843005 0.4017836
[1786] 0.4829177 0.3775172 0.3822556 0.4786806 0.3101117 0.2620350 0.2228400
[1793] 0.2344749 0.4197053 0.2956604 0.1947469 0.2568614 0.2719272 0.3287226
[1800] 0.2561789 0.4531984 0.2526671 0.4192951 0.3024683 0.2677978 0.2197108
[1807] 0.1984068 0.4530200 0.5277227 0.3203049 0.3090252 0.1861044 0.2127591
[1814] 0.2450402 0.3352091 0.6219614 0.2950855 0.2883159 0.2267727 0.1999078
[1821] 0.2815155 0.2341776 0.2129076 0.1912669 0.1829532 0.2607507 0.2680307
[1828] 0.3477850 0.2654191 0.2790189 0.3938153 0.3336358 0.3044053 0.4223614
[1835] 0.5036325 0.3931628 0.2852351 0.1893610 0.3034241 0.4662839 0.2595537
[1842] 0.2347480 0.1818526 0.4369875 0.2581690 0.5249492 0.2671429 0.2885239
[1849] 0.2574487 0.2893805 0.5494975 0.3938090 0.2396020 0.3040088 0.1900472
[1856] 0.3623300 0.6008281 0.5746963 0.2451916 0.3292786 0.2619214 0.2924794
[1863] 0.3874483 0.2664870 0.2764940 0.4381579 0.3736709 0.2385635 0.2338672
[1870] 0.2272073 0.2197982 0.2291698 0.2204991 0.3356806 0.4871241 0.4278433
[1877] 0.4360440 0.3229746 0.3927882 0.2231042 0.2382879 0.3599212 0.5273687
[1884] 0.3203369 0.2764329 0.2401591 0.2157408 0.2961129 0.3625395 0.3279518
[1891] 0.2033560 0.2242332 0.1851481 0.4712810 0.2852904 0.3452135 0.5633265
[1898] 0.3508526 0.4809281 0.2772131 0.4166157 0.2642190 0.2738568 0.3047475
[1905] 0.3459270 0.2731628 0.2116927 0.1992920 0.3175748 0.1954565 0.2780140
[1912] 0.2341563 0.3174331 0.4105553 0.6936781 0.4283448 0.3840187 0.4975585
[1919] 0.3036330 0.2806578 0.3874609 0.2797792 0.3136712 0.2728956 0.2557829
[1926] 0.3916611 0.2636138 0.2431213 0.4930418 0.2943717 0.3409124 0.3472194
[1933] 0.2367818 0.2716712 0.2702111 0.2561015 0.6547293 0.2193772 0.3310648
[1940] 0.2590559 0.2397395 0.2133952 0.2772013 0.4769344 0.3404440 0.3583687
[1947] 0.2515318 0.1963619 0.3120635 0.1811942 0.2127230 0.5571160 0.3780923
[1954] 0.3319234 0.3473893 0.3975351 0.3918113 0.2623238 0.2759832 0.5370505
[1961] 0.1710301 0.2700680 0.4480113 0.5049285 0.3526253 0.2390760 0.4159139
[1968] 0.3269724 0.2923390 0.1385113 0.2020748 0.5245439 0.3474235 0.2619983
[1975] 0.1481387 0.3104660 0.2911286 0.4259435 0.3955058 0.2750572 0.2253100
[1982] 0.2697006 0.2291813 0.2465689 0.3374418 0.2261378 0.5933825 0.3220658
[1989] 0.5076241 0.2069988 0.3377309 0.5098084 0.4256676 0.3121957 0.1948795
[1996] 0.1933622 0.1867504 0.3545424 0.7371031 0.4470760 0.2269230 0.3564960
[2003] 0.2955868 0.2899816 0.2733465 0.2241639 0.3581866 0.4181282 0.2551603
[2010] 0.3192314 0.2539011 0.1943092 0.2486533 0.3988430 0.2371454 0.2141447
[2017] 0.2953289 0.3499895 0.2027244 0.2640477 0.3721407 0.3337149 0.3531808
[2024] 0.2465717 0.3839288 0.4046558 0.3286619 0.3775803 0.2763243 0.2960925
[2031] 0.1633211 0.1714202 0.3135946 0.2635730 0.1684887 0.2708600 0.3691404
[2038] 0.4166028 0.5284763 0.3944257 0.1941803 0.2251770 0.3157851 0.2420082
[2045] 0.5018595 0.2309534 0.2396786 0.3589409 0.5792261 0.3320498 0.3570945
[2052] 0.2801974 0.2284012 0.3567167 0.3661415 0.3129455 0.4545440 0.2838002
[2059] 0.2835190 0.2351542 0.2744259 0.3727834 0.3718042 0.3183171 0.3066649
[2066] 0.3422160 0.4500032 0.2576282 0.2193254 0.3414205 0.2283752 0.2536506
[2073] 0.2782447 0.4240832 0.5942917 0.3334081 0.2412238 0.3187660 0.5806666
[2080] 0.3696428 0.2783457 0.1970477 0.2785947 0.1671097 0.3371758 0.3608466
[2087] 0.2374317 0.4497453 0.2824440 0.2541839 0.2236843 0.3096022 0.3447908
[2094] 0.2999262 0.2769300 0.2871357 0.3623322 0.1929255 0.3184359 0.3923076
[2101] 0.4724380 0.2906816 0.2728816 0.2300595 0.4527091 0.3029485 0.2874163
[2108] 0.3598077 0.3080443 0.2654404 0.3488188 0.3573598 0.3615094 0.2948592
[2115] 0.1925690 0.2369347 0.2874607 0.4649602 0.2588779 0.3268623 0.3039130
[2122] 0.1684318 0.2708325 0.3078845 0.2745812 0.2301244 0.3337583 0.3612200
[2129] 0.4269325 0.3390299 0.2527947 0.2451409 0.3192735 0.2343394 0.2509890
[2136] 0.3341335 0.2514129 0.3325410 0.5688824 0.2224151 0.2146692 0.1956713
[2143] 0.2431210 0.4159472 0.3862818 0.2846764 0.2088594 0.3068325 0.3609649
[2150] 0.3940458 0.3525777 0.3745718 0.3044042 0.2674206 0.4833706 0.2364898
[2157] 0.2607808 0.2300549 0.3664852 0.3487592 0.3070997 0.2927804 0.2153820
[2164] 0.6223030 0.2377197 0.2377240 0.2588996 0.3031192 0.2934819 0.3687949
[2171] 0.3732008 0.1965245 0.2789712 0.1829368 0.3704438 0.3072401 0.2273835
[2178] 0.3737987 0.6757215 0.3166521 0.5213744 0.2918043 0.5379900 0.2864214
[2185] 0.4150331 0.2430011 0.2698083 0.2529106 0.3805381 0.2412048 0.2304458
[2192] 0.2583757 0.2406832 0.3254386 0.3695624 0.2304587 0.2516031 0.5256092
[2199] 0.1507543 0.4289860 0.3605007 0.2255955 0.3126501 0.4590238 0.3642682
[2206] 0.5199768 0.3596042 0.2477657 0.3855282 0.2657205 0.5137384 0.3297047
[2213] 0.3625009 0.3182569 0.5461633 0.1939925 0.5562519 0.4791516 0.2119315
[2220] 0.2883063 0.2185177 0.6417383 0.3040839 0.4247476 0.1961098 0.2432658
[2227] 0.7907062 0.1897006 0.2627336 0.4518118 0.2402780 0.3146494 0.2812489
[2234] 0.3376507 0.2604558 0.3736900 0.2048102 0.2550427 0.1535019 0.2883645
[2241] 0.2325636 0.2773594 0.2366352 0.3138782 0.2443861 0.4083446 0.4151017
[2248] 0.3001063 0.4762455 0.3040920 0.5789637 0.7830795 0.3899166 0.2848799
[2255] 0.3127677 0.1845697 0.4344220 0.3248976 0.2928383 0.1839842 0.3141525
[2262] 0.2037923 0.2515174 0.2286965 0.2868186 0.2803932 0.2527258 0.4509679
[2269] 0.5101120 0.2144989 0.3879751 0.3536335 0.2094539 0.6460185 0.3751659
[2276] 0.2023898 0.2739630 0.1952378 0.2598541 0.6922192 0.7126085 0.3546037
[2283] 0.3046309 0.2364122 0.3854070 0.4001803 0.4762077 0.2650075 0.1965978
[2290] 0.2865501 0.3595002 0.2386682 0.2243287 0.3393199 0.5059933 0.2004355
[2297] 0.3044156 0.2867869 0.3083354 0.2766688 0.2845613 0.3566234 0.3975755
[2304] 0.2957963 0.3033482 0.5523841 0.2782870 0.1617410 0.4098330 0.4629648
[2311] 0.3118647 0.1824653 0.3822748 0.2328584 0.4591098 0.3419394 0.4301291
[2318] 0.4817547 0.8047310 0.2075352 0.3292413 0.3086977 0.4990777 0.2280174
[2325] 0.3555164 0.3628426 0.5505122 0.2669032 0.3095943 0.4452572 0.2573561
[2332] 0.2991919 0.1861246 0.4957710 0.3294077 0.2973617 0.3924899 0.2117860
[2339] 0.1913904 0.2254856 0.2779294 0.4689043 0.3610949 0.3564861 0.3162497
[2346] 0.3225109 0.2600163 0.2709248 0.2298686 0.2386167 0.3720471 0.2820019
[2353] 0.3331879 0.3032076 0.2907132 0.1906147 0.2918517 0.4029100 0.3021064
[2360] 0.2279082 0.3541794 0.3027453 0.3941327 0.2770749 0.3106267 0.3964569
[2367] 0.4060271 0.3013718 0.2300023 0.4103104 0.5971590 0.2861059 0.3238699
[2374] 0.3395888 0.3602755 0.1738433 0.5979814 0.2918396 0.2586355 0.5106156
[2381] 0.2711912 0.2642034 0.2667352 0.4786834 0.2241221 0.3524156 0.2066749
[2388] 0.3701423 0.2520400 0.3519603 0.4962524 0.3346919 0.5630918 0.2249949
[2395] 0.3227947 0.2983855 0.2377679 0.4671677 0.2167093 0.2234112 0.1882189
[2402] 0.3049411 0.2858286 0.3324480 0.3558570 0.3686794 0.2819472 0.2987395
[2409] 0.2877582 0.3629884 0.3146514 0.2935939 0.3657613 0.3197143 0.2574178
[2416] 0.3332926 0.5056988 0.3709975 0.2401031 0.4882179 0.5373113 0.3638225
[2423] 0.2675586 0.4312074 0.4045193 0.3918511 0.3397668 0.2870744 0.2449492
[2430] 0.2042047 0.2547575 0.2715787 0.6572545 0.4206867 0.1776561 0.2734753
[2437] 0.2222764 0.1706541 0.2521833 0.2620174 0.4518748 0.2472326 0.2563031
[2444] 0.2850617 0.4346579 0.2581474 0.3611920 0.2899505 0.3427755 0.3498938
[2451] 0.2654925 0.2913277 0.4134773 0.2807663 0.3966223 0.3407542 0.2992932
[2458] 0.2700350 0.3559319 0.2280357 0.3986435 0.3516414 0.2997656 0.3491775
[2465] 0.3851439 0.1884939 0.2760188 0.2861788 0.2698375 0.3076140 0.1659352
[2472] 0.3144486 0.2232871 0.3577602 0.2470971 0.4558544 0.3978160 0.1824827
[2479] 0.3505401 0.3134866 0.5288719 0.3276078 0.2092471 0.2563694 0.2422609
[2486] 0.3214756 0.4572915 0.4295220 0.5456854 0.2598252 0.3099616 0.2122854
[2493] 0.2646581 0.3074370 0.3118849 0.3321873 0.2948437 0.2501155 0.2072334
[2500] 0.2314974 0.3370178 0.2846307 0.3559062 0.6399887 0.2773774 0.4137617
[2507] 0.4890667 0.2615130 0.5766196 0.2120479 0.3058523 0.3331688 0.2821497
[2514] 0.320237