rFractionalWishart: Random Fractional Wishart Matrix
In rWishart: Random Wishart Matrix Generation
Description
Usage
Arguments
Details
Value
References
Examples
View source: R/rFractionalWishart.R
Description
Generate n random matrices, distributed according to the Wishart distribution with parameters Sigma and df, W_p(Sigma, df).
Usage
1
2
rFractionalWishart(n, df, Sigma, covariance = FALSE,
simplify = "array")
Arguments
n
integer: the number of replications.
df
numeric parameter, “degrees of freedom”.
Sigma
positive definite (p * p) “scale”
matrix, the matrix parameter of the distribution.
covariance
logical on whether a covariance matrix should be generated
simplify
logical or character string; should the result be
simplified to a vector, matrix or higher dimensional array if
possible? For sapply it must be named and not abbreviated.
The default value, TRUE, returns a vector or matrix if appropriate,
whereas if simplify = "array" the result may be an
array of “rank”
(=length(dim(.))) one higher than the result
of FUN(X[[i]]).
Details
If X_1, ..., X_m is a sample of m independent multivariate Gaussians with mean vector 0, and covariance matrix Sigma,
the distribution of M = X'X is W_p(Sigma, m).
Value
A numeric array of dimension p * p * n, where each array is a positive semidefinite matrix, a realization of the Wishart distribution W_p(Sigma, df)
References
Adhikari, S. (2008). Wishart random matrices in probabilistic structural mechanics.
Journal of engineering mechanics, 134(12), doi: 10.1061/(ASCE)0733-9399(2008)134:12(1029).
Examples
1
rFractionalWishart(2, 22.5, diag(1, 20))
Example output
Attaching package: ‘rWishart’
The following object is masked from ‘package:stats’:
rWishart
, , 1
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 227.3400424 -28.92777257 -15.7091314 -19.111657 -1.9955855 11.711521
[2,] -28.9277726 155.46358797 -4.0421071 2.469213 1.7259372 8.675951
[3,] -15.7091314 -4.04210709 79.3414855 -0.574172 2.0931759 -3.348261
[4,] -19.1116566 2.46921324 -0.5741720 140.805629 -4.4858976 1.028657
[5,] -1.9955855 1.72593721 2.0931759 -4.485898 34.2079060 13.145621
[6,] 11.7115212 8.67595088 -3.3482609 1.028657 13.1456213 116.410392
[7,] -3.5855488 10.63878242 1.8020482 -8.343388 3.0907914 -4.627708
[8,] -5.2344835 9.86463813 1.9340584 -12.647050 -5.8572626 -9.867235
[9,] 7.2372063 -5.60585506 6.3486273 -2.641505 -4.9028045 -7.919296
[10,] -0.5218905 -0.59814195 14.4985201 -2.514111 5.6400200 -6.812899
[11,] 5.2447578 2.65628069 6.2800058 -15.612341 -4.6773754 -1.244814
[12,] -10.6679992 -0.35755522 9.6690284 -6.936134 1.8683728 -3.269700
[13,] 12.7987964 -13.08614315 1.3606202 9.678380 0.5190985 2.807234
[14,] 0.5105867 -2.62735811 -0.1968232 2.332331 -5.4638033 3.458920
[15,] 1.0598604 -8.74550233 -7.6071450 -1.306100 -1.2454749 3.752046
[16,] -7.6779368 1.88138198 4.3178483 2.106791 3.2956554 -6.039764
[17,] 0.5569478 -5.36365162 5.1772603 -8.278664 5.1054856 -1.716953
[18,] 1.9432297 -4.75788791 -4.4889020 2.443566 -5.5541954 -2.446559
[19,] -3.3128269 -0.46228373 3.6928392 -1.895497 1.7222935 1.473387
[20,] 0.4281565 0.01054848 0.0507884 -0.178266 0.1904332 1.127288
[,7] [,8] [,9] [,10] [,11]
[1,] -3.58554876 -5.23448354 7.23720633 -0.5218905 5.2447578
[2,] 10.63878242 9.86463813 -5.60585506 -0.5981419 2.6562807
[3,] 1.80204817 1.93405836 6.34862733 14.4985201 6.2800058
[4,] -8.34338803 -12.64704985 -2.64150530 -2.5141109 -15.6123407
[5,] 3.09079136 -5.85726261 -4.90280446 5.6400200 -4.6773754
[6,] -4.62770774 -9.86723515 -7.91929646 -6.8128993 -1.2448139
[7,] 36.05756147 8.83821306 -0.02036627 -1.4088130 -4.7315187
[8,] 8.83821306 58.43231693 1.51155169 1.1402774 5.7875724
[9,] -0.02036627 1.51155169 38.96783632 5.7648532 -1.0135871
[10,] -1.40881300 1.14027740 5.76485319 50.1187563 -5.0144964
[11,] -4.73151868 5.78757243 -1.01358709 -5.0144964 22.3344204
[12,] 2.18936797 4.23787668 -2.72174624 3.9923289 1.4163277
[13,] -14.09025265 -4.26967951 4.74462255 -8.4911253 6.9402579
[14,] -1.75217473 7.20219264 1.07774411 0.0119133 -0.4262292
[15,] -2.66751866 1.99477957 2.31450344 -5.0106841 0.6887500
[16,] 0.75781016 1.74366049 6.85410571 5.1122609 -10.1456736
[17,] 1.03825209 0.32623622 3.98541439 1.0256799 1.3034741
[18,] -6.23978669 0.07492463 1.39258946 -2.2965242 -0.1894124
[19,] -1.63941701 2.00448104 -5.95744293 0.5018147 1.7391015
[20,] 1.48034616 -0.38131004 0.45992364 0.1151233 -0.5743463
[,12] [,13] [,14] [,15] [,16] [,17]
[1,] -10.667999187 12.7987964 0.5105867 1.0598604 -7.6779368 0.55694779
[2,] -0.357555216 -13.0861431 -2.6273581 -8.7455023 1.8813820 -5.36365162
[3,] 9.669028403 1.3606202 -0.1968232 -7.6071450 4.3178483 5.17726034
[4,] -6.936134295 9.6783800 2.3323313 -1.3061005 2.1067905 -8.27866408
[5,] 1.868372814 0.5190985 -5.4638033 -1.2454749 3.2956554 5.10548565
[6,] -3.269699851 2.8072342 3.4589196 3.7520458 -6.0397643 -1.71695282
[7,] 2.189367967 -14.0902526 -1.7521747 -2.6675187 0.7578102 1.03825209
[8,] 4.237876678 -4.2696795 7.2021926 1.9947796 1.7436605 0.32623622
[9,] -2.721746238 4.7446225 1.0777441 2.3145034 6.8541057 3.98541439
[10,] 3.992328912 -8.4911253 0.0119133 -5.0106841 5.1122609 1.02567991
[11,] 1.416327651 6.9402579 -0.4262292 0.6887500 -10.1456736 1.30347408
[12,] 29.882311308 -21.0545280 -5.3831947 -1.5982501 -2.6568437 4.59734742
[13,] -21.054528036 69.3973761 -1.1474795 -2.6948186 -4.2633299 2.44090079
[14,] -5.383194658 -1.1474795 13.5863072 0.8318550 3.4120958 -2.74680221
[15,] -1.598250090 -2.6948186 0.8318550 24.9544400 -2.8435208 0.94310704
[16,] -2.656843691 -4.2633299 3.4120958 -2.8435208 29.8003178 -1.72857328
[17,] 4.597347419 2.4409008 -2.7468022 0.9431070 -1.7285733 13.56240553
[18,] -4.304778978 0.9476917 1.6819331 6.8488828 3.6743205 1.94733871
[19,] 2.223337572 -1.3669113 2.0287242 1.0734772 -3.5060361 -4.47476018
[20,] -0.001546977 -0.6208495 0.4493683 -0.1393863 0.1518481 -0.01395815
[,18] [,19] [,20]
[1,] 1.94322965 -3.3128269 0.428156507
[2,] -4.75788791 -0.4622837 0.010548482
[3,] -4.48890199 3.6928392 0.050788396
[4,] 2.44356574 -1.8954965 -0.178266005
[5,] -5.55419543 1.7222935 0.190433240
[6,] -2.44655899 1.4733865 1.127287970
[7,] -6.23978669 -1.6394170 1.480346162
[8,] 0.07492463 2.0044810 -0.381310039
[9,] 1.39258946 -5.9574429 0.459923637
[10,] -2.29652420 0.5018147 0.115123321
[11,] -0.18941238 1.7391015 -0.574346254
[12,] -4.30477898 2.2233376 -0.001546977
[13,] 0.94769167 -1.3669113 -0.620849529
[14,] 1.68193306 2.0287242 0.449368311
[15,] 6.84888278 1.0734772 -0.139386290
[16,] 3.67432049 -3.5060361 0.151848065
[17,] 1.94733871 -4.4747602 -0.013958149
[18,] 12.39260758 -5.1053840 -0.969000137
[19,] -5.10538401 11.6855792 -0.310388451
[20,] -0.96900014 -0.3103885 0.396357872
, , 2
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 88.8809045 6.9751942 -0.2894928 -12.886513572 13.9374522 -5.1915504
[2,] 6.9751942 134.9840155 -0.9852806 6.437573280 14.4837998 5.8966084
[3,] -0.2894928 -0.9852806 88.8353541 -1.747101856 -10.3461909 -2.7045736
[4,] -12.8865136 6.4375733 -1.7471019 123.456440481 7.9273883 0.8216096
[5,] 13.9374522 14.4837998 -10.3461909 7.927388303 136.9507716 3.0198158
[6,] -5.1915504 5.8966084 -2.7045736 0.821609550 3.0198158 81.8866512
[7,] 6.9133230 -20.3940325 -2.6045770 10.710100324 1.6225417 2.9674880
[8,] 6.7070815 -5.6577463 -0.8260750 3.064446045 0.5412052 -7.7033987
[9,] -8.0404395 8.4104832 5.7524242 4.659974833 1.9649242 12.9848057
[10,] -6.4093079 5.9174432 -3.1795513 -26.280247808 -12.9080088 7.0336563
[11,] 2.0299918 -8.1932757 -7.9295903 0.805616823 -14.7021276 15.1123705
[12,] 4.8345150 3.9643735 2.0421328 -7.049095949 4.2394473 7.0789302
[13,] 3.0963375 5.6211372 -3.1857838 4.464730272 -2.3851926 10.6857388
[14,] -1.3466553 -4.7901904 1.2337572 -0.009624001 -7.1025964 -8.2196241
[15,] 0.5642081 -0.1695940 2.8357109 0.699841235 2.9406989 -1.8211008
[16,] 2.8090635 5.2218430 0.1963142 -3.058618287 -4.7706557 1.1017005
[17,] 0.3734430 4.3391791 -4.5894654 -0.666313432 5.4091743 7.8288676
[18,] -0.5359178 -0.3910417 -0.5029510 0.560287558 -0.8231613 7.4397302
[19,] -1.2879393 1.1781039 0.3916049 -1.058916978 -3.2904659 -0.7993257
[20,] -1.6141693 0.1232961 -5.0378214 -2.253328814 0.7951449 7.3625927
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] 6.9133230 6.7070815 -8.04043951 -6.40930786 2.02999182 4.8345150
[2,] -20.3940325 -5.6577463 8.41048324 5.91744322 -8.19327573 3.9643735
[3,] -2.6045770 -0.8260750 5.75242418 -3.17955133 -7.92959028 2.0421328
[4,] 10.7101003 3.0644460 4.65997483 -26.28024781 0.80561682 -7.0490959
[5,] 1.6225417 0.5412052 1.96492417 -12.90800884 -14.70212761 4.2394473
[6,] 2.9674880 -7.7033987 12.98480570 7.03365627 15.11237051 7.0789302
[7,] 68.0959478 1.1337744 -7.41891741 -13.99137700 5.46751313 -1.7216783
[8,] 1.1337744 23.5197706 -4.41034622 -0.63549225 7.86550000 -1.5017933
[9,] -7.4189174 -4.4103462 78.80418797 5.61196300 -10.58304120 5.4941645
[10,] -13.9913770 -0.6354923 5.61196300 109.92466149 -0.08578358 -2.1395088
[11,] 5.4675131 7.8655000 -10.58304120 -0.08578358 38.85622943 4.0269314
[12,] -1.7216783 -1.5017933 5.49416453 -2.13950876 4.02693143 27.2727720
[13,] 4.8788844 -5.3100586 -7.92258808 -7.44688636 11.54383894 16.2031685
[14,] 7.9241919 -0.8312627 0.90705437 1.81668403 2.92937372 4.9669638
[15,] -2.7985388 1.6536311 0.18756162 -3.30163898 -3.52207773 1.5751812
[16,] -10.6869229 -0.4809266 0.30960002 5.17910698 2.63716466 -4.0714366
[17,] -4.4134743 0.8008605 -3.93074079 -2.61622662 -0.44402282 -2.1093310
[18,] -2.0016753 -1.2657116 -0.02083836 0.72325141 0.73985473 0.7330361
[19,] -0.8085887 -3.5899695 -0.63614908 1.98088577 -0.42668299 1.5841069
[20,] -3.7409792 1.6259225 4.23105301 -1.39835247 0.59041901 -0.9372444
[,13] [,14] [,15] [,16] [,17] [,18]
[1,] 3.0963375 -1.346655346 0.5642081 2.8090635 0.3734430 -0.53591777
[2,] 5.6211372 -4.790190364 -0.1695940 5.2218430 4.3391791 -0.39104167
[3,] -3.1857838 1.233757151 2.8357109 0.1963142 -4.5894654 -0.50295104
[4,] 4.4647303 -0.009624001 0.6998412 -3.0586183 -0.6663134 0.56028756
[5,] -2.3851926 -7.102596437 2.9406989 -4.7706557 5.4091743 -0.82316128
[6,] 10.6857388 -8.219624050 -1.8211008 1.1017005 7.8288676 7.43973018
[7,] 4.8788844 7.924191853 -2.7985388 -10.6869229 -4.4134743 -2.00167530
[8,] -5.3100586 -0.831262683 1.6536311 -0.4809266 0.8008605 -1.26571157
[9,] -7.9225881 0.907054373 0.1875616 0.3096000 -3.9307408 -0.02083836
[10,] -7.4468864 1.816684027 -3.3016390 5.1791070 -2.6162266 0.72325141
[11,] 11.5438389 2.929373720 -3.5220777 2.6371647 -0.4440228 0.73985473
[12,] 16.2031685 4.966963824 1.5751812 -4.0714366 -2.1093310 0.73303609
[13,] 38.3856150 3.196670895 -0.5530011 -4.8802072 0.3174936 -0.51066668
[14,] 3.1966709 16.053774694 -4.1861642 -3.2847040 -8.0739337 -0.31791787
[15,] -0.5530011 -4.186164177 7.5496739 -1.6240941 1.7099876 -1.04294418
[16,] -4.8802072 -3.284704050 -1.6240941 19.8975881 6.8507783 2.08094891
[17,] 0.3174936 -8.073933693 1.7099876 6.8507783 16.4011289 -0.10133546
[18,] -0.5106667 -0.317917872 -1.0429442 2.0809489 -0.1013355 5.04585900
[19,] 0.9914365 2.007574781 -0.9901634 0.8025488 -2.1167750 2.31966980
[20,] -2.4760553 -3.523721873 0.7839629 5.6617202 9.7950246 1.52989672
[,19] [,20]
[1,] -1.2879393 -1.6141693
[2,] 1.1781039 0.1232961
[3,] 0.3916049 -5.0378214
[4,] -1.0589170 -2.2533288
[5,] -3.2904659 0.7951449
[6,] -0.7993257 7.3625927
[7,] -0.8085887 -3.7409792
[8,] -3.5899695 1.6259225
[9,] -0.6361491 4.2310530
[10,] 1.9808858 -1.3983525
[11,] -0.4266830 0.5904190
[12,] 1.5841069 -0.9372444
[13,] 0.9914365 -2.4760553
[14,] 2.0075748 -3.5237219
[15,] -0.9901634 0.7839629
[16,] 0.8025488 5.6617202
[17,] -2.1167750 9.7950246
[18,] 2.3196698 1.5298967
[19,] 4.9065890 -1.8195281
[20,] -1.8195281 9.7533497
rWishart documentation built on Nov. 20, 2019, 1:07 a.m.
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Description Usage Arguments Details Value References Examples
View source: R/rFractionalWishart.R
Description
Generate n random matrices, distributed according to the Wishart distribution with parameters Sigma and df, W_p(Sigma, df).
Usage
1 2 | rFractionalWishart(n, df, Sigma, covariance = FALSE,
simplify = "array")
|
Arguments
n |
integer: the number of replications. |
df |
numeric parameter, “degrees of freedom”. |
Sigma |
positive definite (p * p) “scale” matrix, the matrix parameter of the distribution. |
covariance |
logical on whether a covariance matrix should be generated |
simplify |
logical or character string; should the result be
simplified to a vector, matrix or higher dimensional array if
possible? For |
Details
If X_1, ..., X_m is a sample of m independent multivariate Gaussians with mean vector 0, and covariance matrix Sigma, the distribution of M = X'X is W_p(Sigma, m).
Value
A numeric array of dimension p * p * n, where each array is a positive semidefinite matrix, a realization of the Wishart distribution W_p(Sigma, df)
References
Adhikari, S. (2008). Wishart random matrices in probabilistic structural mechanics. Journal of engineering mechanics, 134(12), doi: 10.1061/(ASCE)0733-9399(2008)134:12(1029).
Examples
1 | rFractionalWishart(2, 22.5, diag(1, 20))
|
Example output
Attaching package: ‘rWishart’
The following object is masked from ‘package:stats’:
rWishart
, , 1
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 227.3400424 -28.92777257 -15.7091314 -19.111657 -1.9955855 11.711521
[2,] -28.9277726 155.46358797 -4.0421071 2.469213 1.7259372 8.675951
[3,] -15.7091314 -4.04210709 79.3414855 -0.574172 2.0931759 -3.348261
[4,] -19.1116566 2.46921324 -0.5741720 140.805629 -4.4858976 1.028657
[5,] -1.9955855 1.72593721 2.0931759 -4.485898 34.2079060 13.145621
[6,] 11.7115212 8.67595088 -3.3482609 1.028657 13.1456213 116.410392
[7,] -3.5855488 10.63878242 1.8020482 -8.343388 3.0907914 -4.627708
[8,] -5.2344835 9.86463813 1.9340584 -12.647050 -5.8572626 -9.867235
[9,] 7.2372063 -5.60585506 6.3486273 -2.641505 -4.9028045 -7.919296
[10,] -0.5218905 -0.59814195 14.4985201 -2.514111 5.6400200 -6.812899
[11,] 5.2447578 2.65628069 6.2800058 -15.612341 -4.6773754 -1.244814
[12,] -10.6679992 -0.35755522 9.6690284 -6.936134 1.8683728 -3.269700
[13,] 12.7987964 -13.08614315 1.3606202 9.678380 0.5190985 2.807234
[14,] 0.5105867 -2.62735811 -0.1968232 2.332331 -5.4638033 3.458920
[15,] 1.0598604 -8.74550233 -7.6071450 -1.306100 -1.2454749 3.752046
[16,] -7.6779368 1.88138198 4.3178483 2.106791 3.2956554 -6.039764
[17,] 0.5569478 -5.36365162 5.1772603 -8.278664 5.1054856 -1.716953
[18,] 1.9432297 -4.75788791 -4.4889020 2.443566 -5.5541954 -2.446559
[19,] -3.3128269 -0.46228373 3.6928392 -1.895497 1.7222935 1.473387
[20,] 0.4281565 0.01054848 0.0507884 -0.178266 0.1904332 1.127288
[,7] [,8] [,9] [,10] [,11]
[1,] -3.58554876 -5.23448354 7.23720633 -0.5218905 5.2447578
[2,] 10.63878242 9.86463813 -5.60585506 -0.5981419 2.6562807
[3,] 1.80204817 1.93405836 6.34862733 14.4985201 6.2800058
[4,] -8.34338803 -12.64704985 -2.64150530 -2.5141109 -15.6123407
[5,] 3.09079136 -5.85726261 -4.90280446 5.6400200 -4.6773754
[6,] -4.62770774 -9.86723515 -7.91929646 -6.8128993 -1.2448139
[7,] 36.05756147 8.83821306 -0.02036627 -1.4088130 -4.7315187
[8,] 8.83821306 58.43231693 1.51155169 1.1402774 5.7875724
[9,] -0.02036627 1.51155169 38.96783632 5.7648532 -1.0135871
[10,] -1.40881300 1.14027740 5.76485319 50.1187563 -5.0144964
[11,] -4.73151868 5.78757243 -1.01358709 -5.0144964 22.3344204
[12,] 2.18936797 4.23787668 -2.72174624 3.9923289 1.4163277
[13,] -14.09025265 -4.26967951 4.74462255 -8.4911253 6.9402579
[14,] -1.75217473 7.20219264 1.07774411 0.0119133 -0.4262292
[15,] -2.66751866 1.99477957 2.31450344 -5.0106841 0.6887500
[16,] 0.75781016 1.74366049 6.85410571 5.1122609 -10.1456736
[17,] 1.03825209 0.32623622 3.98541439 1.0256799 1.3034741
[18,] -6.23978669 0.07492463 1.39258946 -2.2965242 -0.1894124
[19,] -1.63941701 2.00448104 -5.95744293 0.5018147 1.7391015
[20,] 1.48034616 -0.38131004 0.45992364 0.1151233 -0.5743463
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