This is simulated with the fast, thread-safe threefry simulator and can use multiple cores to generate the random deviates.
rxRmvn(
n,
mu = NULL,
sigma,
lower = -Inf,
upper = Inf,
ncores = 1,
isChol = FALSE,
keepNames = TRUE,
a = 0.4,
tol = 2.05,
nlTol = 1e-10,
nlMaxiter = 100L
)| n | Number of random row vectors to be simulated OR the matrix to use for simulation (faster). |
|---|---|
| mu | mean vector |
| sigma | Covariance matrix for multivariate normal or a list
of covariance matrices. If a list of covariance matrix, each
matrix will simulate |
| lower | is a vector of the lower bound for the truncated multivariate norm |
| upper | is a vector of the upper bound for the truncated multivariate norm |
| ncores | Number of cores used in the simulation |
| isChol | A boolean indicating if |
| keepNames | Keep the names from either the mean or covariance matrix. |
| a | threshold for switching between methods; They can be tuned for maximum speed; There are three cases that are considered: case 1: a < l < u case 2: l < u < -a case 3: otherwise where l=lower and u = upper |
| tol | When case 3 is used from the above possibilities, the tol value controls the acceptance rejection and inverse-transformation; When abs(u-l)>tol, uses accept-reject from randn |
| nlTol | Tolerance for newton line-search |
| nlMaxiter | Maximum iterations for newton line-search |
If n==integer (default) the output is an (n x d) matrix
where the i-th row is the i-th simulated vector.
If is.matrix(n) then the random vector are store in n,
which is provided by the user, and the function returns
NULL invisibly.
John K. Salmon, Mark A. Moraes, Ron O. Dror, and David E. Shaw (2011). Parallel Random Numbers: As Easy as 1, 2, 3. D. E. Shaw Research, New York, NY 10036, USA.
The thread safe multivariate normal was inspired from the mvnfast package by Matteo Fasiolo https://CRAN.R-project.org/package=mvnfast
The concept of the truncated multivariate normal was taken from Zdravko Botev Botev (2017) doi: 10.1111/rssb.12162 and Botev and L'Ecuyer (2015) doi: 10.1109/WSC.2015.7408180 and converted to thread safe simulation;
Matthew Fidler, Zdravko Botev and some from Matteo Fasiolo
## From mvnfast
## Unlike mvnfast, uses threefry simulation
d <- 5
mu <- 1:d
# Creating covariance matrix
tmp <- matrix(rnorm(d^2), d, d)
mcov <- tcrossprod(tmp, tmp)
set.seed(414)
rxRmvn(4, 1:d, mcov)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.6136552 1.25812013 5.303832 4.525316 5.365598
#> [2,] 0.2516852 -0.92219464 1.078185 1.306427 2.255198
#> [3,] 3.1149151 0.09902607 -1.774739 4.105226 6.016358
#> [4,] 0.2015307 2.66830901 2.041887 2.379933 3.566044
set.seed(414)
rxRmvn(4, 1:d, mcov)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.6136552 1.25812013 5.303832 4.525316 5.365598
#> [2,] 0.2516852 -0.92219464 1.078185 1.306427 2.255198
#> [3,] 3.1149151 0.09902607 -1.774739 4.105226 6.016358
#> [4,] 0.2015307 2.66830901 2.041887 2.379933 3.566044
set.seed(414)
rxRmvn(4, 1:d, mcov, ncores = 2) # r.v. generated on the second core are different
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.6136552 4.5619767 3.7840009 3.820684 6.181438
#> [2,] 0.3652661 2.3724185 5.0871725 4.070487 5.749454
#> [3,] 0.2516852 0.5206738 -0.4249075 1.026492 1.182587
#> [4,] 1.3164949 2.0964747 1.4628823 3.371607 5.266312
###### Here we create the matrix that will hold the simulated
# random variables upfront.
A <- matrix(NA, 4, d)
class(A) <- "numeric" # This is important. We need the elements of A to be of class "numeric".
set.seed(414)
rxRmvn(A, 1:d, mcov, ncores = 2) # This returns NULL ...
A # ... but the result is here
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.6136552 4.5619767 3.7840009 3.820684 6.181438
#> [2,] 0.3652661 2.3724185 5.0871725 4.070487 5.749454
#> [3,] 0.2516852 0.5206738 -0.4249075 1.026492 1.182587
#> [4,] 1.3164949 2.0964747 1.4628823 3.371607 5.266312
## You can also simulate from a truncated normal:
rxRmvn(10, 1:d, mcov, lower = 1:d - 1, upper = 1:d + 1)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1.40194307 2.188182 2.829579 4.998496 4.804913
#> [2,] 0.02971623 2.555220 2.694816 4.462161 5.022664
#> [3,] 0.73953497 2.082153 2.918758 4.984464 5.057942
#> [4,] 0.18577166 2.453988 2.695229 4.462135 4.990005
#> [5,] 1.00918396 2.113297 3.013401 3.182227 5.226960
#> [6,] 0.02691318 1.336583 3.166658 4.139035 5.284742
#> [7,] 0.75784792 1.776195 3.369402 4.195169 4.996142
#> [8,] 1.12122571 1.662802 2.679519 4.951974 5.025238
#> [9,] 0.65771584 1.992188 2.946981 4.750599 5.124848
#> [10,] 0.08909610 1.817789 2.978310 3.115197 5.301765
# You can also simulate from different matrices (if they match
# dimensions) by using a list of matrices.
matL <- lapply(1:4, function(...) {
tmp <- matrix(rnorm(d^2), d, d)
tcrossprod(tmp, tmp)
})
rxRmvn(4, setNames(1:d, paste0("a", 1:d)), matL)
#> a1 a2 a3 a4 a5
#> [1,] 2.1027689 -3.1277802 -1.7058664 3.877449 6.160238
#> [2,] -0.1528749 0.3372425 1.4079033 3.204818 6.771887
#> [3,] -1.6178920 2.4185331 4.2854089 4.204923 6.115151
#> [4,] 5.2850177 6.0162640 1.1522397 6.009218 8.423744
#> [5,] -0.8389005 1.8108360 3.9390837 2.635257 3.078044
#> [6,] 2.4044119 0.2584573 2.4396218 4.687467 7.747550
#> [7,] 7.2635180 5.5533803 -0.2744354 9.627871 4.788654
#> [8,] -0.3358839 -1.7501935 4.1309667 2.961912 6.318101
#> [9,] 3.4028706 1.1584222 4.5627803 3.408984 3.627014
#> [10,] 3.4927361 -1.5055971 1.0890217 2.867575 4.036955
#> [11,] 2.2089477 -1.0108105 -0.6234824 1.745858 4.178149
#> [12,] 1.9045759 -3.5353019 3.6738287 3.085417 2.755276
#> [13,] -1.0910176 1.6896066 -0.1344867 5.810620 3.303876
#> [14,] 0.7032309 2.5654064 2.7642640 3.706315 5.057585
#> [15,] -3.4067706 2.3051387 4.4260234 6.692458 8.170364
#> [16,] -3.7727314 4.2737997 -0.8379328 6.990844 1.255809