This is simulated with the fast, thread-safe threefry simulator and can use multiple cores to generate the random deviates.
Usage
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
)Arguments
- 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
nmatrices and combine them to a full matrix- 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
sigmais a cholesky decomposition of the covariance matrix.- 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
Value
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.
References
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;
Examples
## 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,] 5.8385385 2.483107 6.938897 6.910732 7.5964797
#> [2,] -0.9739857 3.041282 6.229306 -1.526767 3.8730490
#> [3,] 2.4207266 3.456173 3.313576 5.525857 7.6456551
#> [4,] 1.2860568 1.475712 3.326761 -2.651293 0.7908656
set.seed(414)
rxRmvn(4, 1:d, mcov)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 5.8385385 2.483107 6.938897 6.910732 7.5964797
#> [2,] -0.9739857 3.041282 6.229306 -1.526767 3.8730490
#> [3,] 2.4207266 3.456173 3.313576 5.525857 7.6456551
#> [4,] 1.2860568 1.475712 3.326761 -2.651293 0.7908656
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,] 5.8385385 1.8084689 4.297630 7.977365 7.564832
#> [2,] 5.5150470 0.3966498 8.007903 8.341058 6.026243
#> [3,] -0.9739857 2.4356366 4.731163 3.460645 5.831939
#> [4,] 0.4524881 3.0939983 2.584720 2.797358 5.528742
###### 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,] 5.8385385 1.8084689 4.297630 7.977365 7.564832
#> [2,] 5.5150470 0.3966498 8.007903 8.341058 6.026243
#> [3,] -0.9739857 2.4356366 4.731163 3.460645 5.831939
#> [4,] 0.4524881 3.0939983 2.584720 2.797358 5.528742
## 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,] 0.8049130 1.636456 3.048092 4.282005 4.797902
#> [2,] 1.0226637 1.667080 3.507530 4.459110 4.714118
#> [3,] 1.0579423 1.467899 3.121131 3.239619 4.934069
#> [4,] 0.6999089 2.048211 3.245750 3.275490 4.816539
#> [5,] 1.1674782 2.062341 2.755494 4.859300 5.170974
#> [6,] 1.1400382 1.626747 3.147992 4.157155 4.714692
#> [7,] 1.0986637 2.477932 2.562834 3.159794 5.327605
#> [8,] 0.9468902 1.995504 2.550678 4.921664 4.993267
#> [9,] 1.0225550 2.512505 2.996419 3.260261 4.891580
#> [10,] 0.7723391 2.080293 3.388499 4.736703 4.847944
# 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,] 3.8274046 2.1035743 0.5028009 4.5098402 5.189021
#> [2,] -0.9871330 3.8835057 6.0910523 5.1594862 4.132973
#> [3,] 3.4611290 6.9818905 2.4784421 5.1440327 8.310619
#> [4,] -2.6283293 -5.0190437 2.8076771 -0.5884730 1.060942
#> [5,] 0.3451536 0.5718889 3.7057607 4.3772555 3.829498
#> [6,] -1.1689889 1.9051966 4.0675628 2.0180889 5.571646
#> [7,] -1.7018538 -0.7786124 5.4574824 3.9037163 6.126236
#> [8,] -3.9766942 -0.8582446 5.4820712 -0.5706566 4.047896
#> [9,] 0.8420574 -0.4096991 3.9764994 4.7655857 4.167223
#> [10,] 1.3644751 5.2068446 1.3430378 3.6687705 8.175402
#> [11,] 1.5705584 3.1771677 1.9140454 6.9388794 5.757319
#> [12,] 0.6404211 11.0776336 5.3814729 10.6267879 6.349803
#> [13,] 0.2352059 0.8413157 -0.6291679 3.7003445 4.517157
#> [14,] 3.7622838 -1.0087429 0.1514493 0.7595107 4.988589
#> [15,] 0.4968318 3.1695539 6.2533925 3.9780854 5.781146
#> [16,] -3.7275917 2.3933661 1.3926983 6.3064293 2.905874