R version 2.11.1 (2010-05-31)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> 
> library("mvtnorm")
> set.seed(29)
> 
> ########################################################################
> ## 3 dim example
> corr <- cov2cor(crossprod(matrix(runif(9,-1,1),3,3))+diag(3))
> df <- rpois(1,3)+1
> 
> ## central t distribution (-Inf,upper)
> ctrl <- GenzBretz(maxpts = 2500000, abseps = 0.000001, releps = 0)
> upper <- rexp(3,1)
> pmvt(upper=upper, corr=corr, df = df, algorithm = ctrl)
[1] 0.3920567
attr(,"error")
[1] 6.089669e-07
attr(,"msg")
[1] "Normal Completion"
> pmvt(upper=upper, corr=corr, df = df, algorithm = TVPACK())
[1] 0.3920566
attr(,"error")
[1] 1e-06
attr(,"msg")
[1] "Normal Completion"
> 
> ## central t distribution (lower,Inf)
> lower = -rexp(3,1)
> pmvt(lower=lower, upper=rep(Inf,3), corr=corr, df = df, algorithm = ctrl)
[1] 0.4634843
attr(,"error")
[1] 6.46065e-07
attr(,"msg")
[1] "Normal Completion"
> pmvt(lower=lower, upper=rep(Inf,3), corr=corr, df = df, algorithm = TVPACK())
[1] 0.4634844
attr(,"error")
[1] 1e-06
attr(,"msg")
[1] "Normal Completion"
> 
> ## non-central t (not possible for TVPACK)
> delt <- rexp(3,1/10)
> upper <- delt+runif(3)
> ctrl <- GenzBretz(maxpts = 2500000, abseps = 0.000001, releps = 0)
> pmvt(upper=upper, corr=corr, df = df, algorithm = ctrl, delta = delt)
[1] 0.3235424
attr(,"error")
[1] 9.86407e-07
attr(,"msg")
[1] "Normal Completion"
> try(pmvt(upper=upper, corr=corr, df = df, algorithm = TVPACK(), delta = delt))
Error in probval.TVPACK(algorithm, n, df, lower, upper, infin, corr, corrF,  : 
  TVPACK only possible for the central t-distribution.
> 
> ## central mvn (-Inf, upper)
> upper <- rexp(3,1)
> pmvnorm(upper=upper, corr=corr, algorithm = ctrl)
[1] 0.7733949
attr(,"error")
[1] 6.999168e-07
attr(,"msg")
[1] "Normal Completion"
> pmvnorm(upper=upper, corr=corr, algorithm = TVPACK())
[1] 0.7733949
attr(,"error")
[1] 1e-06
attr(,"msg")
[1] "Normal Completion"
> 
> ## central mvn (lower, Inf)
> lower <- rexp(3,5)
> pmvnorm(lower=lower,upper=rep(Inf, 3), corr=corr, algorithm = ctrl)
[1] 0.0827153
attr(,"error")
[1] 4.969585e-07
attr(,"msg")
[1] "Normal Completion"
> pmvnorm(lower=lower,upper=rep(Inf, 3), corr=corr, algorithm = TVPACK())
[1] 0.08271559
attr(,"error")
[1] 1e-06
attr(,"msg")
[1] "Normal Completion"
> 
> ## non-central mvn
> delt <- rexp(3,1/10)
> upper <- delt+rexp(3,1)
> pmvnorm(upper=upper, corr=corr, algorithm = ctrl, mean = delt)
[1] 0.5824373
attr(,"error")
[1] 9.416391e-07
attr(,"msg")
[1] "Normal Completion"
> try(pmvnorm(upper=upper, corr=corr, algorithm = TVPACK(), mean = delt))
[1] 0.582434
attr(,"error")
[1] 1e-06
attr(,"msg")
[1] "Normal Completion"
> 
> 
> ########################################################################
> ## 2 dim example
> corr <- cov2cor(crossprod(matrix(runif(4,-1,1),2,2))+diag(2))
> upper <- rexp(2,1)
> df <- rpois(1, runif(1, 0, 20))
> 
> ## central t (-Inf, upper)
> pmvt(upper=upper, corr=corr, df = df, algorithm = ctrl)
[1] 0.8656102
attr(,"error")
[1] 1e-15
attr(,"msg")
[1] "Normal Completion"
> pmvt(upper=upper, corr=corr, df = df, algorithm = TVPACK())
[1] 0.8656102
attr(,"error")
[1] NA
attr(,"msg")
[1] "Normal Completion"
> 
> ## central t (lower, Inf)
> pmvt(lower=-upper, upper=rep(Inf, 2), corr=corr, df = df, algorithm = ctrl)
[1] 0.8656102
attr(,"error")
[1] 1e-15
attr(,"msg")
[1] "Normal Completion"
> pmvt(lower=-upper, upper=rep(Inf, 2), corr=corr, df = df, algorithm = TVPACK())
[1] 0.8656102
attr(,"error")
[1] NA
attr(,"msg")
[1] "Normal Completion"
> 
> ## non-central t
> delt <- rexp(2,1/5)
> upper <- delt+rexp(2,1)
> pmvnorm(upper=upper, corr=corr, algorithm = ctrl, mean = delt)
[1] 0.6431222
attr(,"error")
[1] 1e-15
attr(,"msg")
[1] "Normal Completion"
> pmvnorm(upper=upper, corr=corr, algorithm = TVPACK(), mean = delt)
[1] 0.6431222
attr(,"error")
[1] NA
attr(,"msg")
[1] "Normal Completion"
> 
> ########################################################################
> ## comparison with Miwa
> ## 2d
> corr <- cov2cor(crossprod(matrix(runif(4,-1,1),2,2))+diag(2))
> upper <- rexp(2, 1)
> 
> pmvnorm(upper=upper, corr=corr, algorithm = Miwa(steps=128))
[1] 0.7331788
attr(,"error")
[1] NA
attr(,"msg")
[1] "Normal Completion"
> pmvnorm(upper=upper, corr=corr, algorithm = TVPACK())
[1] 0.7331788
attr(,"error")
[1] NA
attr(,"msg")
[1] "Normal Completion"
> 
> ## 3d
> corr <- cov2cor(crossprod(matrix(runif(9,-1,1),3,3))+diag(3))
> upper <- rexp(3, 1)
> 
> ctrl <- Miwa(steps=128)
> pmvnorm(upper=upper, corr=corr, algorithm = ctrl)
[1] 0.8981829
attr(,"error")
[1] NA
attr(,"msg")
[1] "Normal Completion"
> pmvnorm(upper=upper, corr=corr, algorithm = TVPACK())
[1] 0.8981829
attr(,"error")
[1] 1e-06
attr(,"msg")
[1] "Normal Completion"
> 
> proc.time()
   user  system elapsed 
  7.824   0.060   7.850