Description Usage Format Details See also Source Examples
A list of sample counts of a Bernoulli variable with (unnormalized) success and failure probabilities given by Prob{ind=r} and Prob{ind=r+1}.
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A list of two-element integer vectors.
The values of the parameters beta, n, r are specified in the names of the list
elements, which are of the form beta=_,n=_,r=_
with _ replaced by
values. The list contains all combinations of beta=1,2,4
, n=4,5,...,10
,
and r
between floor((n+1)/2)
and n-2
. The remaining values
can be found through the relation Prob{ind=r}=Prob{ind=n-r}.
constr_eigval
Package: symconivol
The samples have been found with the HMC sampler Stan with a model that simulates the eigenvalues of a Gaussian orthogonal/unitary/symplectic ensemble with index constrained to {r,r+1}. The code below shows how this data can be generated.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ## Not run:
library(rstan)
ind_prob <- list()
nmin <- 4
nmax <- 10
filename <- "tmp.stan"
N <- 1e6
warmup <- 1e3
for (n in nmin:nmax) {
for (beta in c(1,2,4)) {
for (r in floor((n+1)/2):(n-2)) {
index <- str_c("beta=",beta,",n=",n,",r=",r)
M <- constr_eigval(beta, n, r, r+1, filename=filename)
stan_samp <- stan( file = filename, data = M$data,
chains = 1, warmup = warmup,
iter = N+warmup, cores = 2, refresh = 1e4 )
ef <- rstan::extract(stan_samp)$ef
indprob[[index]] <- c(length(which(ef<0)),length(which(ef>0)))
}
}
}
file.remove(filename)
## End(Not run)
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