Description Usage Format Details See also Source Examples
A list of reconstructed values of index constrained curvature measures; the constraints being of the form r<=ind(x)<=r+s.
1 |
A list of lists of vectors containing the reconstructed weights; the element names of the outer list are of the form "beta=_,n=", while the the element names of the inner lists are of the form "r=_,s=", the "_" of course replaced by corresponding values.
The values have been found by the following steps:
sample eigenvalues from the index constrained Gaussian orthogonal/unitary/symplectic ensemble using the HMC sampler Stan,
convert the samples samples from the corresponding bivariate chi-bar-squared distribution,
reconstruct the weights of the bivariate chi-bar-squared distribution by running the EM algorithm for 100 steps.
constr_eigval
,
constr_eigval_to_bcbsq
,
estim_em_cm
Package: symconivol
The values have been computed using the HMC sampler stan and functions from the symconivol package. 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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | ## Not run:
library(tidyverse)
library(rstan)
warmup <- 1e3
N <- 1e5
filename_model <- "tmp.stan"
nmin <- 3
nmax <- 10
phi_ind <- list()
for (beta in c(1,2,4)) {
for (n in nmin:nmax) {
pat <- pat_bnd(beta,n)
index_out <- str_c("beta=",beta,",n=",n)
weights <- list()
for (r in floor((n+1)/2):(n-1)) {
for (s in 0:(n-1-r)) {
index_in <- str_c("r=",r,",s=",s)
np <- r
nf <- s
nn <- n-r-s
M <- constr_eigval(pos=(np>0), free=(nf>0), neg=(nn>0),
filename=filename_model, overwrite=TRUE)
stan_samp <- stan( file = filename_model, data = M$data,
chains = 1, warmup = warmup, iter = N+warmup,
cores = 2, refresh = 1e4 )
samp <- list()
if (np>0) samp$ep <- rstan::extract(stan_samp)$ep
if (nf>0) samp$ef <- rstan::extract(stan_samp)$ef
if (nn>0) samp$en <- rstan::extract(stan_samp)$en
m_samp <- constr_eigval_to_bcbsq(pos=(np>0), free=(nf>0), neg=(nn>0),
samp=samp)
em <- estim_em_cm(d=pat$d, low=pat$k_low(r), upp=pat$k_upp(r+s),
m_samp=m_samp, N=100)
weights[[index_in]] <- em[101,]
}
}
phi_ind[[index_out]] <- weights
}
}
file.remove(filename_model)
## End(Not run)
|
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.