constr_eigval generates inputs for Stan (model string or external file)
for sampling eigenvalues from the Gaussian orthogonal/unitary/symplectic ensembles
with prescriped range for the index (number of positive eigenvalues).
constr_eigval(beta, n, ind_low, ind_upp, filename = NA, overwrite = FALSE)
| beta | Dyson index specifying the underlying (skew-) field:
|
|---|---|
| n | size of matrix. |
| ind_low | lower bound for index |
| ind_upp | upper bound for index |
| filename | filename for output |
| overwrite | logical; determines whether the output should overwrite an existing file |
The output of constr_eigval is a list containing the following elements:
model: a string that forms the description of the Stan model,
data: a data list containing the prepared data to be used
for defining a Stan model object (beta, number of positive, free,
negative eigenvalues).
If filename!=NA then the model string will also be written to the file with
the specified name.
constr_eigval_to_bcbsq,
prepare_em_cm,
estim_em_cm
Package: symconivol
# NOT RUN { library(tidyverse) library(rstan) filename <- "tmp.stan" M <- constr_eigval( beta=2, n=12, ind_low=8, ind_upp=9, filename=filename ) stan_samp <- stan( file = filename, data = M$data, chains = 1, warmup = 1e3, iter = 1e5, cores = 2, refresh = 1e4 ) file.remove(filename) tib_ep <- rstan::extract(stan_samp)$ep %>% as_tibble() %>% gather() %>% add_column(type="0") tib_ef <- rstan::extract(stan_samp)$ef %>% as_tibble() %>% gather() %>% add_column(type="1") tib_en <- rstan::extract(stan_samp)$en %>% as_tibble() %>% gather() %>% add_column(type="2") tib <- bind_rows(tib_ep, tib_ef, tib_en) ggplot() + geom_density(data=tib, aes(x=value, y=..count.., group=type, color=type, fill=type), alpha=0.5, bw=0.03) + theme_bw() + theme(axis.title.y=element_blank(), axis.text.y=element_blank(), axis.ticks.y=element_blank(), legend.position="none") # }