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The rust package implements the multivariate generalized ratio-of-uniforms method of simulating random variates from a \(d\)-dimensional continuous distribution. The user specifies (the log of) a positive target function \(f(x)\) proportional to the density function of the distribution. For an introduction to rust see the vignette Introducing rust.
This vignette describes a new feature of rust: the
option for the user to provide a C++ function to evaluate the target
log-density, rather than an R function. The Rcpp Eddelbuettel (2013) and
RcppArmadillo (Eddelbuettel and
Sanderson 2014) packages are used to speed up simulation from the
target density. The improvement results from faster function evaluations
and (in particular) from performing using C++ the looping in the
ratio-of-uniforms algorithm. The new function ru_rcpp
requires the target log-density to be specified using (externals
pointers to) C++ functions, whereas the existing ru
requires input R functions. Otherwise, the functionality of these two
functions is the same. There are also Rcpp-based versions of functions
for setting Box-Cox transformation parameters:
find_lambda_rcpp and
find_lambda_one_d_rcpp
In this vignette we describe in general terms the general setup of the Rcpp-based functions and use examples to illustrate their use. For more information about these examples see the vignette Introducing rust
ru_rcppThe general way that rust enables users to provide their own C++ functions uses external pointers and is based on the Rcpp Gallery article Passing user-supplied C++ functions by Dirk Eddelbuettel. For a detailed case study of the general approach see the RcppDE package (Eddelbuettel 2016) vignette at the RcppDE page on CRAN.
The user writes a C++ function to calculate \(\log f(x)\). The current implementation in
rust requires this function to have a particular
structure: it must take a constant reference to an
Rcpp::NumericVector, say x, a constant
reference to an Rcpp::List, say pars, and
return a double precision scalar. x is the
argument \(x\) of \(f(x)\). pars is a list
containing the values of parameters whose values are not specified
inside the function. This allows the user to change the values of any
parameters in the target density without editing the function. If there
are no such parameters then the user must still include the argument
pars in their function, even though the list provided to
the function when it is called will be empty.
A simple way for the user to provide their C++ functions to create
them in a file, say user_fns.cpp. Example content is
provided below. The full file is available on the rust
Github page. The functions in this file are compiled and made
available to R, either using the Rcpp::sourceCpp function
(e.g. Rcpp::sourceCpp("user_fns.cpp")) or using RStudio’s
Source button on the editor toolbar. The example content below also
includes the function create_xptr, which creates an
external pointer to a C++ function. See Passing
user-supplied C++ functions. It is this external pointer that is
passed to ru_rcpp to perform ratio-of-uniforms sampling. If
the user has written a C++ function, say new_name, then
they need to add to create_xptr two lines of code:
else if (fstr == "new_name")
return(Rcpp::XPtr<funcPtr>(new funcPtr(&new_name))) ;to create an external pointer for new_name using
create_xptr. The following excerpt from the example
user_fns.cpp file contains code for a standard normal
density. Note that for this particular example we don’t need
RcppArmadillo: we could replace
#include <RcppArmadillo.h> with
#include <Rcpp.h> and delete
using namespace arma;. However, RcppArmadillo is used in
the the multivariate normal example below and will be
useful in many examples.
// [[Rcpp::depends(RcppArmadillo)]]
#include <RcppArmadillo.h>
using namespace arma;
using namespace Rcpp;
// [[Rcpp::interfaces(r, cpp)]]
// User-supplied C++ functions for logf.
// Note that currently the only interface available in rust is
// double fun(const Rcpp::NumericVector& x, const Rcpp::List& pars).
// However, as shown in the function logdmvnorm below RcppArmadillo
// functions can be used inside the function.
// Each function must be prefaced by the line: // [[Rcpp::export]]
// One-dimensional standard normal.
// [[Rcpp::export]]
double logdN01(const Rcpp::NumericVector& x, const Rcpp::List& pars) {
return (-pow(x[0], 2.0) / 2.0) ;
}
// A function to create external pointers for any of the functions above.
// See http://gallery.rcpp.org/articles/passing-cpp-function-pointers/
// If you write a new function above called new_name then add the following
//
// else if (fstr == "new_name")
// return(Rcpp::XPtr<funcPtr>(new funcPtr(&new_name))) ;
// [[Rcpp::export]]
SEXP create_xptr(std::string fstr) {
typedef double (*funcPtr)(const Rcpp::NumericVector& x,
const Rcpp::List& pars) ;
if (fstr == "logdN01")
return(Rcpp::XPtr<funcPtr>(new funcPtr(&logdN01))) ;
else
return(Rcpp::XPtr<funcPtr>(R_NilValue)) ;
}
// We could create the external pointers when this file is sourced using
// the embedded R code below and/or (re)create them using create_xptr() in
// an R session or R package..
/*** R
ptr_N01 <- create_xptr("logdN01")
*/ru_rcppAll the examples in the documentation for ru are
replicated in the documentation for ru_rcpp. Here we
consider a subset of the examples from the Introducing rust vignette, to illustrate
how to provide user-supplied C++ functions to ru_rcpp and
to compare the performances of ru and ru_rcpp.
We use the microbenchmark package (Mersmann 2015) to make the comparison.
library(rust)
library(Rcpp)
# Is microbenchmark available?
got_microbenchmark <- requireNamespace("microbenchmark", quietly = TRUE)
if (got_microbenchmark) {
library(microbenchmark)
}
# Set the size of the simulated sample
n <- 1000It is assumed that the user has already compiled their C++ functions
and made them available to their R session, either using the
Rcpp::sourceCpp function
(e.g. Rcpp::sourceCpp("user_fns.cpp")) or using RStudio’s
Source button on the editor toolbar.
We start with a simple example: the (1-dimensional) standard normal
density, based on the C++ function logdN01 in the example
user_fns.cpp file above.
# Normal density ===================
# Create a pointer to the logdN01 C++ function
# (not necessary if this was created when the file of C++ functions was sourced)
ptr_N01 <- create_xptr("logdN01")
# Use ru and ru_rcpp starting from the same random number seed and check
# that the simulated values are the same.
set.seed(47)
x_old <- ru(logf = function(x) -x ^ 2 / 2, d = 1, n = n, init = 0.1)
head(x_old$sim_vals)
#> [,1]
#> [1,] 0.7764728
#> [2,] 0.5310434
#> [3,] -0.1046049
#> [4,] 1.2111509
#> [5,] 1.1391379
#> [6,] 0.5180914
set.seed(47)
x_new <- ru_rcpp(logf = ptr_N01, d = 1, n = n, init = 0.1)
head(x_new$sim_vals)
#> [,1]
#> [1,] 0.7764728
#> [2,] 0.5310434
#> [3,] -0.1046049
#> [4,] 1.2111509
#> [5,] 1.1391379
#> [6,] 0.5180914
# Compare performances of ru and ru_rcpp
if (got_microbenchmark) {
res <- microbenchmark(
old = ru(logf = function(x) -x ^ 2 / 2, d = 1, n = n, init = 0.1),
new = ru_rcpp(logf = ptr_N01, d = 1, n = n, init = 0.1)
)
print(res, signif = 4)
}
#> Unit: milliseconds
#> expr min lq mean median uq max neval
#> old 14.330 15.970 17.410 16.920 18.890 22.490 100
#> new 2.058 2.183 2.436 2.272 2.458 5.092 100As we would hope, ru_rcpp is faster than
ru. If we start from the same random number seed we get the
same simulated values from ru and ru_rcpp.
To execute this example we add the following function to
user_fns.cpp
// d-dimensional normal with zero-mean and covariance matrix sigma.
// [[Rcpp::export]]
double logdmvnorm(const Rcpp::NumericVector& x, const Rcpp::List& pars) {
arma::mat sigma = as<arma::mat>(pars["sigma"]) ;
arma::vec y = Rcpp::as<arma::vec>(x) ;
double qform = arma::as_scalar(y.t() * arma::inv(sigma) * y) ;
return -qform / 2.0 ;
}and add
else if (fstr == "logdmvnorm")
return(Rcpp::XPtr<funcPtr>(new funcPtr(&logdmvnorm))) ;to the function create_xptr in
user_fns.cpp.
# Three-dimensional normal with positive association ----------------
rho <- 0.9
covmat <- matrix(rho, 3, 3) + diag(1 - rho, 3)
# R function
log_dmvnorm <- function(x, mean = rep(0, d), sigma = diag(d)) {
x <- matrix(x, ncol = length(x))
d <- ncol(x)
- 0.5 * (x - mean) %*% solve(sigma) %*% t(x - mean)
}
# Create a pointer to the logdmvnorm C++ function
ptr_mvn <- create_xptr("logdmvnorm")
if (got_microbenchmark) {
res <- microbenchmark(
old = ru(logf = log_dmvnorm, sigma = covmat, d = 3, n = n,
init = c(0, 0, 0)),
new = ru_rcpp(logf = ptr_mvn, sigma = covmat, d = 3, n = n,
init = c(0, 0, 0))
)
print(res, signif = 4)
}
#> Unit: milliseconds
#> expr min lq mean median uq max neval
#> old 177.900 185.200 197.800 189.600 194.200 560.70 100
#> new 8.451 8.902 9.741 9.242 9.873 13.74 100Again, the improvement in speed obtained using Rcpp is clear.
In this example we use a log transform (Box-Cox parameter \(\lambda = 0\)) so that the ratio-of-uniforms sampling is based on a normal distribution. The C++ function to calculate the log-density of a lognormal distribution is:
// Lognormal(mu, sigma).
// [[Rcpp::export]]
double logdlnorm(const Rcpp::NumericVector& x, const Rcpp::List& pars) {
double mu = pars["mu"] ;
double sigma = pars["sigma"] ;
if (x[0] > 0)
return -log(x[0]) - pow(log(x[0]) - mu, 2.0) / (2.0 * pow(sigma, 2.0)) ;
else
return R_NegInf ;
}ptr_lnorm <- create_xptr("logdlnorm")
if (got_microbenchmark) {
res <- microbenchmark(
old = ru(logf = dlnorm, log = TRUE, d = 1, n = n, lower = 0, init = 0.1,
trans = "BC", lambda = 0),
new = ru_rcpp(logf = ptr_lnorm, mu = 0, sigma = 1, d = 1, n = n,
lower = 0, init = 0.1, trans = "BC", lambda = 0)
)
print(res, signif = 4)
}
#> Unit: milliseconds
#> expr min lq mean median uq max neval
#> old 33.450 37.03 39.180 38.900 40.710 58.21 100
#> new 4.828 5.04 6.229 5.282 5.625 69.34 100The C++ function to calculate the log-posterior density is:
// Generalized Pareto posterior based on an MDI prior truncated to
// shape parameter xi >= -1.
// [[Rcpp::export]]
double loggp(const Rcpp::NumericVector& x, const Rcpp::List& ss) {
Rcpp::NumericVector gpd_data = ss["gpd_data"] ;
int m = ss["m"] ;
double xm = ss["xm"] ;
double sum_gp = ss["sum_gp"] ;
if (x[0] <= 0 || x[1] <= -x[0] / xm)
return R_NegInf ;
double loglik ;
Rcpp::NumericVector sdat = gpd_data / x[0] ;
Rcpp::NumericVector zz = 1 + x[1] * sdat ;
if (std::abs(x[1]) > 1e-6) {
loglik = -m * log(x[0]) - (1.0 + 1.0 / x[1]) * sum(log(zz)) ;
} else {
double t1, t2, sdatj ;
double total = 0;
for(int j = 0; j < m; ++j) {
sdatj = sdat[j] ;
for(int i = 1; i < 5; ++i) {
t1 = pow(sdatj, i) ;
t2 = (i * sdatj - i - 1) ;
total += pow(-1.0, i) * t1 * t2 * pow(x[1], i) / i / (i + 1) ;
}
}
loglik = -m * log(x[0]) - sum_gp / x[0] - total ;
}
// MDI prior.
if (x[1] < -1)
return R_NegInf ;
double logprior = -log(x[0]) - x[1] - 1 ;
return (logprior + loglik) ;
}We simulate some data from a Generalized Pareto distribution, calculate summary statistics involved in the likelihood and calculate an initial value in the search for the posterior mode.
set.seed(46)
# Sample data from a GP(sigma, xi) distribution
gpd_data <- rgpd(m = 100, xi = -0.5, sigma = 1)
# Calculate summary statistics for use in the log-likelihood
ss <- gpd_sum_stats(gpd_data)
# Calculate an initial estimate
init <- c(mean(gpd_data), 0)Again we see that ru_rcpp is substantially faster than
ru.
# Arguments for ru_rcpp
ptr_gp <- create_xptr("loggp")
for_ru_rcpp <- c(list(logf = ptr_gp, init = init, d = 2, n = n,
lower = c(0, -Inf)), ss)
if (got_microbenchmark) {
res <- microbenchmark(
old = ru(logf = gpd_logpost, ss = ss, d = 2, n = n, init = init,
lower = c(0, -Inf)),
new = do.call(ru_rcpp, for_ru_rcpp)
)
print(res, signif = 4)
}
#> Unit: milliseconds
#> expr min lq mean median uq max neval
#> old 70.10 74.89 77.41 76.59 78.22 130.00 100
#> new 15.15 16.05 17.34 16.65 18.24 24.91 100find_lambda_one_d_rcpp and
find_lambda_rcppWe repeat two examples from the Introducing rust vignette.
find_lambda_one_d_rcppWe make use of the Rcpp
sugar function dgamma.
// Gamma(alpha, 1).
// [[Rcpp::export]]
double logdgamma(const Rcpp::NumericVector& x, const Rcpp::List& pars) {
double shp = pars["alpha"] ;
return Rcpp::dgamma(x, shp, 1.0, 1)[0] ;
}alpha <- 1
max_phi <- qgamma(0.999, shape = alpha)
ptr_gam <- create_xptr("logdgamma")
lambda <- find_lambda_one_d_rcpp(logf = ptr_gam, alpha = alpha,
max_phi = max_phi)
lambda
#> $lambda
#> [1] 0.2727968
#>
#> $gm
#> [1] 0.5689906
#>
#> $init_psi
#> [1] -0.2016904
#>
#> $sd_psi
#> [1] 0.7835109
#>
#> $user_args
#> list()find_lambda_rcppIn this example we supply an external pointer to a C++ function
phi_to_theta that ensures that both parameters of the model
are strictly positive, a requirement for the Box-Cox transformation to
be applicable. The function phi_to_theta must have the same
structure as the function used to calculate \(\log f\). See Providing
a C++ function to ru_rcpp for details. See the Introducing rust vignette for the form
of the transformation.
temp <- do.call(gpd_init, ss)
min_phi <- pmax(0, temp$init_phi - 2 * temp$se_phi)
max_phi <- pmax(0, temp$init_phi + 2 * temp$se_phi)
# Create external pointers
ptr_gp <- create_xptr("loggp")
ptr_phi_to_theta_gp <- create_phi_to_theta_xptr("gp")
# Note: log_j is set to zero by default inside find_lambda_rcpp()
lambda <- find_lambda_rcpp(logf = ptr_gp, ss = ss, d = 2, min_phi = min_phi,
max_phi = max_phi, user_args = list(xm = ss$xm),
phi_to_theta = ptr_phi_to_theta_gp)
lambda
#> $lambda
#> [1] 0.1624226 0.3678549
#>
#> $gm
#> [1] 1.10542493 0.03225836
#>
#> $init_psi
#> [1] 0.1054021 -0.2184344
#>
#> $sd_psi
#> Var1 Var2
#> 0.12670792 0.02477219
#>
#> $phi_to_theta
#> <pointer: 0x000002574a6fd920>
#>
#> $log_j
#> <pointer: 0x000002574a6fd880>
#>
#> $user_args
#> $user_args$xm
#> [1] 1.846219These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.