更新：
我试图实施 Dirk 的建议。注释？我现在在 JSM 很忙，但我想在为画廊编织 Rmd 之前获得一些反馈。我从犰狳切换回正常的 Rcpp，因为它没有增加任何价值。带有 R:: 的标量版本非常好。如果将均值/标准差输入为标量，而不是作为所需输出长度的向量，我可能应该为绘制次数输入参数 n。
有许多 MCMC 应用程序需要从截断的正态分布中抽取样本。我建立在 TN 的现有实现之上，并向其中添加了并行计算。
问题：
- 有没有人看到进一步的潜在速度改进？
在基准测试的最后一种情况下，rtruncnorm 有时更快。Rcpp 的实现总是比现有的包更快，但它可以进一步改进吗？ - 我在一个我无法共享的复杂模型中运行它，我的 R 会话崩溃了。但是，我无法系统地重现它，因此它可能是代码的另一部分。如果有人正在使用 TN，请对其进行测试并告诉我。更新：我对更新的代码没有任何问题，但请告诉我。
我是如何把东西放在一起的：据我所知，最快的实现不是在 CRAN 上，但可以下载源代码OSU stat。在我的基准测试中， msm和truncorm中的竞争实现较慢。诀窍是有效地调整提议分布，其中指数很好地适用于截断法线的尾部。因此，我采用了 Chris 的代码，“Rcpp'ed”并添加了一些 openMP 香料。动态调度在这里是最佳的，因为采样可能需要更多或更少的时间，具体取决于边界。我发现一件令人讨厌的事情：当我想使用双打时，许多统计分布都是基于 NumericVector 类型的。我只是用我的方式编码。
这是 Rcpp 代码：
#include <Rcpp.h>
#include <omp.h>
// norm_rs(a, b)
// generates a sample from a N(0,1) RV restricted to be in the interval
// (a,b) via rejection sampling.
// ======================================================================
// [[Rcpp::export]]
double norm_rs(double a, double b)
{
double x;
x = Rf_rnorm(0.0, 1.0);
while( (x < a) || (x > b) ) x = norm_rand();
return x;
}
// half_norm_rs(a, b)
// generates a sample from a N(0,1) RV restricted to the interval
// (a,b) (with a > 0) using half normal rejection sampling.
// ======================================================================
// [[Rcpp::export]]
double half_norm_rs(double a, double b)
{
double x;
x = fabs(norm_rand());
while( (x<a) || (x>b) ) x = fabs(norm_rand());
return x;
}
// unif_rs(a, b)
// generates a sample from a N(0,1) RV restricted to the interval
// (a,b) using uniform rejection sampling.
// ======================================================================
// [[Rcpp::export]]
double unif_rs(double a, double b)
{
double xstar, logphixstar, x, logu;
// Find the argmax (b is always >= 0)
// This works because we want to sample from N(0,1)
if(a <= 0.0) xstar = 0.0;
else xstar = a;
logphixstar = R::dnorm(xstar, 0.0, 1.0, 1.0);
x = R::runif(a, b);
logu = log(R::runif(0.0, 1.0));
while( logu > (R::dnorm(x, 0.0, 1.0,1.0) - logphixstar))
{
x = R::runif(a, b);
logu = log(R::runif(0.0, 1.0));
}
return x;
}
// exp_rs(a, b)
// generates a sample from a N(0,1) RV restricted to the interval
// (a,b) using exponential rejection sampling.
// ======================================================================
// [[Rcpp::export]]
double exp_rs(double a, double b)
{
double z, u, rate;
// Rprintf("in exp_rs");
rate = 1/a;
//1/a
// Generate a proposal on (0, b-a)
z = R::rexp(rate);
while(z > (b-a)) z = R::rexp(rate);
u = R::runif(0.0, 1.0);
while( log(u) > (-0.5*z*z))
{
z = R::rexp(rate);
while(z > (b-a)) z = R::rexp(rate);
u = R::runif(0.0,1.0);
}
return(z+a);
}
// rnorm_trunc( mu, sigma, lower, upper)
//
// generates one random normal RVs with mean 'mu' and standard
// deviation 'sigma', truncated to the interval (lower,upper), where
// lower can be -Inf and upper can be Inf.
//======================================================================
// [[Rcpp::export]]
double rnorm_trunc (double mu, double sigma, double lower, double upper)
{
int change;
double a, b;
double logt1 = log(0.150), logt2 = log(2.18), t3 = 0.725;
double z, tmp, lograt;
change = 0;
a = (lower - mu)/sigma;
b = (upper - mu)/sigma;
// First scenario
if( (a == R_NegInf) || (b == R_PosInf))
{
if(a == R_NegInf)
{
change = 1;
a = -b;
b = R_PosInf;
}
// The two possibilities for this scenario
if(a <= 0.45) z = norm_rs(a, b);
else z = exp_rs(a, b);
if(change) z = -z;
}
// Second scenario
else if((a * b) <= 0.0)
{
// The two possibilities for this scenario
if((R::dnorm(a, 0.0, 1.0,1.0) <= logt1) || (R::dnorm(b, 0.0, 1.0, 1.0) <= logt1))
{
z = norm_rs(a, b);
}
else z = unif_rs(a,b);
}
// Third scenario
else
{
if(b < 0)
{
tmp = b; b = -a; a = -tmp; change = 1;
}
lograt = R::dnorm(a, 0.0, 1.0, 1.0) - R::dnorm(b, 0.0, 1.0, 1.0);
if(lograt <= logt2) z = unif_rs(a,b);
else if((lograt > logt1) && (a < t3)) z = half_norm_rs(a,b);
else z = exp_rs(a,b);
if(change) z = -z;
}
double output;
output = sigma*z + mu;
return (output);
}
// rtnm( mu, sigma, lower, upper, cores)
//
// generates one random normal RVs with mean 'mu' and standard
// deviation 'sigma', truncated to the interval (lower,upper), where
// lower can be -Inf and upper can be Inf.
// mu, sigma, lower, upper are vectors, and vectorized calls of this function
// speed up computation
// cores is an intege, representing the number of cores to be used in parallel
//======================================================================
// [[Rcpp::export]]
Rcpp::NumericVector rtnm(Rcpp::NumericVector mus, Rcpp::NumericVector sigmas, Rcpp::NumericVector lower, Rcpp::NumericVector upper, int cores){
omp_set_num_threads(cores);
int nobs = mus.size();
Rcpp::NumericVector out(nobs);
double logt1 = log(0.150), logt2 = log(2.18), t3 = 0.725;
double a,b, z, tmp, lograt;
int change;
#pragma omp parallel for schedule(dynamic)
for(int i=0;i<nobs;i++) {
a = (lower(i) - mus(i))/sigmas(i);
b = (upper(i) - mus(i))/sigmas(i);
change=0;
// First scenario
if( (a == R_NegInf) || (b == R_PosInf))
{
if(a == R_NegInf)
{
change = 1;
a = -b;
b = R_PosInf;
}
// The two possibilities for this scenario
if(a <= 0.45) z = norm_rs(a, b);
else z = exp_rs(a, b);
if(change) z = -z;
}
// Second scenario
else if((a * b) <= 0.0)
{
// The two possibilities for this scenario
if((R::dnorm(a, 0.0, 1.0,1.0) <= logt1) || (R::dnorm(b, 0.0, 1.0, 1.0) <= logt1))
{
z = norm_rs(a, b);
}
else z = unif_rs(a,b);
}
// Third scenario
else
{
if(b < 0)
{
tmp = b; b = -a; a = -tmp; change = 1;
}
lograt = R::dnorm(a, 0.0, 1.0, 1.0) - R::dnorm(b, 0.0, 1.0, 1.0);
if(lograt <= logt2) z = unif_rs(a,b);
else if((lograt > logt1) && (a < t3)) z = half_norm_rs(a,b);
else z = exp_rs(a,b);
if(change) z = -z;
}
out(i)=sigmas(i)*z + mus(i);
}
return(out);
}
这是基准：
libs=c("truncnorm","msm","inline","Rcpp","RcppArmadillo","rbenchmark")
if( sum(!(libs %in% .packages(all.available = TRUE)))>0){ install.packages(libs[!(libs %in% .packages(all.available = TRUE))])}
for(i in 1:length(libs)) {library(libs[i],character.only = TRUE,quietly=TRUE)}
#needed for openMP parallel
Sys.setenv("PKG_CXXFLAGS"="-fopenmp")
Sys.setenv("PKG_LIBS"="-fopenmp")
#no of cores for openMP version
cores = 4
#surce code from same dir
Rcpp::sourceCpp('truncnorm.cpp')
#sample size
nn=1000000
bb= 100
aa=-100
benchmark( rtnm(rep(0,nn),rep(1,nn),rep(aa,nn),rep(100,nn),cores), rtnm(rep(0,nn),rep(1,nn),rep(aa,nn),rep(100,nn),1),rtnorm(nn,rep(0,nn),rep(1,nn),rep(aa,nn),rep(100,nn)),rtruncnorm(nn, a=aa, b=100, mean = 0, sd = 1) , order="relative", replications=3 )[,1:4]
aa=0
benchmark( rtnm(rep(0,nn),rep(1,nn),rep(aa,nn),rep(100,nn),cores), rtnm(rep(0,nn),rep(1,nn),rep(aa,nn),rep(100,nn),1),rtnorm(nn,rep(0,nn),rep(1,nn),rep(aa,nn),rep(100,nn)),rtruncnorm(nn, a=aa, b=100, mean = 0, sd = 1) , order="relative", replications=3 )[,1:4]
aa=2
benchmark( rtnm(rep(0,nn),rep(1,nn),rep(aa,nn),rep(100,nn),cores), rtnm(rep(0,nn),rep(1,nn),rep(aa,nn),rep(100,nn),1),rtnorm(nn,rep(0,nn),rep(1,nn),rep(aa,nn),rep(100,nn)),rtruncnorm(nn, a=aa, b=100, mean = 0, sd = 1) , order="relative", replications=3 )[,1:4]
aa=50
benchmark( rtnm(rep(0,nn),rep(1,nn),rep(aa,nn),rep(100,nn),cores), rtnm(rep(0,nn),rep(1,nn),rep(aa,nn),rep(100,nn),1),rtnorm(nn,rep(0,nn),rep(1,nn),rep(aa,nn),rep(100,nn)),rtruncnorm(nn, a=aa, b=100, mean = 0, sd = 1) , order="relative", replications=3 )[,1:4]
由于速度取决于上限/下限，因此需要进行多次基准测试。对于不同的情况，算法的不同部分会起作用。