导入 R 函数时，Rcpp 中的实现比 R 慢

Question

我尝试使用 Rcpp 重写一些 R 代码。但是，我发现性能有所下降。我已经针对有问题的代码的特定部分。在这一部分中，我从 R 中的stats 包中导入了optimise 函数。

我要重写的 R 代码是：

###################################
# R implementation

phi_R <- function(x, mean = 0, beta) {
  return(2*(beta^2)*((x-mean)^6) - 3*beta*((x-mean)^2))
}

bound_phi_R <- function(beta, mean = 0, lower, upper) {
  # finding maxima and minimma in the interval
  maxim <- optimise(function(x) phi_R(x, mean, beta), interval = c(lower, upper), 
                    maximum = TRUE)$objective
  minim <- optimise(function(x) phi_R(x, mean, beta), interval = c(lower, upper), 
                    maximum = FALSE)$objective

  # checking end points
  at_lower <- phi_R(lower, mean, beta)
  at_upper <- phi_R(upper, mean, beta)

  # obtaining upper and lower bounds
  upper_bound <- max(maxim, at_lower, at_upper)
  lower_bound <- min(minim, at_lower, at_upper)

  return(list('low_bound' = lower_bound, 'up_bound' = upper_bound))
}

这个函数试图找到一个特定的一维函数的上限和下限，称为 phi。 我的 Rcpp 实现是：

#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::plugins("cpp17")]]
// [[Rcpp::depends(stats)]]

double phi_rcpp(const double &x,
                             const double &mean,
                             const double &beta) {
  return ((2*beta*beta*pow(x-mean, 6))-(3*beta*(x-mean)*(x-mean)));
}

// [[Rcpp::export]]
Rcpp::List bound_phi_rcpp(const double &mean,
                                const double &beta,
                                const double &lower,
                                const double &upper) {
  // Obtaining namespace of stats package in R
  Rcpp::Environment stats("package:stats");
  // Picking up optimise function
  Function optimise = stats["optimise"];

  // using optimise to find the maximum and minimum of phi within the interval
  Rcpp::List maxim = optimise(_["f"] = Rcpp::InternalFunction(&phi_rcpp),
                              _["lower"] = lower,
                              _["upper"] = upper,
                              _["maximum"] = true,
                              _["mean"] = mean,
                              _["beta"] = beta);
  Rcpp::List minim = optimise(_["f"] = Rcpp::InternalFunction(&phi_rcpp),
                              _["lower"] = lower,
                              _["upper"] = upper,
                              _["maximum"] = false,
                              _["mean"] = mean,
                              _["beta"] = beta);

  // check the end points are not greater or less than the minimum and maximums from optimise
  double at_upper = phi_rcpp(upper, mean, beta);
  double at_lower = phi_rcpp(lower, mean, beta);

  double upper_bound = std::max(as<double>(maxim[1]), std::max(at_lower, at_upper));
  double lower_bound = std::min(as<double>(minim[1]), std::min(at_lower, at_upper));

  // return bounds as vector
  return Rcpp::List::create(Named("low_bound") = lower_bound,
                            Named("up_bound") = upper_bound);
}

接下来，我做一些基准测试：

library(Rcpp)
sourceCpp(file = 'rcpp.cpp')

pcm <- proc.time()
set.seed(42)
for (i in 1:10000) {
  limits <- runif(2, -2, 2)
  bound_phi_rcpp(beta = 1/4, mean = 0, lower = min(limits), upper = max(limits))
}
test1_time <- proc.time()-pcm

pcm <- proc.time()
set.seed(42)
for (i in 1:10000) {
  limits <- runif(2, -2, 2)
  bound_phi_R(beta = 1/4, mean = 0, lower = min(limits), upper = max(limits))
}
test2time <- proc.time()-pcm

print(paste('rcpp:', test1_time['elapsed'])) # 5.69 on my machine
print(paste('R:', test2_time['elapsed'])) # 0.0749 on my machine

# benchmarking with rbenchmark
set.seed(42)
limits <- runif(2, -2, 2)
identical(bound_phi_rcpp(beta = 1/4, mean = 0, lower = min(limits), upper = max(limits)),
          bound_phi_R(beta = 1/4, mean = 0, lower = min(limits), upper = max(limits)))
rbenchmark::benchmark(cpp = bound_phi_rcpp(beta = 1/4, mean = 0, lower = min(limits), upper = max(limits)),
                      R = bound_phi_R(beta = 1/4, mean = 0, lower = min(limits), upper = max(limits)), 
                      replications = 1000)

我得到以下基准：

  test replications elapsed relative user.self sys.self user.child sys.child
1  cpp         1000   0.532   10.231     0.532    0.001          0         0
2    R         1000   0.052    1.000     0.052    0.000          0         0

从 stats 导入函数似乎有相当多的开销。有什么方法可以加快这个过程，或者 Rcpp 中是否有等效的优化功能？

Answer 1

你的 C++ 代码很慢并不奇怪，因为你要在 R 和 C++ 之间切换很多次。每一次这样的转变都有其代价。但是，可以使用仅在 C++ 中实现的优化算法，例如https://www.boost.org/doc/libs/1_70_0/libs/math/doc/html/math_toolkit/brent_minima.html 似乎与 R 使用的算法相同，并且包含在 BH 包中。事实证明它也很容易使用：

#include <Rcpp.h>
// [[Rcpp::plugins(cpp11)]]
// [[Rcpp::depends(BH)]]
#include <boost/math/tools/minima.hpp>

class phi_rcpp {
private:
    double mean;
    double beta;
public:
    phi_rcpp(double _mean, double _beta) : mean(_mean), beta(_beta) {}
    double operator()(const double &x) {
        double y = x - mean;
        return (2*beta*beta*pow(y, 6))-(3*beta*y*y);
    }
};

template<class T>
class negate : public T {
public:
    using T::T;
    double operator() (const double &x) {
        return - T::operator()(x);
    }
};

// [[Rcpp::export]]
Rcpp::List bound_phi_rcpp(const double &mean,
                          const double &beta,
                          const double &lower,
                          const double &upper) {
    using boost::math::tools::brent_find_minima;
    const int double_bits = std::numeric_limits<double>::digits;
    phi_rcpp func(mean, beta);
    negate<phi_rcpp> nfunc(mean, beta);
    std::pair<double, double> min = brent_find_minima(func, lower, upper, double_bits);
    std::pair<double, double> max = brent_find_minima(nfunc, lower, upper, double_bits);

    double at_upper = func(upper);
    double at_lower = func(lower);

    return Rcpp::List::create(Rcpp::Named("low_bound") = std::min(min.second, std::min(at_upper, at_lower)),
                              Rcpp::Named("up_bound") =  std::max(max.second, std::max(at_upper, at_lower)));
}

/*** R
phi_R <- function(x, mean = 0, beta) {
    return(2*(beta^2)*((x-mean)^6) - 3*beta*((x-mean)^2))
}

bound_phi_R <- function(beta, mean = 0, lower, upper) {
    # finding maxima and minimma in the interval
    maxim <- optimise(function(x) phi_R(x, mean, beta), interval = c(lower, upper), 
                      maximum = TRUE)$objective
    minim <- optimise(function(x) phi_R(x, mean, beta), interval = c(lower, upper), 
                      maximum = FALSE)$objective

    # checking end points
    at_lower <- phi_R(lower, mean, beta)
    at_upper <- phi_R(upper, mean, beta)

    # obtaining upper and lower bounds
    upper_bound <- max(maxim, at_lower, at_upper)
    lower_bound <- min(minim, at_lower, at_upper)

    return(list('low_bound' = lower_bound, 'up_bound' = upper_bound))
}


set.seed(42)
limits <- runif(2, -2, 2)
bench::mark(cpp = bound_phi_rcpp(beta = 1/4, mean = 0, lower = min(limits), upper = max(limits)),
            R = bound_phi_R(beta = 1/4, mean = 0, lower = min(limits), upper = max(limits)))

*/

这里唯一棘手的是用于否定函子的模板。基准测试结果：

# A tibble: 2 x 13
  expression     min  median `itr/sec` mem_alloc `gc/sec` n_itr  n_gc total_time result memory time 
  <bch:expr> <bch:t> <bch:t>     <dbl> <bch:byt>    <dbl> <int> <dbl>   <bch:tm> <list> <list> <lis>
1 cpp         6.26µs  7.94µs   117496.    2.49KB     11.8  9999     1     85.1ms <list… <Rpro… <bch…
2 R          61.51µs 72.31µs    11279.  124.98KB     11.1  5102     5    452.4ms <list… <Rpro… <bch…
# … with 1 more variable: gc <list>

注意bench::mark 默认检查相同的结果。