Kolmogorov-Smirnov 测试：C 到 R 的翻译问题

Question

我在将算法从 C 转换为 R 时遇到困难。这是关于 Kolmogorov Smirnov 检验，更具体地说是 KS 概率函数

在'Numerical Recipes in C'、'probks'中编码为

#include <math.h>
#define EPS1 0.001
#define EPS2 1.0e-8
float probks(float alam)
/*Kolmogorov-Smirnov probability function.*/
{
   int j;
   float a2,fac=2.0,sum=0.0,term,termbf=0.0;

   a2 = -2.0*alam*alam;
   for (j=1;j<=100;j++) {
      term=fac*exp(a2*j*j);
      sum += term;
      if (fabs(term) <= EPS1*termbf || fabs(term) <= EPS2*sum) return sum;
      fac = -fac; /*Alternating signs in sum.*/
      termbf=fabs(term);
   }
   return 1.0; /* Get here only by failing to converge. */
}

我不知道如何处理最后几行在 R 中的翻译，我现在只有

PROBKS <- function(lambda) {

  EPS1 <- 0.001; EPS2 <- 1.0e-8;
  sum <- 0.0; fac <- 2.0; termbf <- 0.0; 
  a2 <- -2*lambda*lambda 

  for (j in 1:100) {
    term <- fac * exp(a2*j*j)
    sum <- sum + term
    if ( (abs(term) <= EPS1*termbf) || (abs(term) <= EPS2*sum) ) {
      break
    } else {
      fac <- -fac
    }
  }
  termbf <- abs(term)
  return(sum)
}

但这会产生一个非单调的概率函数

它应该是 $Q_KS(0) = 1$ 和 $Q_KS(\infty) = 0$。显然，这是关于如何 interpret/encode 最后一个 'if' 语句。

如有任何帮助，我们将不胜感激。 M

编辑 1： 这是我的会话信息

> sessionInfo()
R version 3.4.4 (2018-03-15)
Platform: i386-w64-mingw32/i386 (32-bit)
Running under: Windows >= 8 x64 (build 9200)

Matrix products: default

locale:
[1] LC_COLLATE=English_United Kingdom.1252 
[2] LC_CTYPE=English_United Kingdom.1252   
[3] LC_MONETARY=English_United Kingdom.1252
[4] LC_NUMERIC=C                           
[5] LC_TIME=English_United Kingdom.1252    

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] reshape2_1.4.3  forcats_0.3.0   stringr_1.3.1   dplyr_0.7.7    
 [5] purrr_0.2.5     readr_1.1.1     tidyr_0.8.1     tibble_1.4.2   
 [9] ggplot2_3.1.0   tidyverse_1.2.1

loaded via a namespace (and not attached):
 [1] withr_2.1.2      rvest_0.3.2      tidyselect_0.2.5 lattice_0.20-35 
 [5] pkgconfig_2.0.2  xml2_1.2.0       compiler_3.4.4   readxl_1.1.0    
 [9] Rcpp_0.12.19     cli_1.0.1        plyr_1.8.4       cellranger_1.1.0
[13] httr_1.3.1       tools_3.4.4      nlme_3.1-131.1   broom_0.5.0     
[17] R6_2.3.0         bindrcpp_0.2.2   bindr_0.1.1      scales_1.0.0    
[21] assertthat_0.2.0 gtable_0.2.0     stringi_1.1.7    rstudioapi_0.8  
[25] backports_1.1.2  hms_0.4.2        munsell_0.5.0    grid_3.4.4      
[29] colorspace_1.3-2 glue_1.3.0       lubridate_1.7.4  rlang_0.3.0.1   
[33] magrittr_1.5     lazyeval_0.2.1   yaml_2.2.0       crayon_1.3.4    
[37] haven_1.1.2      modelr_0.1.2     pillar_1.3.0     jsonlite_1.5

编辑 2 使用 Konrad 函数 ks_cdf 和

x = seq(0, 1, by = 0.01)
plot(x, ks_cdf(x))

仍然在 0 处给出 0

编辑 3 升级到 3.6.1 后

> sessionInfo()
R version 3.6.1 (2019-07-05)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows >= 8 x64 (build 9200)
...

我仍然得到与上面相同的情节，即 ks_cdf(0)=0 而它应该是 ks_sdf(0)=1

Answer 1

代码几乎可以按字面意思翻译成 R——不清楚你为什么无缘无故地偏离 C 代码。这是一个字面的，稍微清理过的翻译：

ks_cdf = function (lambda) {
  EPS1 = 0.001
  EPS2 = 1.0e-8
  sum = 0
  fac = 2
  termbf = 0
  a2 = -2 * lambda ^ 2

  for (j in 1 : 100) {
    term = fac * exp(a2 * j ^ 2)
    sum = sum + term
    if ((abs(term) <= EPS1 * termbf) || (abs(term) <= EPS2 * sum)) {
      return(sum)
    } else {
      fac = -fac
      termbf = abs(term)
    }
  }
  1 # Failed to converge.
}

此代码有效但未矢量化，这是我为实际实现而更改的内容（但是，这样做，我们将失去提前退出）。

这是使用向量化算术和矩阵乘法的惯用 R 实现：

ks_cdf = function (λ) {
  eps1 = 0.001
  eps2 = 1E-8

  range = seq(1, 100)
  terms = (-1) ^ (range - 1) * exp(-2 * range ^ 2 %*% t(λ ^ 2))
  sums = 2 * colSums(terms)
  pterms = abs(terms)
  prev_pterms = rbind(0, pterms[-nrow(pterms), , drop = FALSE])
  converged = apply(pterms <= eps1 * prev_pterms | pterms <= eps2 * sums, 2L, any)
  sums[! converged] = 1
  sums
}

并展示它的矢量化有多好，这实际上是一件大事：

x = seq(0, 1, by = 0.01)
plot(x, ks_cdf(x))

Kolmogorov-Smirnov 测试：C 到 R 的翻译问题

Kolomogorov-Smirnov test: C to R translation issue

c

r

kolmogorov-smirnov