# Is the pain worth it?: Can Rcpp speed up Passing Bablok Regression?

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### Background

R dogma is that for loops are bad because they are slow but this is not the case in C++. I had never programmed a line of C++ as of last week but my beloved firstborn started university last week and is enrolled in a C++ intro course, so I thought I would try to learn some and see if it would speed up Passing Bablok regression.

### Passing Bablok Regression

As mentioned in the past, the field of Clinical Chemistry has a peculiar devotion to Passing Bablok regression… and hey, why not?

Here is the code for a minimal implementation of Passing Bablok regression as discussed in this paper. This is the scale-invariant version.

PB.reg <- function(x,y){ lx <- length(x) l <- lx*(lx - 1)/2 k <- 0 S <- rep(NA, lx) for (i in 1:(lx - 1)) { for (j in (i + 1):lx) { k <- k + 1 S[k] <- (y[i] - y[j])/(x[i] - x[j]) } } S.sort <- sort(S) N <- length(S.sort) neg <- length(subset(S.sort,S.sort < 0)) K <- floor(neg/2) if (N %% 2 == 1) { b <- S.sort[(N+1)/2+K] } else { b <- sqrt(S.sort[N / 2 + K]*S.sort[N / 2 + K + 1]) } a <- median(y - b * x) return(as.vector(c(a,b))) }

So let’s make some fake data and see what we get:

set.seed(314) x <- seq(1, 100, length.out = 100) y <- 1.1* x + 20 + x*rnorm(100,0,0.10) reg <- PB.reg(x,y) round(reg,2)

## [1] 18.90 1.14

Just to sanity check, we can get the coefficients from the `mcr()`

package.

library(mcr) reg.mcr <- mcreg(x,y) round([email protected],2)

## [1] 18.90 1.14

Ok, looks good.

### Rcpp

The Rcpp package permits compiling and execution of C++ code from within R. This can be good for computationally intensive tasks. Here is my child-like attempt at recapitulation of the R script above.

#include#include #include #include #include #include #include "Rcpp.h" using namespace std; using namespace Rcpp; // [[Rcpp::plugins("cpp11")]] // [[Rcpp::export]] vector PB(vector x,vector y){ int lx=x.size(); int l=lx*(lx-1)/2; int k=-1; vector S(l,numeric_limits ::quiet_NaN()); vector sortS; vector neg; double b; double a; vector aVec(x.size()); vector coef(2); // Calculate the components of the S Matrix for(int i=0; i :: iterator it = S.begin(); it != S.end(); ++it){ if (!isnan(*it)) sortS.push_back((*it)); } // Put all the negative values into a vector called neg for(vector :: iterator it = S.begin(); it != S.end(); ++it){ if ((*it)<0) neg.push_back((*it)); } // Calculate N and K int K=int(floor(float(neg.size()/2))); int N=sortS.size(); // Calculate the slope if (N%2==1) { b=S[static_cast ((N+1)/2+K-1)]; } else { b=sqrt(S[static_cast (N/2+K-1)]*S[static_cast (N/2+K)]); } // Make a vector aVec of the estimates of the intercept for(int i=0; i ((x.size()+1.0)/2.0-1.0)]; }else{ a=(aVec[static_cast (x.size()/2.0-1.0)] + aVec[static_cast (x.size()/2.0)])/2.0; } // Report results coef[0]=a; coef[1]=b; return coef; } int main(){ return 0; }

Saving this to a local directory as PB_Reg.cpp, we can compile it and call the function into the R session as follows:

library(Rcpp) sourceCpp("PB_Reg.cpp")

And run it:

round(PB(x,y),2)

## [1] 18.90 1.14

Looks good! But is it faster? Like really faster? Let’s find out. And let’s also compare it to what the `compiler()`

package produces:

library(compiler) PB.reg.cmpfun <- cmpfun(PB.reg) library(rbenchmark) bmark <- benchmark( Rscript = PB.reg(x,y), `Compiler Package` = PB.reg.cmpfun(x,y), Rcpp = PB(x,y), replications = 100, order = "relative" ) knitr::kable(bmark)

test | replications | elapsed | relative | user.self | sys.self | user.child | sys.child | |
---|---|---|---|---|---|---|---|---|

3 | Rcpp | 100 | 0.024 | 1.000 | 0.024 | 0.000 | 0 | 0 |

2 | Compiler Package | 100 | 0.214 | 8.917 | 0.214 | 0.000 | 0 | 0 |

1 | Rscript | 100 | 0.217 | 9.042 | 0.213 | 0.004 | 0 | 0 |

So this makes C++ code about 9x faster than R source code. Not bad but in this case it was probably not worth the effort. Oh well. I learned something. Incidentally, the `compiler()`

package did not help much in this case as it is only marginally better than raw R source. I have seen better results from `compiler()`

in other cases.

### Final thought

Speaking of speed:

*“Free yourself, like a gazelle from the hand of the hunter, like a bird from the snare of the fowler.”*

*Proverbs 6:5*

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