Fastest way to compute Gaussian kernel vector in CppArmadillo? - c++

Question

I am trying to compute a vector of gaussian kernel evaluations as quickly as possible. I have a data point x in R^p, and a matrix X of n vectors x_i. I would like to compute exp( -||x-x_i||^2 / t) for every x_i and return the result as a vector.
I have tried implementing this in both R and RcppArmadillo via the following code
R CODE:
kernel <- function(x, Data, sigma){
if(sigma <= 0 ) stop('Gaussian kernel parameter <= 0.')
DiffPart <- (t(t(Data) - x))^2 ## Computes the distance squared of the data and point x
DiffPart <- rowSums(DiffPart) # Sum of squares
exp( - DiffPart / sigma) #Divide by kernel parameter and evluate exponential function
}
RcppArmadillo:
arma::Col<double> kernelCPP(arma::Row<double> x, arma::Mat<double> Data, double sigma){
arma::Mat<double> Diff=Data.each_row()-x;
int n = Data.n_rows;
arma::Col<double> kern(n);
for(int k = 0 ; k < n; k++){
kern(k) = exp(-arma::accu(square(Diff.row(k)))/sigma);
}
return(kern);
}
Unfortunately, my RcppArmadillo code is not much faster than the original R code. I'll be computing kernel vectors hundreds of thousands of times in future code/computation, and so I would like this to be as fast of a process as I can make it.
When microbenchmarking, I get the following results:
> microbenchmark(
+ kernel(x= TrainX1[1,], Data = TrainX1, sigma = 100)
+ )
Unit: milliseconds
min lq mean median
2.223359 2.274559 2.5199 2.308052
uq max neval
2.575144 4.73301 100
and
> microbenchmark(
+ kernelCPP(x= TrainX1[1,], Data = TrainX1, sigma = 100)
+ )
Unit: milliseconds
min lq mean
1.697706 1.732053 1.826743
median uq max neval
1.775786 1.871786 2.493439 100
A little faster, but not by much.