RcppArmadillo ifft2与R的原生mvfft

Question

I have noticed that RcppArmadillo supports FFT & 2-D FFT. Unfortunately there is a significant difference between ifft2 ( RcppArmadillo ) and R's native mvfft(..., inverse = TRUE) with my data. This is especially large in the zeroth bin (which is incredibly important in my application). The difference is not a scalar multiple. I cannot find any documentation or account for these deviations especially in the zeroth bin.

I have debugged the issue specifically to the ifft(arma::cx_mat input) function call. Unless perhaps there is an unforeseen memory management issue, this is the culprit.

Example: ifft2 result(1 column first 5 entries):

[1] 0.513297156-0.423498014i -0.129250939+0.300225299i  
0.039722228-0.093052563i -0.007956237+0.018643534i 0.001181177-0.002768473i

mvfft inverse result (1 column first 5 entries):

[1] 0.278131988-0.633838170i -0.195699114+0.445980950i  
0.060070320-0.136894940i -0.011924932+0.027175865i 0.001754788-0.003999007i

Questions

• Is the RcppArmadillo FFT still in development?
• Is this a common issue across FFT variants(numerical deviations outside of FP or DP noise)?
• Is there a 'low-level' function call from Rcpp or RcppArmadillo to call R's native FFT?

Reproducibility - Below I condensed the problem as much as I could and reproduced the issue. Updated for minimal code Rcpp code:

#include <RcppArmadillo.h>
// [[Rcpp::depends(RcppArmadillo)]]

using namespace Rcpp;
 // [[Rcpp::export]]
 //profile is the dependent variable of a given variable x,
 //q is a vector containing complex valued information for a single column after a tcrossprod
 //Size is a scalar value which the FFT depends upon.
 arma::cx_mat DebugLmnCPP( arma::cx_vec Profile, arma::cx_vec q) {
   std::complex<double> oneeye (0,1);//Cmplx number (0 + 1i)
   arma::cx_mat qFFT = ifft2( exp( oneeye * (Profile * q.st() )  ) );
   return(qFFT );
 }
 // [[Rcpp::export]]
 //For pedagogical purposes
 arma::cx_mat DebugIFFTRCPP( arma::cx_mat input) {
   arma::cx_mat qFFT = ifft2( input );
   return( qFFT );
 }

RCode (sorry this is sloppy)

library(Rcpp)
library(RcppArmadillo)
sourceCpp("/home/FILE.cpp")

#Use C++ function
qt <- c(6.0+0i, 5.95+0i, 0.10+0i)
prof <-  0.25* sin( (1:512)*(2*3.1415)/512 )  + 0.25#Offset Sine wave
Debug1 <- DebugLmnCPP( Profile = prof, q = qt )

#Use R function
FFTSize <- 2^9
DebugLmnR <- function(Profile, q) {
  g <- (0+1i)*(as.matrix(Profile ) %*% t(q))
  qFFT <- mvfft( exp(g) , inverse = TRUE) / FFTSize 
  return( qFFT )
}
#Call function
Debug2 <- DebugLmnR( Profile = prof, q = qt )

#Use R and C++
DebugLmnRC <- function(Profile, q) {
  g <- (0+1i)*(as.matrix(Profile ) %*% t(q))
  qFFT <-  DebugIFFTRCPP(exp(g))
  return( qFFT )
}
#Call function
Debug3 <- DebugLmnRC( Profile = prof, q = qt )
#Compare Results
Debug1[1:5,1] #CPP
Debug2[1:5,1] #R
Debug3[1:5,1] #R and CPP

yields :

> Debug1[1:5,1]
[1]  0.359632774+0.35083419i -0.037254305-0.36995074i  0.015576046+0.15288379i -0.004552119-0.03992962i
[5]  0.000967252+0.00765564i
> Debug2[1:5,1]
[1]  0.03620451+0.51053116i -0.04624384-0.55604273i  0.02204910+0.23101589i -0.00653108-0.06061692i
[5]  0.00140213+0.01167389i
> Debug3[1:5,1]
[1]  0.359632774+0.35083419i -0.037254305-0.36995074i  0.015576046+0.15288379i -0.004552119-0.03992962i
[5]  0.000967252+0.00765564i

Answer 1

I don't particularly like your example:

• as it is still way too complex
• you are transforming data in the functions you are comparing -- generally a bad idea
• so I would suggest you fix your inputs

Here is a simpler example. help(fft) in R leads of with this example

fftR> x <- 1:4

fftR> fft(x)
[1] 10+0i -2+2i -2+0i -2-2i

fftR> fft(fft(x), inverse = TRUE)/length(x)
[1] 1+0i 2+0i 3+0i 4+0i

which we can easily reproduce using RcppArmadillo:

R> cppFunction("arma::cx_mat armafft(arma::vec x) { return fft(x); }", 
+              depends="RcppArmadillo")
R> armafft(1:4)
      [,1]
[1,] 10+0i
[2,] -2+2i
[3,] -2+0i
[4,] -2-2i
R> 

and adding the inverse

R> cppFunction("arma::cx_mat armaifft(arma::cx_mat x) { return ifft(x); }", 
+              depends="RcppArmadillo")
R> armaifft(armafft(1:4))
     [,1]
[1,] 1+0i
[2,] 2+0i
[3,] 3+0i
[4,] 4+0i
R> 

recovering our input as in the R example.

No bug as far as I can tell, and I have no reason to believe this is any different for the 2d case...

Edit/Followup: The error is with the OP, and not with Armadillo. The primary issues here are

• not reading the documentation carefully
• not working with a minimal examples

The main issue here is that Armadillo's fft() can work on vectors or matrices and does hence (in the matrix case) correspond to R's mvfft() . Armadillo's fft2() is simply something else and not relevant here.

Let us continue / extend our previous example. We redefine our accessor to use complex matrix values:

R> cppFunction("arma::cx_mat armafft(arma::cx_mat x) { return fft(x); }",
+              depends="RcppArmadillo")
R>

and then define a complex array of dimension 5 x 2 which we feed to it:

R> z <- array(1:10 + 1i, dim=c(5,2))
R> z
     [,1]  [,2]
[1,] 1+1i  6+1i
[2,] 2+1i  7+1i
[3,] 3+1i  8+1i
[4,] 4+1i  9+1i
[5,] 5+1i 10+1i
R> 
R> armafft(z)
              [,1]          [,2]
[1,] 15.0+5.00000i 40.0+5.00000i
[2,] -2.5+3.44095i -2.5+3.44095i
[3,] -2.5+0.81230i -2.5+0.81230i
[4,] -2.5-0.81230i -2.5-0.81230i
[5,] -2.5-3.44095i -2.5-3.44095i
R> 

This is the same output we would get from running the function separately on each column. And that is also what R does for mvfft() (cf help(fft) )

R> mvfft(z)
              [,1]          [,2]
[1,] 15.0+5.00000i 40.0+5.00000i
[2,] -2.5+3.44095i -2.5+3.44095i
[3,] -2.5+0.81230i -2.5+0.81230i
[4,] -2.5-0.81230i -2.5-0.81230i
[5,] -2.5-3.44095i -2.5-3.44095i
R> 

Same result, different libraries / packages, no bug as far as I can see.