More on convolution

Often you need to convolve a particular vector with a lot of other vectors of equal length, then the program below can be used. It illustrates the use of Rcpp/inline and FFTW used from within R.

### The program below can be used, when a vector is convolved several times ### with vectors of equal length

### In the first step the FFT of x is stored and FFTW plans are created, ### in subsequent steps the FFT of x is reused and FFTW plans recalled.

library(Rcpp) require(inline)

### Definition of plugin, makes linkage to FFTW possible plug <- Rcpp:::Rcpp.plugin.maker(include.before = "#include “, libs = paste(“-L/usr/local/lib/R/site-library/Rcpp/lib -lRcpp”, “-Wl,-rpath,/usr/local/lib/R/site-library/Rcpp/lib”, “-lfftw3 -lm -L/usr/lib”)) registerPlugin(“FFTWconv”, plug )

### Convolution function used after initiation convFFTW <- cxxfunction( signature(x_fftIn = “numeric”, yIn = “numeric”), body = ‘ Rcpp::NumericMatrix x_fft(x_fftIn); Rcpp::NumericVector y(yIn); int ny=y.size(); int n=x_fft.ncol(); Rcpp:NumericVector retPar(n);

double in_1[n]; double out_2[n];

FILE *inputfile;

fftw_complex *in_2,*out_1,*y_fft; in_2=(fftw_complex*) fftw_malloc(sizeof(fftw_complex) * n); out_1=(fftw_complex*) fftw_malloc(sizeof(fftw_complex) * n);

fftw_plan forward; fftw_plan backward;

inputfile = fopen(“stored.wisdom”, “r”); fftw_import_wisdom_from_file(inputfile); fclose(inputfile);

forward=fftw_plan_dft_r2c_1d(n, in_1, out_1, FFTW_MEASURE); backward=fftw_plan_dft_c2r_1d(n, in_2, out_2, FFTW_MEASURE);

for(int i=0;i<ny;i++) in_1[i]=y[i]; for(int i=ny;i<n;i++) in_1[i]=0.0; fftw_execute(forward);

for(int i=0;i<n;i++){ in_2[i][0]=x_fft(0,i)*out_1[i][0]+x_fft(1,i)*out_1[i][1]; in_2[i][1]=x_fft(1,i)*out_1[i][0]-x_fft(0,i)*out_1[i][1]; } fftw_execute(backward);

for(int i=0;i<n;i++) retPar[i]=out_2[i]/((double)n);

fftw_destroy_plan(forward); fftw_destroy_plan(backward);

return retPar; ‘, plugin=”FFTWconv”)

### Convolution function used for initiation / creation of FFTW plans convFFTWstart <- cxxfunction( signature(xIn = “numeric”, yIn = “numeric”), body = ‘ Rcpp::NumericVector x(xIn); Rcpp::NumericVector y(yIn); int nx=x.size(); int ny=y.size(); int n=nx+ny-1; Rcpp:NumericMatrix retPar(3,n);

double in_1[n]; double out_2[n];

FILE *inputfile;

fftw_complex *in_2,*out_1,*x_fft,*y_fft; in_2=(fftw_complex*) fftw_malloc(sizeof(fftw_complex) * n); out_1=(fftw_complex*) fftw_malloc(sizeof(fftw_complex) * n);

fftw_plan forward; fftw_plan backward;

forward=fftw_plan_dft_r2c_1d(n, in_1, out_1, FFTW_MEASURE); backward=fftw_plan_dft_c2r_1d(n, in_2, out_2, FFTW_MEASURE); inputfile = fopen(“stored.wisdom”, “w”); fftw_export_wisdom_to_file(inputfile); fclose(inputfile);

for(int i=0;i<(n-nx);i++) in_1[i]=0.0; for(int i=(n-nx);i<n;i++) in_1[i]=x[i-n+nx]; fftw_execute(forward); x_fft=(fftw_complex*) fftw_malloc(sizeof(fftw_complex) * n); for(int i=0;i<n;i++) for(int j=0;j<2;j++) x_fft[i][j]=out_1[i][j];

for(int i=0;i<ny;i++) in_1[i]=y[i]; for(int i=ny;i<n;i++) in_1[i]=0.0; fftw_execute(forward);

for(int i=0;i<n;i++){ in_2[i][0]=x_fft[i][0]*out_1[i][0]+x_fft[i][1]*out_1[i][1]; in_2[i][1]=x_fft[i][1]*out_1[i][0]-x_fft[i][0]*out_1[i][1]; } fftw_execute(backward);

for(int i=0;i<n;i++){ retPar(0,i)=out_2[i]/((double)n); retPar(1,i)=x_fft[i][0]; retPar(2,i)=x_fft[i][1]; }

fftw_destroy_plan(forward); fftw_destroy_plan(backward);

return retPar; ‘, plugin=”FFTWconv”)

convolve_fftw=function(x,y){ return(convFFTW(x,rev(y))) }

###R function which handles Rcpp/inline functions above conv.iteration <<- 0

convolve_fftw=function(x,y){ if(conv.iteration==0){ conv.start <<- convFFTWstart(x,rev(y)) conv.iteration <<- 1 return(conv.start[1,]) } else return(convFFTW(conv.start[2:3,],rev(y))) }