R/conv.R

In dSTEM: Multiple Testing of Local Extrema for Detection of Change Points

#' Compute convolution function using FFT
#' @description Compute convolution function using FFT, similar to \code{'conv'} in matlab
#' @references Matlab document on \code{'conv'}: \url{https://www.mathworks.com/help/matlab/ref/conv.html}
#' @param u numerical vector
#' @param v numerical vector, don't need to have the same length as \code{u}
#' @param shape if 'same', return central part of the convolution and has the same size as \code{u};
#'              otherwise return the whole sequence of size \eqn{lenth(u)+length(v)-1}.
#'
#' @return a vector of convolution, as specified by shape.
#' @export
#' @examples
#' u = c(-1,2,3,-2,0,1,2)
#' v = c(2,4,-1,1)
#' w = conv(u,v,'same')
conv = function(u, v, shape = c("same","full")){
  shape <- match.arg(shape)
  lx <- length(u)
  ly <- length(v)
  n <- lx + ly - 1
  w <- fft(fft(c(u,rep(0,n-lx))) * fft(c(v,rep(0,n-ly))),inverse=TRUE)/n
  w <- Re(w)
  if(shape=="same") w <- w[floor(ly/2+1):(floor(ly/2)+lx)]
  return(w)
}