On May 18, 2011, at 15:47 , Alex Hofmann wrote: > Hi, > > I'm new to R, and I'm a bit confused with the "convolve()" function. > If I do: > x<-c(1, 2, 3) > convolve(x, rev(x), TRUE, "open") > = 9 12 10 4 1 > > But I expected: 3 8 14 8 3 (like in Octave/MATLAB - conv(x, reverse(x)) ) > > 3 2 1 x 1 2 3 > = 3 2 1 > 0 6 4 2 > 0 0 9 6 3 > = 3 8 14 8 3 > > The thing is, that "convolve(x, x, TRUE, "open")" works. > For me it feels very confusing, that convolution does the reverse itself but > the help suggest to reverse it again. > > The help file says: "Note that the usual definition of convolution of two > sequences x and y is given by convolve(x, rev(y), type = "o")." > > Thanks for your help,
This confuses me every time as well. One way of putting it is that R's "convolve" is really what others call "correlate": the product-sum between x and y shifted by k, for k=(1-n):(n-1) (adding appropriate padding): > z <- 1:3 > crossprod(z,z) [,1] [1,] 14 > crossprod(c(z,0),c(0,z)) [,1] [1,] 8 > crossprod(c(z,0,0),c(0,0,z)) [,1] [1,] 3 Notice that this always comes out symmetric if x==y. However in convolution you want sum(x_j, y_(k-j)) so y is used in reverse order. One way of spotting the issue is that if x represents the distribution of a binary random variable X, then the convolution of x with itself should be the distribution of the sum of two independent such variables. > x [1] 0.05 0.95 > convolve(x,x,type="o") [1] 0.0475 0.9050 0.0475 > convolve(x,rev(x),type="o") [1] 0.0025 0.0950 0.9025 ... and it is pretty obviously not the case that the sum of two highly skewed distributions is symmetric, so the 2nd line is right. > dbinom(0:2,p=.95,size=2) [1] 0.0025 0.0950 0.9025 -- Peter Dalgaard Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.