On Fri, Feb 04, 2011 at 02:03:22PM -0500, sudhir cr wrote:
> Hello,
>
> I have a R code for doing convolution of two functions:
>
> convolveSlow <- function(x, y) {
> nx <- length(x); ny <- length(y)
> xy <- numeric(nx + ny - 1)
> for(i in seq(length = nx)) {
> xi <- x[[i]]
> for(j in seq(length = ny)) {
> ij <- i+j-1
> xy[[ij]] <- xy[[ij]] + xi * y[[j]]
> }
> }
> xy
> }
>
> How do I reduce the 2 loops so that I can run the code faster?
Hello:
Convolution of two vectors may be computed also using matrix reshaping
without a loop. For example
convolution <- function(x, y)
{
# more efficient if length(x) >= length(y)
m <- length(x)
n <- length(y)
zero <- matrix(0, nrow=n, ncol=n)
a <- rbind(x %o% y, zero)
k <- m + n - 1
b <- matrix(c(a)[1:(n*k)], nrow=k, ncol=n)
rowSums(b)
}
Testing this on computing the product of the polynomials (1+t)^4 (1+t)^3
yields
x <- choose(4, 0:4)
y <- choose(3, 0:3)
convolution(x, y)
[1] 1 7 21 35 35 21 7 1
which is the same as choose(7, 0:7).
See also ?convolve.
Hope this helps.
Petr Savicky.
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