On Sat, Apr 02, 2011 at 08:24:07AM -0400, ivo welch wrote:
> curiosity---given that vector operations are so much faster than
> scalar operations, would it make sense to make uniroot vectorized? if
> I read the uniroot docs correctly, uniroot() calls an external C
> routine which seems to be a scalar function. that must be slow. I am
> thinking a vectorized version would be useful for an example such as
>
> of <- function(x,a) ( log(x)+x+a )
> uniroot( of, c( 1e-7, 100 ), a=rnorm(1000000) )
Hi.
The slowest part of the solution using uniroot() is the repeated
evaluation of the R level input function. If this can be vectorized,
then a faster algorithm could be possible. The following is an
example of a vectorized bisection, which is simpler and less
efficient than "zeroin" used in uniroot().
of <- function(x,a) { log(x)+x+a }
a <- rnorm(1000)
x1 <- rep(1e-7, times=length(a))
x2 <- rep(100, times=length(a))
stopifnot(of(x1, a) < 0)
stopifnot(of(x2, a) > 0)
for (i in 1:60) {
x3 <- (x1 + x2)/2
pos <- of(x3, a) > 0
y1 <- ifelse(pos, x1, x3)
y2 <- ifelse(pos, x3, x2)
x1 <- y1
x2 <- y2
}
print(range(of(x1, a)))
print(range(of(x2, a)))
It can be more efficient to find approximations of the roots
using a few iterations of the above approach and then switch
to the Newton method, which can be vectorized easily.
Hope this helps for a start.
Petr Savicky.
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