On Jun 4, 2013, at 10:15 PM, Hans W Borchers wrote:
Bert Gunter <gunter.berton <at> gene.com> writes:
1. This looks like a homework question. We should not do homework
here.
2. optim() will only approximate the max.
3. optim() is not the right numerical tool for this anyway.
optimize() is.
4. There is never a guarantee numerical methods will find the max.
5. This can (and should?) be done exactly using elementary math
rather
than numerical methods.
Cheers,
Bert
In the case of polynomials, "elementary math ... methods" can
actually be
executed with R:
library(polynomial) # -6 + 11*x - 6*x^2 + x^3
p0 <- polynomial(c(-6, 11, -6, 1)) # has zeros at 1, 2, and 3
p1 <- deriv(p0); p2 <- deriv(p1) # first and second derivative
xm <- solve(p1) # maxima and minima of p0
xmax = xm[predict(p2, xm) < 0] # select the maxima
xmax # [1] 1.42265
Obviously, the same procedure will work for polynomials p0 of higher
orders.
These look like the functions present in the 'polynom' package
authored by Bill Venables [aut] (S original), Kurt Hornik [aut, cre]
(R port), Martin Maechler. I wasn't able to find a 'polynomial'
package on CRAN. The 'mpoly' package by David Kahle offers
multivariate symbolic operations as well.
--
David.
Hans Werner
Em 04-06-2013 21:32, Joseph Clark escreveu:
My script fits a third-order polynomial to my data with something
like
this:
model <- lm( y ~ poly(x, 3) )
What I'd like to do is find the theoretical maximum of the
polynomial
(i.e. the x at which "model" predicts the highest y).
Specifically, I'd
like to predict the maximum between 0 <= x <= 1.
What's the best way to accomplish that in R?
Bonus question: can R give me the derivative or 2nd derivative of
the
polynomial? I'd like to be able to compute these at that maximum
point.
Thanks in advance!
--
David Winsemius, MD
Alameda, CA, USA
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