Re: [R] easy way to do a 2-D fit to an array of data?

From: Ravi Varadhan <rvaradhan_at_jhmi.edu>
Date: Mon, 02 May 2011 23:55:18 -0400

Hi Carl,

Here is another slightly different (not necessarily the easiest) approach that uses a profiling technique. An advantage is that you get the maximum location directly.

n <- 20

x <- sort(rnorm(n))

y <- sort(rnorm(n))

xy <- expand.grid(x, y)

zfn <- function(x) 0.5 - 2.2 * (x[1] - 0.5)^2 - 0.9 * (x[2] + 0.5)^2

z <- rep(NA, length=n^2)

for (i in 1:nrow(xy)) z[i] <- zfn(xy[i, ])

z <- z + rnorm(n^2, sd=0.3)

obj <- function(par, x, y, z) {
-summary(lm(z ~ I((x - par[1])^2) + I((y - par[2])^2)))$r.sq }

require(dfoptim)

ans <- nmk(par=colMeans(xy), fn=obj, x=xy[,1], y=xy[,2], z=z)

ans$par # location of the maximum

summary(lm(z ~ I((xy[,1] - ans$par[1])^2) + I((xy[,2] - ans$par[2])^2)))

Ravi.



From: r-help-bounces_at_r-project.org [r-help-bounces_at_r-project.org] On Behalf Of Carl Witthoft [carl_at_witthoft.com] Sent: Monday, May 02, 2011 7:14 PM
To: r-help_at_r-project.org
Subject: [R] easy way to do a 2-D fit to an array of data?

Hi,
I've got a matrix, Z, of values representing (as it happens) optical power at each pixel location. Since I know in advance I've got a single, convex peak, I would like to do a 2D parabolic fit of the form Z = poly((x+y),2) where x and y are the x,y coordinates of each pixel (or equivalently, the row, column numbers). Is there an R function that lets me easily implement that? I've started down the path of something like

zvec <- as.vector(Z), and creating applicable x,y vectors by something like (where for the sake of argument Z is 128x128)

foo<-matrix(seq(1,128),128,128)

xvec <- as.vector(foo)
yvec <- as.vector(t(foo))

at which point I can feed zvec, xvec, yvec to lm() .

I'm hopeful someone can point me to a much easier way to do the same thing. Oh, and if there's a 2-D splinefunction generator, that would work for me as well.

thanks
Carl



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