R help - May 2011 - 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

You may want to consider spatial::surf.ls  

Or, a simplistic approach where you fit a model such as using `lm':

E[Z | x, y] = a + b(x - x0)^2 + c(y - y0)^2 

where (x0, y0) is the location of maximum.

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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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

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

______________________________________________
R-help at 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.