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fit polynomial surface to 2d data?

From: george young
Subject: fit polynomial surface to 2d data?
Date: Fri, 6 Jul 2001 16:26:39 -0400

I have an array of floating-point measurements on a square (5 by 5) 2d grid.
I need to find any significant spatial trend, e.g. bigger on the
left, bigger in the middle, etc.  I have many thousands of these data sets
that need to be scanned for 'interesting' spatial variations, reporting the
few that are beyond some criterion of flatness.

My thought was to fit a 2'nd order polynomial with least-squares or some
such metric, and scan for coefficients bigger than some cutoff.  I think
a paraboloid is probably as complex a surface as the small amount of data 

I found "polyfit", but that seems only to work on 1d data.  Is there some
octave package for fitting a simple surface to 2d noisy data?

Is there some other approach anyone would suggest for the general task?
I'm not very experienced in data crunching, so any suggestion would
be appreciated.

I don't mind committing a lot of cpu to the task, if that helps.

-- George Young
   MIT Lincoln Laboratory

 I cannot think why the whole bed of the ocean is
 not one solid mass of oysters, so prolific they seem. Ah,
 I am wandering! Strange how the brain controls the brain!
        -- Sherlock Holmes in "The Dying Detective"

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