Presently available EOF external functions

[kessler@xxxxxxxxxxxxx (Billy Kessler)]

Hello Ferreters -

This seems to be an appropriate time to say a few things about the
EOF external functions available in V5.n of Ferret. These are
EOF_SPACE, EOF_STAT, and EOF_TFUNC. See the V5 documentation for
descriptions of the use of these.

These EOF routines were originally designed for a special purpose:
to compute EOFs on gappy time series. Gaps in the time series
introduce special complications which require a much more difficult
(and CPU-consuming) code to deal with. Briefly, it is possible to
make estimates of the EOFs and time functions (PCs) that minimize 
the expected square error in a least squares sense. (Ask me for 
details; the algebra is not easy to write down in an e-mail). I 
wrote these routines in fortran about 15 years ago, based on 
unpublished notes by Dudley Chelton.

These EOF routines are now in ferret because someone asked the PMEL 
ferret team to make them into external functions. A more systematic 
approach would have made the more usual (and MUCH faster) type of 
EOF routines external functions first, but the squeaky wheel gets 
the grease, so this is the way it turned out. We are now working
on making better EOF external functions available.

So while the present routines definitely work, they are not ideal for 
probably the great majority of EOF work that most of us encounter.
For complete time series, they are far slower than a usual EOF
routine (roughly nx*nt times slower). Lots of needless computation
is being done if there are no gaps. On the other hand, if you DO 
have a gappy time series, then these routines are very useful and
hard to come by otherwise.

Billy K
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
William S. Kessler
NOAA / Pacific Marine Environmental Laboratory
7600 Sand Point Way NE
Seattle Wa 98115 USA

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