Re: eofs and current vectors

[Mick.Spillane@xxxxxxxx]

On Wed, 17 Mar 2004, Vincent Le Fouest wrote:
>
> Would you have an idea whether it is be possible to use the EOF
> functions (eof_space, eof_tfunc and eof_stat) with vector fields (u,v)?
>
Hi Vincent,

	What you need I believe is a complex EOF of the vector
field U + iV.
	If there is a way to do it I suspect it would be rather
cumbersome and heavy on memory, with the interpretation of the
results awkward too, if one relied on the existing "real" EOF
tools (eof_space, eof_tfunc and eof_stat).  Rather, a separate
set of external functions for the complex case would need to
be set up, to implement something like the scheme suggested in
"Numerical Recipes".

	If you look at "Numerical Recipes" by Press et al you will
find under "Hermitian Matrices" in the Eigensystems that the n x n
COMPLEX eigenvalue problem
	(A+iB)(U+iV) = k (U+iV)
is equivalent to the 2n x 2n REAL problem
         | A  -B |   | U |     | U |
         |       | . |   | = k |   |
         | B   A |   | V |     | V |

	I have implemented in Fortran using their "jacobi" subroutine
but as a standalone program rather than an external function. In
light of recent correspondence regarding the size and time required
for eof analyses of large spatial fields, doing the analysis
outside of ferret may be the best at present.  But Ferret remains
tops in my book when it comes to visualizing the results of the
analysis.

And in light of the day that's in it, begorrah ...

May the road rise for you, (actually a more rational translation
of the Gaelic fortune cookie "Go n-eiri an bothar leat" might be
"May your path be successful".) And may the (vector) wind be always
at your back.

Mick