🚀 go-pugleaf

To all and sundry out there who replied to my request,

Thanks a bundle for all your help, the response was overwhelming!!!!

I had better let you all know what I am trying to do with this algorithm.
I am analysing a neutron Time-of-flight spectrum (TOF) using the Maximum
Entropy Principle to deconvolute spin-flip and non-spin-flip scattering
cross-sections from measured counts.  The data is taken by impressing a
pseudo-random sequence upon the polarisation of the neutrons, and then
analysing the scattered neutrons with an MCA.  I end up with something like
the following, (don't quote me here - I'm still fighting my supervisor over
the form)	 	

	y(k) = {sigma j} ( R(k,j)( f(j) - g(j) ) + Q(k,j)( g(j) - f(j) ) + e(k)

where R, Q are convolution matrices formed from the pseudo-random sequences, and
f, g are the SF and NSF cross-sections ( e(k) is error with normal distribution
)

The technique consists of maximising the entropy of the system (or information)
WRT the measured values and also the chi-square of the errors.

This becomes a 1000 x 1000 quasi-linear system with (f|g) as the eigenvectors.

Memory is tight in the PC but I am loath to transfer all my C to the Vax as I
have a lot of graphics code that would be a bit messy to port.  So I am using 
a custom designed virtual memory driver to store the big matrices (NB. the
system is symmetric and block-diagonal, and has been reduced as much as poss.)
, and am solving the system by SOR with my relaxation parameter calculated by
estimating the spectral radius of the system.

Because of the entropy calculations, I end up with

ln( f.2.mu.B(j,j) ) + f.2.mu.B(j,j) = .....(calculated const.)
By changing variables I solve for f.

The const. changes as f and g change and has a range over all allowed values of
the function.
I am currently using the WEW algorithm, which I have seen before but don't
understand as I just have the code and not the reasoning. It's fast, but I
want to rewrite it in assembler to use the 80287 more.

I hope that's enough info for all those who asked.  Thanks again for your 
answers, they were most encouraging.

Daffy.

PS. All those who suggested a table, Perhaps now you see why I hadn't used that
one before!  Also Newton-Raphson was a strong contender, but I'll stick to WEW. 

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