Dear Richard,

It is funny. I have to perform the approach of sediment fingerprinting for
my master thesis. Mr. Hasselman gave me the advice to take a closer look
into the limSolve package a few days ago. 
http://cran.r-project.org/web/packages/limSolve/index.html

I guess, the lsei-function of this package is exactly what  you and i are
looking for. I have tried it out today and compared the lsei-results with
the results of the MS-Excel solver. They are the same!
You will find in the manual (Chemtax example), how to define the
constraints, that every unknown is >= 0 and the sum of unknowns is always 1.
http://cran.r-project.org/web/packages/limSolve/limSolve.pdf

Try to get familiar with the lsei-function and if you still need help, i can
send you my code.

Bearing the Monte-Carlo simulation in mind, the package could offer some
nice functions too.

Have a nice day and best regards
Thomas



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