Function parametrization: Difference between revisions

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== Method ==
== Method ==
                                                                               
The method of function parameterization (FP) consists of the                   
numerical determination,                                                       
by statistical regression on a database of                                     
simulated states, of  simple functional representations of                     
parameters characterizing the state of a particular physical                 
system, where                                                                 
the arguments of the functions are statistically independent                   
combinations of diagnostic raw measurements                                   
of the system whose geometry is                                               
fixed.  The technique,  developed by H. Wind                                   
for the purpose of momentum determination from spark chamber data             
<ref>    Wind, H.,                                                               
    `Function Parametrization'                                               
in ``Proceedings of the 1972 CERN Computing and Data Processing School'',     
CERN 72--21, 1972, pp.~53--106.} </ref> , <ref>Wind, H.,                                                               
(a)`Principal component analysis and its application to track           
finding',  (b) `interpolation and function representation'                 
in ``Formulae and Methods in Experimental Data Evaluation'',                   
Vol.~3, European Physical Society, Geneva, 1984</ref>,
was                                             
introduced by B. Braams to plasma physics, where its  first                   
application (to the analysis of equilibrium magnetic                           
measurements on ASDEX) together with an admirably succinct                     
mathematical description, appeared in ref. <ref>B.J. Braams, W. Jilge, and K. Lackner, ''Fast determination of plasma parameters through function parametrization'', Nucl. Fusion '''26''' (1986) 699</ref>.


The application of the technique requires that a model exists to compute the response of the measurements (''q'') to variations of the system parameters (''p''), i.e. the mapping ''q = M(p)'' is known.
The application of the technique requires that a model exists to compute the response of the measurements (''q'') to variations of the system parameters (''p''), i.e. the mapping ''q = M(p)'' is known.
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