Function parametrization: Difference between revisions

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The method of function parameterization (FP) consists of the numerical determination, by statistical regression on a database of simulated states, of  simple functional representations  
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
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'
the system whose geometry is fixed.  The technique,  developed by H. Wind for the purpose of momentum determination from spark chamber data
in ``Proceedings of the 1972 CERN Computing and Data Processing School'', CERN 72--21, 1972, pp.~53--106.} </ref> , <ref>Wind, H.,  
<ref>    Wind, H.,                                                                
(a)`Principal component analysis and its application to track finding',  (b) `interpolation and function representation'
    `Function Parametrization'                                                
in ``Formulae and Methods in Experimental Data Evaluation'',Vol. 3, European Physical Society, Geneva, 1984</ref>, was introduced by B. Braams to plasma physics,  
in ``Proceedings of the 1972 CERN Computing and Data Processing School'',      
where its  first application (to the analysis of equilibrium magnetic measurements on ASDEX) together with a succinct mathematical description, appeared in ref. <sup>[1]</sup>.  
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 a succinct mathematical description, appeared in ref. <sup>[1]</sup>.  


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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