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Function Parametrization (FP) is a technique to provide fast (real-time) construction of system parameters from a set of diverse measurements.
Function Parametrization (FP) is a technique to provide fast (real-time) construction of system parameters from a set of diverse measurements. It consists of the numerical determination, by statistical regression on a database of simulated states, of  simple functional representations
<ref>B.J. Braams, W. Jilge, and K. Lackner, ''Fast determination of plasma parameters through function parametrization'', Nucl. Fusion '''26''' (1986) 699</ref>
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.
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 the circular cross-section ASDEX tokamak) together with a succinct mathematical description, appeared in
<ref>B.J. Braams, W. Jilge, and K. Lackner, ''Fast determination of plasma parameters through function parametrization'', Nucl. Fusion '''26''' (1986) 699</ref>.
 
 


== 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 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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