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. | ||