Name

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ROBUST_POLY_FIT

Purpose

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An outlier-resistant polynomial fit.

Calling Sequence

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COEFF = ROBUST_POLY_FIT(X,Y,NDEGREE ,[ YFIT,SIG, /DOULBE, NUMIT=] )

Inputs

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X = Independent variable vector, floating-point or double-precision
Y = Dependent variable vector
      NDEGREE - integer giving degree of polynomial to fit, maximum = 6

Outputs

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Function result = coefficient vector, length NDEGREE+1.
IF COEFF=0.0, NO FIT! If N_ELEMENTS(COEFF) > degree+1, the fit is poor
(in this case the last element of COEFF=0.)
Either floating point or double precision.

Optional Output Parameters

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YFIT = Vector of calculated y's
SIG = the "standard deviation" of the residuals

Optional Input Keyword

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      /DOUBLE - If set, then force all computations to double precision.
      NUMIT - Maximum number of iterations to perform, default = 25

Restrictions

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Large values of NDEGREE should be avoided. This routine works best
when the number of points >> NDEGREE.

Procedure

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For the initial estimate, the data is sorted by X and broken into
NDEGREE+2 sets. The X,Y medians of each set are fitted to a polynomial
via POLY_FIT. Bisquare ("Tukey's Biweight") weights are then
calculated, using a limit of 6 outlier-resistant standard deviations.
The fit is repeated iteratively until the robust standard deviation of
the residuals changes by less than .03xSQRT(.5/(N-1)).

Procedures Called

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        POLY(), POLY_FIT()
      ROB_CHECKFIT()

Revision History

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Written, H. Freudenreich, STX, 8/90. Revised 4/91.
2/94 -- changed convergence criterion
        Added /DOUBLE keyword, remove POLYFITW call W. Landsman Jan 2009