NAME: goodpoly PURPOSE: (one line) Robust fitting of a polynomial to data. DESCRIPTION: This is a multi-pass fitting routine that fits a fixed order polynomial to the input data. After each pass, the scatter of the fit relative to the fitted line is computed. Each point is examined to see if it falls beyond THRESH sigma from the line. If is does, it is removed from the data and the fit is tried again. This will make up to two attempts to remove bad data. CATEGORY: Function fitting CALLING SEQUENCE: coeff = goodpoly(x,y,order,thresh,yfit,newx,newy,newerr) INPUTS: x - Input dataset, independant values. y - Input dataset, dependant values. order - Order of the polynomial fit (linear = 1). thresh - Sigma threshold for removing outliers. OPTIONAL INPUT PARAMETERS: KEYWORD INPUT PARAMETERS: BAD - Vector of flags, same length as x and y, that indicate bad values in the y vector. The default is that all points are considered good at the stars. If supplied, any additional bad values found will be marked as bad in this vector upon output. Also, any NaN values found in either the x or y vector will be trimmed from the data (and marked bad) prior to any processing. EXCLUDE - Number of points to exclude from initial pass fit. This number is rounded up to the next even number. Then EXCLUDE/2 of the highest and lowest points are removed before the first fit. If these numbers are reasonable, they will not be excluded in the second pass. This helps prevent biasing the first fit with the worst points in the array. Default is to not exclude any points on the first pass. MAX_VALUE - The maximum value to be fitted. If this keyword is provided, data values greater than MAX_VALUE are treated as missing and are not used in the fit at any pass. MIN_VALUE - The minimum value to be fitted. If this keyword is provided, data values greater than MIN_VALUE are treated as missing and are not used in the fit at any pass. YERR - Uncertainties on the y values. Default=no weighting. The point-to-point scatter from the fit is still used for the threshold. After all editing is done on this basis, a last poly_fit is run using the errors on the surviving points to do a final weighted fit. This is not a perfect solution to this desired feature but it's reasonably close. The down side is that large error points are more likely to be removed than would be truly justified. OUTPUTS: yfit - Fitted values for y that match the input vector. newx - X values from input that were considered good. newy - Y values from input that were considered good. newerr - uncertainties from input that were considered good. Return value is the set of polynomial coefficients. KEYWORD OUTPUT PARAMETERS: COEFFSIG - Uncertainty on the final returned coefficients SIGMA - Standard deviation of difference between good points and the fitted curve. COMMON BLOCKS: SIDE EFFECTS: RESTRICTIONS: PROCEDURE: MODifICATION HISTORY: Written 1991 Feb., Marc W. Buie, Lowell Observatory 93/11/12, MWB, Program fixed to return a computed y for all input x. 95/09/20, MWB, Added EXCLUDE keyword. 98/02/09, MWB, Added SIGMA keyword. 98/06/08, MWB, Added MIN/MAX_VALUE keywords. 98/08/12, MWB, Revamped some logic plus added direct support for badflags. The new version is probably a tad faster and more robust than the old version. 2009/10/02, MWB, removed obsolete Poly_fit arguments 2010/04/29, MWB, added a trimrank call on the return value 2011/04/29, MWB, added COEFFSIG keyword 2013/07/19, MWB, added YERR keyword and newerr argument 2013/11/21, MWB, the previous modification to add YERR had some really bad logic. This has been fixed now but please read the documentation carefully to understand what it really does.