#378 Some polynomial fit equations produce incorrect an plot.

Defect
closed-fixed
nobody
None
9
2013-07-11
2013-05-19
David Benn
No

Compare the 7 degree polynomial fit of omi Cet data (see attached). The fit is fine but the equation is clearly wrong. Also, the zero point being subtracted from each time parameter is near the mid-point of the date range.

Compare this to the 23 degree polynomial fit of Kepler RR Lyr data, which is correct. The zero point being subtracted from each time parameter is near the start of the date range. The other major difference is that it is quite a short range compared to the omi Cet data; a short filtered single-cycle section was filtered for analysis. What would this look like if the whole FITS file's range was used?

4 Attachments

Discussion

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  • David Benn
    David Benn
    2013-05-19

     
  • David Benn
    David Benn
    2013-05-19

    • Description has changed:

    Diff:

    --- old
    +++ new
    @@ -1,3 +1,3 @@
     Compare the 7 degree polynomial fit of omi Cet data (see attached). The fit is fine but the equation is clearly wrong. Also, the zero point being subtracted from each time parameter is near the mid-point of the date range.
    
    -Compare this to the 23 degree polynomial fit of Kepler RR Lyr data, which looks fine. The zero point being subtracted from each time parameter is near the start of the date range. The other major difference is that it is quite a short range compared to the omi Cet data.
    +Compare this to the 23 degree polynomial fit of Kepler RR Lyr data, which is correct. The zero point being subtracted from each time parameter is near the start of the date range. The other major difference is that it is quite a short range compared to the omi Cet data; a short filtered single-cycle section was filtered for analysis. What would this look like if the whole FITS file's range was used?
    
    • Priority: 8 --> 9
     
  • David Benn
    David Benn
    2013-05-19

     
  • Doug Welch
    Doug Welch
    2013-05-19

    Comment: High-order polynomials produce very, very large (t-t0)**n terms. To produce precision, the best strategy is to always make t0 the mid-time of the series.

     
    • David Benn
      David Benn
      2013-05-23

      Doug, would you recommend the mid-point element, i.e. t[size(t)/2] or the mean time value, i.e. sum(t)/size(t)?

       
      • Doug Welch
        Doug Welch
        2013-05-23

        Hi David, I would recommend the mean time value. All coefficients will be determined with maximum possible precision in that case, since the largest abs(t-tmean) will be smaller that the largest abs(t - t[size(t)/2]).

         
        • David Benn
          David Benn
          2013-05-23

          Thanks Doug. That's what I was wondering too and it makes sense. I suppose that for some particular distributions of times, these values could be equivalent, but not in the general case.

           
          • Doug Welch
            Doug Welch
            2013-05-23

            Hi David - I expect that you are well aware of how to nest polynomial calculations to maintain precision since you are a skilled programmer.
            But if that doesn't sound familiar, let me know!

             
            • David Benn
              David Benn
              2013-05-24

              Hi Doug. If you're referring to Horner's method/scheme/rule, then yep. I can generate this form of the polynomial equation in the model dialog.

               
  • David Benn
    David Benn
    2013-05-23

    For various reasons, including the stability, and ability to determine derivatives and apply optimisation algorithms, the current TS based polyfit implementation will probably be replaced by the apache commons math implementation. This will also allow me to add extrema finding and goodness of fit functionality for EB and other analysis.

     
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