Re: Singular matrix in Invert_RtR

Am 07.08.2007, 10:28 Uhr, schrieb Dan Hatton <vi5u0-gnuplot@xxxxxxxxxxx>:


Dear All,

With a particulalrly tricky fitting problem, I keep getting the error
message

Singular matrix in Invert_RtR

just after the fit converges.

The problem is that Gnuplot's fit uses a procedure known as Marquard-Levenberg algorithm, which is sometimes very ill-behaved. There is an alternative fitting algorithm, Simplex by Nelson & Mead, which is much more stable and can also minimise Chi^2 or the median of residuals in those cases where minimising the sum of squares is statistically inappropriate. Unfortunately, Simplex can not directly calculate the standard deviations for the parameters, that is probably the reason why many scientific fitting programs (like Gnuplot) do not use it.

Byte Magazine in 1985 had a nice paper on Simplex by Caceci & Cacheris together with an implementation of that algorithm.

Sometimes it is possible to use Marquard with the parameters estimated by Simplex in order to get the standard deviations of the params, but frequently one runs into either of two problems:
- the fit aborts with a singular matrix
- the sum of squares for the parameters calculated by Marquard is several times larger than that calculated by Simplex

The alternative is to bite the bullet and calculate standard deviations by bootstrapping, that is computationally expensive but after all we no longer use 8088 processors.
.

Relevant Pages

  • Re: Update Query; But keep rest of field...
    ... Left$ and Right$ act like a scissors, counting from left or right, and cutting the string at that point, returning just that portion of the string. ... Comparing "Fitting ABS" with Left$will tell you if the beginning matches the eleven characters in "Fitting ABS". ... Will take "Fit ABS", and add everything except the first eleven characters, of tblItem.to it. ... Using the Design View to create a query, ...
    (microsoft.public.access.queries)
  • Re: Update Query; But keep rest of field...
    ... Using the Design View to create a query, ... UPDATE tblItem SET tblItem.itemMfgItemNumber = "Fit ABS" ... The goal is to find all items that START with "Fitting ABS" and change them ... Fitting PVC Sch40 1" 90 ELL SxS ...
    (microsoft.public.access.queries)
  • Re: how can I alter the x-data of a cfit object after fitting?
    ... These three numbers correspond to the coefficients ... improve the quality of the fit. ... I am fitting histogram data with a Gaussian, ... calibration first and then feed the data to the fitting ...
    (comp.soft-sys.matlab)
  • Re: Fitting Nonlinear Complex Data(How do you do this?)
    ... Matlab documentation provides a 'curve fitting guide' where ... "For fitting curves in a case involving complex data set, ... I saw the help on how to fit nonlinear parameters I did not ...
    (comp.soft-sys.matlab)