PS: The same indpendence from the y values is true for ANY least squares
fit, or even for the case of a completely determined system. The covariance
matrix for a system defined by
A x = y
is always independent of the y values. It simply measures the
appropriateness of a chosen set of basis functions, not how well they fit
the data... That goodness of fit is measured by the ChiSquare estimate!
- DM
Justin <justin_ashmall@hotmail.com> wrote in message
8EF66B4F8ltbyltbmltbouts@155.198.199.181">news:8EF66B4F8ltbyltbmltbouts@155.198.199.181...
> Greetings all,
> I came across what looks like a bug in SVDFIT. I submitted it to RSI a
week
> ago now but haven't heard back (except for a confirmation of receipt) and
> thought it might of interest to The Group. The bug appears to be in the
> errors given for the coefficients returned by SVDFIT. Below is the email I
> sent to RSI explaining the problem. I'm using IDL5.3 on an NT box.
>
> Justin
>
>
>
>
> I've used LINFIT to fit a straight line to some data, and done the same
> using SVDFIT (with M set to 2 for a linear fit). Whilst I get exactly the
> same coefficients returned from both routines, the standard deviations
> (errors) of the coefficients vary between routines. It looks to me that
> the SVDFIT errors are incorrect.
>
> Strangely it seems that the errors of the coefficients from SVDFIT do not
> depend on the y values. I've included a short prog to demonstrate the
> problem. The results it produces are shown below:
>
>
> IDL> lin_test
> Fitting y = a + bx
> Showing: a, b, a_err, b_err
>
> Fitting (x, y1):
> SVDFIT: -0.084282358 0.14992642 0.42803180 0.010803003
> LINFIT: -0.084282358 0.14992642 0.085521095 0.0021584486
> Fitting (x, y2)
> SVDFIT: 0.15193113 3.5026045 0.42803180 0.010803003
> LINFIT: 0.15193113 3.5026045 0.58222837 0.014694737
>
>
> You can see that the last two numbers (the errors) vary between LINFIT and
> SVDFIT. Notice also that the error values from SVDFIT are the same with
> two different sets of y values (but the same x values).
>
> From the documentation we see that the SIGMA keyword returns a "vector of
> standard deviations for the returned coefficients" with SVDFIT. With
> LINFIT the SIGMA keyword returns a "vector of probable uncertainties for
> the model parameters." Given this maybe we should not expect the values to
> be the same, however order of magnitude differences and the independece of
> the y values suggest something is amiss. Also, since both routines appear
> to use code lifted or translated from Numerical Recipes, we might expect
> the same values back.
>
>
> PRO lin_test
>
> ;Create some data
> x =DOUBLE([85, 76, 24, 21, 8.6, 5.7, 1.6, 1.2, 0.6 ])
> y1=DOUBLE([13, 11, 3.3, 3.0, 1.3, 0.8, 0.2, 0.1, 0.08])
> y2=DOUBLE([296, 268, 84, 76, 30, 19, 5.6, 4.3, 2.0 ])
>
> PRINT, "Fitting y = a + bx"
> PRINT, "Showing: a, b, a_err, b_err"
> PRINT
>
> PRINT,"Fitting (x, y1):"
> ;Make linear fit using SVDFIT, setting M = 2
> svd_vals1 = SVDFIT( x, y1, 2, /DOUBLE, SIGMA=svd_sig1)
> PRINT, "SVDFIT:", svd_vals1[0], svd_vals1[1], svd_sig1[0], svd_sig1[1]
>
> ;Fit same data using LINFIT
> lin_vals1 = LINFIT( x, y1, /DOUBLE, SIGMA=lin_sig1)
> PRINT, "LINFIT:", lin_vals1[0], lin_vals1[1], lin_sig1[0], lin_sig1[1]
>
>
> PRINT, "Fitting (x, y2)"
> ;SAme as above with y2 data
> svd_vals2 = SVDFIT( x, y2, 2, /DOUBLE, SIGMA=svd_sig2)
> PRINT, "SVDFIT:", svd_vals2[0], svd_vals2[1], svd_sig2[0], svd_sig2[1]
>
> ;Fit y2 data using LINFIT
> lin_vals2 = LINFIT( x, y2, /DOUBLE, SIGMA=lin_sig2)
> PRINT, "LINFIT:", lin_vals2[0], lin_vals2[1], lin_sig2[0], lin_sig2[1]
>
>
> END
>
>