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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.


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,"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]