[Gnuplot-bugs] fit.c duplicate extimation of error?

[Isao S. <sa...@bi...>]

Dear maintainers of gnuplot.

In fit.c: The covar matrix is calculated base on err_data if given by a 
user. Thus, scaling of parameter errors occurs twice and cancels out 
each other if err_data are explicitly given.

For example, if you fit the data,
# fit data (data.dat)
0	1.1	100
1	1.9	100
2	5.1	100
3	9.9	100
4	17.1	100
With the function f(x) = a * x**2 + b, results of fitting from "fit f(x)
 'data.dat' using 1:2 via a, b" and "fit f(x) 'data.dat' using 1:2:3 via
 a, b" are identical (except for sum of squares of residuals). However, 
"Asymptotic Standard Error" of parameters should increase as errors 
increase.

I think this bug can be resolved with a patch attached below.
I don't subscribe this mailing list. Please inform me if there is 
something with this patch.

Regards.
----
Isao Sakane <sa...@bi...>
Tottori University, Faculty of Engineering, Dept. of Biotechnology,
Koyamacyo-minami 4-101, Tottori-city, Tottori, Japan. ZIP:680-8552

----
Hear is a patch.
--- fit.c.old	2004-04-05 09:22:07.000000000 +0900
+++ fit.c	2004-04-05 12:09:29.000000000 +0900
@@ -745,7 +745,17 @@
 	covar = C + num_data;
 	Invert_RtR(C, covar, num_params);
 
-	/* calculate unscaled parameter errors in dpar[]: */
+	if (columns <= 2) {
+	    /* scale covar matrix based on chisq */
+	    chisq /= (num_data - num_params);
+	    for (i = 0; i < num_params; i++) {
+		/* only lower triangle needs to be handled */
+		for (j = 0; j <= i; j++)
+		    covar[i][j] *= chisq;
+	    }
+	}
+
+	/* calculate parameter errors in dpar[]: */
 	dpar = vec(num_params);
 	for (i = 0; i < num_params; i++) {
 	    /* FIXME: can this still happen ? */
@@ -761,11 +771,6 @@
 		covar[i][j] /= dpar[i] * dpar[j];
 	}
 
-	/* scale parameter errors based on chisq */
-	chisq = sqrt(chisq / (num_data - num_params));
-	for (i = 0; i < num_params; i++)
-	    dpar[i] *= chisq;
-
 	Dblf("Final set of parameters            Asymptotic Standard 
Error\n");
 	Dblf("=======================            =======================
===\n\n");