Weighted orthogonal least squares without constant term

Question

This post Estimate error on slope of linear regression given data with associated uncertainty gives the function for the linear regression in the case where both x- and y- data are affected by errors.

I wonder if someone known/has a function that does the same but for the case of no-constant term (similar to the option IncludeConstantBasis -> False in LinearModelFit).

Thanks.

Edit: Random Data Sample

SeedRandom[1]
n = 10;
x = Range[n];
y = x + 0.1 RandomVariate[NormalDistribution[], n];
data = {x, y}\[Transpose]
ex = Abs[0.03*RandomVariate[NormalDistribution[], n]];
ey = Abs[0.1 RandomVariate[NormalDistribution[], n]];
err = {ex, ey}\[Transpose]

Answer 1

Well, I've used a trick by performing the fit over the original data extended to included the reflected data about the constrained point. This is the code using the original solution posted by JM, with the trick for constraining the fit passing through (0,0).

n = 20;
\[Alpha] = 2;
x = N[Range[n]];
y = \[Alpha]*x + 5 RandomVariate[NormalDistribution[], n];
ex = Abs[RandomVariate[NormalDistribution[], n]];
ey = Abs[RandomVariate[NormalDistribution[], n]];
data = {Flatten@{x, -x}, Flatten@{y, -y}}\[Transpose];
err = {Flatten@{ex, ex}, Flatten@{ey, ey}}\[Transpose];
{lin, {sm, sk}} = ortlinfit[data, err]
Show[
 ListPlot[data],
 Plot[lin[x], {x, 0, n}, PlotStyle -> Black],     
 Graphics[MapThread[Circle, {data, err}]],
 PlotRange -> {{0, n}, {0, \[Alpha] n}}, Frame -> True, 
 PlotRangePadding -> 0, Axes -> None
 ]