Re: [Gnuplot-info] fit by varying the data

[Hans-Bernhard B. <HBB...@t-...>]

Am 19.06.2019 um 00:36 schrieb Patrick Dupre:

> I do not have a 3D cloud of points, just 2 sets of points (same length) with the
> same x, 

Whether you admit it or not: that _is_ a cloud of points in 3D space.
It's just represented a bit disjointedly.

> I "just need" to minimize the sum  of the square between a given function
> and a set of data (which depend on 1 parameter).

And that's, again, where this fails to make sense.  If something depends
on a parameter, it's not a set of data --- it's a function of said
parameter, and the actual data.  Just like it's normal for the model
function of a fit.

Your linear combination of y1 and y2 is a projection of the (y1,y2)
plane onto a straight line rotated at angle \theta.  Then you compare
this projected value to a function depending on x.  In the end, this
means the function you need to minimize would actually be one of three
variables, something like

	projection(theta; y1, y2) - function(a, x0; x) = min!

or possibly

	projection^2(theta; y1, y2) - function^2(a, x0; x) = min!