gnuplot: Plot and fit 2d function with two variables

Question

Is its possible in gnuplot to plot and fit a function that has two variables? For example, a physical function that depends on hight h and Temperature T where the T dependence should only be calculated but not plotted (for f, h and T experimental data exists):

f(h,T) = a * h * (1 + alpha * T) + f0

where a and f0 are to be determined by the fit, alpha is known. In the end I need a plot with f on the y-axis and h on the x-axis. The whole T dependence should be taken care of in the fit, but I don't need it displayed with splot.

The following is what I tried and failed. I assume because one can't set two dummy variables:

set term png;
set output 'test.png';
set dummy h;
set dummy T;
f(h,T) = a * h * (1 + alpha * T) + f0;
fit f(h,T) 'data.txt' using 2:4:1 via a, f0;
plot f(h,T);

gives undefined variable: h. Any ideas?

have you tried removing the set dummy stuff and just do fit f(x,y) 'data.txt' using 2:4:1:(1) via a,f0? — mgilson
– mgilson, Commented Feb 6, 2013 at 16:49

mgilson · Accepted Answer · 2013-02-06 19:43:21Z

3

From examples in the documentation:

Examples:
       f(x) = a*x**2 + b*x + c
       g(x,y) = a*x**2 + b*y**2 + c*x*y
       FIT_LIMIT = 1e-6
       fit f(x) 'measured.dat' via 'start.par'
       fit f(x) 'measured.dat' using 3:($7-5) via 'start.par'
       fit f(x) './data/trash.dat' using 1:2:3 via a, b, c
       fit g(x,y) 'surface.dat' using 1:2:3:(1) via a, b, c

I would expect your script to work if you simply did:

set term png
set output 'test.png'
f(h,T) = a * h * (1 + alpha * T) + f0
fit f(x,y) 'data.txt' using 2:4:1:(1) via a, f0

set view 90,0  #possibly `set view 0,90` or `set view map`?
splot f(x,y)

edited Feb 6, 2013 at 19:43

answered Feb 6, 2013 at 16:51

mgilson

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9 Comments

Foo Bar Over a year ago

What does the ":(1)" mean in "using"?

mgilson Over a year ago

It's the weight that each point should be given (e.g. for error). see help fit in gnuplot. This weights each point the same.

Foo Bar Over a year ago

Ah, ok. But nevertheless. If I switch all to x and y and remove the dummy, it get the error line 5: undefined variable: y (line 5 is plot). Do I have to enable multi variable plots somewhere first? Fitting seems to works just fine (I get reasonable values), but plotting does not.

mgilson Over a year ago

@FooBar -- Sorry, I wasn't thinking. You're plotting a function of 2 variables, so you're going to need splot instead of plot. Then instead of x and y, the variables become u and v. I've updated so hopefully it'll work now.

Foo Bar Over a year ago

But splot plots a surface plot (3D), but I want to fit f(h,T), but plot only the projection on f(h) (2D). So the projection from the 3D vector (h, T, f(h,T)) on (h, 0, f(h,T)) -> (h, f(h,T)). Such that if I'd look at the 3D f(h,T) plot from the specific angle that shows only the f(h) part.

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