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?

Answer 1

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)