Fitotron

Fitotron provides ordinary least squares for 2D data with a simple interface. It uses by default a Nelder-Mead method (or a Brent method, in univariate fits) to find the optimum parameters of the fit, thanks to the Optim library.

It can rescale the parameter uncertainties using the minimum value of the sum of residuals function; this is the default behaviour when y errors are not provided, although it can be disabled.

Usage

In a REPL, type:

using Fitotron

N = 50
x = linspace(0,2π,N)
y = sin(x) + 0.5randn(N)

fun(x,p) = p[1] + p[2]*x
model = CustomModel(fun,2,x,y)
fit = fitmodel(model)

p = plotfit(fit)
c = plotcost(fit)

p,c will be two Gadfly.Plot like the following:

And a fit a FitResult that shows like

Fit results:
───────────────────────────────────────────────────────────────
Param. 1:                       +1.14e+00 ± 1.86e-01 (16.3%)
Param. 2:                       -3.49e-01 ± 5.11e-02 (14.6%)
Reduced χ²                      0.4467
Errors were rescaled so χ²=d.o.f.

in the REPL. A fit to a sine would be better, indeed:

sine(x,p) = p[1] + p[2]*sin(p[3]*x+p[4])
model = CustomModel(sine,4,x,y)
fit = fitmodel(model)

p = plotfit(fit)

Which gives:

Fit results:
───────────────────────────────────────────────────────────────
Param. 1:                       +4.48e-02 ± 7.30e-02 (163.0%)
Param. 2:                       +1.07e+00 ± 1.04e-01 (9.8%)
Param. 3:                       +9.27e-01 ± 5.42e-02 (5.9%)
Param. 4:                       +2.11e-01 ± 1.96e-01 (92.8%)
Reduced χ²                      0.2645
Errors were rescaled so χ²=d.o.f.

and

TODO/Bugs:

Cost function plot

• It has two legends
• Works only for functions of 2 parameters, it should let the user choose which dimensions should it choose for models of higher dimensionality and be a 1D plot for 1D models.

Linear models

• Uncertainties are way smaller than the CustomModel ones. Is that the expected behaivour?

Ideas

• Add x error capabilities, via Orear's method of effective variances.