GModelFit is a general purpose, data-driven model fitting framework for Julia.
Install with:
]add GModelFitusing GModelFit
# Prepare vectors with domain points, empirical measures and uncertainties
x = [0.1, 1.1, 2.1, 3.1, 4.1]
meas = [6.29, 7.27, 10.41, 18.67, 25.3]
unc = [1.1, 1.1, 1.1, 1.2, 1.2]
dom = Domain(x)
data = Measures(dom, meas, unc)
# Create a model using an explicit mathematical expression, and provide the
# initial guess values:
model = Model(dom, @λ (x, a2=1, a1=1, a0=5) -> (a2 .* x.^2 .+ a1 .* x .+ a0))
# Fit model to the data
best, res = fit(model, data)The output is as follows:
(Components:
╭───────────┬────────────┬─────────────┬───────────┬───────────┬───────────┬─────────╮
│ Component │ Type │ Eval. count │ Min │ Max │ Mean │ NaN/Inf │
├───────────┼────────────┼─────────────┼───────────┼───────────┼───────────┼─────────┤
│ main │ GModelFit.FComp │ 76 │ 6.088 │ 25.84 │ 13.56 │ 0 │
╰───────────┴────────────┴─────────────┴───────────┴───────────┴───────────┴─────────╯
Parameters:
╭───────────┬────────┬───────┬───────────┬───────────┬────────┬───────╮
│ Component │ Param. │ Range │ Value │ Uncert. │ Actual │ Patch │
├───────────┼────────┼───────┼───────────┼───────────┼────────┼───────┤
│ main │ a2 │ │ 1.201 │ 0.3051 │ │ │
│ │ a1 │ │ -0.106 │ 1.317 │ │ │
│ │ a0 │ │ 6.087 │ 1.142 │ │ │
╰───────────┴────────┴───────┴───────────┴───────────┴────────┴───────╯
, Fit results:
#Data : 5 Red. fit stat.: 1.0129 (DOF: 2)
#Free : 3 Elapsed time : 0.004
Status: OK