Multi-dataset fitting
GModelFit.jl is able to simultaneously fit several models against a corresponding number of datasets, while placing constraints among the models. Typical use cases are:
- a single phenomenon is observed with two (or more) instruments/detectors;
- a single phenomenon is observed at different times;
Fitting multiple datasets simultaneously may provide tighter constraints on the best fit parameters under the assumption that the models are somehow related, i.e. that their parameters are constrained (or patched).
To perform a multi-dataset fitting we should create one Model for each dataset in the usual way, collect them in a Vector{Model}, and define patch constraints among models. The following example shows how to fit two Gaussian curves under the hypotesis that the center and normalization parameters are the same:
using GModelFit
# Create individual models and the Vector{Model} container
model1 = Model(GModelFit.Gaussian(1, 0., 1.))
model2 = Model(GModelFit.Gaussian(1, 0., 1.))
multi = [model1, model2]
# Patch parameters
multi[2][:main].norm.mpatch = @fd m -> m[1][:main].norm
multi[2][:main].center.mpatch = @fd m -> m[1][:main].center
# Create datasets and fit
dom = Domain(-5.:5)
data1 = Measures(dom, [-0.006, 0.015, 0.001, 0.049, 0.198, 0.430, 0.226, 0.048, 0.017, -0.001, -0.006], 0.04)
data2 = Measures(dom, [-0.072, -0.033, -0.070, 0.108, 0.168, 0.765, 0.113, -0.054, 0.032, 0.013, 0.015], 0.04)
bestfit, stats = fit(multi, [data1, data2])(
============================== Model 1 ==============================
Components:
╭───────────┬─────────────┬───────┬─────────────┬───────────┬───────────┬───────────┬─────────╮
│ Component │ Type │ #Free │ Eval. count │ Min │ Max │ Mean │ NaN/Inf │
├───────────┼─────────────┼───────┼─────────────┼───────────┼───────────┼───────────┼─────────┤
│ main │ Gaussian_1D │ 3 │ 104 │ 1.965e-07 │ 0.4286 │ 0.09098 │ 0 │
╰───────────┴─────────────┴───────┴─────────────┴───────────┴───────────┴───────────┴─────────╯
Parameters:
╭───────────┬─────────────┬────────┬──────────┬───────────┬───────────┬────────┬───────╮
│ Component │ Type │ Param. │ Range │ Value │ Uncert. │ Actual │ Patch │
├───────────┼─────────────┼────────┼──────────┼───────────┼───────────┼────────┼───────┤
│ main │ Gaussian_1D │ norm │ 0:Inf │ 1.001 │ 0.05878 │ │ │
│ │ │ center │ -Inf:Inf │ -0.03039 │ 0.05462 │ │ │
│ │ │ sigma │ 0:Inf │ 0.931 │ 0.08751 │ │ │
╰───────────┴─────────────┴────────┴──────────┴───────────┴───────────┴────────┴───────╯
============================== Model 2 ==============================
Components:
╭───────────┬─────────────┬───────┬─────────────┬───────────┬───────────┬───────────┬─────────╮
│ Component │ Type │ #Free │ Eval. count │ Min │ Max │ Mean │ NaN/Inf │
├───────────┼─────────────┼───────┼─────────────┼───────────┼───────────┼───────────┼─────────┤
│ main │ Gaussian_1D │ 1 │ 105 │ 1.963e-20 │ 0.7525 │ 0.09168 │ 0 │
╰───────────┴─────────────┴───────┴─────────────┴───────────┴───────────┴───────────┴─────────╯
Parameters:
╭───────────┬─────────────┬────────┬──────────┬───────────┬───────────┬───────────┬───────────────────────────╮
│ Component │ Type │ Param. │ Range │ Value │ Uncert. │ Actual │ Patch │
├───────────┼─────────────┼────────┼──────────┼───────────┼───────────┼───────────┼───────────────────────────┤
│ main │ Gaussian_1D │ norm │ 0:Inf │ 1 │ (fixed) │ 1.001 │ m->((m[1])[:main]).norm │
│ │ │ center │ -Inf:Inf │ 0 │ (fixed) │ -0.03039 │ m->((m[1])[:main]).center │
│ │ │ sigma │ 0:Inf │ 0.5297 │ 0.03196 │ │ │
╰───────────┴─────────────┴────────┴──────────┴───────────┴───────────┴───────────┴───────────────────────────╯
, Fit results: #data: 22, #free pars: 4, red. fit stat.: 1.0839, Status: OK
)The best fit models and values are returned as a Vector{ModelSnapshot} in bestfit, i.e.:
println("Width of Gaussian 1: ", bestfit[1][:main].sigma.val, " ± ", bestfit[1][:main].sigma.unc)
println("Width of Gaussian 2: ", bestfit[2][:main].sigma.val, " ± ", bestfit[2][:main].sigma.unc)
println("Reduced χ^2: ", stats.fitstat)Width of Gaussian 1: 0.9310421973929704 ± 0.08750812769577807
Width of Gaussian 2: 0.5296953759086085 ± 0.031957107728184504
Reduced χ^2: 1.0839282826923964