MWE fitting a model with a known parameter

General Usage
15

As a simple MWE, the following synthax seems to work fine to fix the 3rd parameter of a LsqFit.jl model with 4 parameters:

using LsqFit
@. model(t, p) = p[1] + p[2]*sin(2π*p[3]*t)*exp(-t*p[4])

tdata = LinRange(0,4,1000)
ydata = model(tdata, [1.0 2.0 30.0 0.5]) + 0.01*randn(length(tdata))
lb = [0, 0.0, 0.0, 0.0]
ub = [Inf, Inf, Inf,Inf]
p0 = [1.2, 1.2, 27.0, 0.1]
fit_bounds = curve_fit(model, tdata, ydata, p0, lower=lb, upper=ub)
fit_bounds.param    # 1.0003, 2.0001, 30.000, 0.4996

# Fix 3rd parameter (which disappears from constraints):
lb = [0, 0.0, 0.0]
ub = [Inf, Inf, Inf]
p0 = [1.2, 1.2, 0.1]
modelfixparam3(t,p) = model(t, (p[1], p[2], 30.0, p[3]))
fit_bounds2 = curve_fit(modelfixparam3, tdata, ydata, p0, lower=lb, upper=ub)
fit_bounds2.param  # 1.0000, 2.0013, 0.5004
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