I'm looking for an analog to Matlab's lsqnonlin function in Julia.
LsqFit.jl looks great, but doesn't accept the same arguments Matlab's implementation does; specifically:
where initial conditions, lower, and upper bounds are vectors of length 6.
Any advice would be awesome. Thanks!
Actually, it does, it's just not explained in the readme (for good measure, here is a stable link README.md).
It is unclear what you mean by initial conditions. If you mean initial parameters, this is very much possible.
using LsqFit
# a two-parameter exponential model
# x: array of independent variables
# p: array of model parameters
model(x, p) = p[1]*exp.(-x.*p[2])
# some example data
# xdata: independent variables
# ydata: dependent variable
xdata = linspace(0,10,20)
ydata = model(xdata, [1.0 2.0]) + 0.01*randn(length(xdata))
p0 = [0.5, 0.5]
fit = curve_fit(model, xdata, ydata, p0)
(taken from the manual). Here p0 is the initial parameter vector.
This will give you something very close to [1.0, 2.0]. But what if we want to constrain the parameter to be in [0,1]x[0,1]? Then we simply set the keyword arguments lower and upper to be vectors of lower and upper bounds
fit = curve_fit(model, xdata, ydata, p0; lower = zeros(2), upper = ones(2))
That should give something like [1.0, 1.0] depending on your exact data.