How to add constraints to "Fitting unknown number of Gaussians to data"?

Question

This question of how to fit a sum Gaussians, where the number of Gaussians is to be determined, to data is answered nicely already by Fittting data with combination of an unknown number of Gaussians, but including constraints seems difficult. Here is an attempt:

g[x_, xo_, σ_, a_] := {a Exp[-((x - xo)^2/(2 σ^2))]/(σ Sqrt[2 π]), a > 0} 

When running the code at the link with this change get the following error:

NonlinearModelFit::eqineq: Constraints in {(a[1]>0)+(a[2]>0)} are not all equality or inequality constraints. With the exception of integer domain constraints for linear programming, domain constraints or constraints with Unequal (!=) are not supported.

How to add constraints?

Answer 1

This is how you can generate an expression with constraints in the appropriate form:

gmodel[n_Integer] := Module[{forms, cons},
  {forms, cons} = Transpose@Table[g[x, Sequence @@ kvar[i]], {i, 1, n}];
  {Total[forms], Sequence @@ cons}
  ]

gmodel[3]

This assumes that we're using the definition of g given in your question, and all the other definitions needed from the answer to the linked question by rhermans.

When I run this on his example, I get a warning message saying that AIC assumes an unconstrained model and the fitting doesn't seem to work. But that's another problem, this should solve the problem of how to provide constraints.