(* ::Package:: *)

BeginPackage["extrapolation`"]


simul::usage = "simul[a0,b0,x,\[Sigma]] returns the object from the fit of a,b 
of expression a+bx to a simulated dataset with y=a0+b0+error, where error
is drawn accordign the normal distribution with standard deviation \[Sigma].
x is the independent data vector, hence it gives the number of data points to use."


value::usage = "value[fit,x] returns  a list with the interpolated value using the 
fitted parameters and the fit chi-square"


\[Sigma]value::usage = "\[Sigma]value[fit,x] gives the calculated standard deviation in
the value interpolated in point x."


Begin["Private`"]


simul[a0_,b0_,x_,\[Sigma]_]:=Module[{dado},\[Sigma]i=\[Sigma];
dado=Table[{x[[i]],RandomVariate[ NormalDistribution[a0+b0 x[[i]],\[Sigma]] ]},{i,Length[x]}];
LinearModelFit[dado,{z},z,Weights->1/ConstantArray[\[Sigma]^2,Length[x] ],VarianceEstimatorFunction->(1&) ]
]


value[fit_,x_]:=Module[{v,y},v={1,x};{fit[x],Total[(fit["FitResiduals"]/\[Sigma]i)^2]} ]


\[Sigma]value[fit_,x_]:=Module[{v,y},v={1,x};Sqrt[ v.fit["CovarianceMatrix"].v ] ]


End[]


EndPackage[]