void VF_linfitwW( fVector A, fMatrix Covar, iVector AStatus, unsigned npars, fVector X, fVector Y, fVector InvVar, ui sizex,
void funcs(fVector BasFuncs, float x, unsigned nfuncs));

void vector<T>::linfitwW( matrix<T>* Covar, const vector<int>& AStatus, const vector<T>& X, const vector<T>& Y, const vector<T>& InvVar,
void funcs(fVector BasFuncs, float x, unsigned nfuncs));

procedure VF_linfitwW( A:fVector; Covar:fMatrix; AStatus:iVector; npars:UInt; X, Y, InvVar:fVector; sizex:UInt; funcs:Pointer );

Arguments:

A	vector of size npars; returns the coefficients
Covar	matrix of dimensions [npars, npars]; returns the covariances of the coefficients
AStatus	vector of size npars; decides which parameters are treated as free or as fixed
npars	total number of parameters
X, Y, InvVar	vectors of size sizex, holding the input data
funcs	user-defined model function

 
Your model function may actually contain more parameters than you wish to treat as adjustable. This is why you have to provide the vector AStatus, which contains the necessary information about which parameters are to be held fixed at their input values (AStatus[i] = 0) and which are free (AStatus[i] = 1). Any fixed parameters must be initialized in A prior to calling VF_linfit. npars denotes the total number of parameters in A (not only the free parameters!).

The model function funcs must calculate the individual f_i(x) for any argument x and store the f_i(x) in a vector BasFuncs of size npars. In C/C++, it has to be defined as
void MyFunc( fVector BasFuncs, float x, unsigned nfuncs)
{
  BasFuncs[0] = f0( x );
  BasFuncs[1] = f1( x);
  . . .
}
and shall be passed to VF_linfit by calling
VF_linfit( A, AStatus, npars, X, Y, sizex, MyFunc );
In Pascal/Delphi, the model function has to be defined as
procedure MyFunc( BasFuncs:fVector; x:Single; nfuncs:UInt );
begin
  VF_Pelement( BasFuncs, 0 )^ := f0( x );
  VF_Pelement( BasFuncs, 1 )^ := f1( x );
  . . .
end;
and shall be passed to VF_linfit by calling
VF_linfit( A, AStatus, npars, X, Y, sizex, @MyFunc );
Note the address-of operator in front of "MyFunc.". In Turbo Pascal, the model function must be compiled with the Force-Far-Calls option {$F+}.

The functions f0( x ) etc. must not contain the parameters a_i.
In the weighted variant, VF_linfitwW, the vector InvVar has to contain the inverse of the variances of the individual X-Y data points, and the matrix Covar will be filled with the covariances of the parameters a_i on output: MCovar_i,j = covariance( a_i, a_j ).

Internally, VF_linfit employs a Singular Value Decomposition algorithm to obtain a solution even for (near-)singular linear systems. Thereby, coefficients a_i whose significance is lower than a threshold, Thresh, are set to 0 instead of infinity. This threshold can be modified by calling VF_setLinfitNeglect. The current threshold can be retrieved by VF_getLinfitNeglect.