float MF_multiNonlinfitwW( fVector A, fMatrix Covar, iVector AStatus, unsigned npars,
    MF_EXPERIMENT *ListOfExperiments, unsigned nexperiments,
    void (*modelfunc)(fMatrix ZModel, ui htZ, ui lenZ, fVector X, fVector Y, unsigned iexperiment ),
    void (*derivatives)(fMatrix dZdAi, ui htZ, ui lenZ, fVector X, fVector Y, unsigned ipar, unsigned iexperiment),
    VF_NONLINFITOPTIONS *FitOpts,
    MF_NONLINFITWORKSPACE *WorkSpace );

float MF_multiNonlinfitwW( fVector A, fMatrix Covar, iVector AStatus, unsigned npars,
    MF_EXPERIMENT *ListOfExperiments, unsigned nexperiments,
    void (*modelfunc)(fMatrix ZModel, ui htZ, ui lenZ, fVector X, fVector Y, unsigned iexperiment ),
    void (*derivatives)(fMatrix dZdAi, ui htZ, ui lenZ, fVector X, fVector Y, unsigned ipar, unsigned iexperiment) );

function MF_multiNonlinfitwW( A: fVector; Covar: fMatrix; AStatus: iVector; nParameters: UInt;
    ListOfExperiments: PMF_EXPERIMENT; nexperiments: UInt;
    ModelFunc, Derivatives: Pointer;
    FitOpts: PVF_NONLINFITOPTIONS; WorkSpace: PMF_NONLINFITWORKSPACE ): Single;

function MF_multiNonlinfitwW( A: fVector; Covar: fMatrix; AStatus: iVector; nParameters: UInt;
    ListOfExperiments: PMF_EXPERIMENT; nexperiments: UInt;
    ModelFunc, Derivatives: Pointer ): Single;

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
ListOfExperiments	input data, see chap. 13.4
nexperiments	number of data sets in ListOfExperiments
modelfunc	user-defined model function
derivatives	user-defined function, calculating the partial derivatives with respect to all parameters
FitOpts	pointer to a structure containing options, see chap. 13.3
WorkSpace	pointer to a structure holding internal variables, see chap. 13.3

 
The model function (and, consequently, the vector A as well) may actually contain more parameters than you wish to treat as adjustable. This is why you have to provide an additional 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). All parameters must be initialized in A prior to calling MF_multiNonlinfit. The better your initial guess of the parameters, the faster MF_multiNonlinfit shall converge. The argument npars denotes the total number of parameters in A (not only the free parameters!).

The input data must be combined into sets of the type MF_EXPERIMENT. Let us assume you have two sets of X-Y-Z data, each with the vectors X and Y for the independent variables, the matrix MZ for the z=f(x,y) values and, for MF_multiLinfitwW, the weights of all points in MInvVar. The matrix dimensions are htZ (equal to sizeY) and lenZ (equal to sizeX). Now you have to construct a list of experiments as in the following example:

The argument iexperiment with which MyFunc shall be called by MF_multiNonlinfit allows to distinguish between parameters that are common to all experiments and others that belong to individual experiments. For example, each experiment's MZ values might be scaled by an individual constant C. In this case, A has to contain as many scales C as there are experiments. In MyFunc, you would have to code this as something like:
  if( iexperiment == 0 ) MZ[i][j] *= A[5];  else MZ[i][j] *= A[6];

In addition to the model function, MF_multiNonlinfit needs the partial derivatives of MZ with respect to all parameters A[ipar], according to your model. If you know them analytically, you should write a function MyDerivs. If you happen to know only some, but not all of the partial derivatives, you may rely on MF_multiNonlinfit_autoDeriv to calculate the unknown derivatives numerically.

void _cdecl MyDerivs( fMatrix dZdAi, ui htZ, ui lenZ, fVector X, fVector Y, unsigned ipar, unsigned iexperiment )
{
  ui i;
  switch( ipar )
  {
    case 0:
    for(i=0; i<htZ; i++ )
      for( j=0; j<lenZ; j++ )
        dZdAi[i][j] = part_derv_MZ_w_resp_to_A₀( X[j], Y[i] );
    break;
    case 1:
    for(i=0; i<htZ; i++ )
      for( j=0; j<lenZ; j++ )
        dZdAi[i][j] = part_derv_MZ_w_resp_to_A₁( X[j], Y[i] );
    break;
    default: /* for all derivatives we don't know: */
      MF_multiNonlinfit_autoDeriv( dZdAi, htZ, lenZ, X, Y, ipar, iexperiment, &WorkSpace );
  }
}
Again, the argument iexperiment allows you to treat "private" parameters of the individual experiments differently from the shared parameters.
A call to MF_multiNonlinfit will look like:
MF_multiNonlinfit( A, AStatus, npars, ExpList, 2, MyFunc, MyDerivs, &FitOpts, &WorkSpace );
or, with simplified syntax:
MF_multiNonlinfit( A, AStatus, npars, ExpList, 2, MyFunc, MyDerivs );
In case you do not know any of the partial derivatives, do not define MyDerivs, but call MF_multiNonlinfit with derivatives = NULL:
MF_multiNonlinfit( A, AStatus, npars, ExpList, 2, MyFunc, NULL );
 

The argument iexperiment with which MyFunc shall be called by MF_multiNonlinfit allows to distinguish between parameters that are common to all experiments and others that belong to individual experiments. For example, each experiment's MZ values might be scaled by an individual constant C. In this case, A has to contain as many scales C as there are experiments. In MyFunc, you would have to code this as something like:
  if iexperiment = 0 then
         MF_Pelement(MZ, htZ, lenZ, i, j)^ :=
         MF_element(MZ, htZ, lenZ, i, j) * VF_element(A,5)
  else MF_Pelement(MZ, htZ, lenZ, i, j)^ :=
         MF_element(MZ, htZ, lenZ, i, j) * VF_element(A,6);

In addition to the model function, MF_multiNonlinfit needs the partial derivatives of MZ with respect to all parameters A[ipar], according to your model. If you know them analytically, you should write a function MyDerivs. If you happen to know only some, but not all of the partial derivatives, you may rely on MF_multiNonlinfit_autoDeriv to calculate the unknown derivatives numerically.

procedure MyDerivs( dZdAi:fMatrix; htZ, lenZ:UIntSize; X, Y:fVector; ipar, iexperiment:UInt );
var i, j:UIntSize;
begin
  case ipar of
    0: begin
      for i:=0 to htZ-1 do
        for j:=0 to lenZ-1 do
          MF_Pelement( dZdAi, htZ, lenZ, i, j )^ :=
          part_derv_MZ_w_resp_to_A₀(VF_element( X, j ), VF_element( Y, i ));
       end;
    1: begin
      for i:=0 to htZ-1 do
        for j:=0 to lenZ-1 do
          MF_Pelement( dZdAi, htZ, lenZ, i, j )^ :=
          part_derv_MZ_w_resp_to_A₁(VF_element( X, j ), VF_element( Y, i ));
       end;
  else (* for all derivatives we don't know: *)
    MF_multiNonlinfit_autoDeriv( dZdAi, htZ, lenZ, X, Y, ipar, @WorkSpace );
  end;
end;
Again, the argument iexperiment allows you to treat "private" parameters of the individual experiments differently from the shared parameters.
A call to MF_multiNonlinfit will look like:
MF_multiNonlinfit( A, AStatus, npars, @ExpList, 2, @MyFunc, @MyDerivs, @FitOpts, @WorkSpace );
or, in simplified syntax,
MF_multiNonlinfit( A, AStatus, npars, @ExpList, 2, @MyFunc, @MyDerivs );
Note the address-of operator in front of "ExpList", "MyFunc.", and "MyDerivs". In case you do not know any of the partial derivatives, do not define MyDerivs, but call MF_multiNonlinfit with derivatives = nil:
MF_multiNonlinfit( A, AStatus, npars, @ExpList, 2, @MyFunc, nil );

In the weighted variant, MF_multiNonlinfitwW, the matrix ExpList[i].MInvVar of each experiment has to contain the inverse of the variances of the individual X-Y-Z data points, and the matrix MCovar will be filled with the covariances of the parameters a_i on output: MCovar_i,j = covariance( a_i, a_j ).
 

These functions may not be called while the FPU is set to reduced accuracy, or else they might hang in an infinite loop. See V_setFPAccuracy.