MF_multiNonlinfit MD_multiNonlinfit ME_multiNonlinfit
MF_multiNonlinfitwW MD_multiNonlinfitwW ME_multiNonlinfitwW
Functionfit multiple X-Y-Z data sets to a common model function, possibly non-linear in its parameters
Syntax C/C++#include <MFstd.h>
float MF_multiNonlinfit( fVector A, 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),
    VF_NONLINFITOPTIONS *FitOpts,
    MF_NONLINFITWORKSPACE *WorkSpace );

Syntax C/C++ simplified#include <MFstd.h>
float MF_multiNonlinfit( fVector A, 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) );

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) );

Pascal/Delphiuses MFmnlfit;
function MF_multiNonlinfit( A: fVector; 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;
    FitOpts: PVF_NONLINFITOPTIONS; WorkSpace: PMF_NONLINFITWORKSPACE ): Single;

Pascal/Delphi simplifieduses MFmnlfit;
function MF_multiNonlinfit( A: fVector; AStatus: iVector; nParameters: UInt;
    ListOfExperiments: PMF_EXPERIMENT; nexperiments: UInt;
    ModelFunc, Derivatives: Pointer ): Single;

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

DescriptionThe input data, contained in ListOfExperiments, are used to evaluate the parameter array A with npars elements ai of an arbitrary model function z = f(x, y).

Arguments:
Avector of size npars; returns the coefficients
Covarmatrix of dimensions [npars, npars]; returns the covariances of the coefficients
AStatusvector of size npars; decides which parameters are treated as free or as fixed
nparstotal number of parameters
ListOfExperimentsinput data, see chap. 13.4
nexperimentsnumber of data sets in ListOfExperiments
modelfuncuser-defined model function
derivativesuser-defined function, calculating the partial derivatives with respect to all parameters
FitOptspointer to a structure containing options, see chap. 13.3
WorkSpacepointer 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:

Constructing list of experiments in C/C++ MF_EXPERIMENT ExpList[2];
ExpList[0].X = X1;  ExpList[0].Y = Y1;  
ExpList[0].MZ = MZ1;
ExpList[0].htZ = htZ1;  ExpList[0].lenZ = lenZ1;
ExpList[1].X = X1;  ExpList[1].Y = Y2;  
ExpList[1].MZ = MZ2;
ExpList[1].htZ = htZ2;  ExpList[1].lenZ = lenZ2;
/* for the weighted variant, set additionally: */
ExpList[0].MInvVar = MInvVar1;  
ExpList[0].WeightOfExperiment = wt1;
ExpList[1].MInvVar = MInvVar2;  
ExpList[1].WeightOfExperiment = wt2;
 
Constructing list of experiments in Pascal/Delphi var ExpList: array[0..1] of MF_EXPERIMENT;
begin
  ...
  ExpList[0].X := X1;  ExpList[0].Y := Y1;  
  ExpList[0].MZ := MZ1;
  ExpList[0].htZ := htZ1;  ExpList[0].lenZ := lenZ1;
  ExpList[1].X := X2;  ExpList[1].Y := Y2;  
  ExpList[1].MZ := MZ2;
  ExpList[1].htZ := htZ2;  ExpList[1].lenZ := lenZ2;
    /* for the weighted variant, set additionally: */
  ExpList[0].MInvVar := MInvVar1;  
  ExpList[0].WeightOfExperiment := wt1;
  ExpList[1].MInvVar := MInvVar2;  
  ExpList[1].WeightOfExperiment := wt2;
  ...
end;

 

Both C/C++ and Pascal/Delphi You must provide a model function "modelfunc" which, for a given pair of X, Y vectors, must calculate the corresponding "theoretical" z-values. In C/C++, it has to be defined as
 
Model function for C/C++ void _cdecl MyFunc( fMatrix Z, ui htZ, ui lenZ, fVector X, fVector Y, unsigned iexperiment )
{
  for (ui i=0; i<htZ; i++ )
    for (ui j=0; j<lenZ; j++ )
      MZ[i][j] = f( X[j], Y[i] );
}
f( X[j], Y[i] )
is any arbitrary function, which may be as complicated as you like and your application needs. The only condition is that it have no singularities, at least within the parameter space specified by upper and lower boundaries (see NONLINFITOPTIONS).

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.

Partial derivatives coded for C/C++ MF_NONLINFITWORKSPACE WorkSpace; /* this should be a global variable, the same as passed to MF_multiNonlinfit */

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 );
 

Model function for Pascal/Delphi In Pascal/Delphi, the model function has to be defined as
procedure MyFunc( MZ:fMatrix; htZ, lenZ:UIntSize; X, Y:fVector; iexperiment:UInt );
var i, j:UIntSize;
begin
  for i:=0 to htZ-1 do
    for j:=0 to lenZ-1 do
      MF_Pelement( MZ, htZ, lenZ, i, j )^ :=
        f( VF_element( X, j ), VF_element( Y, i ) );
end;
f( Xj, Yi )
is any arbitrary function, which may be as complicated as you like and your application needs. The only condition is that it have no singularities, at least within the parameter space specified by upper and lower boundaries (see NONLINFITOPTIONS).

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.

Partial derivatives coded for Pascal/Delphi var WorkSpace: MF_NONLINFITWORKSPACE; (* this should be a global variable, the same as passed to MF_multiNonlinfit *)

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 ai on output: MCovari,j = covariance( ai, aj ).
 

Both C/C++ and Pascal/Delphi: For the many different options controlling nonlinear data-fitting functions, please consult chapter 13.3. Helper functions for breaking off excessively long fitting runs and for the monitoring of these often very time-consuming procedures are summarized in chapter 13.5 and, in the special case of MF_multiNonlinfit, described here.
Multi-threading restrictionsThe multi-threading restrictions, present in OptiVec versions up to and including 6.1, have been lifted with v6.2.

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.

Error handlingIf the number of free parameters (i.e., those with AStatus[i] = 1) exceeds the total number of data points, an error message "Invalid parameter(s)" is generated and the program aborted.
Return valuein case of success: goodness-of-fit parameter c2 (chi-square);
in case of failure: -1
See alsoVF_setNonlinfitOptions,   VF_multiNonlinfit,   MF_linfit,   chapter 13,  FITDEMO*.*

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