TMtxMultiNonLinReg Class

type TMtxMultiNonLinReg = class(TMtxComponent);

Performs multiple-nonlinear regression.

How to use TMtxMultiNonLinReg component?
1. Drop a TMtxMultiNonLinReg component on the form. 2. Define TMtxMultiNonLinReg.X the vector of independent variables. 3. Define TMtxMultiNonLinReg.Y the vector of dependent variables. Make sure that X and Y have the same length. 4. Define initial estimates for TMtxMultiNonLinReg.B regression parameters. 5. (Optionaly) define TMtxMultiNonLinReg.Weights. If you'll use weights, set TMtxMultiNonLinReg.UseWeights property to true. 6. Define regression function. 7. (Optionally) define the derivative procedure. If you don't define derivative procedure then the numeric approximation will be used to calculate the derivative at specific point. 8. Define the optimization method. Depending on your function different methods will give better/worse results. 9. (Optionally) define desired tolerance for result. 10. Define the maximum number of steps for optimization method. Internal optimization method will stop when number of iterations exceeds MaxIter or internal minimum precision is within Tolerance. 11. Verbose property, if assigned, stores Fun, evaluated at each iteration step. Optionally, you can also assign TOptControl object to the Verbose property. This allows the optimization procedure to be interrupted from another thread and optionally also allows logging and iteration count monitoring.

Results:
1. TMtxMultiNonLinReg.B : Regression coefficients estimates. 2. TMtxMultiNonLinReg.YCalc : Fitted Y values.

The component internally performs vectorized optimization process. It can also be used to speed-up nonlinear regression with only one independent variable by 10-20x.

Examples

delphi

// regress function
procedure Rat43(const B: TVec; const X: TVecList; const y: TVec);
begin
    // Rat43 := B[0] / Power((1.0 + Exp(B[1]-B[2]*X)),1/B[3]);

    y.Mul(x[0], -B[2]);
    y.Add(B[1]);
    y.Exp();
    y.Add(1);
    y.Power(1/B[3]);
    y.DivideBy(B[0]);
end;

procedure TfrmNonLinTest.FormCreate(Sender: TObject);
var MtxNonLinReg: TMtxMultiNonLinReg;
begin
    MtxNonLinReg := TMtxMultiNonLinReg.Create;
    try
        // Load data - independent variable
        MtxNonLinReg.X.Add(); //add one variable
        MtxNonLinReg.X[0].SetIt(false,[9.000, 14.000, 21.000, 28.000,
        42.000, 57.000, 63.000, 70.000,
        79.000]);
        // Load data - dependent variable
        MtxNonLinReg.Y.SetIt(false,[8.930, 10.800, 18.590, 22.330,
        39.350, 56.110, 61.730, 64.620,
        67.080]);
        // Initial estimates for regression coefficients
        MtxNonLinReg.b.SetIt(false,[100,10,1,1]);
        // setup optimization parameters
        MtxNonLinReg.Tolerance := 1.0e-6; // 6 digits should do the trick
        MtxNonLinReg.GradTolerance := 1.0e-3 // 3 digits
        MtxNonLinReg.MaxIterations := 400;
        MtxNonLinReg.RegressFunction := Rat43; // regression function
        // Marquardt method
        MtxNonLinReg.OptMethod := optMarquardt;
        MtxNonLinReg.Recalc;
        // MtxNinLinReg.b now stores calculated regression parameter estimates
    finally
        MtxNonLinReg.Free;
    end;
end;

Properties

Name	Type	Description
AutoUpdate	Boolean	If true then changing any of the TMtxMultiNonLinReg properties will trigger the TMtxMultiNonLinReg.Recalc method.
B	TVec	Stores the regression coefficients.
BlockAssign	Boolean	Block streaming of specific properties when storing only a "template".
DeriveProcedure	TMultiDeriveProc	Defines derivatives of regression function.
Dirty	Boolean	When any of the TMtxNonLinReg properties changes, this property is automatically set to true.
EditorActive	Boolean	Returns True, if the component editor is displayed.
GradTolerance	Double	Defines minimal allowed gradient C-Norm.
MaxIteration	Integer	Defines one of the conditions for terminating the regression coefficient calculation.
OptMethod	TOptMethod	Optimization method used.
Reference	TReferenceList	Stores a list of components that have to be notified, when this component is destroyed.
RegressFunction	TMultiRegressFun	Defines the regression function of several regression parameters.
SoftSearch	Boolean	Defines line search algorithm for Quasi-Newton and Conjugate methods.
StopReason	TOptStopReason	Returns the reason why regression parameters calculation stopped.
Tolerance	Double	Defines one of the conditions for terminating the regression coefficient calculation.
UseWeights	Boolean	Weighted non-linear regression.
Verbose	TStrings	If not nil then the optimization method uses it for logging each optimization step.
Weights	TVec	Weights.
X	TVecList	Vector of independant variables.
Y	TVec	Vector of dependant variables.
YCalc	TVec	Vector of calculated values.

Methods

Name	Description
AllowStreaming	Returns the negatated value of BlockAssign.
Assign	Assign values of all published properties from Source.
AssignTemplate	Assign values of "template-like" published properties from Source.
EditorClass	To be overriden in descendanr classses.
LoadFromStream	Load the component from Src stream.
LoadTemplateFromFile	Load a template from file.
LoadTemplateFromStream	Load a template from stream.
Recalc	Triggers non-linear regression recalculation.
Reset	Reset is called after loading the data from stream or file.
SaveTemplateToFile	Save template to file.
SaveTemplateToStream	Save template to stream.
SaveToStream	Save the component to Dst stream.