Overload List
Overload 1: function NLinRegress(const X: TVec; const Y: TVec; RegFun: TRegressFun; DeriveProc: TDeriveProc; const B: TVec; Method: TOptMethod; out StopReason: TOptStopReason; const Weights: TVec; const YCalc: TVec; SoftSearch: Boolean; MaxIter: Integer; Tol: Double; GradTol: Double; const Verbose: TStrings): Integer;
General non-linear regression.
| # | Name | Description |
|---|---|---|
| 1 | X | Vector of the independent variable. |
| 2 | Y | Vector of dependent variable. |
| 3 | RegFun | Regression function. |
| 4 | DeriveProc | Procedure to calculate the derivatives of RegFun. You can define the exact derivative or use Regress.NumericDerive routine as numerical approximation. |
| 5 | B | Holds initial estimate for regression parameters. After the call to NLinRegress b returns calculated regression parameters. |
| 6 | Method | Defines which optimization method will be used to find regression parameters (see MtxVec.hlp TOptMethod type to learn more about this). |
| 7 | StopReason | Returns why regression parameters search stopped (see MtxVec.hlp TOptStopReason type to learn more about different stop reasons). |
| 8 | Weights | Weights (optional). |
| 9 | YCalc | Returns calculated values (optional). |
| 10 | SoftSearch | If true, internal line search algoritm will use soft line search method. Set this parameter to true if you're using numerical approximation for derivative. If this parameter is set to false, internal line search algorithm will use exact line search method. Set this parameter to false if you're using *exact* derivative. |
| 11 | MaxIter | Maximum allowed numer of allowed iterations. |
| 12 | Tol | Desired regression parameters tolerance. |
| 13 | GradTol | Minimum allowed gradient C-Norm. |
| 14 | Verbose | If assigned, stores Fun, evaluated at each iteration step. Optionally, you can also pass TOptControl object to the Verbose parameter. This allows the optimization procedure to be interrupted from another thread and optionally also allows logging and iteration count monitoring. |
Returns: Int32 - Number of iterations needed to calculate regression parameters with specified tolerance.
Remarks:
The routine fits equations to data by minimizing the sum of squared residuals :
SS = Sum [y(k) - ycalc(k)]^2 ,
where y(k) and ycalc(k) are respectively the observed and calculated value of the dependent variable for observation k. ycalc(k) is a function of the regression parameters b(0), b(1) ... Here the observed values obey the following (non-linear) equation:
y(k) = RegFun[x(k), b(0), b(1), ... ]
Y = RegFun[X,b(0),b(1), ...]
where RegFun is the regression function and b(0),..b(i) are the regression parameters.
Examples
Uses MtxExp, Math387, Regress, Optimization, MtxVecTee;
// function definition
function Eckerle4(const B: TVec; X: double): double;
begin
Eckerle4 := B[0]/B[1] * Exp(-0.5*Sqr((X-B[2])/B[1]));
end;
procedure Example;
var x,y,b,yhat: Vector;
StopReason: TOptStopReason;
begin
x.SetIt(false,[400.0, 405.0, 410.0, 415.0,
420.0, 425.0, 430.0, 435.0,
436.5, 438.0, 439.5, 441.0,
442.5, 444.0, 445.5, 447.0,
448.5, 450.0, 451.5, 453.0,
454.5, 456.0, 457.5, 459.0,
460.5, 462.0, 463.5, 465.0,
470.0, 475.0, 480.0, 485.0,
490.0, 495.0, 500.0]);
y.SetIt(false,[0.0001575, 0.0001699, 0.0002350, 0.0003102,
0.0004917, 0.0008710, 0.0017418, 0.0046400,
0.0065895, 0.0097302, 0.0149002, 0.0237310,
0.0401683, 0.0712559, 0.1264458, 0.2073413,
0.2902366, 0.3445623, 0.3698049, 0.3668534,
0.3106727, 0.2078154, 0.1164354, 0.0616764,
0.0337200, 0.0194023, 0.0117831, 0.0074357,
0.0022732, 0.0008800, 0.0004579, 0.0002345,
0.0001586, 0.0001143, 0.0000710]);
b.SetIt(false,[1.0, 10.0, 500.0]); // initial estimates
NLinRegress(x,y,Eckerle4,nil,b,optMarquardt, StopReason,
nil,yhat,false,300,1e-8,1e-10);
DrawValues(x,y,Series1,false); // draw data
DrawValues(x,yhat,Series2,false); // draw fitted values
end;See Also: Regress.NumericDerive
Overload 2: function NLinRegress(const X: TVec; const Y: TVec; RegFun: TRegressFun; DeriveProc: TDeriveProc; const B: TVec; const BLowerB: TVec; const BUpperB: TVec; Method: TOptMethod; out StopReason: TOptStopReason; const Weights: TVec; const YCalc: TVec; SoftSearch: Boolean; MaxIter: Integer; Tol: Double; GradTol: Double; const Verbose: TStrings): Integer;
Non-linear regression with lower and upper bounds.
| # | Name | Description |
|---|---|---|
| 1 | X | Vector of the independent variable. |
| 2 | Y | Vector of the dependent variable. |
| 3 | RegFun | Regression function. |
| 4 | DeriveProc | Procedure to calculate the derivatives of RegFun. You can define the exact derivative or use Regress.NumericDerive routine as numerical approximation. |
| 5 | B | Holds initial estimate for regression parameters. After the call to NLinRegress b returns calculated regression parameters. |
| 6 | BLowerB | Holds lower bounds for regression parameters. If there are no lower bounds, set BLowerB values to -INF. |
| 7 | BUpperB | Holds upper bounds for regression parameters. If there are no upper bounds, set BUpperB values to +INF. |
| 8 | Method | Defines which optimization method will be used to find regression parameters (see MtxVec.hlp TOptMethod type to learn more about this). |
| 9 | StopReason | Returns why regression parameters search stopped (see MtxVec.hlp TOptStopReason type to learn more about different stop reasons). |
| 10 | Weights | Weights (optional). |
| 11 | YCalc | Returns calculated values (optional). |
| 12 | SoftSearch | If true, internal line search algoritm will use soft line search method. Set this parameter to true if you're using numerical approximation for derivative. If this parameter is set to false, internal line search algorithm will use exact line search method. Set this parameter to false if you're using *exact* derivative. |
| 13 | MaxIter | Maximum allowed numer of allowed iterations. |
| 14 | Tol | Desired regression parameters tolerance. |
| 15 | GradTol | Minimum allowed gradient C-Norm. |
| 16 | Verbose | If assigned, stores Fun, evaluated at each iteration step. Optionally, you can also pass TOptControl object to the Verbose parameter. This allows the optimization procedure to be interrupted from another thread and optionally also allows logging and iteration count monitoring. |
Returns: Int32 - Number of iterations needed to calculate regression parameters with specified tolerance.
Remarks:
General non-linear regression with lower and upper bounds for regression coefficients.
Examples
Uses MtxExp, Math387, Regress, Optimization, MtxVecTee;
// function definition
procedure Eckerle4(const B: TVec; const X: TVecList; const Y: TVec);
begin
//= B[0]/B[1] * Exp(-0.5*Sqr((X-B[2])/B[1]));
y.Normalize(X[0], B[2], B[1]);
y.Sqr;
y.Scale(-0.5);
y.Exp;
y.Scale(B[0]/B[1]);
end;
procedure Example;
var x0,y,b,yhat: Vector;
StopReason: TOptStopReason;
x: TVecList;
begin
x := TVecList.Create;
x.Add; //add
x[0].SetIt(false,[400.0, 405.0, 410.0, 415.0,
420.0, 425.0, 430.0, 435.0,
436.5, 438.0, 439.5, 441.0,
442.5, 444.0, 445.5, 447.0,
448.5, 450.0, 451.5, 453.0,
454.5, 456.0, 457.5, 459.0,
460.5, 462.0, 463.5, 465.0,
470.0, 475.0, 480.0, 485.0,
490.0, 495.0, 500.0]);
y.SetIt(false,[0.0001575, 0.0001699, 0.0002350, 0.0003102,
0.0004917, 0.0008710, 0.0017418, 0.0046400,
0.0065895, 0.0097302, 0.0149002, 0.0237310,
0.0401683, 0.0712559, 0.1264458, 0.2073413,
0.2902366, 0.3445623, 0.3698049, 0.3668534,
0.3106727, 0.2078154, 0.1164354, 0.0616764,
0.0337200, 0.0194023, 0.0117831, 0.0074357,
0.0022732, 0.0008800, 0.0004579, 0.0002345,
0.0001586, 0.0001143, 0.0000710]);
b.SetIt(false,[1.0, 10.0, 500.0]); // initial estimates
NLinRegress(x,y,Eckerle4,nil,b,optMarquardt, StopReason,
nil,yhat,false,300,1e-8,1e-10);
DrawValues(x[0],y,Series1,false); // draw data
DrawValues(x[0],yhat,Series2,false); // draw fitted values
x.Free;
end;Overload 3: function NLinRegress(const X: TVecList; const Y: TVec; RegFun: TMultiRegressFun; DeriveProc: TMultiDeriveProc; const B: TVec; Method: TOptMethod; out StopReason: TOptStopReason; const Weights: TVec; const YCalc: TVec; SoftSearch: Boolean; MaxIter: Integer; Tol: Double; GradTol: Double; const Verbose: TStrings): Integer;
General vectorized non-linear regression.
| # | Name | Description |
|---|---|---|
| 1 | X | List of vectors of independent variable(s). |
| 2 | Y | Vector of the dependent variable. |
| 3 | RegFun | Regression function. |
| 4 | DeriveProc | Procedure to calculate the derivatives of RegFun. You can define the exact derivative or use Regress.MultiNumericDerive routine as numerical approximation. |
| 5 | B | Holds initial estimate for regression parameters. After the call to NLinRegress b returns calculated regression parameters. |
| 6 | Method | Defines which optimization method will be used to find regression parameters (see MtxVec.hlp TOptMethod type to learn more about this). |
| 7 | StopReason | Returns why regression parameters search stopped (see MtxVec.hlp TOptStopReason type to learn more about different stop reasons). |
| 8 | Weights | Weights of X values (optional). |
| 9 | YCalc | Returns calculated values (optional). |
| 10 | SoftSearch | If true, internal line search algoritm will use soft line search method. Set this parameter to true if you're using numerical approximation for derivative. If this parameter is set to false, internal line search algorithm will use exact line search method. Set this parameter to false if you're using *exact* derivative. |
| 11 | MaxIter | Maximum allowed numer of allowed iterations. |
| 12 | Tol | Desired regression parameters tolerance. |
| 13 | GradTol | Minimum allowed gradient C-Norm. |
| 14 | Verbose | If assigned, stores Fun, evaluated at each iteration step. Optionally, you can also pass TOptControl object to the Verbose parameter. This allows the optimization procedure to be interrupted from another thread and optionally also allows logging and iteration count monitoring. |
Returns: Int32 - Number of iterations needed to calculate regression parameters with specified tolerance.
Remarks:
The routine fits equations to data by minimizing the sum of squared residuals :
SS = Sum [y(k) - ycalc(k)]^2 ,
where y(k) and ycalc(k) are respectively the observed and calculated value of the dependent variable for observation k. ycalc(k) is a function of the regression parameters b(0), b(1) ... Here the observed values obey the following (non-linear) equation:
y(k) = RegFun[x(k), b(0), b(1), ... ]
Y = RegFun[X,b(0),b(1), ...]
where RegFun is the regression function and b(0),..b(i) are the regression parameters.
See Also: Regress.NumericDerive
Overload 4: function NLinRegress(const X: TVecList; const Y: TVec; RegFun: TMultiRegressFun; DeriveProc: TMultiDeriveProc; const B: TVec; const BLowerB: TVec; const BUpperB: TVec; Method: TOptMethod; out StopReason: TOptStopReason; const Weights: TVec; const YCalc: TVec; SoftSearch: Boolean; MaxIter: Integer; Tol: Double; GradTol: Double; const Verbose: TStrings): Integer;
Non-linear regression with lower and upper bounds.
| # | Name | Description |
|---|---|---|
| 1 | X | List of vectors of independent variable(s). |
| 2 | Y | Vector of dependent variable. |
| 3 | RegFun | Regression function. |
| 4 | DeriveProc | Procedure to calculate the derivatives of RegFun. You can define the exact derivative or use Regress.NumericDerive routine as numerical approximation. |
| 5 | B | Holds initial estimate for regression parameters. After the call to NLinRegress b returns calculated regression parameters. |
| 6 | BLowerB | Holds lower bounds for regression parameters. If there are no lower bounds, set BLowerB values to -INF. |
| 7 | BUpperB | Holds upper bounds for regression parameters. If there are no upper bounds, set BUpperB values to +INF. |
| 8 | Method | Defines which optimization method will be used to find regression parameters (see MtxVec.hlp TOptMethod type to learn more about this). |
| 9 | StopReason | Returns why regression parameters search stopped (see MtxVec.hlp TOptStopReason type to learn more about different stop reasons). |
| 10 | Weights | Weights (optional). |
| 11 | YCalc | Returns calculated values (optional). |
| 12 | SoftSearch | If true, internal line search algoritm will use soft line search method. Set this parameter to true if you're using numerical approximation for derivative. If this parameter is set to false, internal line search algorithm will use exact line search method. Set this parameter to false if you're using *exact* derivative. |
| 13 | MaxIter | Maximum allowed numer of allowed iterations. |
| 14 | Tol | Desired regression parameters tolerance. |
| 15 | GradTol | Minimum allowed gradient C-Norm. |
| 16 | Verbose | If assigned, stores Fun, evaluated at each iteration step. Optionally, you can also pass TOptControl object to the Verbose parameter. This allows the optimization procedure to be interrupted from another thread and optionally also allows logging and iteration count monitoring. |
Returns: Int32 - Number of iterations needed to calculate regression parameters with specified tolerance.
Remarks:
General non-linear regression with lower and upper bounds for regression coefficients.