94 lines
3 KiB
Text
94 lines
3 KiB
Text
|
// This is an example of a non-linear least squares fit. The example
|
||
|
|
// is from "Nonlinear estimation" by Gavin Ross (Springer,1990), p 63.
|
||
|
|
// There are better ways of doing the fit in this case so this
|
||
|
|
// example is just an example.
|
||
|
|
|
||
|
|
// The model is E(y) = a + b exp(-kx) and there are 6 data points.
|
||
|
|
|
||
|
|
#define WANT_STREAM
|
||
|
|
#define WANT_MATH
|
||
|
|
#include "newmatnl.h"
|
||
|
|
#include "newmatio.h"
|
||
|
|
|
||
|
|
#ifdef use_namespace
|
||
|
|
using namespace RBD_LIBRARIES;
|
||
|
|
#endif
|
||
|
|
|
||
|
|
|
||
|
|
// first define the class describing the predictor function
|
||
|
|
|
||
|
|
class Model_3pe : public R1_Col_I_D
|
||
|
|
{
|
||
|
|
ColumnVector x_values; // the values of "x"
|
||
|
|
RowVector deriv; // values of derivatives
|
||
|
|
public:
|
||
|
|
Model_3pe(const ColumnVector& X_Values)
|
||
|
|
: x_values(X_Values) { deriv.ReSize(3); }
|
||
|
|
// load X data
|
||
|
|
Real operator()(int);
|
||
|
|
bool IsValid() { return para(3)>0; }
|
||
|
|
// require "k" > 0
|
||
|
|
ReturnMatrix Derivatives() { return deriv; }
|
||
|
|
};
|
||
|
|
|
||
|
|
Real Model_3pe::operator()(int i)
|
||
|
|
{
|
||
|
|
Real a = para(1); Real b = para(2); Real k = para(3);
|
||
|
|
Real xvi = x_values(i);
|
||
|
|
Real e = exp(-k * xvi);
|
||
|
|
deriv(1) = 1.0; // calculate derivatives
|
||
|
|
deriv(2) = e;
|
||
|
|
deriv(3) = - b * e * xvi;
|
||
|
|
return a + b * e; // function value
|
||
|
|
}
|
||
|
|
|
||
|
|
int main()
|
||
|
|
{
|
||
|
|
{
|
||
|
|
// Get the data
|
||
|
|
ColumnVector X(6);
|
||
|
|
ColumnVector Y(6);
|
||
|
|
X << 1 << 2 << 3 << 4 << 6 << 8;
|
||
|
|
Y << 3.2 << 7.9 << 11.1 << 14.5 << 16.7 << 18.3;
|
||
|
|
|
||
|
|
|
||
|
|
// Do the fit
|
||
|
|
Model_3pe model(X); // the model object
|
||
|
|
NonLinearLeastSquares NLLS(model); // the non-linear least squares
|
||
|
|
// object
|
||
|
|
ColumnVector Para(3); // for the parameters
|
||
|
|
Para << 9 << -6 << .5; // trial values of parameters
|
||
|
|
cout << "Fitting parameters\n";
|
||
|
|
NLLS.Fit(Y,Para); // do the fit
|
||
|
|
|
||
|
|
// Inspect the results
|
||
|
|
ColumnVector SE; // for the standard errors
|
||
|
|
NLLS.GetStandardErrors(SE);
|
||
|
|
cout << "\n\nEstimates and standard errors\n" <<
|
||
|
|
setw(10) << setprecision(2) << (Para | SE) << endl;
|
||
|
|
Real ResidualSD = sqrt(NLLS.ResidualVariance());
|
||
|
|
cout << "\nResidual s.d. = " << setw(10) << setprecision(2) <<
|
||
|
|
ResidualSD << endl;
|
||
|
|
SymmetricMatrix Correlations;
|
||
|
|
NLLS.GetCorrelations(Correlations);
|
||
|
|
cout << "\nCorrelationMatrix\n" <<
|
||
|
|
setw(10) << setprecision(2) << Correlations << endl;
|
||
|
|
ColumnVector Residuals;
|
||
|
|
NLLS.GetResiduals(Residuals);
|
||
|
|
DiagonalMatrix Hat;
|
||
|
|
NLLS.GetHatDiagonal(Hat);
|
||
|
|
cout << "\nX, Y, Residual, Hat\n" << setw(10) << setprecision(2) <<
|
||
|
|
(X | Y | Residuals | Hat.AsColumn()) << endl;
|
||
|
|
// recover var/cov matrix
|
||
|
|
SymmetricMatrix D;
|
||
|
|
D << SE.AsDiagonal() * Correlations * SE.AsDiagonal();
|
||
|
|
cout << "\nVar/cov\n" << setw(14) << setprecision(4) << D << endl;
|
||
|
|
}
|
||
|
|
|
||
|
|
#ifdef DO_FREE_CHECK
|
||
|
|
FreeCheck::Status();
|
||
|
|
#endif
|
||
|
|
|
||
|
|
return 0;
|
||
|
|
}
|