3dpcp/.svn/pristine/24/247a47058db146ee1b4f85c65a7a6e35ba33d0a0.svn-base
2012-09-16 14:33:11 +02:00

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// 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;
}