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