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259 lines
7.3 KiB
C++
259 lines
7.3 KiB
C++
//$$ newmatnl.cpp Non-linear optimisation
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// Copyright (C) 1993,4,5,6: R B Davies
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#define WANT_MATH
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#define WANT_STREAM
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#include "newmatap.h"
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#include "newmatnl.h"
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#ifdef use_namespace
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namespace NEWMAT {
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#endif
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void FindMaximum2::Fit(ColumnVector& Theta, int n_it)
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{
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Tracer tr("FindMaximum2::Fit");
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enum State {Start, Restart, Continue, Interpolate, Extrapolate,
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Fail, Convergence};
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State TheState = Start;
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Real z,w,x,x2,g,l1,l2,l3,d1,d2=0,d3;
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ColumnVector Theta1, Theta2, Theta3;
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int np = Theta.Nrows();
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ColumnVector H1(np), H3, HP(np), K, K1(np);
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bool oorg, conv;
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int counter = 0;
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Theta1 = Theta; HP = 0.0; g = 0.0;
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// This is really a set of gotos and labels, but they do not work
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// correctly in AT&T C++ and Sun 4.01 C++.
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for(;;)
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{
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switch (TheState)
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{
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case Start:
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tr.ReName("FindMaximum2::Fit/Start");
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Value(Theta1, true, l1, oorg);
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if (oorg) Throw(ProgramException("invalid starting value\n"));
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case Restart:
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tr.ReName("FindMaximum2::Fit/ReStart");
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conv = NextPoint(H1, d1);
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if (conv) { TheState = Convergence; break; }
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if (counter++ > n_it) { TheState = Fail; break; }
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z = 1.0 / sqrt(d1);
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H3 = H1 * z; K = (H3 - HP) * g; HP = H3;
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g = 0.0; // de-activate to use curved projection
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if (g==0.0) K1 = 0.0; else K1 = K * 0.2 + K1 * 0.6;
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// (K - K1) * alpha + K1 * (1 - alpha)
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// = K * alpha + K1 * (1 - 2 * alpha)
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K = K1 * d1; g = z;
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case Continue:
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tr.ReName("FindMaximum2::Fit/Continue");
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Theta2 = Theta1 + H1 + K;
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Value(Theta2, false, l2, oorg);
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if (counter++ > n_it) { TheState = Fail; break; }
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if (oorg)
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{
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H1 *= 0.5; K *= 0.25; d1 *= 0.5; g *= 2.0;
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TheState = Continue; break;
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}
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d2 = LastDerivative(H1 + K * 2.0);
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case Interpolate:
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tr.ReName("FindMaximum2::Fit/Interpolate");
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z = d1 + d2 - 3.0 * (l2 - l1);
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w = z * z - d1 * d2;
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if (w < 0.0) { TheState = Extrapolate; break; }
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w = z + sqrt(w);
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if (1.5 * w + d1 < 0.0)
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{ TheState = Extrapolate; break; }
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if (d2 > 0.0 && l2 > l1 && w > 0.0)
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{ TheState = Extrapolate; break; }
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x = d1 / (w + d1); x2 = x * x; g /= x;
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Theta3 = Theta1 + H1 * x + K * x2;
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Value(Theta3, true, l3, oorg);
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if (counter++ > n_it) { TheState = Fail; break; }
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if (oorg)
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{
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if (x <= 1.0)
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{ x *= 0.5; x2 = x*x; g *= 2.0; d1 *= x; H1 *= x; K *= x2; }
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else
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{
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x = 0.5 * (x-1.0); x2 = x*x; Theta1 = Theta2;
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H1 = (H1 + K * 2.0) * x;
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K *= x2; g = 0.0; d1 = x * d2; l1 = l2;
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}
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TheState = Continue; break;
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}
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if (l3 >= l1 && l3 >= l2)
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{ Theta1 = Theta3; l1 = l3; TheState = Restart; break; }
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d3 = LastDerivative(H1 + K * 2.0);
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if (l1 > l2)
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{ H1 *= x; K *= x2; Theta2 = Theta3; d1 *= x; d2 = d3*x; }
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else
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{
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Theta1 = Theta2; Theta2 = Theta3;
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x -= 1.0; x2 = x*x; g = 0.0; H1 = (H1 + K * 2.0) * x;
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K *= x2; l1 = l2; l2 = l3; d1 = x*d2; d2 = x*d3;
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if (d1 <= 0.0) { TheState = Start; break; }
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}
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TheState = Interpolate; break;
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case Extrapolate:
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tr.ReName("FindMaximum2::Fit/Extrapolate");
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Theta1 = Theta2; g = 0.0; K *= 4.0; H1 = (H1 * 2.0 + K);
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d1 = 2.0 * d2; l1 = l2;
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TheState = Continue; break;
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case Fail:
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Throw(ConvergenceException(Theta));
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case Convergence:
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Theta = Theta1; return;
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}
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}
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}
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void NonLinearLeastSquares::Value
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(const ColumnVector& Parameters, bool, Real& v, bool& oorg)
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{
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Tracer tr("NonLinearLeastSquares::Value");
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Y.ReSize(n_obs); X.ReSize(n_obs,n_param);
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// put the fitted values in Y, the derivatives in X.
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Pred.Set(Parameters);
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if (!Pred.IsValid()) { oorg=true; return; }
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for (int i=1; i<=n_obs; i++)
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{
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Y(i) = Pred(i);
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X.Row(i) = Pred.Derivatives();
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}
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if (!Pred.IsValid()) { oorg=true; return; } // check afterwards as well
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Y = *DataPointer - Y; Real ssq = Y.SumSquare();
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errorvar = ssq / (n_obs - n_param);
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cout << "\n" << setw(15) << setprecision(10) << " " << errorvar;
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Derivs = Y.t() * X; // get the derivative and stash it
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oorg = false; v = -0.5 * ssq;
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}
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bool NonLinearLeastSquares::NextPoint(ColumnVector& Adj, Real& test)
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{
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Tracer tr("NonLinearLeastSquares::NextPoint");
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QRZ(X, U); QRZ(X, Y, M); // do the QR decomposition
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test = M.SumSquare();
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cout << " " << setw(15) << setprecision(10)
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<< test << " " << Y.SumSquare() / (n_obs - n_param);
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Adj = U.i() * M;
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if (test < errorvar * criterion) return true;
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else return false;
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}
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Real NonLinearLeastSquares::LastDerivative(const ColumnVector& H)
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{ return (Derivs * H).AsScalar(); }
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void NonLinearLeastSquares::Fit(const ColumnVector& Data,
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ColumnVector& Parameters)
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{
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Tracer tr("NonLinearLeastSquares::Fit");
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n_param = Parameters.Nrows(); n_obs = Data.Nrows();
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DataPointer = &Data;
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FindMaximum2::Fit(Parameters, Lim);
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cout << "\nConverged\n";
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}
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void NonLinearLeastSquares::MakeCovariance()
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{
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if (Covariance.Nrows()==0)
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{
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UpperTriangularMatrix UI = U.i();
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Covariance << UI * UI.t() * errorvar;
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SE << Covariance; // get diagonals
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for (int i = 1; i<=n_param; i++) SE(i) = sqrt(SE(i));
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}
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}
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void NonLinearLeastSquares::GetStandardErrors(ColumnVector& SEX)
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{ MakeCovariance(); SEX = SE.AsColumn(); }
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void NonLinearLeastSquares::GetCorrelations(SymmetricMatrix& Corr)
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{ MakeCovariance(); Corr << SE.i() * Covariance * SE.i(); }
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void NonLinearLeastSquares::GetHatDiagonal(DiagonalMatrix& Hat) const
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{
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Hat.ReSize(n_obs);
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for (int i = 1; i<=n_obs; i++) Hat(i) = X.Row(i).SumSquare();
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}
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// the MLE_D_FI routines
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void MLE_D_FI::Value
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(const ColumnVector& Parameters, bool wg, Real& v, bool& oorg)
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{
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Tracer tr("MLE_D_FI::Value");
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if (!LL.IsValid(Parameters,wg)) { oorg=true; return; }
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v = LL.LogLikelihood();
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if (!LL.IsValid()) { oorg=true; return; } // check validity again
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cout << "\n" << setw(20) << setprecision(10) << v;
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oorg = false;
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Derivs = LL.Derivatives(); // Get derivatives
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}
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bool MLE_D_FI::NextPoint(ColumnVector& Adj, Real& test)
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{
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Tracer tr("MLE_D_FI::NextPoint");
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SymmetricMatrix FI = LL.FI();
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LT = Cholesky(FI);
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ColumnVector Adj1 = LT.i() * Derivs;
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Adj = LT.t().i() * Adj1;
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test = SumSquare(Adj1);
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cout << " " << setw(20) << setprecision(10) << test;
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return (test < Criterion);
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}
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Real MLE_D_FI::LastDerivative(const ColumnVector& H)
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{ return (Derivs.t() * H).AsScalar(); }
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void MLE_D_FI::Fit(ColumnVector& Parameters)
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{
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Tracer tr("MLE_D_FI::Fit");
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FindMaximum2::Fit(Parameters,Lim);
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cout << "\nConverged\n";
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}
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void MLE_D_FI::MakeCovariance()
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{
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if (Covariance.Nrows()==0)
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{
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LowerTriangularMatrix LTI = LT.i();
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Covariance << LTI.t() * LTI;
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SE << Covariance; // get diagonal
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int n = Covariance.Nrows();
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for (int i=1; i <= n; i++) SE(i) = sqrt(SE(i));
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}
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}
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void MLE_D_FI::GetStandardErrors(ColumnVector& SEX)
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{ MakeCovariance(); SEX = SE.AsColumn(); }
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void MLE_D_FI::GetCorrelations(SymmetricMatrix& Corr)
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{ MakeCovariance(); Corr << SE.i() * Covariance * SE.i(); }
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#ifdef use_namespace
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}
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#endif
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