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newmatnl.cpp

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00001 //$$ newmatnl.cpp         Non-linear optimisation
00002 
00003 // Copyright (C) 1993,4,5,6: R B Davies
00004 
00005 
00006 #ifndef WANT_MATH
00007 #define WANT_MATH
00008 #endif
00009 
00010 #ifndef WANT_STREAM
00011 #define WANT_STREAM
00012 #endif
00013 
00014 #include "newmatap.h"
00015 #include "newmatnl.h"
00016 #include <iomanip>
00017 
00018 using namespace std;
00019 
00020 #ifdef use_namespace
00021 namespace NEWMAT {
00022 #endif
00023 
00024 void FindMaximum2::Fit(ColumnVector& Theta, int n_it)
00025 {
00026    Tracer tr("FindMaximum2::Fit");
00027    enum State {Start, Restart, Continue, Interpolate, Extrapolate,
00028       Fail, Convergence};
00029    State TheState = Start;
00030    Real z,w,x,x2,g,l1,l2,l3,d1,d2=0,d3;
00031    ColumnVector Theta1, Theta2, Theta3;
00032    int np = Theta.Nrows();
00033    ColumnVector H1(np), H3, HP(np), K, K1(np);
00034    bool oorg, conv;
00035    int counter = 0;
00036    Theta1 = Theta; HP = 0.0; g = 0.0;
00037 
00038    // This is really a set of gotos and labels, but they do not work
00039    // correctly in AT&T C++ and Sun 4.01 C++.
00040 
00041    for(;;)
00042    {
00043       switch (TheState)
00044       {
00045       case Start:
00046    tr.ReName("FindMaximum2::Fit/Start");
00047    Value(Theta1, true, l1, oorg);
00048    if (oorg) Throw(ProgramException("invalid starting value\n"));
00049 
00050       case Restart:
00051    tr.ReName("FindMaximum2::Fit/ReStart");
00052    conv = NextPoint(H1, d1);
00053    if (conv) { TheState = Convergence; break; }
00054    if (counter++ > n_it) { TheState = Fail; break; }
00055 
00056    z = 1.0 / sqrt(d1);
00057    H3 = H1 * z; K = (H3 - HP) * g; HP = H3;
00058    g = 0.0;                     // de-activate to use curved projection
00059    if (g==0.0) K1 = 0.0; else K1 = K * 0.2 + K1 * 0.6;
00060    // (K - K1) * alpha + K1 * (1 - alpha)
00061    //     = K * alpha + K1 * (1 - 2 * alpha)
00062    K = K1 * d1; g = z;
00063 
00064       case Continue:
00065    tr.ReName("FindMaximum2::Fit/Continue");
00066    Theta2 = Theta1 + H1 + K;
00067    Value(Theta2, false, l2, oorg);
00068    if (counter++ > n_it) { TheState = Fail; break; }
00069    if (oorg)
00070    {
00071       H1 *= 0.5; K *= 0.25; d1 *= 0.5; g *= 2.0;
00072       TheState =  Continue; break;
00073    }
00074    d2 = LastDerivative(H1 + K * 2.0);
00075 
00076       case Interpolate:
00077    tr.ReName("FindMaximum2::Fit/Interpolate");
00078    z = d1 + d2 - 3.0 * (l2 - l1);
00079    w = z * z - d1 * d2;
00080    if (w < 0.0) { TheState = Extrapolate; break; }
00081    w = z + sqrt(w);
00082    if (1.5 * w + d1 < 0.0)
00083       { TheState = Extrapolate; break; }
00084    if (d2 > 0.0 && l2 > l1 && w > 0.0)
00085       { TheState = Extrapolate; break; }
00086    x = d1 / (w + d1); x2 = x * x; g /= x;
00087    Theta3 = Theta1 + H1 * x + K * x2;
00088    Value(Theta3, true, l3, oorg);
00089    if (counter++ > n_it) { TheState = Fail; break; }
00090    if (oorg)
00091    {
00092       if (x <= 1.0)
00093          { x *= 0.5; x2 = x*x; g *= 2.0; d1 *= x; H1 *= x; K *= x2; }
00094       else
00095       {
00096          x = 0.5 * (x-1.0); x2 = x*x; Theta1 = Theta2;
00097          H1 = (H1 + K * 2.0) * x;
00098          K *= x2; g = 0.0; d1 = x * d2; l1 = l2;
00099       }
00100       TheState = Continue; break;
00101    }
00102 
00103    if (l3 >= l1 && l3 >= l2)
00104       { Theta1 = Theta3; l1 = l3; TheState =  Restart; break; }
00105 
00106    d3 = LastDerivative(H1 + K * 2.0);
00107    if (l1 > l2)
00108       { H1 *= x; K *= x2; Theta2 = Theta3; d1 *= x; d2 = d3*x; }
00109    else
00110    {
00111       Theta1 = Theta2; Theta2 = Theta3;
00112       x -= 1.0; x2 = x*x; g = 0.0; H1 = (H1 + K * 2.0) * x;
00113       K *= x2; l1 = l2; l2 = l3; d1 = x*d2; d2 = x*d3;
00114       if (d1 <= 0.0) { TheState = Start; break; }
00115    }
00116    TheState =  Interpolate; break;
00117 
00118       case Extrapolate:
00119    tr.ReName("FindMaximum2::Fit/Extrapolate");
00120    Theta1 = Theta2; g = 0.0; K *= 4.0; H1 = (H1 * 2.0 + K);
00121    d1 = 2.0 * d2; l1 = l2;
00122    TheState = Continue; break;
00123 
00124       case Fail:
00125    Throw(ConvergenceException(Theta));
00126 
00127       case Convergence:
00128    Theta = Theta1; return;
00129       }
00130    }
00131 }
00132 
00133 
00134 
00135 void NonLinearLeastSquares::Value
00136    (const ColumnVector& Parameters, bool, Real& v, bool& oorg)
00137 {
00138    Tracer tr("NonLinearLeastSquares::Value");
00139    Y.ReSize(n_obs); X.ReSize(n_obs,n_param);
00140    // put the fitted values in Y, the derivatives in X.
00141    Pred.Set(Parameters);
00142    if (!Pred.IsValid()) { oorg=true; return; }
00143    for (int i=1; i<=n_obs; i++)
00144    {
00145       Y(i) = Pred(i);
00146       X.Row(i) = Pred.Derivatives();
00147    }
00148    if (!Pred.IsValid()) { oorg=true; return; }  // check afterwards as well
00149    Y = *DataPointer - Y; Real ssq = Y.SumSquare();
00150    errorvar =  ssq / (n_obs - n_param);
00151    cout << endl;
00152    cout << setw(15) << setprecision(10) << " " << errorvar;
00153    Derivs = Y.t() * X;          // get the derivative and stash it
00154    oorg = false; v = -0.5 * ssq;
00155 }
00156 
00157 bool NonLinearLeastSquares::NextPoint(ColumnVector& Adj, Real& test)
00158 {
00159    Tracer tr("NonLinearLeastSquares::NextPoint");
00160    QRZ(X, U); QRZ(X, Y, M);     // do the QR decomposition
00161    test = M.SumSquare();
00162    cout << " " << setw(15) << setprecision(10)
00163       << test << " " << Y.SumSquare() / (n_obs - n_param);
00164    Adj = U.i() * M;
00165    if (test < errorvar * criterion) return true;
00166    else return false;
00167 }
00168 
00169 Real NonLinearLeastSquares::LastDerivative(const ColumnVector& H)
00170 { return (Derivs * H).AsScalar(); }
00171 
00172 void NonLinearLeastSquares::Fit(const ColumnVector& Data,
00173    ColumnVector& Parameters)
00174 {
00175    Tracer tr("NonLinearLeastSquares::Fit");
00176    n_param = Parameters.Nrows(); n_obs = Data.Nrows();
00177    DataPointer = &Data;
00178    FindMaximum2::Fit(Parameters, Lim);
00179    cout << "\nConverged" << endl;
00180 }
00181 
00182 void NonLinearLeastSquares::MakeCovariance()
00183 {
00184    if (Covariance.Nrows()==0)
00185    {
00186       UpperTriangularMatrix UI = U.i();
00187       Covariance << UI * UI.t() * errorvar;
00188       SE << Covariance;                 // get diagonals
00189       for (int i = 1; i<=n_param; i++) SE(i) = sqrt(SE(i));
00190    }
00191 }
00192 
00193 void NonLinearLeastSquares::GetStandardErrors(ColumnVector& SEX)
00194    { MakeCovariance(); SEX = SE.AsColumn(); }
00195 
00196 void NonLinearLeastSquares::GetCorrelations(SymmetricMatrix& Corr)
00197    { MakeCovariance(); Corr << SE.i() * Covariance * SE.i(); }
00198 
00199 void NonLinearLeastSquares::GetHatDiagonal(DiagonalMatrix& Hat) const
00200 {
00201    Hat.ReSize(n_obs);
00202    for (int i = 1; i<=n_obs; i++) Hat(i) = X.Row(i).SumSquare();
00203 }
00204 
00205 
00206 // the MLE_D_FI routines
00207 
00208 void MLE_D_FI::Value
00209    (const ColumnVector& Parameters, bool wg, Real& v, bool& oorg)
00210 {
00211    Tracer tr("MLE_D_FI::Value");
00212    if (!LL.IsValid(Parameters,wg)) { oorg=true; return; }
00213    v = LL.LogLikelihood();
00214    if (!LL.IsValid()) { oorg=true; return; }     // check validity again
00215    cout << endl;
00216    cout << setw(20) << setprecision(10) << v;
00217    oorg = false;
00218    Derivs = LL.Derivatives();                    // Get derivatives
00219 }
00220 
00221 bool MLE_D_FI::NextPoint(ColumnVector& Adj, Real& test)
00222 {
00223    Tracer tr("MLE_D_FI::NextPoint");
00224    SymmetricMatrix FI = LL.FI();
00225    LT = Cholesky(FI);
00226    ColumnVector Adj1 = LT.i() * Derivs;
00227    Adj = LT.t().i() * Adj1;
00228    test = SumSquare(Adj1);
00229    cout << "   " << setw(20) << setprecision(10) << test;
00230    return (test < Criterion);
00231 }
00232 
00233 Real MLE_D_FI::LastDerivative(const ColumnVector& H)
00234 { return (Derivs.t() * H).AsScalar(); }
00235 
00236 void MLE_D_FI::Fit(ColumnVector& Parameters)
00237 {
00238    Tracer tr("MLE_D_FI::Fit");
00239    FindMaximum2::Fit(Parameters,Lim);
00240    cout << "\nConverged" << endl;
00241 }
00242   
00243 void MLE_D_FI::MakeCovariance()
00244 {
00245    if (Covariance.Nrows()==0)
00246    {
00247       LowerTriangularMatrix LTI = LT.i();
00248       Covariance << LTI.t() * LTI;
00249       SE << Covariance;                // get diagonal
00250       int n = Covariance.Nrows();
00251       for (int i=1; i <= n; i++) SE(i) = sqrt(SE(i));
00252    }
00253 }
00254 
00255 void MLE_D_FI::GetStandardErrors(ColumnVector& SEX)
00256 { MakeCovariance(); SEX = SE.AsColumn(); }
00257    
00258 void MLE_D_FI::GetCorrelations(SymmetricMatrix& Corr)
00259 { MakeCovariance(); Corr << SE.i() * Covariance * SE.i(); }
00260 
00261 
00262 
00263 #ifdef use_namespace
00264 }
00265 #endif
00266 

newmat11b
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