newmatnl.cppGo to the documentation of this file.00001
00002
00003
00004
00005
00006 #define WANT_MATH
00007 #define WANT_STREAM
00008
00009 #include "newmatap.h"
00010 #include "newmatnl.h"
00011
00012 #ifdef use_namespace
00013 namespace NEWMAT {
00014 #endif
00015
00016
00017
00018 void FindMaximum2::Fit(ColumnVector& Theta, int n_it)
00019 {
00020 Tracer tr("FindMaximum2::Fit");
00021 enum State {Start, Restart, Continue, Interpolate, Extrapolate,
00022 Fail, Convergence};
00023 State TheState = Start;
00024 Real z,w,x,x2,g,l1,l2,l3,d1,d2=0,d3;
00025 ColumnVector Theta1, Theta2, Theta3;
00026 int np = Theta.Nrows();
00027 ColumnVector H1(np), H3, HP(np), K, K1(np);
00028 bool oorg, conv;
00029 int counter = 0;
00030 Theta1 = Theta; HP = 0.0; g = 0.0;
00031
00032
00033
00034
00035 for(;;)
00036 {
00037 switch (TheState)
00038 {
00039 case Start:
00040 tr.ReName("FindMaximum2::Fit/Start");
00041 Value(Theta1, true, l1, oorg);
00042 if (oorg) Throw(ProgramException("invalid starting value\n"));
00043
00044 case Restart:
00045 tr.ReName("FindMaximum2::Fit/ReStart");
00046 conv = NextPoint(H1, d1);
00047 if (conv) { TheState = Convergence; break; }
00048 if (counter++ > n_it) { TheState = Fail; break; }
00049
00050 z = 1.0 / sqrt(d1);
00051 H3 = H1 * z; K = (H3 - HP) * g; HP = H3;
00052 g = 0.0;
00053 if (g==0.0) K1 = 0.0; else K1 = K * 0.2 + K1 * 0.6;
00054
00055
00056 K = K1 * d1; g = z;
00057
00058 case Continue:
00059 tr.ReName("FindMaximum2::Fit/Continue");
00060 Theta2 = Theta1 + H1 + K;
00061 Value(Theta2, false, l2, oorg);
00062 if (counter++ > n_it) { TheState = Fail; break; }
00063 if (oorg)
00064 {
00065 H1 *= 0.5; K *= 0.25; d1 *= 0.5; g *= 2.0;
00066 TheState = Continue; break;
00067 }
00068 d2 = LastDerivative(H1 + K * 2.0);
00069
00070 case Interpolate:
00071 tr.ReName("FindMaximum2::Fit/Interpolate");
00072 z = d1 + d2 - 3.0 * (l2 - l1);
00073 w = z * z - d1 * d2;
00074 if (w < 0.0) { TheState = Extrapolate; break; }
00075 w = z + sqrt(w);
00076 if (1.5 * w + d1 < 0.0)
00077 { TheState = Extrapolate; break; }
00078 if (d2 > 0.0 && l2 > l1 && w > 0.0)
00079 { TheState = Extrapolate; break; }
00080 x = d1 / (w + d1); x2 = x * x; g /= x;
00081 Theta3 = Theta1 + H1 * x + K * x2;
00082 Value(Theta3, true, l3, oorg);
00083 if (counter++ > n_it) { TheState = Fail; break; }
00084 if (oorg)
00085 {
00086 if (x <= 1.0)
00087 { x *= 0.5; x2 = x*x; g *= 2.0; d1 *= x; H1 *= x; K *= x2; }
00088 else
00089 {
00090 x = 0.5 * (x-1.0); x2 = x*x; Theta1 = Theta2;
00091 H1 = (H1 + K * 2.0) * x;
00092 K *= x2; g = 0.0; d1 = x * d2; l1 = l2;
00093 }
00094 TheState = Continue; break;
00095 }
00096
00097 if (l3 >= l1 && l3 >= l2)
00098 { Theta1 = Theta3; l1 = l3; TheState = Restart; break; }
00099
00100 d3 = LastDerivative(H1 + K * 2.0);
00101 if (l1 > l2)
00102 { H1 *= x; K *= x2; Theta2 = Theta3; d1 *= x; d2 = d3*x; }
00103 else
00104 {
00105 Theta1 = Theta2; Theta2 = Theta3;
00106 x -= 1.0; x2 = x*x; g = 0.0; H1 = (H1 + K * 2.0) * x;
00107 K *= x2; l1 = l2; l2 = l3; d1 = x*d2; d2 = x*d3;
00108 if (d1 <= 0.0) { TheState = Start; break; }
00109 }
00110 TheState = Interpolate; break;
00111
00112 case Extrapolate:
00113 tr.ReName("FindMaximum2::Fit/Extrapolate");
00114 Theta1 = Theta2; g = 0.0; K *= 4.0; H1 = (H1 * 2.0 + K);
00115 d1 = 2.0 * d2; l1 = l2;
00116 TheState = Continue; break;
00117
00118 case Fail:
00119 Throw(ConvergenceException(Theta));
00120
00121 case Convergence:
00122 Theta = Theta1; return;
00123 }
00124 }
00125 }
00126
00127
00128
00129 void NonLinearLeastSquares::Value
00130 (const ColumnVector& Parameters, bool, Real& v, bool& oorg)
00131 {
00132 Tracer tr("NonLinearLeastSquares::Value");
00133 Y.ReSize(n_obs); X.ReSize(n_obs,n_param);
00134
00135 Pred.Set(Parameters);
00136 if (!Pred.IsValid()) { oorg=true; return; }
00137 for (int i=1; i<=n_obs; i++)
00138 {
00139 Y(i) = Pred(i);
00140 X.Row(i) = Pred.Derivatives();
00141 }
00142 if (!Pred.IsValid()) { oorg=true; return; }
00143 Y = *DataPointer - Y; Real ssq = Y.SumSquare();
00144 errorvar = ssq / (n_obs - n_param);
00145 cout << endl;
00146 cout << setw(15) << setprecision(10) << " " << errorvar;
00147 Derivs = Y.t() * X;
00148 oorg = false; v = -0.5 * ssq;
00149 }
00150
00151 bool NonLinearLeastSquares::NextPoint(ColumnVector& Adj, Real& test)
00152 {
00153 Tracer tr("NonLinearLeastSquares::NextPoint");
00154 QRZ(X, U); QRZ(X, Y, M);
00155 test = M.SumSquare();
00156 cout << " " << setw(15) << setprecision(10)
00157 << test << " " << Y.SumSquare() / (n_obs - n_param);
00158 Adj = U.i() * M;
00159 if (test < errorvar * criterion) return true;
00160 else return false;
00161 }
00162
00163 Real NonLinearLeastSquares::LastDerivative(const ColumnVector& H)
00164 { return (Derivs * H).AsScalar(); }
00165
00166 void NonLinearLeastSquares::Fit(const ColumnVector& Data,
00167 ColumnVector& Parameters)
00168 {
00169 Tracer tr("NonLinearLeastSquares::Fit");
00170 n_param = Parameters.Nrows(); n_obs = Data.Nrows();
00171 DataPointer = &Data;
00172 FindMaximum2::Fit(Parameters, Lim);
00173 cout << "\nConverged" << endl;
00174 }
00175
00176 void NonLinearLeastSquares::MakeCovariance()
00177 {
00178 if (Covariance.Nrows()==0)
00179 {
00180 UpperTriangularMatrix UI = U.i();
00181 Covariance << UI * UI.t() * errorvar;
00182 SE << Covariance;
00183 for (int i = 1; i<=n_param; i++) SE(i) = sqrt(SE(i));
00184 }
00185 }
00186
00187 void NonLinearLeastSquares::GetStandardErrors(ColumnVector& SEX)
00188 { MakeCovariance(); SEX = SE.AsColumn(); }
00189
00190 void NonLinearLeastSquares::GetCorrelations(SymmetricMatrix& Corr)
00191 { MakeCovariance(); Corr << SE.i() * Covariance * SE.i(); }
00192
00193 void NonLinearLeastSquares::GetHatDiagonal(DiagonalMatrix& Hat) const
00194 {
00195 Hat.ReSize(n_obs);
00196 for (int i = 1; i<=n_obs; i++) Hat(i) = X.Row(i).SumSquare();
00197 }
00198
00199
00200
00201
00202 void MLE_D_FI::Value
00203 (const ColumnVector& Parameters, bool wg, Real& v, bool& oorg)
00204 {
00205 Tracer tr("MLE_D_FI::Value");
00206 if (!LL.IsValid(Parameters,wg)) { oorg=true; return; }
00207 v = LL.LogLikelihood();
00208 if (!LL.IsValid()) { oorg=true; return; }
00209 cout << endl;
00210 cout << setw(20) << setprecision(10) << v;
00211 oorg = false;
00212 Derivs = LL.Derivatives();
00213 }
00214
00215 bool MLE_D_FI::NextPoint(ColumnVector& Adj, Real& test)
00216 {
00217 Tracer tr("MLE_D_FI::NextPoint");
00218 SymmetricMatrix FI = LL.FI();
00219 LT = Cholesky(FI);
00220 ColumnVector Adj1 = LT.i() * Derivs;
00221 Adj = LT.t().i() * Adj1;
00222 test = SumSquare(Adj1);
00223 cout << " " << setw(20) << setprecision(10) << test;
00224 return (test < Criterion);
00225 }
00226
00227 Real MLE_D_FI::LastDerivative(const ColumnVector& H)
00228 { return (Derivs.t() * H).AsScalar(); }
00229
00230 void MLE_D_FI::Fit(ColumnVector& Parameters)
00231 {
00232 Tracer tr("MLE_D_FI::Fit");
00233 FindMaximum2::Fit(Parameters,Lim);
00234 cout << "\nConverged" << endl;
00235 }
00236
00237 void MLE_D_FI::MakeCovariance()
00238 {
00239 if (Covariance.Nrows()==0)
00240 {
00241 LowerTriangularMatrix LTI = LT.i();
00242 Covariance << LTI.t() * LTI;
00243 SE << Covariance;
00244 int n = Covariance.Nrows();
00245 for (int i=1; i <= n; i++) SE(i) = sqrt(SE(i));
00246 }
00247 }
00248
00249 void MLE_D_FI::GetStandardErrors(ColumnVector& SEX)
00250 { MakeCovariance(); SEX = SE.AsColumn(); }
00251
00252 void MLE_D_FI::GetCorrelations(SymmetricMatrix& Corr)
00253 { MakeCovariance(); Corr << SE.i() * Covariance * SE.i(); }
00254
00255
00256
00257 #ifdef use_namespace
00258 }
00259 #endif
00260
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