| 1 | /// \ingroup newmat
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| 2 | ///@{
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| 3 |
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| 4 | /// \file newmatnl.cpp
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| 5 | /// Non-linear optimisation.
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| 6 |
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| 7 | // Copyright (C) 1993,4,5,6: R B Davies
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| 8 |
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| 9 |
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| 10 | #define WANT_MATH
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| 11 | #define WANT_STREAM
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| 12 |
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| 13 | #include "newmatap.h"
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| 14 | #include "newmatnl.h"
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| 15 |
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| 16 | #ifdef use_namespace
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| 17 | namespace NEWMAT {
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| 18 | #endif
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| 19 |
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| 20 |
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| 21 |
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| 22 | void FindMaximum2::Fit(ColumnVector& Theta, int n_it)
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| 23 | {
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| 24 | Tracer tr("FindMaximum2::Fit");
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| 25 | enum State {Start, Restart, Continue, Interpolate, Extrapolate,
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| 26 | Fail, Convergence};
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| 27 | State TheState = Start;
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| 28 | Real z,w,x,x2,g,l1,l2,l3,d1,d2=0,d3;
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| 29 | ColumnVector Theta1, Theta2, Theta3;
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| 30 | int np = Theta.Nrows();
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| 31 | ColumnVector H1(np), H3, HP(np), K, K1(np);
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| 32 | bool oorg, conv;
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| 33 | int counter = 0;
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| 34 | Theta1 = Theta; HP = 0.0; g = 0.0;
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| 35 |
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| 36 | // This is really a set of gotos and labels, but they do not work
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| 37 | // correctly in AT&T C++ and Sun 4.01 C++.
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| 38 |
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| 39 | for(;;)
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| 40 | {
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| 41 | switch (TheState)
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| 42 | {
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| 43 | case Start:
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| 44 | tr.ReName("FindMaximum2::Fit/Start");
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| 45 | Value(Theta1, true, l1, oorg);
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| 46 | if (oorg) Throw(ProgramException("invalid starting value\n"));
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| 47 |
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| 48 | case Restart:
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| 49 | tr.ReName("FindMaximum2::Fit/ReStart");
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| 50 | conv = NextPoint(H1, d1);
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| 51 | if (conv) { TheState = Convergence; break; }
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| 52 | if (counter++ > n_it) { TheState = Fail; break; }
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| 53 |
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| 54 | z = 1.0 / sqrt(d1);
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| 55 | H3 = H1 * z; K = (H3 - HP) * g; HP = H3;
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| 56 | g = 0.0; // de-activate to use curved projection
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| 57 | if ( g == 0.0 ) K1 = 0.0; else K1 = K * 0.2 + K1 * 0.6;
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| 58 | // (K - K1) * alpha + K1 * (1 - alpha)
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| 59 | // = K * alpha + K1 * (1 - 2 * alpha)
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| 60 | K = K1 * d1; g = z;
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| 61 |
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| 62 | case Continue:
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| 63 | tr.ReName("FindMaximum2::Fit/Continue");
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| 64 | Theta2 = Theta1 + H1 + K;
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| 65 | Value(Theta2, false, l2, oorg);
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| 66 | if (counter++ > n_it) { TheState = Fail; break; }
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| 67 | if (oorg)
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| 68 | {
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| 69 | H1 *= 0.5; K *= 0.25; d1 *= 0.5; g *= 2.0;
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| 70 | TheState = Continue; break;
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| 71 | }
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| 72 | d2 = LastDerivative(H1 + K * 2.0);
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| 73 |
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| 74 | case Interpolate:
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| 75 | tr.ReName("FindMaximum2::Fit/Interpolate");
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| 76 | z = d1 + d2 - 3.0 * (l2 - l1);
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| 77 | w = z * z - d1 * d2;
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| 78 | if (w < 0.0) { TheState = Extrapolate; break; }
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| 79 | w = z + sqrt(w);
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| 80 | if (1.5 * w + d1 < 0.0)
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| 81 | { TheState = Extrapolate; break; }
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| 82 | if (d2 > 0.0 && l2 > l1 && w > 0.0)
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| 83 | { TheState = Extrapolate; break; }
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| 84 | x = d1 / (w + d1); x2 = x * x; g /= x;
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| 85 | Theta3 = Theta1 + H1 * x + K * x2;
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| 86 | Value(Theta3, true, l3, oorg);
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| 87 | if (counter++ > n_it) { TheState = Fail; break; }
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| 88 | if (oorg)
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| 89 | {
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| 90 | if (x <= 1.0)
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| 91 | { x *= 0.5; x2 = x*x; g *= 2.0; d1 *= x; H1 *= x; K *= x2; }
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| 92 | else
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| 93 | {
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| 94 | x = 0.5 * (x-1.0); x2 = x*x; Theta1 = Theta2;
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| 95 | H1 = (H1 + K * 2.0) * x;
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| 96 | K *= x2; g = 0.0; d1 = x * d2; l1 = l2;
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| 97 | }
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| 98 | TheState = Continue; break;
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| 99 | }
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| 100 |
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| 101 | if (l3 >= l1 && l3 >= l2)
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| 102 | { Theta1 = Theta3; l1 = l3; TheState = Restart; break; }
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| 103 |
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| 104 | d3 = LastDerivative(H1 + K * 2.0);
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| 105 | if (l1 > l2)
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| 106 | { H1 *= x; K *= x2; Theta2 = Theta3; d1 *= x; d2 = d3*x; }
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| 107 | else
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| 108 | {
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| 109 | Theta1 = Theta2; Theta2 = Theta3;
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| 110 | x -= 1.0; x2 = x*x; g = 0.0; H1 = (H1 + K * 2.0) * x;
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| 111 | K *= x2; l1 = l2; l2 = l3; d1 = x*d2; d2 = x*d3;
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| 112 | if (d1 <= 0.0) { TheState = Start; break; }
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| 113 | }
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| 114 | TheState = Interpolate; break;
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| 115 |
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| 116 | case Extrapolate:
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| 117 | tr.ReName("FindMaximum2::Fit/Extrapolate");
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| 118 | Theta1 = Theta2; g = 0.0; K *= 4.0; H1 = (H1 * 2.0 + K);
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| 119 | d1 = 2.0 * d2; l1 = l2;
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| 120 | TheState = Continue; break;
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| 121 |
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| 122 | case Fail:
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| 123 | Throw(ConvergenceException(Theta));
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| 124 |
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| 125 | case Convergence:
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| 126 | Theta = Theta1; return;
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| 127 | }
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| 128 | }
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| 129 | }
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| 130 |
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| 131 |
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| 132 |
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| 133 | void NonLinearLeastSquares::Value
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| 134 | (const ColumnVector& Parameters, bool, Real& v, bool& oorg)
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| 135 | {
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| 136 | Tracer tr("NonLinearLeastSquares::Value");
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| 137 | Y.resize(n_obs); X.resize(n_obs,n_param);
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| 138 | // put the fitted values in Y, the derivatives in X.
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| 139 | Pred.Set(Parameters);
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| 140 | if (!Pred.IsValid()) { oorg=true; return; }
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| 141 | for (int i=1; i<=n_obs; i++)
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| 142 | {
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| 143 | Y(i) = Pred(i);
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| 144 | X.Row(i) = Pred.Derivatives();
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| 145 | }
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| 146 | if (!Pred.IsValid()) { oorg=true; return; } // check afterwards as well
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| 147 | Y = *DataPointer - Y; Real ssq = Y.SumSquare();
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| 148 | errorvar = ssq / (n_obs - n_param);
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| 149 | cout << endl;
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| 150 | cout << setw(15) << setprecision(10) << " " << errorvar;
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| 151 | Derivs = Y.t() * X; // get the derivative and stash it
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| 152 | oorg = false; v = -0.5 * ssq;
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| 153 | }
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| 154 |
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| 155 | bool NonLinearLeastSquares::NextPoint(ColumnVector& Adj, Real& test)
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| 156 | {
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| 157 | Tracer tr("NonLinearLeastSquares::NextPoint");
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| 158 | QRZ(X, U); QRZ(X, Y, M); // do the QR decomposition
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| 159 | test = M.SumSquare();
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| 160 | cout << " " << setw(15) << setprecision(10)
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| 161 | << test << " " << Y.SumSquare() / (n_obs - n_param);
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| 162 | Adj = U.i() * M;
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| 163 | if (test < errorvar * criterion) return true;
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| 164 | else return false;
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| 165 | }
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| 166 |
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| 167 | Real NonLinearLeastSquares::LastDerivative(const ColumnVector& H)
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| 168 | { return (Derivs * H).AsScalar(); }
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| 169 |
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| 170 | void NonLinearLeastSquares::Fit(const ColumnVector& Data,
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| 171 | ColumnVector& Parameters)
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| 172 | {
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| 173 | Tracer tr("NonLinearLeastSquares::Fit");
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| 174 | n_param = Parameters.Nrows(); n_obs = Data.Nrows();
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| 175 | DataPointer = &Data;
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| 176 | FindMaximum2::Fit(Parameters, Lim);
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| 177 | cout << "\nConverged" << endl;
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| 178 | }
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| 179 |
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| 180 | void NonLinearLeastSquares::MakeCovariance()
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| 181 | {
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| 182 | if (Covariance.Nrows()==0)
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| 183 | {
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| 184 | UpperTriangularMatrix UI = U.i();
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| 185 | Covariance << UI * UI.t() * errorvar;
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| 186 | SE << Covariance; // get diagonals
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| 187 | for (int i = 1; i<=n_param; i++) SE(i) = sqrt(SE(i));
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| 188 | }
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| 189 | }
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| 190 |
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| 191 | void NonLinearLeastSquares::GetStandardErrors(ColumnVector& SEX)
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| 192 | { MakeCovariance(); SEX = SE.AsColumn(); }
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| 193 |
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| 194 | void NonLinearLeastSquares::GetCorrelations(SymmetricMatrix& Corr)
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| 195 | { MakeCovariance(); Corr << SE.i() * Covariance * SE.i(); }
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| 196 |
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| 197 | void NonLinearLeastSquares::GetHatDiagonal(DiagonalMatrix& Hat) const
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| 198 | {
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| 199 | Hat.resize(n_obs);
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| 200 | for (int i = 1; i<=n_obs; i++) Hat(i) = X.Row(i).SumSquare();
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| 201 | }
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| 202 |
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| 203 |
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| 204 | // the MLE_D_FI routines
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| 205 |
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| 206 | void MLE_D_FI::Value
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| 207 | (const ColumnVector& Parameters, bool wg, Real& v, bool& oorg)
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| 208 | {
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| 209 | Tracer tr("MLE_D_FI::Value");
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| 210 | if (!LL.IsValid(Parameters,wg)) { oorg=true; return; }
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| 211 | v = LL.LogLikelihood();
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| 212 | if (!LL.IsValid()) { oorg=true; return; } // check validity again
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| 213 | cout << endl;
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| 214 | cout << setw(20) << setprecision(10) << v;
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| 215 | oorg = false;
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| 216 | Derivs = LL.Derivatives(); // Get derivatives
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| 217 | }
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| 218 |
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| 219 | bool MLE_D_FI::NextPoint(ColumnVector& Adj, Real& test)
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| 220 | {
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| 221 | Tracer tr("MLE_D_FI::NextPoint");
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| 222 | SymmetricMatrix FI = LL.FI();
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| 223 | LT = Cholesky(FI);
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| 224 | ColumnVector Adj1 = LT.i() * Derivs;
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| 225 | Adj = LT.t().i() * Adj1;
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| 226 | test = SumSquare(Adj1);
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| 227 | cout << " " << setw(20) << setprecision(10) << test;
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| 228 | return (test < Criterion);
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| 229 | }
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| 230 |
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| 231 | Real MLE_D_FI::LastDerivative(const ColumnVector& H)
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| 232 | { return (Derivs.t() * H).AsScalar(); }
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| 233 |
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| 234 | void MLE_D_FI::Fit(ColumnVector& Parameters)
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| 235 | {
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| 236 | Tracer tr("MLE_D_FI::Fit");
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| 237 | FindMaximum2::Fit(Parameters,Lim);
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| 238 | cout << "\nConverged" << endl;
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| 239 | }
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| 240 |
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| 241 | void MLE_D_FI::MakeCovariance()
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| 242 | {
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| 243 | if (Covariance.Nrows()==0)
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| 244 | {
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| 245 | LowerTriangularMatrix LTI = LT.i();
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| 246 | Covariance << LTI.t() * LTI;
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| 247 | SE << Covariance; // get diagonal
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| 248 | int n = Covariance.Nrows();
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| 249 | for (int i=1; i <= n; i++) SE(i) = sqrt(SE(i));
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| 250 | }
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| 251 | }
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| 252 |
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| 253 | void MLE_D_FI::GetStandardErrors(ColumnVector& SEX)
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| 254 | { MakeCovariance(); SEX = SE.AsColumn(); }
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| 255 |
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| 256 | void MLE_D_FI::GetCorrelations(SymmetricMatrix& Corr)
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| 257 | { MakeCovariance(); Corr << SE.i() * Covariance * SE.i(); }
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| 258 |
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| 259 |
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| 260 |
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| 261 | #ifdef use_namespace
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| 262 | }
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| 263 | #endif
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| 264 |
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| 265 |
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| 266 | ///@}
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