3dpcp/.svn/pristine/c0/c038fd22c6c89deb39477b7bd9ee169af6b50931.svn-base
2012-09-16 14:33:11 +02:00

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