Gabriele Cosmo
444 lines
12 KiB
Plaintext
444 lines
12 KiB
Plaintext
//
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// ********************************************************************
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// * License and Disclaimer *
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// * *
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// * The Geant4 software is copyright of the Copyright Holders of *
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// * the Geant4 Collaboration. It is provided under the terms and *
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// * conditions of the Geant4 Software License, included in the file *
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// * LICENSE and available at http://cern.ch/geant4/license . These *
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// * include a list of copyright holders. *
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// * *
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// * Neither the authors of this software system, nor their employing *
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// * institutes,nor the agencies providing financial support for this *
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// * work make any representation or warranty, express or implied, *
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// * regarding this software system or assume any liability for its *
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// * use. Please see the license in the file LICENSE and URL above *
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// * for the full disclaimer and the limitation of liability. *
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// * *
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// * This code implementation is the result of the scientific and *
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// * technical work of the GEANT4 collaboration. *
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// * By using, copying, modifying or distributing the software (or *
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// * any work based on the software) you agree to acknowledge its *
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// * use in resulting scientific publications, and indicate your *
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// * acceptance of all terms of the Geant4 Software license. *
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// ********************************************************************
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//
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//
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// $Id: G4SimplexDownhill.icc,v 1.2 2007/05/11 13:05:53 gcosmo Exp $
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// GEANT4 tag $Name: geant4-09-01 $
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//
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// Author: Tatsumi Koi (SLAC/SCCS), 2007
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// --------------------------------------------------------------------------
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#include <iostream>
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#include <numeric>
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#include <cfloat>
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template<class T> void G4SimplexDownhill<T>::init()
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{
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alpha = 2.0; // refrection coefficient: 0 < alpha
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beta = 0.5; // contraction coefficient: 0 < beta < 1
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gamma = 2.0; // expantion coefficient: 1 < gamma
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maximum_no_trial = 10000;
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max_se = FLT_MIN;
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//max_ratio = FLT_EPSILON/1;
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max_ratio = DBL_EPSILON/1;
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minimized = false;
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}
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/*
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void G4SimplexDownhill<class T>::
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SetFunction( G4int n , G4double( *afunc )( std::vector < G4double > ) )
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{
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numberOfVariable = n;
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theFunction = afunc;
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minimized = false;
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}
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*/
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template<class T>
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G4double G4SimplexDownhill<T>::GetMinimum()
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{
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initialize();
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// First Tryal;
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//G4cout << "Begin First Trials" << G4endl;
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doDownhill();
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//G4cout << "End First Trials" << G4endl;
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std::vector< G4double >::iterator it_minh =
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std::min_element( currentHeights.begin() , currentHeights.end() );
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G4int imin = -1;
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G4int i = 0;
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for ( std::vector< G4double >::iterator it = currentHeights.begin();
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it != currentHeights.end(); it++ )
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{
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if ( it == it_minh )
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{
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imin = i;
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}
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i++;
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}
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std::vector< G4double > minimumPoint = currentSimplex[ imin ];
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// Second Trial
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//std::vector< G4double > minimumPoint = currentSimplex[ 0 ];
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initialize();
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currentSimplex[ numberOfVariable ] = minimumPoint;
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//G4cout << "Begin Second Trials" << G4endl;
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doDownhill();
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//G4cout << "End Second Trials" << G4endl;
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G4double sum = std::accumulate( currentHeights.begin() ,
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currentHeights.end() , 0.0 );
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G4double average = sum/(numberOfVariable+1);
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G4double minimum = average;
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minimized = true;
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return minimum;
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}
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template<class T>
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void G4SimplexDownhill<T>::initialize()
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{
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currentSimplex.resize( numberOfVariable+1 );
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currentHeights.resize( numberOfVariable+1 );
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for ( G4int i = 0 ; i < numberOfVariable ; i++ )
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{
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std::vector< G4double > avec ( numberOfVariable , 0.0 );
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avec[ i ] = 1.0;
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currentSimplex[ i ] = avec;
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}
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//std::vector< G4double > avec ( numberOfVariable , 0.0 );
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std::vector< G4double > avec ( numberOfVariable , 1 );
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currentSimplex[ numberOfVariable ] = avec;
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}
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template<class T>
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void G4SimplexDownhill<T>::calHeights()
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{
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for ( G4int i = 0 ; i <= numberOfVariable ; i++ )
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{
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currentHeights[i] = getValue ( currentSimplex[i] );
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}
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}
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template<class T>
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std::vector< G4double > G4SimplexDownhill<T>::calCentroid( G4int ih )
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{
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std::vector< G4double > centroid ( numberOfVariable , 0.0 );
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G4int i = 0;
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for ( std::vector< std::vector< G4double > >::iterator
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it = currentSimplex.begin(); it != currentSimplex.end() ; it++ )
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{
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if ( i != ih )
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{
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for ( G4int j = 0 ; j < numberOfVariable ; j++ )
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{
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centroid[j] += (*it)[j]/numberOfVariable;
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}
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}
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i++;
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}
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return centroid;
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}
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template<class T>
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std::vector< G4double > G4SimplexDownhill<T>::
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getReflectionPoint( std::vector< G4double > p ,
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std::vector< G4double > centroid )
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{
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//G4cout << "Reflection" << G4endl;
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std::vector< G4double > reflectionP ( numberOfVariable , 0.0 );
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for ( G4int i = 0 ; i < numberOfVariable ; i++ )
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{
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reflectionP[ i ] = ( 1 + alpha ) * centroid[ i ] - alpha * p[ i ];
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}
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return reflectionP;
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}
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template<class T>
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std::vector< G4double > G4SimplexDownhill<T>::
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getExpansionPoint( std::vector< G4double > p ,
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std::vector< G4double > centroid )
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{
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//G4cout << "Expantion" << G4endl;
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std::vector< G4double > expansionP ( numberOfVariable , 0.0 );
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for ( G4int i = 0 ; i < numberOfVariable ; i++ )
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{
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expansionP[i] = ( 1 - gamma ) * centroid[i] + gamma * p[i];
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}
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return expansionP;
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}
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template<class T>
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std::vector< G4double > G4SimplexDownhill<T>::
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getContractionPoint( std::vector< G4double > p ,
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std::vector< G4double > centroid )
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{
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//G4cout << "Contraction" << G4endl;
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std::vector< G4double > contractionP ( numberOfVariable , 0.0 );
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for ( G4int i = 0 ; i < numberOfVariable ; i++ )
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{
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contractionP[i] = ( 1 - beta ) * centroid[i] + beta * p[i];
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}
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return contractionP;
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}
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template<class T>
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G4bool G4SimplexDownhill<T>::isItGoodEnough()
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{
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G4bool result = false;
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G4double sum = std::accumulate( currentHeights.begin() ,
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currentHeights.end() , 0.0 );
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G4double average = sum/(numberOfVariable+1);
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//G4cout << "average " << average << G4endl;
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G4double delta = 0.0;
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for ( G4int i = 0 ; i <= numberOfVariable ; i++ )
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{
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delta += std::abs ( currentHeights[ i ] - average );
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}
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//G4cout << "ratio of delta to average is "
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// << delta / (numberOfVariable+1) / average << G4endl;
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if ( delta/(numberOfVariable+1)/average < max_ratio )
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{
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result = true;
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}
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/*
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G4double sigma = 0.0;
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G4cout << "average " << average << G4endl;
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for ( G4int i = 0 ; i <= numberOfVariable ; i++ )
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{
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sigma += ( currentHeights[ i ] - average )
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*( currentHeights[ i ] - average );
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}
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G4cout << "standard error of hs "
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<< std::sqrt ( sigma ) / (numberOfVariable+1) << G4endl;
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if ( std::sqrt ( sigma ) / (numberOfVariable+1) < max_se )
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{
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result = true;
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}
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*/
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return result;
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}
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template<class T>
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void G4SimplexDownhill<T>::doDownhill()
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{
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G4int nth_trial = 0;
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while ( nth_trial < maximum_no_trial )
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{
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/*
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G4cout << "Begining " << nth_trial << "th trial " << G4endl;
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for ( G4int j = 0 ; j <= numberOfVariable ; j++ )
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{
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G4cout << "SimplexPoint " << j << ": ";
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for ( G4int i = 0 ; i < numberOfVariable ; i++ )
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{
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G4cout << currentSimplex[j][i]
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<< " ";
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}
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G4cout << G4endl;
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}
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*/
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calHeights();
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if ( isItGoodEnough() )
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{
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break;
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}
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std::vector< G4double >::iterator it_maxh =
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std::max_element( currentHeights.begin() , currentHeights.end() );
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std::vector< G4double >::iterator it_minh =
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std::min_element( currentHeights.begin() , currentHeights.end() );;
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G4double h_H = *it_maxh;
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G4double h_L = *it_minh;
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G4int ih = 0;;
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G4int il = 0;
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G4double h_H2 =0.0;
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G4int i = 0;
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for ( std::vector< G4double >::iterator
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it = currentHeights.begin(); it != currentHeights.end(); it++ )
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{
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if ( it == it_maxh )
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{
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ih = i;
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}
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else
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{
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h_H2 = std::max( h_H2 , *it );
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}
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if ( it == it_minh )
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{
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il = i;
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}
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i++;
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}
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//G4cout << "max " << h_H << " " << ih << G4endl;
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//G4cout << "max-dash " << h_H2 << G4endl;
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//G4cout << "min " << h_L << " " << il << G4endl;
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std::vector< G4double > centroidPoint = calCentroid ( ih );
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// REFLECTION
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std::vector< G4double > reflectionPoint =
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getReflectionPoint( currentSimplex[ ih ] , centroidPoint );
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G4double h = getValue( reflectionPoint );
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if ( h <= h_L )
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{
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// EXPANSION
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std::vector< G4double > expansionPoint =
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getExpansionPoint( reflectionPoint , centroidPoint );
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G4double hh = getValue( expansionPoint );
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if ( hh <= h_L )
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{
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// Replace
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currentSimplex[ ih ] = expansionPoint;
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//G4cout << "A" << G4endl;
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}
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else
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{
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// Replace
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currentSimplex[ ih ] = reflectionPoint;
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//G4cout << "B1" << G4endl;
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}
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}
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else
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{
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if ( h <= h_H2 )
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{
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// Replace
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currentSimplex[ ih ] = reflectionPoint;
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//G4cout << "B2" << G4endl;
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}
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else
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{
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if ( h <= h_H )
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{
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// Replace
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currentSimplex[ ih ] = reflectionPoint;
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//G4cout << "BC" << G4endl;
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}
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// CONTRACTION
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std::vector< G4double > contractionPoint =
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getContractionPoint( currentSimplex[ ih ] , centroidPoint );
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G4double hh = getValue( contractionPoint );
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if ( hh <= h_H )
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{
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// Replace
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currentSimplex[ ih ] = contractionPoint;
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//G4cout << "C" << G4endl;
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}
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else
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{
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// Replace
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for ( G4int j = 0 ; j <= numberOfVariable ; j++ )
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{
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std::vector< G4double > vec ( numberOfVariable , 0.0 );
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for ( G4int k = 0 ; k < numberOfVariable ; k++ )
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{
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vec[ k ] = ( currentSimplex[ j ][ k ]
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+ currentSimplex[ il ][ k ] ) / 2.0;
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}
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currentSimplex[ j ] = vec;
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}
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//G4cout << "D" << G4endl;
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}
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}
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}
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nth_trial++;
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}
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}
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template<class T>
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std::vector< G4double > G4SimplexDownhill<T>::GetMinimumPoint()
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{
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if ( minimized != true )
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{
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GetMinimum();
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}
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std::vector< G4double >::iterator it_minh =
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std::min_element( currentHeights.begin() , currentHeights.end() );;
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G4int imin = -1;
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G4int i = 0;
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for ( std::vector< G4double >::iterator
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it = currentHeights.begin(); it != currentHeights.end(); it++ )
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{
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if ( it == it_minh )
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{
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imin = i;
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}
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i++;
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}
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std::vector< G4double > minimumPoint = currentSimplex[ imin ];
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return minimumPoint;
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}
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