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/////////////////////////////////////////////////////////////
// //
// Copyright (c) 2007-2014 by The University of Queensland //
// Centre for Geoscience Computing //
// http://earth.uq.edu.au/centre-geoscience-computing //
// //
// Primary Business: Brisbane, Queensland, Australia //
// Licensed under the Open Software License version 3.0 //
// http://www.opensource.org/licenses/osl-3.0.php //
// //
/////////////////////////////////////////////////////////////
template<class T,int n>
simplex_method<T,n>::simplex_method(nfunction<T,n>* f)
{
m_func=f;
}
template<class T,int n>
nvector<T,n> simplex_method<T,n>::reflect(int idx)
{
nvector<T,n> sum=nvector<T,n>(T(0));
for(int i=0;i<n+1;i++){
if(i!=idx){
sum+=m_vert[i];
}
}
sum+=sum;
sum=sum/T(n);
return sum-m_vert[idx];
}
template<class T,int n>
void simplex_method<T,n>::insert(const nvector<T,n>& vert,T val,int idx)
{
bool up=true;
bool down=true;
m_vert[idx]=vert;
m_val[idx]=val;
int i=idx;
while(up && (i<n)){
if(m_val[i]>m_val[i+1]){
up=false;
} else {
// swap
nvector<T,n> h_vert=m_vert[i];
T h_val=m_val[i];
m_vert[i]=m_vert[i+1];
m_val[i]=m_val[i+1];
m_vert[i+1]=h_vert;
m_val[i+1]=h_val;
i++;
}
}
while(down && (i>0)){
if(m_val[i]<m_val[i-1]){
down=false;
} else {
// swap
nvector<T,n> h_vert=m_vert[i];
T h_val=m_val[i];
m_vert[i]=m_vert[i-1];
m_val[i]=m_val[i-1];
m_vert[i-1]=h_vert;
m_val[i-1]=h_val;
i--;
}
}
}
template<class T,int n>
void simplex_method<T,n>::shrink()
{
nvector<T,n> center=m_vert[0];
for(int i=1;i<n+1;i++){
center+=m_vert[i];
}
center=center/T(n+1);
for(int i=0;i<n+1;i++){
m_vert[i]=center+(m_vert[i]-center)/T(2);
m_val[i]=(*m_func)(m_vert[i]);
}
sort();
}
template<class T,int n>
void simplex_method<T,n>::sort()
{
for(int i=0;i<n-1;i++){
for(int j=i;j<n;j++){
if(m_val[j]<m_val[j+1]){
nvector<T,n> h_vert=m_vert[j];
T h_val=m_val[j];
m_vert[j]=m_vert[j+1];
m_val[j]=m_val[j+1];
m_vert[j+1]=h_vert;
m_val[j+1]=h_val;
}
}
}
}
template<class T,int n>
nvector<T,n> simplex_method<T,n>::solve(T lim, const nvector<T,n> & start,int max)
{
int idx;
for(int i=0;i<n+1;i++){
m_val[i]=T(0);
}
// set initial simplex vertices
insert(start,(*m_func)(start),0);
for(int i=0;i<n;i++){
nvector<T,n> temp_vert=start+nvector<T,n>::unit(i);
T temp_val=(*m_func)(temp_vert);
insert(temp_vert,temp_val,i+1);
}
T eps=m_val[0];
int count=0;
while((eps>lim)&&((count<max)||(max==-1))){
idx=0;
bool found=false;
while((idx<n+1) && !found){
nvector<T,n> temp_vert=reflect(idx);
T temp_val=(*m_func)(temp_vert);
if(temp_val<m_val[idx]){
insert(temp_vert,temp_val,idx);
found=true;
} else {
idx++;
}
}
if(idx==n+1) shrink();
//for(int i=0;i<n+1;i++){
// cout << m_vert[i] << " " << m_val[i] << endl;
//}
//cout << "------------" << endl;
eps=m_val[n];
count++;
//std::cout << "step : " << count << " eps : " << eps << std::endl;
}
return m_vert[n];
}
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