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// Copyright (C) 2018 EDF
// All Rights Reserved
// This code is published under the GNU Lesser General Public License (GNU LGPL)
#include <vector>
#include <memory>
#include <algorithm>
#include <Eigen/Dense>
#include <iostream>
using namespace std;
using namespace Eigen ;
namespace StOpt
{
// To ease sorting of points in each dimension
double lesserPair(const pair<double, int > &c1, const pair<double, int> &c2)
{
return c1.first < c2.first ;
}
/// p_pt size (2,NnbSimul)
/// p_iSort1 first set of points of size (nbSimul,2)
/// p_iSort2 second set of points of size (nbSimul,2)
/// p_valToAdd size (P, nbSimul)
/// p_fDominLoc size (nbFunc, N)
/// merge the two set in first direction for the last dimension
void merge1D1(const ArrayXXd &p_pt,
const ArrayXXi &p_iSort1,
const ArrayXXi &p_iSort2,
const ArrayXXd &p_valToAdd,
ArrayXXd &p_fDominLoc)
{
int i1 = p_iSort1.rows();
int i2 = p_iSort2.rows();
int iloc = 0 ;
ArrayXd sumToAdd = ArrayXd::Zero(p_valToAdd.rows());
for (int i = 0; i < i2 ; ++i)
{
int ipt2 = p_iSort2(i, 0);
int ipt1 = p_iSort1(iloc, 0);
while (p_pt(0, ipt2) >= p_pt(0, ipt1))
{
sumToAdd += p_valToAdd.col(ipt1);
iloc += 1;
if (iloc == i1)
break;
ipt1 = p_iSort1(iloc, 0);
}
// add contribution
p_fDominLoc.col(ipt2) += sumToAdd;
// last points to treat
if (iloc == i1)
{
for (int j = i + 1; j < i2; ++j)
{
p_fDominLoc.col(p_iSort2(j, 0)) += sumToAdd;
}
break;
}
}
}
/// p_pt size (2,nbSimul)
/// p_iSort1 first set of points of size (nbSimul,2)
/// p_iSort2 second set of points of size (nbSimul,2)
/// p_valToAdd size (P, nbSimul)
/// p_fDominLoc size (P, N)
/// merge the two set in second direction for the last dimension
void merge1D2(const ArrayXXd &p_pt,
const ArrayXXi &p_iSort1,
const ArrayXXi &p_iSort2,
const ArrayXXd &p_valToAdd,
ArrayXXd &p_fDominLoc)
{
int i1 = p_iSort1.rows();
int i2 = p_iSort2.rows();
int iloc = i1 - 1 ;
ArrayXd sumToAdd = ArrayXd::Zero(p_valToAdd.rows());
for (int i = i2 - 1; i >= 0; --i)
{
int ipt2 = p_iSort2(i, 0);
int ipt1 = p_iSort1(iloc, 0);
while (p_pt(0, ipt1) >= p_pt(0, ipt2))
{
sumToAdd += p_valToAdd.col(ipt1);
iloc -= 1;
if (iloc == -1)
break;
ipt1 = p_iSort1(iloc, 0);
}
// add contribution
p_fDominLoc.col(ipt2) += sumToAdd;
// last points to treat
if (iloc == -1)
{
for (int j = 0; j < i; ++j)
{
p_fDominLoc.col(p_iSort2(j, 0)) += sumToAdd;
}
break;
}
}
}
/// Merge nD procedure between two sets of point to calculate all summations
/// dimension above 2
/// Set A is dominated by set B in the current dimension
/// p_pt size (d,nbSimul)
/// p_iSort1 first set of points A size (nbSimul,d)
/// p_iSort2 second set of points B size (nbSimul,d
/// p_idim current dimension treated
/// p_valToAdd vector of size 2^{p_dim} of arrays of size (P, nbSimul)
/// p_fDomin vector of size 2^{p_dim} of arrays of size (P, nbSimul)
void mergeND(const ArrayXXd &p_pt,
const ArrayXXi &p_iSort1,
const ArrayXXi &p_iSort2,
const int &p_idim,
const std::vector< shared_ptr< ArrayXXd > > &p_valToAdd,
std::vector< shared_ptr< ArrayXXd > > &p_fDomin)
{
int i1 = p_iSort1.rows();
int i2 = p_iSort2.rows();
// merge the two set to find the median point of the union
int nbPoints = i1 + i2;
int nbPtsDiv2 = nbPoints / 2;
int iPos1 = 0; //position in array1
int iPos2 = 0 ; // position in array 2
int iPos = 0;
int nDimMu = p_idim - 1;
while ((iPos1 < i1) && (iPos2 < i2) && (iPos < nbPtsDiv2))
{
if (p_pt(nDimMu, p_iSort1(iPos1, nDimMu)) < p_pt(nDimMu, p_iSort2(iPos2, nDimMu)))
iPos1++;
else
iPos2++;
iPos++ ;
}
if (iPos1 == i1)
iPos2 += nbPtsDiv2 - iPos;
else if (iPos2 == i2)
iPos1 += nbPtsDiv2 - iPos;
double xMin = 0. ;
if (iPos1 > 0)
{
if (iPos2 > 0)
xMin = max(p_pt(nDimMu, p_iSort1(iPos1 - 1, nDimMu)), p_pt(nDimMu, p_iSort2(iPos2 - 1, nDimMu)));
else
xMin = p_pt(nDimMu, p_iSort1(iPos1 - 1, nDimMu));
}
else
xMin = p_pt(nDimMu, p_iSort2(iPos2 - 1, nDimMu));
double xMax = 0;
if (iPos1 < i1)
{
if (iPos2 < i2)
xMax = min(p_pt(nDimMu, p_iSort1(iPos1, nDimMu)), p_pt(nDimMu, p_iSort2(iPos2, nDimMu)));
else
xMax = p_pt(nDimMu, p_iSort1(iPos1, nDimMu));
}
else
xMax = p_pt(nDimMu, p_iSort2(iPos2, nDimMu));
// xMed permist to seperate two sets with roughly the same number of particles
double xMed = 0.5 * (xMin + xMax) ;
// 4 sets
ArrayXXi iSort11(iPos1, p_idim) ; // set A below : A1
iSort11.col(nDimMu) = p_iSort1.col(nDimMu).head(iPos1);
ArrayXXi iSort21(iPos2, p_idim) ; // set B below: B1
iSort21.col(nDimMu) = p_iSort2.col(nDimMu).head(iPos2);
ArrayXXi iSort12(i1 - iPos1, p_idim); // set A above: A2
iSort12.col(nDimMu) = p_iSort1.col(nDimMu).tail(i1 - iPos1);
ArrayXXi iSort22(i2 - iPos2, p_idim) ; // set B above: B2
iSort22.col(nDimMu) = p_iSort2.col(nDimMu).tail(i2 - iPos2);
// now keep sorted point on dimension 0
for (int id = 0 ; id < p_idim - 1; ++id)
{
int iloc11 = 0;
int iloc12 = 0;
int iloc21 = 0;
int iloc22 = 0;
// Set A
for (int i = 0; i < i1; ++i)
{
int ipt = p_iSort1(i, id); // point number
if (((p_pt(nDimMu, ipt) <= xMed) && (iloc11 < iPos1)) || (iloc12 == iSort12.rows()))
{
// under the median
iSort11(iloc11++, id) = ipt;
}
else
{
iSort12(iloc12++, id) = ipt;
}
}
// set B
for (int i = 0; i < i2; ++i)
{
int ipt = p_iSort2(i, id); // point number
if (((p_pt(nDimMu, ipt) <= xMed) && (iloc21 < iPos2)) || (iloc22 == iSort22.rows()))
{
// under the median
iSort21(iloc21++, id) = ipt;
}
else
{
iSort22(iloc22++, id) = ipt;
}
}
}
// merge on the two set A1 and B1
if ((iPos1 > 0) && (iPos2 > 0))
{
mergeND(p_pt, iSort11, iSort21, p_idim, p_valToAdd, p_fDomin);
}
// merge on teh two set A2 and B2
if ((iPos1 < i1) && (iPos2 < i2))
{
mergeND(p_pt, iSort12, iSort22, p_idim, p_valToAdd, p_fDomin);
}
if (p_idim == 2)
{
// merge on inferior dimension : we know that point in iSort22 dominate iSort11 in dimension 2 and 3
if ((iSort11.rows() > 0) && (iSort22.rows() > 0))
{
// merge 1D for the direction (x_j<x) (y_j<y) (z_j< z) : 0
merge1D1(p_pt, iSort11, iSort22, *p_valToAdd[0], *p_fDomin[0]) ;
// merge 1D for the direction (x_j>x) (y_j<y) (z_j< z) : 1
merge1D2(p_pt, iSort11, iSort22, *p_valToAdd[1], *p_fDomin[1]);
// merge 1D for the direction (x_j<x) (y_j>y) (z_j> z) : 6
merge1D1(p_pt, iSort22, iSort11, *p_valToAdd[6], *p_fDomin[6]);
// merge 1D for the direction (x_j>x) (y_j>x) (z_j> z) : 7
merge1D2(p_pt, iSort22, iSort11, *p_valToAdd[7], *p_fDomin[7]);
}
if ((iSort12.rows() > 0) && (iSort21.rows() > 0))
{
// merge 1D for the direction (x_j<x) (y_j>y) (z_j< z) : 2
merge1D1(p_pt, iSort12, iSort21, *p_valToAdd[2], *p_fDomin[2]) ;
// merge 1D for the direction (x_j>x) (y_j>y) (z_j< z) : 3
merge1D2(p_pt, iSort12, iSort21, *p_valToAdd[3], *p_fDomin[3]) ;
// merge 1D for the direction (x_j<x) (y_j<y) (z_j> z) : 4
merge1D1(p_pt, iSort21, iSort12, *p_valToAdd[4], *p_fDomin[4]) ;
// merge 1D for the direction (x_j>x) (y_j<y) (z_j> z) : 5
merge1D2(p_pt, iSort21, iSort12, *p_valToAdd[5], *p_fDomin[5]) ;
}
}
else
{
/// merge in dimension below
int iSizeV = pow(2, p_idim);
int iSizeVS2 = pow(2, p_idim - 1);
if ((iSort11.rows() > 0) && (iSort22.rows() > 0))
{
// we know a domination of iSort22 on iSort11
std::vector<shared_ptr< ArrayXXd > > valToAdd1(iSizeV);
std::vector<shared_ptr< ArrayXXd > > fDomin1(iSizeV);
for (int id = 0; id < iSizeVS2 ; ++id)
{
valToAdd1[id] = p_valToAdd[id];
fDomin1[id] = p_fDomin[id];
valToAdd1[id + iSizeVS2] = p_valToAdd[id + 3 * iSizeVS2];
fDomin1[id + iSizeVS2] = p_fDomin[id + 3 * iSizeVS2];
}
mergeND(p_pt, iSort11, iSort22, nDimMu, valToAdd1, fDomin1);
}
if ((iSort12.rows() > 0) && (iSort21.rows() > 0))
{
// we know that iSort12 dominated in last coordinate and dominates is the previous iSort21
std::vector<shared_ptr< ArrayXXd > > valToAdd3(iSizeV);
std::vector<shared_ptr< ArrayXXd > > fDomin3(iSizeV);
for (int id = 0; id < iSizeVS2 ; ++id)
{
valToAdd3[id] = p_valToAdd[id + iSizeV];
fDomin3[id] = p_fDomin[id + iSizeV];
valToAdd3[id + iSizeVS2] = p_valToAdd[id + iSizeVS2];
fDomin3[id + iSizeVS2] = p_fDomin[id + iSizeVS2];
}
mergeND(p_pt, iSort21, iSort12, nDimMu, valToAdd3, fDomin3);
}
}
}
/// p_pt size (d,nbSimul)
/// p_iSort first set of points A size (nbSimul,d)
/// p_valToAdd vector of size 2^{d} of arrays of size (P, nbSimul)
/// p_fDomin vector of size 2^{d} of arrays of size (P, nbSimul)
void recursiveCallND(const ArrayXXd &p_pt,
const ArrayXXi &p_iSort,
const std::vector< shared_ptr< ArrayXXd > > &p_valToAdd,
std::vector< shared_ptr< ArrayXXd > > &p_fDomin)
{
if (p_iSort.cols() == 1)
{
for (int is = 1; is < p_pt.cols(); ++is)
p_fDomin[0]->col(p_iSort(is, 0)) = p_fDomin[0]->col(p_iSort(is - 1, 0)) + p_valToAdd[0]->col(p_iSort(is - 1, 0)) ;
for (int is = p_pt.cols() - 2; is >= 0; --is)
p_fDomin[1]->col(p_iSort(is, 0)) = p_fDomin[1]->col(p_iSort(is + 1, 0)) + p_valToAdd[1]->col(p_iSort(is + 1, 0)) ;
}
else if (p_iSort.rows() > 1)
{
// split into two part
int iSize1 = p_iSort.rows() / 2 ;
int iSize2 = p_iSort.rows() - iSize1 ;
int nDimM1 = p_iSort.cols() - 1;
// position valeu of splitting position
double xMedium = 0.5 * (p_pt(nDimM1, p_iSort(iSize1 - 1, nDimM1)) + p_pt(nDimM1, p_iSort(iSize1, nDimM1)));
// utilitary for sorted particles
ArrayXXi iSort1(iSize1, p_iSort.cols());
ArrayXXi iSort2(iSize2, p_iSort.cols());
// copy last dimenson
iSort1.col(nDimM1) = p_iSort.col(nDimM1).head(iSize1);
iSort2.col(nDimM1) = p_iSort.col(nDimM1).tail(iSize2);
// two first dimensions
for (int id = 0; id < nDimM1; ++id)
{
int iLoc1 = 0 ;
int iLoc2 = 0 ;
for (int i = 0 ; i < p_iSort.rows() ; ++i)
{
int iPoint = p_iSort(i, id) ; // get back point number
// decide in which set to add the point
if (((p_pt(nDimM1, iPoint) < xMedium) && (iLoc1 < iSize1)) || (iLoc2 == iSize2))
iSort1(iLoc1++, id) = iPoint;
else
iSort2(iLoc2++, id) = iPoint;
}
}
// call on the two set
recursiveCallND(p_pt, iSort1, p_valToAdd, p_fDomin);
recursiveCallND(p_pt, iSort2, p_valToAdd, p_fDomin);
// merge nD for the 2 set
if (p_iSort.cols() > 2)
mergeND(p_pt, iSort1, iSort2, nDimM1, p_valToAdd, p_fDomin);
else
{
// 2D merge
// merge 1D for direction 1
merge1D1(p_pt, iSort1, iSort2, *p_valToAdd[0], *p_fDomin[0]) ;
// merge 1D for direction 2
merge1D2(p_pt, iSort1, iSort2, *p_valToAdd[1], *p_fDomin[1]);
// merge 1D for direction 3
merge1D1(p_pt, iSort2, iSort1, *p_valToAdd[2], *p_fDomin[2]) ;
// merge 1D for direction 4
merge1D2(p_pt, iSort2, iSort1, *p_valToAdd[3], *p_fDomin[3]) ;
}
}
}
/// \brief Dominance for kernel
/// \param p_pt arrays of point coordinates (d, nbSimul)
/// \param p_valToAdd terms to add (exponential in summation above) : vector of \f$2^d \f kinds of terms of size ( P, nbSimul)
/// \param p_fDomin result of summation \f$2^d \f terms of size ( P, nbSimul)
void nDDominanceKernel(const ArrayXXd &p_pt,
const std::vector< shared_ptr< ArrayXXd > > &p_valToAdd,
std::vector< shared_ptr< ArrayXXd > > &p_fDomin)
{
int nbSim = p_pt.cols();
int nDim = p_pt.rows();
// sort
ArrayXXi iSort(nbSim, nDim);
for (int id = 0; id < nDim; ++id)
{
vector< std::pair< double, int> > xSDim(nbSim);
for (int i = 0; i < nbSim ; ++i)
{
xSDim[i] = make_pair(p_pt(id, i), i);
}
// sort
sort(xSDim.begin(), xSDim.end(), lesserPair);
for (int i = 0; i < nbSim ; ++i)
iSort(i, id) = xSDim[i].second ;
}
for (int ip = 0; ip < pow(2, nDim); ++ip)
p_fDomin[ip] = make_shared<ArrayXXd>(ArrayXXd::Zero(p_valToAdd[ip]->rows(), p_valToAdd[ip]->cols()));
// recursive call with divide and conquer
recursiveCallND(p_pt, iSort, p_valToAdd, p_fDomin);
}
}
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