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// Copyright (C) 2016 EDF
// All Rights Reserved
// This code is published under the GNU Lesser General Public License (GNU LGPL)
#include <vector>
#include <memory>
#include <functional>
#include <array>
#include <math.h>
#include <boost/lexical_cast.hpp>
#include <Eigen/Dense>
#include <Eigen/Eigenvalues>
#include "StOpt/core/utils/comparisonUtils.h"
#include "StOpt/core/grids/RegularGrid.h"
#include "StOpt/core/grids/FullLegendreGridIterator.h"
#include "StOpt/core/grids/LegendreInterpolator.h"
#include "StOpt/core/grids/LegendreInterpolatorSpectral.h"
#include "StOpt/core/grids/RegularLegendreGrid.h"
#include "StOpt/core/utils/AnalyticLegendre.h"
using namespace StOpt;
using namespace Eigen;
using namespace std;
RegularLegendreGrid::RegularLegendreGrid(const ArrayXd &p_lowValues, const ArrayXd &p_step, const ArrayXi &p_nbStep, const ArrayXi &p_poly):
RegularGrid(p_lowValues, p_step, p_nbStep), m_poly(p_poly),
m_gllPoints(p_lowValues.size()),
m_legendre(new array< function< double(const double &) >, 11 >
{
{
Legendre0(), Legendre1(), Legendre2(), Legendre3(), Legendre4(), Legendre5(), Legendre6(), Legendre7(), Legendre8(), Legendre9(), Legendre10()
}
}),
m_fInterpol(make_shared< vector< ArrayXXd > >(p_poly.size())), m_firstPoints(ArrayXi::Zero(p_lowValues.size())), m_lastPoints(p_lowValues.size())
{
m_lastPoints = p_poly ;
for (size_t id = 0; id < m_gllPoints.size(); ++id)
{
m_gllPoints[id].resize(p_poly(id) + 1);
m_gllPoints[id](0) = -1. ;
m_gllPoints[id](p_poly(id)) = 1. ;
if (p_poly(id) == 2)
m_gllPoints[id](1) = 0. ;
else if (p_poly(id) > 2)
{
int n = p_poly(id) - 1;
MatrixXd mat = MatrixXd::Zero(n, n);
for (int i = 0; i < n - 1; ++i)
{
double util = 0.5 * sqrt((i + 1) * (i + 3.) / ((i + 1.5) * (i + 2.5)));
mat(i + 1, i) = util;
mat(i, i + 1) = util;
}
SelfAdjointEigenSolver<MatrixXd> es(mat);
// eigen values
m_gllPoints[id].segment(1, p_poly(id) - 1) = es.eigenvalues().array();
}
}
// function used for interpolations
for (int id = 0; id < p_poly.size(); ++id)
{
(*m_fInterpol)[id].resize(p_poly(id) + 1, p_poly(id) + 1);
ArrayXd rho(p_poly(id) + 1);
for (int i = 0; i <= p_poly(id); ++i)
rho(i) = 2. / ((p_poly(id) + 1) * p_poly(id) * pow((*m_legendre)[p_poly(id)](m_gllPoints[id](i)), 2.));
for (int k = 0; k <= p_poly(id); ++k)
{
double weight = 0;
for (int i = 0; i <= p_poly(id); ++i)
weight += pow((*m_legendre)[k](m_gllPoints[id](i)), 2.) * rho(i);
weight = 1. / weight;
for (int i = 0; i <= p_poly(id); ++i)
{
(*m_fInterpol)[id](k, i) = weight * rho(i) * (*m_legendre)[k](m_gllPoints[id](i));
}
}
}
// update dimension
m_dimensions = m_nbStep * p_poly + 1;
m_nbPoints = m_dimensions.prod();
}
RegularLegendreGrid::RegularLegendreGrid(const ArrayXd &p_lowValues, const ArrayXd &p_step, const ArrayXi &p_nbStep, const vector< ArrayXd > &p_gllPoints,
shared_ptr< vector< ArrayXXd > > p_fInterpol, const ArrayXi &p_firstPoints, const ArrayXi &p_lastPoints):
RegularGrid(p_lowValues, p_step, p_nbStep), m_poly(p_lowValues.size()), m_gllPoints(p_gllPoints),
m_legendre(new array< function< double(const double &) >, 11 >
{
{
Legendre0(), Legendre1(), Legendre2(), Legendre3(), Legendre4(), Legendre5(), Legendre6(), Legendre7(), Legendre8(), Legendre9(), Legendre10()
}
}),
m_fInterpol(p_fInterpol), m_firstPoints(p_firstPoints), m_lastPoints(p_lastPoints)
{
for (size_t id = 0; id < m_gllPoints.size(); ++id)
{
m_poly(id) = p_gllPoints[id].size() - 1;
}
// update dimension
m_dimensions = m_nbStep * m_poly + 1 - m_firstPoints - (m_poly - m_lastPoints);
m_nbPoints = m_dimensions.prod();
}
ArrayXi RegularLegendreGrid::lowerPositionCoord(const Ref<const ArrayXd > &p_point) const
{
#ifndef NOCHECK_GRID
assert(isInside(p_point)) ;
#endif
ArrayXi intCoord(p_point.size());
for (int i = 0; i < p_point.size(); ++i)
{
intCoord(i) = max(min(roundIntAbove((p_point(i) - m_lowValues(i)) / m_step(i)), m_nbStep(i) - 1), 0) * m_poly(i);
}
return intCoord;
}
ArrayXi RegularLegendreGrid::upperPositionCoord(const Ref<const ArrayXd > &p_point) const
{
#ifndef NOCHECK_GRID
assert(isInside(p_point)) ;
#endif
ArrayXi intCoord(p_point.size());
for (int i = 0; i < p_point.size(); ++i)
{
intCoord(i) = max(min(roundIntAbove((p_point(i) - m_lowValues(i)) / m_step(i)) + 1, m_nbStep(i)) * m_poly(i), 0);
}
return intCoord;
}
ArrayXd RegularLegendreGrid::getCoordinateFromIntCoord(const ArrayXi &p_icoord) const
{
ArrayXd ret(p_icoord.size());
for (int i = 0; i < p_icoord.size(); ++i)
{
int nPoint = m_poly(i);
int coordRec = p_icoord(i) + m_firstPoints(i);
int imesh = coordRec / nPoint;
int ipoint = coordRec % nPoint;
ret(i) = m_lowValues(i) + m_step(i) * (imesh + 0.5 * (1 + m_gllPoints[i](ipoint)));
}
return ret;
}
shared_ptr<FullGrid> RegularLegendreGrid::getSubGrid(const Array< array<int, 2>, Dynamic, 1> &p_mesh) const
{
if (p_mesh.size() == 0)
{
return make_shared<RegularLegendreGrid>();
}
ArrayXd lowValues(p_mesh.size()) ;
ArrayXi nbStep(p_mesh.size()) ;
ArrayXi firstPoint(p_mesh.size());
ArrayXi lastPoint(p_mesh.size());
for (int id = 0; id < p_mesh.size(); ++id)
{
firstPoint(id) = p_mesh(id)[0] % m_poly(id);
lastPoint(id) = (p_mesh(id)[1] - 1) % m_poly(id);
if (lastPoint(id) == 0)
lastPoint(id) = m_poly(id);
nbStep(id) = (p_mesh(id)[1] - 1 + m_poly(id) - lastPoint(id) - p_mesh(id)[0] + firstPoint(id)) / m_poly(id);
lowValues(id) = m_lowValues(id) + p_mesh(id)[0] / m_poly(id) * m_step(id);
}
return make_shared<RegularLegendreGrid>(lowValues, m_step, nbStep, m_gllPoints, m_fInterpol, firstPoint, lastPoint);
}
shared_ptr< GridIterator> RegularLegendreGrid::getGridIteratorInc(const int &p_iThread) const
{
return make_shared<FullLegendreGridIterator>(m_lowValues, m_step, m_nbStep, m_poly, m_gllPoints, m_firstPoints, m_lastPoints, p_iThread) ;
}
shared_ptr< GridIterator> RegularLegendreGrid::getGridIterator() const
{
return make_shared<FullLegendreGridIterator>(m_lowValues, m_step, m_nbStep, m_poly, m_gllPoints, m_firstPoints, m_lastPoints) ;
}
shared_ptr<Interpolator> RegularLegendreGrid::createInterpolator(const ArrayXd &p_coord) const
{
return make_shared<LegendreInterpolator>(this, p_coord) ;
}
shared_ptr<InterpolatorSpectral> RegularLegendreGrid::createInterpolatorSpectral(const Eigen::ArrayXd &p_values) const
{
return make_shared<LegendreInterpolatorSpectral>(this, p_values);
}
void RegularLegendreGrid::rescalepoint(const double &p_point, const int &p_idim, double &p_coordLoc, int &p_iCoord)const
{
p_iCoord = max(min(roundIntAbove((p_point - m_lowValues(p_idim)) / m_step(p_idim)), m_nbStep(p_idim) - 1), 0) * m_poly(p_idim);
int coordRec = p_iCoord + m_firstPoints(p_idim);
int imesh = coordRec / m_poly(p_idim);
int ipoint = coordRec % m_poly(p_idim);
double coordMin = m_lowValues(p_idim) + m_step(p_idim) * (imesh + 0.5 * (1 + m_gllPoints[p_idim](ipoint)));
p_coordLoc = 2.*(p_point - coordMin) / m_step(p_idim) - 1.;
}
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