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/*
* TPSInterpolate.hpp
* license: http://www.boost.org/LICENSE_1_0.txt
* Created on: 18 Aug 2010
* Author: Peter Stroia-Williams
*/
#ifndef TPSINTERPOLATE_HPP_
#define TPSINTERPOLATE_HPP_
#include <vector>
#include <cmath>
#include <boost/array.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/vector_expression.hpp>
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/vector_proxy.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/triangular.hpp>
#include <boost/numeric/ublas/lu.hpp>
#include <boost/numeric/ublas/io.hpp>
using namespace boost::numeric::ublas;
using namespace boost;
using namespace std;
double
radial_basis(double r)
{
if(r==0.0)
return 0.0;
return pow(r, 2) * log(r);
}
template<typename T1, typename T2, int Dim>
double
radialbasis(const array<T1, Dim> & v1, const array<T2, Dim> & v2)
{
boost::numeric::ublas::vector<double> v(Dim);
for(unsigned int i(0); i < v.size(); ++i)
{
v(i) = v1[i] - v2[i];
}
return radial_basis(norm_2(v));
}
template<int PosDim, int ValDim, typename WorkingType = double>
class ThinPlateSpline
{
public:
matrix<WorkingType> Wa;
std::vector<array<WorkingType, PosDim> > refPositions;
ThinPlateSpline()
{}
ThinPlateSpline(std::vector<array<WorkingType, PosDim> > positions,
std::vector<array<WorkingType, ValDim> > values)
{
matrix<WorkingType> L;
refPositions = positions;
const int numPoints(refPositions.size());
const int WaLength(numPoints + PosDim + 1);
L = matrix<WorkingType> (WaLength, WaLength);
// Calculate K and store in L
for(int i(0); i < numPoints; i++)
{
L(i,i) = 0.0;
// K is symmetrical so no point in calculating things twice
int j(i + 1);
for(; j < numPoints; ++j)
{
L(i,j) = L(j,i) = radialbasis<WorkingType, WorkingType, PosDim>(refPositions[i], refPositions[j]);
}
// construct P and store in K
L(j,i) = L(i,j) = 1.0;
++j;
for(int posElm(0); j < WaLength; ++posElm, ++j)
L(j,i) = L(i,j) = positions[i][posElm];
}
// O
for(int i(numPoints); i < WaLength; i++)
for(int j(numPoints); j < WaLength; j++)
L(i,j) = 0.0;
// Solve L^-1 Y = W^T
typedef permutation_matrix<std::size_t> pmatrix;
matrix<WorkingType> A(L);
pmatrix pm(A.size1());
int res = lu_factorize(A, pm);
if(res != 0)
;//TODO catch this error
matrix<WorkingType> invL(identity_matrix<WorkingType>(A.size1()));
lu_substitute(A, pm, invL);
Wa = matrix<WorkingType>(WaLength, ValDim );
matrix <WorkingType> Y(WaLength, ValDim);
int i(0);
for(; i < numPoints; i++)
for(int j(0); j < ValDim; ++j)
Y(i, j) = values[i][j];
for(; i < WaLength; i++)
for(int j(0); j < ValDim; ++j)
Y(i, j) = 0.0;
Wa = prod(invL,Y);
}
array<WorkingType, ValDim>
interpolate(const array<WorkingType, PosDim> &position) const
{
array<WorkingType, ValDim> result;
// Init result
for(int j(0); j < ValDim; ++j)
result[j] = 0;
unsigned int i(0);
for(; i < Wa.size1() - (PosDim+1); ++i)
{
for(int j(0); j < ValDim; ++j)
result[j] += Wa(i,j) * radialbasis<WorkingType, WorkingType, PosDim>(refPositions[i], position);
}
for(int j(0); j < ValDim; ++j)
result[j] += Wa(i,j);
++i;
for(int k(0); k < PosDim; ++k, ++i)
{
for(int j(0); j < ValDim; ++j)
result[j] += Wa(i,j) * position[k];
}
return result;
}
};
#endif /* TPSINTERPOLATE_HPP_ */
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