/usr/include/ql/math/interpolations/kernelinterpolation2d.hpp is in libquantlib0-dev 1.7.1-1.
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/*
Copyright (C) 2009 Dimitri Reiswich
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
/*! \file kernelinterpolation2d.hpp
\brief 2D Kernel interpolation
*/
#ifndef quantlib_kernel_interpolation2D_hpp
#define quantlib_kernel_interpolation2D_hpp
#include <ql/math/interpolations/interpolation2d.hpp>
#include <ql/math/matrixutilities/qrdecomposition.hpp>
/*
Grid Explanation:
Grid=[ (x1,y1) (x1,y2) (x1,y3)... (x1,yM);
(x2,y1) (x2,y2) (x2,y3)... (x2,yM);
.
.
.
(xN,y1) (xN,y2) (xN,y3)... (xN,yM);
]
The Passed variables are:
- x which is N dimensional
- y which is M dimensional
- zData which is NxM dimensional and has the z values
corresponding to the grid above.
- kernel is a template which needs a Real operator()(Real x) implementation
*/
namespace QuantLib {
namespace detail {
template <class I1, class I2, class M, class Kernel>
class KernelInterpolation2DImpl
: public Interpolation2D::templateImpl<I1,I2,M> {
public:
KernelInterpolation2DImpl(const I1& xBegin, const I1& xEnd,
const I2& yBegin, const I2& yEnd,
const M& zData,
const Kernel& kernel)
: Interpolation2D::templateImpl<I1,I2,M>(xBegin, xEnd,
yBegin, yEnd, zData),
xSize_(Size(xEnd-xBegin)), ySize_(Size(yEnd-yBegin)),
xySize_(xSize_*ySize_), invPrec_(1.0e-10),
alphaVec_(xySize_), yVec_(xySize_),
M_(xySize_,xySize_),
kernel_(kernel) {
QL_REQUIRE(zData.rows()==xSize_,
"Z value matrix has wrong number of rows");
QL_REQUIRE(zData.columns()==ySize_,
"Z value matrix has wrong number of columns");
}
void calculate() {
updateAlphaVec();
}
Real value(Real x1, Real x2) const {
Real res=0.0;
Array X(2),Xn(2);
X[0]=x1;X[1]=x2;
Size cnt=0; // counter
for( Size j=0; j< ySize_;++j){
for( Size i=0; i< xSize_;++i){
Xn[0]=this->xBegin_[i];
Xn[1]=this->yBegin_[j];
res+=alphaVec_[cnt]*kernelAbs(X,Xn);
cnt++;
}
}
return res/gammaFunc(X);
}
// the calculation will solve y=M*a for a. Due to
// singularity or rounding errors the recalculation
// M*a may not give y. Here, a failure will be thrown if
// |M*a-y|>=invPrec_
void setInverseResultPrecision(Real invPrec){
invPrec_=invPrec;
}
private:
// returns K(||X-Y||) where X,Y are vectors
Real kernelAbs(const Array& X, const Array& Y)const{
return kernel_(vecNorm(X-Y));
}
Real vecNorm(const Array& X)const{
return std::sqrt(DotProduct(X,X));
}
Real gammaFunc(const Array& X)const{
Real res=0.0;
Array Xn(X.size());
for(Size j=0; j< ySize_;++j){
for(Size i=0; i< xSize_;++i){
Xn[0]=this->xBegin_[i];
Xn[1]=this->yBegin_[j];
res+=kernelAbs(X,Xn);
}
}
return res;
}
void updateAlphaVec(){
// Function calculates the alpha vector with given
// fixed pillars+values
Array Xk(2),Xn(2);
Size rowCnt=0,colCnt=0;
Real tmpVar=0.0;
// write y-vector and M-Matrix
for(Size j=0; j< ySize_;++j){
for(Size i=0; i< xSize_;++i){
yVec_[rowCnt]=this->zData_[i][j];
// calculate X_k
Xk[0]=this->xBegin_[i];
Xk[1]=this->yBegin_[j];
tmpVar=1/gammaFunc(Xk);
colCnt=0;
for(Size jM=0; jM< ySize_;++jM){
for(Size iM=0; iM< xSize_;++iM){
Xn[0]=this->xBegin_[iM];
Xn[1]=this->yBegin_[jM];
M_[rowCnt][colCnt]=kernelAbs(Xk,Xn)*tmpVar;
colCnt++; // increase column counter
}// end iM
}// end jM
rowCnt++; // increase row counter
} // end i
}// end j
alphaVec_=qrSolve(M_, yVec_);
// check if inversion worked up to a reasonable precision.
// I've chosen not to check determinant(M_)!=0 before solving
Array diffVec=Abs(M_*alphaVec_ - yVec_);
for (Size i=0; i<diffVec.size(); ++i) {
QL_REQUIRE(diffVec[i]<invPrec_,
"inversion failed in 2d kernel interpolation");
}
}
private:
Size xSize_,ySize_,xySize_;
Real invPrec_;
Array alphaVec_, yVec_;
Matrix M_;
Kernel kernel_;
};
} // end namespace detail
/*! Implementation of the 2D kernel interpolation approach, which
can be found in "Foreign Exchange Risk" by Hakala, Wystup page
256.
The kernel in the implementation is kept general, although a
Gaussian is considered in the cited text.
*/
class KernelInterpolation2D : public Interpolation2D{
public:
/*! \pre the \f$ x \f$ values must be sorted.
\pre kernel needs a Real operator()(Real x) implementation
*/
template <class I1, class I2, class M, class Kernel>
KernelInterpolation2D(const I1& xBegin, const I1& xEnd,
const I2& yBegin, const I2& yEnd,
const M& zData,
const Kernel& kernel) {
impl_ = boost::shared_ptr<Interpolation2D::Impl>(new
detail::KernelInterpolation2DImpl<I1,I2,M,Kernel>(xBegin, xEnd,
yBegin, yEnd,
zData, kernel));
this->update();
}
};
}
#endif
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