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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2007 François du Vignaud
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.
*/
#include <ql/math/matrixutilities/tapcorrelations.hpp>
#include <cmath>
namespace QuantLib {
Matrix triangularAnglesParametrization(const Array& angles,
Size matrixSize,
Size rank) {
// what if rank == 1?
QL_REQUIRE((rank-1) * (2*matrixSize - rank) == 2*angles.size(),
"rank-1) * (matrixSize - rank/2) == angles.size()");
Matrix m(matrixSize, matrixSize);
// first row filling
m[0][0] = 1.0;
for (Size j=1; j<matrixSize; ++j)
m[0][j] = 0.0;
// next ones...
Size k = 0; //angles index
for (Size i=1; i<m.rows(); ++i) {
Real sinProduct = 1.0;
Size bound = std::min(i,rank-1);
for (Size j=0; j<bound; ++j) {
m[i][j] = std::cos(angles[k]);
m[i][j] *= sinProduct;
sinProduct *= std::sin(angles[k]);
++k;
}
m[i][bound] = sinProduct;
for (Size j=bound+1; j<m.rows(); ++j)
m[i][j] = 0;
}
return m;
}
Matrix lmmTriangularAnglesParametrization(const Array& angles,
Size matrixSize,
Size) {
Matrix m(matrixSize, matrixSize);
for (Size i=0; i<m.rows(); ++i) {
Real cosPhi, sinPhi;
if (i>0) {
cosPhi = std::cos(angles[i-1]);
sinPhi = std::sin(angles[i-1]);
} else {
cosPhi = 1.0;
sinPhi = 0.0;
}
for (Size j=0; j<i; ++j)
m[i][j] = sinPhi * m[i-1][j];
m[i][i] = cosPhi;
for (Size j=i+1; j<m.rows(); ++j)
m[i][j] = 0.0;
}
return m;
}
Matrix triangularAnglesParametrizationUnconstrained(const Array& x,
Size matrixSize,
Size rank) {
Array angles(x.size());
//we convert the unconstrained parameters in angles
for (Size i = 0; i < x.size(); ++i)
angles[i] = M_PI*.5 - std::atan(x[i]);
return triangularAnglesParametrization(angles, matrixSize, rank);
}
Matrix lmmTriangularAnglesParametrizationUnconstrained(const Array& x,
Size matrixSize,
Size rank) {
Array angles(x.size());
//we convert the unconstrained parameters in angles
for (Size i = 0; i < x.size(); ++i)
angles[i] = M_PI*.5 - std::atan(x[i]);
return lmmTriangularAnglesParametrization(angles, matrixSize, rank);
}
Matrix triangularAnglesParametrizationRankThree(Real alpha, Real t0,
Real epsilon, Size matrixSize) {
Matrix m(matrixSize, 3);
for (Size i=0; i<m.rows(); ++i) {
Real t = t0 * (1 - std::exp(epsilon*Real(i)));
Real phi = std::atan(alpha * t);
m[i][0] = std::cos(t)*std::cos(phi);
m[i][1] = std::sin(t)*std::cos(phi);
m[i][2] = -std::sin(phi);
}
return m;
}
Matrix triangularAnglesParametrizationRankThreeVectorial(const Array& parameters,
Size nbRows) {
QL_REQUIRE(parameters.size() == 3,
"the parameter array must contain exactly 3 values" );
return triangularAnglesParametrizationRankThree(parameters[0],
parameters[1],
parameters[2],
nbRows);
}
Real FrobeniusCostFunction::value(const Array& x) const {
Array temp = values(x);
return DotProduct(temp, temp);
}
Array FrobeniusCostFunction::values(const Array& x) const {
Array result((target_.rows()*(target_.columns()-1))/2);
Matrix pseudoRoot = f_(x, matrixSize_, rank_);
Matrix differences = pseudoRoot * transpose(pseudoRoot) - target_;
Size k = 0;
// then we store the elementwise differences in a vector.
for (Size i=0; i<target_.rows(); ++i) {
for (Size j=0; j<i; ++j){
result[k] = differences[i][j];
++k;
}
}
return result;
}
}
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