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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2004 Ferdinando Ametrano
Copyright (C) 2004 Gianni Piolanti
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/randomnumbers/faurersg.hpp>
#include <ql/math/primenumbers.hpp>
namespace QuantLib {
FaureRsg::FaureRsg(Size dimensionality)
: dimensionality_(dimensionality),
// sequenceCounter_(0),
sequence_(std::vector<Real> (dimensionality), 1.0),
integerSequence_(dimensionality, 0) {
QL_REQUIRE(dimensionality>0,
"dimensionality must be greater than 0");
// base is the lowest prime number >= dimensionality_
Size i, j, k=1;
base_=2;
while (base_<dimensionality_) {
base_ = (Size)PrimeNumbers::get(k);
k++;
}
mbit_=(Size)(std::log((double)std::numeric_limits<long int>::max())/
std::log((double)base_));
gray_ = std::vector<std::vector<long int> >(dimensionality_,
std::vector<long int>(mbit_+1, 0));
bary_ = std::vector<long int>(mbit_+1, 0);
//setMatrixValues();
powBase_ = std::vector<std::vector<long int> >(mbit_,
std::vector<long int>(2*base_-1, 0));
powBase_[mbit_-1][base_] = 1;
for (int i2=mbit_-2; i2>=0; --i2)
powBase_[i2][base_] = powBase_[i2+1][base_] * base_;
for (int ii=0; ii<(int)mbit_; ii++) {
for (int j1=base_+1; j1<2*(int)base_-1; j1++ )
powBase_[ii][j1] = powBase_[ii][j1-1] + powBase_[ii][base_];
for (int j2=base_-1; j2>=0; --j2)
powBase_[ii][j2] = powBase_[ii][j2+1] - powBase_[ii][base_];
}
addOne_.resize(base_);
for (j=0; j<base_ ; j++)
addOne_[j] = (j+1) % base_;
//setPascalMatrix();
for (k=0; k<mbit_; k++) {
std::vector<std::vector<long int> > mm(dimensionality_+1,
std::vector<long int>(k+1, 0));
pascal3D.push_back(mm);
pascal3D[k][0][k] = 1;
pascal3D[k][1][0] = 1;
pascal3D[k][1][k] = 1;
}
long int p1, p2;
for (k=2; k<mbit_ ; k++) {
for (i=1; i<k ; i++) {
p1 = pascal3D[k-1][1][i-1];
p2 = pascal3D[k-1][1][i];
pascal3D[k][1][i] = (p1+p2) % base_;
}
}
long int fact = 1, diag;
for (j=2; j<dimensionality_; j++) {
for (long int kk=mbit_-1; kk>=0 ; --kk) {
diag = mbit_ - kk - 1;
if (diag==0)
fact = 1;
else
fact = (fact*j) % base_;
for (long int ii=0; ii<=kk; ii++)
pascal3D[diag+ii][j][ii] = (fact*
pascal3D[diag+ii][1][ii]) % base_;
}
}
normalizationFactor_ = (double)base_ * (double)powBase_[0][base_];
// std::cout << IntegerFormatter::toString(dimensionality_) << ", " ;
// std::cout << IntegerFormatter::toString(normalizationFactor_);
// std::cout << std::endl;
}
void FaureRsg::generateNextIntSequence() const {
// sequenceCounter_++;
Size bit = 0;
bary_[bit] = addOne_[bary_[bit]];
while (bary_[bit] == 0) {
bit++;
bary_[bit] = addOne_[bary_[bit]];
};
QL_REQUIRE(bit != mbit_,
"Error processing Faure sequence." );
long int tmp, g1, g2;
for (Size i=0; i<dimensionality_ ; i++) {
for (Size j=0; j<=bit ; j++) {
tmp = gray_[i][j];
gray_[i][j] = (pascal3D[bit][i][j] + tmp) % base_;
g1 = gray_[i][j];
g2 = base_ - 1 + g1 - tmp;
integerSequence_[i] += powBase_[j][g2];
}
}
}
}
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