422 lines
18 KiB
C++
422 lines
18 KiB
C++
/*
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* Portable Agile C++ Classes (PACC)
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* Copyright (C) 2001-2003 by Marc Parizeau
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* http://manitou.gel.ulaval.ca/~parizeau/PACC
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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*
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* Contact:
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* Laboratoire de Vision et Systemes Numeriques
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* Departement de genie electrique et de genie informatique
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* Universite Laval, Quebec, Canada, G1K 7P4
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* http://vision.gel.ulaval.ca
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*
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*/
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/*!
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* \file PACC/Math/QRandSequencer.cpp
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* \brief Class methods for the Scrambled Halton quasi-random sequence generator.
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* \author Christian Gagne <cgagne@gmail.com>
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* \author Olivier Teytaud <olivier.teytaud@lri.fr>
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* \author Marc Parizeau <marc.parizeau@gel.ulaval.ca>
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* $Revision: 1.6.2.1 $
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* $Date: 2007/09/10 18:24:08 $
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*/
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#include "Util/Assert.hpp"
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#include "Math/QRandSequencer.hpp"
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#include <cmath>
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#include <sstream>
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#ifndef M_PI
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#define M_PI 3.14159265358979323846
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#endif
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using namespace PACC;
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/*!
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* \brief Construct a low-discrepancy sequence generator of the specified dimensionality.
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* \param inDimensionality Dimensionality for the generated sequences.
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* \param inRand Random number generator.
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*/
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QRandSequencer::QRandSequencer(unsigned int inDimensionality, PACC::Randomizer& inRand) :
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mDimensionality(inDimensionality),
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mCount(0)
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{
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if(inDimensionality != 0) reset(mDimensionality, inRand);
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}
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/*!
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* \brief Compute square root of covariance matrix.
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* \param outSqRootCovar Output square root matrix.
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* \param inCovar Input covariance matrix.
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*/
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void QRandSequencer::computeSqRootCovar(PACC::Matrix& outSqRootCovar, PACC::Matrix& inCovar)
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{
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Vector lValues;
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inCovar.computeEigens(lValues, outSqRootCovar);
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for(unsigned int j = 0; j < lValues.size(); ++j) {
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double lStDev = std::sqrt(lValues[j]);
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for(unsigned int i = 0; i < lValues.size(); ++i) outSqRootCovar(i,j) *= lStDev;
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}
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}
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/*!
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* \brief Generate a low-discrepancy sequence.
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* \param outValues Generated values of the sequence
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* \param outMaxValues Max range for each value.
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*/
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void QRandSequencer::generateSequence(std::vector<unsigned long>& outValues, std::vector<unsigned long>& outMaxValues)
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{
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outValues.resize(mBases.size());
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outMaxValues.resize(mBases.size());
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bool lShouldReset=false;
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for(unsigned int i = 0; i < mBases.size(); ++i) {
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// Increment the counter values according to their basis.
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unsigned int lIndex = 0;
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while((lIndex<mCounters[i].size()) && (mCounters[i][lIndex]==(mBases[i]-1))) {
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mCounters[i][lIndex] = 0;
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++lIndex;
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}
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if(lIndex==mCounters[i].size()) mCounters[i].push_back(1);
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else ++mCounters[i][lIndex];
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// Unscramble the counter value and convert it from its prime basis.
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const unsigned int lCountSizeI = mCounters[i].size();
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unsigned long lBasesPow = mBases[i];
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outValues[i] = mPermutations[i][mCounters[i][lCountSizeI-1]];
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for(unsigned int j = lCountSizeI-1; j >= 1; --j) {
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outValues[i] += (mPermutations[i][mCounters[i][j-1]] * lBasesPow);
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lBasesPow *= mBases[i];
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}
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outMaxValues[i] = lBasesPow;
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// Check if we should reset counters.
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if(lBasesPow >= (LONG_MAX/mBases[i])) lShouldReset = true;
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}
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// Reset counters when we are getting near LONG_MAX on one component.
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if(lShouldReset) {
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for(unsigned int i = 0; i < mCounters.size(); ++i) mCounters.clear();
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mCount = 0;
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}
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else ++mCount;
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}
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/*!
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* \brief Generate a point vector of Gaussian distribution N(0,I).
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* \param outVector Generated vector point.
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*/
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void QRandSequencer::getGaussianVector(PACC::Vector& outVector)
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{
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std::vector<unsigned long> lValues, lMaxValues;
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generateSequence(lValues, lMaxValues);
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PACC_AssertM((lValues.size()%2)==0 && (lMaxValues.size()%2)==0, "getGaussianVector() internal error");
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outVector.resize(lValues.size());
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// Box-Muller method to get gaussian distributions.
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for(unsigned int i = 0; i < lValues.size(); i+=2) {
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const double lX1 = double(lValues[i]) / double(lMaxValues[i]);
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const double lX2 = double(lValues[i+1]) / double(lMaxValues[i+1]);
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const double lR = std::sqrt(-2.0 * std::log(1.0 - lX1));
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const double lPhi = 2.0 * M_PI * lX2;
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outVector[i] = lR * std::cos(lPhi);
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outVector[i+1] = lR * std::sin(lPhi);
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}
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outVector.resize(mDimensionality);
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}
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/*!
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* \brief Generate a point vector of gaussian distribution \c N(inCenter,inStdDev*I).
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* \param outVector Generated vector point.
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* \param inCenter Center of the gaussian distribution.
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* \param inStDev Vector of standard deviations for the Gaussian distribution.
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The covariance of the generated distribution is a diagonal matrix with the values in \c inStDev.
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\attention The size of arguments \c inCenter and \c inStdDev must be equal to the
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dimensionality of this sequencer.
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*/
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void QRandSequencer::getGaussianVector(PACC::Vector& outVector, const PACC::Vector& inCenter, const PACC::Vector& inStDev)
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{
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PACC_AssertM(inCenter.size() == mDimensionality, "getGaussianVector() invalid size for the center vector");
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PACC_AssertM(inStDev.size() == mDimensionality, "getGaussianVector() invalid size for the stdev vector");
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// generate N(0,I) vector
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getGaussianVector(outVector);
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// apply scales
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for(unsigned int i = 0; i < outVector.size(); ++i) outVector *= inStDev[i];
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// apply translation
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outVector += inCenter;
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}
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/*!
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* \brief Generate a point vector of gaussian distribution N(inCenter,inCovar).
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* \param outVector Generated vector point.
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* \param inCenter Center of the gaussian distribution.
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* \param inSqRootCovar Square root of the covariance matrix.
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This method must be invoqued with the square root of the distribution covariance matrix C:
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\code
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C^0.5 = ZD
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\endcode
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where Z is the matrix of the eigen vectors of C, and D is the diagonal matrix that
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contains the square roots of its eigen values. To compute this matrix, the user
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should call the QRandSequencer::computeSqRootCovar helper method.
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\attention The size of arguments \c inCenter and \c inSqRootCovar must be compatible
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with the dimensionality of this sequencer.
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*/
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void QRandSequencer::getGaussianVector(PACC::Vector& outVector, const PACC::Vector& inCenter, const PACC::Matrix& inSqRootCovar)
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{
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PACC_AssertM(inCenter.size() == mDimensionality, "getGaussianVector() invalid size for the center vector");
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PACC_AssertM((inSqRootCovar.getCols() == mDimensionality) && (inSqRootCovar.getRows()==mDimensionality),
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"getGaussianVector() invalid size for the covariance matrix");
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// generate N(0,I) vector
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getGaussianVector(outVector);
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// apply transform matrix
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outVector = inCenter + inSqRootCovar*outVector;
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}
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/*!
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* \brief Get a new integer low-discrepancy sequence.
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* \param outSequence Generated integer sequence.
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* \param inMinValue Minimum value for all components of the sequence.
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* \param inMaxValue Maximum value for all components of the sequence.
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*/
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void QRandSequencer::getIntegerSequence(std::vector<long>& outSequence, long inMinValue, long inMaxValue)
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{
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PACC_AssertM(inMinValue < inMaxValue, "getIntegerSequence() min value must be less than max value");
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std::vector<long> lMinValues(mDimensionality, inMinValue);
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std::vector<long> lMaxValues(mDimensionality, inMaxValue);
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getIntegerSequence(outSequence, lMinValues, lMaxValues);
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}
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/*!
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* \brief Get a new integer low-discrepancy sequence.
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* \param outSequence Generated integer sequence.
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* \param inMinValues Minimum value for each component value of the sequence.
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* \param inMaxValues Maximum value for each component value of the sequence.
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\attention The size of arguments \c inMinValues and \c inMaxValues must be equal to the dimensionality of this sequencer.
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*/
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void QRandSequencer::getIntegerSequence(std::vector<long>& outSequence, const std::vector<long>& inMinValues, const std::vector<long>& inMaxValues)
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{
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PACC_AssertM(inMinValues.size() == mDimensionality, "getIntegerSequence() invalid min value vector size");
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PACC_AssertM(inMaxValues.size() == mDimensionality, "getIntegerSequence() invalid max value vector size");
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std::vector<unsigned long> lValues, lMaxValues;
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generateSequence(lValues, lMaxValues);
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outSequence.resize(mDimensionality);
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for(unsigned int i = 0; i < mDimensionality; ++i) {
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PACC_AssertM(inMinValues[i] < inMaxValues[i], "getIntegerSequence() min value must be less than max value");
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const unsigned long lMaxMinRange = inMaxValues[i] - inMinValues[i];
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if(lMaxMinRange < (LONG_MAX/20000)) {
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outSequence[i] = (lValues[i] * lMaxMinRange) / lMaxValues[i];
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} else {
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outSequence[i] = (long)std::floor(double(lValues[i]) / double(lMaxValues[i]) * double(lMaxMinRange));
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}
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outSequence[i] += inMinValues[i];
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}
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}
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/*!
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* \brief Return the internal state of the quasi-random numbers generator.
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*/
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std::string QRandSequencer::getState(void) const
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{
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if(mBases.size()==0) return std::string("");
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std::ostringstream lOSS;
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lOSS << mDimensionality << ',';
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for(unsigned int i=0; i<mBases.size(); ++i) {
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lOSS << mBases[i] << ',';
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for(unsigned int j=1; j<mBases[i]; ++j) lOSS << mPermutations[i][j] << ',';
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}
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lOSS << mCount;
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return lOSS.str();
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}
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/*!
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* \brief Generate a point vector of uniform distribution.
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* \param outVector Generated point vector.
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* \param inMinValue Minimum value for all components of the vector.
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* \param inMaxValue Maximum value for all components of the vector.
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*/
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void QRandSequencer::getUniformVector(PACC::Vector& outVector, double inMinValue, double inMaxValue)
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{
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PACC_AssertM(inMinValue < inMaxValue, "getUniformVector() min value must be less than max value");
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Vector lMinValues(mDimensionality, inMinValue);
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Vector lMaxValues(mDimensionality, inMaxValue);
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getUniformVector(outVector, lMinValues, lMaxValues);
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}
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/*!
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* \brief Generate a point vector of uniform distribution.
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* \param outVector Generated point vector.
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* \param inMinValues Minimum value for each components of the point.
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* \param inMaxValues Maximum value for each components of the point.
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\attention The size of arguments \c inMinValues and \c inMaxValues must be equal to the dimensionality of this sequencer.
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*/
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void QRandSequencer::getUniformVector(PACC::Vector& outVector, const PACC::Vector& inMinValues, const PACC::Vector& inMaxValues)
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{
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PACC_AssertM(inMinValues.size() == mDimensionality, "getUniformVector() invalid min value vector size");
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PACC_AssertM(inMaxValues.size() == mDimensionality, "getUniformVector() invalid max value vector size");
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std::vector<unsigned long> lValues, lMaxValues;
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generateSequence(lValues, lMaxValues);
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outVector.resize(mDimensionality);
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for(unsigned int i = 0; i < mDimensionality; ++i) {
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PACC_AssertM(inMinValues[i] < inMaxValues[i], "getUniformVector() min value must be less than max value");
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const double lMaxMinRange = inMaxValues[i] - inMinValues[i];
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outVector[i] = lMaxMinRange * (double(lValues[i]) / double(lMaxValues[i]));
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outVector[i] += inMinValues[i];
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}
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}
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/*!
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* \brief Reset the low-discrepancy sequence generator.
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* \param inDimensionality Dimensionality of the quasirandom number generator.
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* \param inRand Random number generator used to scrambled the bases.
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*/
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void QRandSequencer::reset(unsigned int inDimensionality, PACC::Randomizer& inRand)
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{
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// 1000 first prime numbers.
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static const unsigned short l1000FirstPrimes[1000] = {
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2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,
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131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,
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263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,
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409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,
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569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,
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719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,
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881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,
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1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,
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1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,
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1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,
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1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,
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1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,
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1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,
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1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,
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2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,
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2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,
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2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,
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2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,
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2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,
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2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,
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2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,
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3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,
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3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,
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3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,
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3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,
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3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,
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3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,
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4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,
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4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,
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4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,
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4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,
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4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,
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4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,
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4993,4999,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,
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5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,
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5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,
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5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,5651,
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5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,
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5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,5953,
|
|
5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,6131,6133,
|
|
6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,
|
|
6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,
|
|
6469,6473,6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,6637,6653,
|
|
6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,6763,6779,6781,6791,6793,6803,
|
|
6823,6827,6829,6833,6841,6857,6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,
|
|
6971,6977,6983,6991,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,
|
|
7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,7307,7309,7321,
|
|
7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507,7517,
|
|
7523,7529,7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,
|
|
7669,7673,7681,7687,7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,
|
|
7841,7853,7867,7873,7877,7879,7883,7901,7907,7919
|
|
};
|
|
|
|
// Get prime numbers used as basis.
|
|
PACC_AssertM(inDimensionality <= 1000, "reset() dimensionality cannot exceed 1000");
|
|
const unsigned int lDim = inDimensionality + (inDimensionality % 2);
|
|
mBases.resize(lDim);
|
|
for(unsigned int i=0; i < lDim; ++i) mBases[i] = l1000FirstPrimes[i];
|
|
std::random_shuffle(mBases.begin(), mBases.end(), inRand);
|
|
// Reset counters to 0.
|
|
mCounters.resize(lDim);
|
|
for(unsigned int i=0; i<lDim; ++i) mCounters[i].clear();
|
|
// Set permutations for the different basis.
|
|
mPermutations.resize(lDim);
|
|
for(unsigned int i=0; i<lDim; ++i) {
|
|
mPermutations[i].resize(mBases[i]);
|
|
for(unsigned int j=0; j < mPermutations[i].size(); ++j) mPermutations[i][j] = j;
|
|
std::random_shuffle(mPermutations[i].begin()+1, mPermutations[i].end(), inRand);
|
|
}
|
|
// Set dimensionality and counter values.
|
|
mDimensionality = inDimensionality;
|
|
mCount = 0;
|
|
}
|
|
|
|
/*!
|
|
* \brief Set the state of the quasi-random numbers generator to \c inState.
|
|
*/
|
|
void QRandSequencer::setState(const std::string& inState)
|
|
{
|
|
// Reset to empty state.
|
|
mBases.clear();
|
|
mCounters.clear();
|
|
mPermutations.clear();
|
|
|
|
// If string empty, exit from function
|
|
if(inState.empty()) return;
|
|
|
|
// Read prime basis and permutations from state string.
|
|
std::istringstream lISS(inState);
|
|
mDimensionality = 0;
|
|
lISS >> mDimensionality;
|
|
lISS.get();
|
|
const unsigned int lDim = mDimensionality + (mDimensionality % 2);
|
|
mBases.resize(lDim);
|
|
mPermutations.resize(lDim);
|
|
for(unsigned int i=0; i<lDim; ++i) {
|
|
lISS >> mBases[i];
|
|
lISS.get();
|
|
mPermutations[i].resize(mBases[i]);
|
|
mPermutations[i][0] = 0;
|
|
for(unsigned int j=1; j<mPermutations[i].size(); ++j) {
|
|
lISS >> mPermutations[i][j];
|
|
lISS.get();
|
|
}
|
|
}
|
|
mCount = 0;
|
|
lISS >> mCount;
|
|
|
|
// Set counters values.
|
|
mCounters.resize(lDim);
|
|
for(unsigned int i=0; i<lDim; ++i) {
|
|
mCounters[i].clear();
|
|
unsigned int lCounterI = mCount;
|
|
while(lCounterI > 0) {
|
|
const unsigned int lRemaining = lCounterI % mBases[i];
|
|
mCounters[i].push_back(lRemaining);
|
|
lCounterI = (lCounterI-lRemaining) / mBases[i];
|
|
}
|
|
}
|
|
}
|