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/* -*- C++ -*- |
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* |
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* This file is a part of LEMON, a generic C++ optimization library |
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* |
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* Copyright (C) 2003-2008 |
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* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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* (Egervary Research Group on Combinatorial Optimization, EGRES). |
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* |
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* Permission to use, modify and distribute this software is granted |
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* provided that this copyright notice appears in all copies. For |
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* precise terms see the accompanying LICENSE file. |
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* |
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* This software is provided "AS IS" with no warranty of any kind, |
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* express or implied, and with no claim as to its suitability for any |
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* purpose. |
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* |
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*/ |
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#ifndef LEMON_MATH_H |
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#define LEMON_MATH_H |
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///\ingroup misc |
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///\file |
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///\brief Some extensions to the standard \c cmath library. |
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/// |
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///Some extensions to the standard \c cmath library. |
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/// |
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///This file includes the standard math library (cmath). |
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#include<cmath> |
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namespace lemon { |
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/// \addtogroup misc |
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/// @{ |
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/// The Euler constant |
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const long double E = 2.7182818284590452353602874713526625L; |
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/// log_2(e) |
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const long double LOG2E = 1.4426950408889634073599246810018921L; |
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/// log_10(e) |
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const long double LOG10E = 0.4342944819032518276511289189166051L; |
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/// ln(2) |
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const long double LN2 = 0.6931471805599453094172321214581766L; |
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/// ln(10) |
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const long double LN10 = 2.3025850929940456840179914546843642L; |
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/// pi |
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const long double PI = 3.1415926535897932384626433832795029L; |
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/// pi/2 |
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const long double PI_2 = 1.5707963267948966192313216916397514L; |
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/// pi/4 |
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const long double PI_4 = 0.7853981633974483096156608458198757L; |
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/// sqrt(2) |
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const long double SQRT2 = 1.4142135623730950488016887242096981L; |
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/// 1/sqrt(2) |
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const long double SQRT1_2 = 0.7071067811865475244008443621048490L; |
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/// @} |
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} //namespace lemon |
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#endif //LEMON_TOLERANCE_H |
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EXTRA_DIST += \ |
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lemon/Makefile \ |
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lemon/lemon.pc.in |
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pkgconfig_DATA += lemon/lemon.pc |
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lib_LTLIBRARIES += lemon/libemon.la |
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lemon_libemon_la_SOURCES = \ |
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lemon/base.cc \ |
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lemon/random.cc |
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lemon_libemon_la_CXXFLAGS = $(GLPK_CFLAGS) $(CPLEX_CFLAGS) $(SOPLEX_CXXFLAGS) |
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lemon_libemon_la_LDFLAGS = $(GLPK_LIBS) $(CPLEX_LIBS) $(SOPLEX_LIBS) |
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lemon_HEADERS += \ |
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lemon/dim2.h \ |
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lemon/maps.h \ |
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lemon/math.h \ |
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lemon/random.h \ |
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lemon/list_graph.h \ |
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lemon/tolerance.h |
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bits_HEADERS += \ |
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lemon/bits/alteration_notifier.h \ |
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lemon/bits/array_map.h \ |
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lemon/bits/base_extender.h \ |
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lemon/bits/default_map.h \ |
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lemon/bits/graph_extender.h \ |
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lemon/bits/invalid.h \ |
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lemon/bits/map_extender.h \ |
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lemon/bits/traits.h \ |
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lemon/bits/utility.h \ |
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lemon/bits/vector_map.h |
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concept_HEADERS += \ |
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lemon/concept_check.h \ |
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lemon/concepts/digraph.h \ |
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lemon/concepts/graph.h \ |
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lemon/concepts/maps.h \ |
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lemon/concepts/graph_components.h |
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@@ -38,67 +38,68 @@ |
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* |
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* 3. The names of its contributors may not be used to endorse or promote |
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* products derived from this software without specific prior written |
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* permission. |
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* |
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS |
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE |
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, |
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
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* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR |
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* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
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* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
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* OF THE POSSIBILITY OF SUCH DAMAGE. |
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* |
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* |
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* Any feedback is very welcome. |
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* http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html |
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* email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space) |
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*/ |
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#ifndef LEMON_RANDOM_H |
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#define LEMON_RANDOM_H |
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#include <algorithm> |
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#include <iterator> |
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#include <vector> |
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#include <ctime> |
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#include <cmath> |
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#include <lemon/math.h> |
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#include <lemon/dim2.h> |
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///\ingroup misc |
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///\file |
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///\brief Mersenne Twister random number generator |
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namespace lemon { |
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namespace _random_bits { |
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template <typename _Word, int _bits = std::numeric_limits<_Word>::digits> |
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struct RandomTraits {}; |
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template <typename _Word> |
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struct RandomTraits<_Word, 32> { |
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typedef _Word Word; |
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static const int bits = 32; |
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static const int length = 624; |
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static const int shift = 397; |
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static const Word mul = 0x6c078965u; |
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static const Word arrayInit = 0x012BD6AAu; |
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static const Word arrayMul1 = 0x0019660Du; |
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static const Word arrayMul2 = 0x5D588B65u; |
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static const Word mask = 0x9908B0DFu; |
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static const Word loMask = (1u << 31) - 1; |
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static const Word hiMask = ~loMask; |
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static Word tempering(Word rnd) { |
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rnd ^= (rnd >> 11); |
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/// This function generates an exponential distribution random number |
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/// with mean <tt>1/lambda</tt>. |
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/// |
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double exponential(double lambda=1.0) |
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{ |
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return -std::log(1.0-real<double>())/lambda; |
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} |
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/// Gamma distribution with given integer shape |
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/// This function generates a gamma distribution random number. |
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/// |
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///\param k shape parameter (<tt>k>0</tt> integer) |
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double gamma(int k) |
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{ |
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double s = 0; |
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for(int i=0;i<k;i++) s-=std::log(1.0-real<double>()); |
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return s; |
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} |
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/// Gamma distribution with given shape and scale parameter |
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/// This function generates a gamma distribution random number. |
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/// |
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///\param k shape parameter (<tt>k>0</tt>) |
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///\param theta scale parameter |
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/// |
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double gamma(double k,double theta=1.0) |
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{ |
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double xi,nu; |
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const double delta = k-std::floor(k); |
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const double v0= |
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const double v0=E/(E-delta); |
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do { |
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double V0=1.0-real<double>(); |
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double V1=1.0-real<double>(); |
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double V2=1.0-real<double>(); |
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if(V2<=v0) |
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{ |
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xi=std::pow(V1,1.0/delta); |
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nu=V0*std::pow(xi,delta-1.0); |
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} |
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else |
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{ |
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xi=1.0-std::log(V1); |
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nu=V0*std::exp(-xi); |
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} |
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} while(nu>std::pow(xi,delta-1.0)*std::exp(-xi)); |
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return theta*(xi-gamma(int(std::floor(k)))); |
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} |
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/// Weibull distribution |
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/// This function generates a Weibull distribution random number. |
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/// |
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///\param k shape parameter (<tt>k>0</tt>) |
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///\param lambda scale parameter (<tt>lambda>0</tt>) |
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/// |
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double weibull(double k,double lambda) |
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{ |
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return lambda*pow(-std::log(1.0-real<double>()),1.0/k); |
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} |
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/// Pareto distribution |
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