922 lines
25 KiB
C++
922 lines
25 KiB
C++
// ____ ______ __
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// / __ \ / ____// /
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// / /_/ // / / /
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// / ____// /___ / /___ PixInsight Class Library
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// /_/ \____//_____/ PCL 2.4.23
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// ----------------------------------------------------------------------------
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// pcl/Random.h - Released 2022-03-12T18:59:29Z
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// ----------------------------------------------------------------------------
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// This file is part of the PixInsight Class Library (PCL).
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// PCL is a multiplatform C++ framework for development of PixInsight modules.
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//
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// Copyright (c) 2003-2022 Pleiades Astrophoto S.L. All Rights Reserved.
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//
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// Redistribution and use in both source and binary forms, with or without
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// modification, is permitted provided that the following conditions are met:
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//
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// 1. All redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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//
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// 2. All redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// 3. Neither the names "PixInsight" and "Pleiades Astrophoto", nor the names
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// of their contributors, may be used to endorse or promote products derived
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// from this software without specific prior written permission. For written
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// permission, please contact info@pixinsight.com.
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//
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// 4. All products derived from this software, in any form whatsoever, must
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// reproduce the following acknowledgment in the end-user documentation
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// and/or other materials provided with the product:
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//
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// "This product is based on software from the PixInsight project, developed
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// by Pleiades Astrophoto and its contributors (https://pixinsight.com/)."
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//
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// Alternatively, if that is where third-party acknowledgments normally
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// appear, this acknowledgment must be reproduced in the product itself.
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//
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// THIS SOFTWARE IS PROVIDED BY PLEIADES ASTROPHOTO AND ITS CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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// TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL PLEIADES ASTROPHOTO OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, BUSINESS
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// INTERRUPTION; PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; AND LOSS OF USE,
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// DATA OR PROFITS) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, 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 OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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// ----------------------------------------------------------------------------
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#ifndef __PCL_Random_h
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#define __PCL_Random_h
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/// \file pcl/Random.h
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#include <pcl/Defs.h>
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#include <pcl/Diagnostics.h>
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#include <pcl/AutoPointer.h>
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#include <pcl/Vector.h>
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namespace pcl
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{
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// ----------------------------------------------------------------------------
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/*!
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* \defgroup random_numbers Random Number Generation
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*/
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/*!
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* Returns a 64-bit random generator seed.
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*
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* On UNIX/Linux platforms, this function reads the /dev/urandom system device
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* to acquire a high-quality random seed. On Windows, the rand_s() CRT function
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* is invoked with the same purpose.
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*
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* In the extremely rare cases where a system random seed cannot be obtained,
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* the time() function is used to get a unique initialization value.
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*
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* Subsequent calls to this function are guaranteed to return unique values.
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*
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* This function is thread-safe. It can be safely called from multiple
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* execution threads running concurrently.
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*
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* \ingroup random_numbers
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*/
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extern uint64 RandomSeed64();
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/*!
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* Returns a 32-bit random generator seed.
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*
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* This function simply calls RandomSeed64() and returns the XOR combination of
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* the 32-bit words in the 64-bit random seed.
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*
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* As RandomSeed64(), this function is thread-safe and is guaranteed to return
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* a unique value on each call.
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*
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* \ingroup random_numbers
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*/
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inline uint32 RandomSeed32()
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{
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union { uint64 u64; uint32 u32[ 2 ]; } seed;
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seed.u64 = RandomSeed64();
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return seed.u32[0] ^ seed.u32[1];
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}
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// ----------------------------------------------------------------------------
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class FastMersenneTwister;
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// ----------------------------------------------------------------------------
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/*!
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* \class RandomNumberGenerator
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* \brief Mersenne Twister (MT19937) pseudo-random number generator.
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*
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* \deprecated This class has been deprecated. Use the XoShiRo256ss and
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* XoRoShiRo1024ss classes for all newly produced code.
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*
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* Generation of pseudo-random numbers with user-selectable range and
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* probability distributions.
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*
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* This generator supports the uniform, normal (Gaussian) and Poisson
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* distributions. In addition, the upper range of generated uniform deviates
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* can be arbitrarily defined.
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*
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* %RandomNumberGenerator is a functional class. The function call operator()()
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* returns pseudo-random numbers in the range [0,ymax], where ymax is the
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* user-defined arbitrary upper range.
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*
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* Example of use:
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*
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* \code
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* RandomNumberGenerator R, R1( 10 ); // R's ymax = 1, R1's ymax = 10
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* // ...
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* double y = R(); // y = random uniform deviate in the range [0,1]
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* double z = R1(); // z = random uniform deviate in the range [0,10]
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* \endcode
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*
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* <b>References</b>
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*
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* Based on an adaptation of SIMD-oriented Fast Mersenne Twister (SFMT) by
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* Mutsuo Saito and Makoto Matsumoto (Hiroshima University).
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*
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* Currently PCL implements a SFMT generator with a period of 2^19937-1.
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*
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* SFMT Copyright (C) 2006, 2007 Mutsuo Saito, Makoto Matsumoto and Hiroshima
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* University. All rights reserved.
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*
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* \ingroup random_numbers
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*/
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class PCL_CLASS RandomNumberGenerator
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{
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public:
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/*!
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* Constructs a %RandomNumberGenerator object.
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*
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* \param ymax Upper bound of uniform deviates. The function call
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* operator double operator()() and the Uniform() member
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* function (which are synonyms) will return uniform
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* pseudo-random deviates in the range [0,ymax]. The default
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* value is 1.0.
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*
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* \param seed 32-bit initialization seed. If this parameter is zero, a
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* unique random seed will be generated automatically. The
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* default value is zero.
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*/
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RandomNumberGenerator( double ymax = 1.0, uint32 seed = 0 );
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/*!
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* Destroys a %RandomNumberGenerator object.
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*/
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virtual ~RandomNumberGenerator();
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/*!
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* Generates a floating point uniform deviate in the range [0,UpperBound()]
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*/
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double operator ()()
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{
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return m_rmax*Rand32();
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}
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/*!
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* Generates a 32-bit unsigned integer uniform deviate.
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*/
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uint32 Rand32();
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/*!
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* Generates a floating point uniform deviate in the range [0,1] (i.e.,
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* ignoring UpperBound()).
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*/
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double Rand1()
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{
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return double( Rand32() )/uint32_max;
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}
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/*!
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* Generates a floating point uniform deviate in the range [0,UpperBound()]
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*
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* This is a convenience alias for operator()().
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*/
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double Uniform()
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{
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return operator()();
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}
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/*!
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* Generates a floating point normal deviate with the specified \a mean and
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* standard deviation \a sigma.
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*/
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double Normal( double mean = 0, double sigma = 1 );
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/*!
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* Generates a floating point normal deviate with the specified \a mean and
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* standard deviation \a sigma.
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*
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* This is a convenience alias for Normal( mean, sigma ).
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*/
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double Gaussian( double mean = 0, double sigma = 1 )
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{
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return Normal( mean, sigma );
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}
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/*!
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* Generates a discrete random deviate from a Poisson distribution with the
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* specified expected value \a lambda.
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*/
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int Poisson( double lambda );
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/*!
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* Returns the current upper bound of this random number generator.
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*/
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double UpperBound() const
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{
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return m_ymax;
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}
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/*!
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* Sets the upper bound \a ymax > 0 for this random number generator.
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*/
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void SetUpperBound( double ymax )
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{
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PCL_PRECONDITION( ymax > 0 )
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PCL_PRECONDITION( 1 + ymax != 1 )
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m_rmax = (m_ymax = ymax)/double( uint32_max );
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m_normal = false;
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}
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private:
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AutoPointer<FastMersenneTwister> m_generator;
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double m_ymax;
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double m_rmax;
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bool m_normal;
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double m_vs; // second result from Box–Muller transform
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DVector m_lambda; // precalculated for current Poisson lambda
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};
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// ----------------------------------------------------------------------------
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/*!
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* \class XorShift1024
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* \brief Implementation of the XorShift1024* pseudo-random number generator.
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*
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* \deprecated This class has been deprecated. Use the XoShiRo256ss and
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* XoRoShiRo1024ss classes for all newly produced code.
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*
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* Generation of pseudo-random uniform deviates using the xorshift1024*
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* generator developed in 2014 by Sebastiano Vigna. This is a fast, top-quality
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* generator with a period of 2^1024-1, passing strong statistical test suites.
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*
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* Examples of use:
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*
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* \code
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* XorShift1024 X; // initialized automatically
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* // ...
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* double x = X(); // x = random uniform deviate in the range [0,1)
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* uint64 y = X.UI64(); // y = 64-bit unsigned integer random uniform deviate
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* uint32 z = X.UI32(); // z = 32-bit unsigned integer random uniform deviate
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* uint32 t = X.UIN( 100 ); // t = integer uniform deviate in the range [0,99]
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* \endcode
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*
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* <b>References</b>
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*
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* Sebastiano Vigna (2014), <em>An experimental exploration of Marsaglia's
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* xorshift generators, scrambled</em>, arXiv:1402.6246
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*
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* Sebastiano Vigna (2014), <em>Further scramblings of Marsaglia's xorshift
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* generators</em>, arXiv:1404.0390
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*
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* See also: http://xorshift.di.unimi.it/
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*
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* \ingroup random_numbers
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*/
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class PCL_CLASS XorShift1024
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{
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public:
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/*!
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* Constructs a %XorShift1024 pseudo-random number generator.
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*
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* \param seed 64-bit initialization seed. If this parameter is zero, a
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* unique random seed will be generated automatically. The
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* default value is zero.
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*/
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XorShift1024( uint64 seed = 0 ) noexcept( false )
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{
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Initialize( seed );
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}
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/*!
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* Returns a double precision uniform random deviate in the [0,1) range.
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*/
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double operator ()() noexcept
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{
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return 5.4210108624275221703311e-20 * UI64(); // 1.0/(2^64 -1)
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}
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/*!
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* Returns a 64-bit unsigned integer uniform random deviate.
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*/
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uint64 UI64() noexcept
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{
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uint64 s0 = m_s[m_p];
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uint64 s1 = m_s[m_p = (m_p + 1) & 15];
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s1 ^= s1 << 31; // a
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s1 ^= s1 >> 11; // b
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s0 ^= s0 >> 30; // c
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return (m_s[m_p] = s0 ^ s1) * 1181783497276652981ull;
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}
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/*!
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* Returns a 32-bit unsigned integer uniform random deviate.
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*/
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uint32 UI32() noexcept
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{
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return uint32( UI64() );
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}
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/*!
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* Returns a 64-bit unsigned integer uniform random deviate in the range
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* [0,n-1].
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*/
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uint64 UI64N( uint64 n ) noexcept
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{
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return UI64() % n;
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}
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/*!
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* Returns an unsigned integer uniform random deviate in the range [0,n-1].
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*/
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uint32 UIN( uint32 n ) noexcept
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{
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return UI64() % n;
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}
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||
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/*!
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* A synonym for UIN().
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*/
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uint32 UI32N( uint32 n ) noexcept
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{
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return UIN( n );
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}
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/*!
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* Reinitializes this generator with a new \a seed.
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||
*
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* If the specified \a seed is zero, a unique, high-quality random seed will
|
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* be generated automatically by calling RandomSeed64().
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*/
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void Initialize( uint64 x )
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{
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if ( x == 0 )
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x = RandomSeed64();
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// Use a xorshift64* generator to initialize the state space.
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for ( int i = 0; i < 16; ++i )
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{
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x ^= x >> 12; // a
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x ^= x << 25; // b
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x ^= x >> 27; // c
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m_s[i] = x * 2685821657736338717ull;
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}
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m_p = 0;
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||
}
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||
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||
private:
|
||
|
||
uint64 m_s[ 16 ]; // state space
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||
int m_p; // current index
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||
};
|
||
|
||
// ----------------------------------------------------------------------------
|
||
|
||
/*!
|
||
* \class XoRoShiRo1024ss
|
||
* \brief Base class of xoshiro and xoroshiro pseudo-random number generators.
|
||
*/
|
||
class PCL_CLASS XoShiRoBase
|
||
{
|
||
public:
|
||
|
||
/*!
|
||
* Default constructor.
|
||
*/
|
||
XoShiRoBase() = default;
|
||
|
||
protected:
|
||
|
||
/*!
|
||
* \internal
|
||
* The left rotation function used by the generator.
|
||
*/
|
||
static uint64 RotL( const uint64 x, int k ) noexcept
|
||
{
|
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return (x << k) | (x >> (64 - k));
|
||
}
|
||
|
||
/*!
|
||
* \internal
|
||
* The SplitMix64 generator used for state space initialization, as
|
||
* recommended by Blackman/Vigna.
|
||
*/
|
||
static uint64 SplitMix64( uint64& x ) noexcept
|
||
{
|
||
uint64 z = (x += 0x9e3779b97f4a7c15);
|
||
z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
|
||
z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
|
||
return z ^ (z >> 31);
|
||
}
|
||
|
||
/*!
|
||
* \internal
|
||
* Conversion of a 64-bit unsigned inteter to 64-bit floating point with
|
||
* uniform probability over the entire 53-bit significant digits.
|
||
* See: http://prng.di.unimi.it/#remarks
|
||
*/
|
||
static double UI64ToDouble( uint64 x ) noexcept
|
||
{
|
||
return (x >> 11) * 0x1.0p-53;
|
||
}
|
||
};
|
||
|
||
// ----------------------------------------------------------------------------
|
||
|
||
/*!
|
||
* \class XoShiRo256ss
|
||
* \brief Implementation of the xoshiro256** pseudo-random number generator.
|
||
*
|
||
* Generation of pseudo-random uniform deviates using the xoroshiro1024**
|
||
* generator developed in 2019 by David Blackman and Sebastiano Vigna. This is
|
||
* a fast, top-quality generator with a period of 2^256-1, passing strong
|
||
* statistical test suites—actually, it passes all tests we are aware of.
|
||
*
|
||
* Examples of use:
|
||
*
|
||
* \code
|
||
* XoShiRo256ss X; // initialized automatically
|
||
* // ...
|
||
* double x = X(); // x = random uniform deviate in the range [0,1)
|
||
* uint64 y = X.UI64(); // y = 64-bit unsigned integer random uniform deviate
|
||
* uint32 z = X.UI32(); // z = 32-bit unsigned integer random uniform deviate
|
||
* uint32 t = X.UIN( 100 ); // t = integer uniform deviate in the range [0,99]
|
||
* \endcode
|
||
*
|
||
* <b>References</b>
|
||
*
|
||
* David Blackman and Sebastiano Vigna (2019), <em>Scrambled linear
|
||
* pseudorandom number generators</em> (preprint).
|
||
*
|
||
* See also: http://prng.di.unimi.it/
|
||
*
|
||
* \ingroup random_numbers
|
||
*/
|
||
class PCL_CLASS XoShiRo256ss : public XoShiRoBase
|
||
{
|
||
public:
|
||
|
||
/*!
|
||
* Constructs a %XoShiRo256ss pseudo-random number generator.
|
||
*
|
||
* \param seed 64-bit initialization seed. If this parameter is zero, a
|
||
* unique random seed will be generated automatically. The
|
||
* default value is zero.
|
||
*/
|
||
XoShiRo256ss( uint64 seed = 0 ) noexcept( false )
|
||
{
|
||
Initialize( seed );
|
||
}
|
||
|
||
/*!
|
||
* Returns a double precision uniform random deviate in the [0,1) range.
|
||
*/
|
||
double operator ()() noexcept
|
||
{
|
||
return UI64ToDouble( UI64() );
|
||
}
|
||
|
||
/*!
|
||
* Returns a 64-bit unsigned integer uniform random deviate.
|
||
*/
|
||
uint64 UI64() noexcept
|
||
{
|
||
const uint64 result = RotL( m_s[1]*5, 7 ) * 9;
|
||
const uint64 t = m_s[1] << 17;
|
||
m_s[2] ^= m_s[0];
|
||
m_s[3] ^= m_s[1];
|
||
m_s[1] ^= m_s[2];
|
||
m_s[0] ^= m_s[3];
|
||
m_s[2] ^= t;
|
||
m_s[3] = RotL( m_s[3], 45 );
|
||
return result;
|
||
}
|
||
|
||
/*!
|
||
* Returns a 32-bit unsigned integer uniform random deviate.
|
||
*/
|
||
uint32 UI32() noexcept
|
||
{
|
||
return uint32( UI64() );
|
||
}
|
||
|
||
/*!
|
||
* Returns a 64-bit unsigned integer uniform random deviate in the range
|
||
* [0,n-1].
|
||
*/
|
||
uint64 UI64N( uint64 n ) noexcept
|
||
{
|
||
return UI64() % n;
|
||
}
|
||
|
||
/*!
|
||
* Returns an unsigned integer uniform random deviate in the range [0,n-1].
|
||
*/
|
||
uint32 UIN( uint32 n ) noexcept
|
||
{
|
||
return UI64() % n;
|
||
}
|
||
|
||
/*!
|
||
* A synonym for UIN().
|
||
*/
|
||
uint32 UI32N( uint32 n ) noexcept
|
||
{
|
||
return UIN( n );
|
||
}
|
||
|
||
/*!
|
||
* Reinitializes this generator with a new \a seed.
|
||
*
|
||
* If the specified \a seed is zero, a unique, high-quality random seed will
|
||
* be generated automatically by calling RandomSeed64().
|
||
*/
|
||
void Initialize( uint64 x )
|
||
{
|
||
if ( x == 0 )
|
||
x = RandomSeed64();
|
||
// Use a SplitMix64 generator to initialize the state space.
|
||
for ( int i = 0; i < 4; ++i )
|
||
m_s[i] = SplitMix64( x );
|
||
}
|
||
|
||
private:
|
||
|
||
uint64 m_s[ 4 ];
|
||
};
|
||
|
||
// ----------------------------------------------------------------------------
|
||
|
||
/*!
|
||
* \class XoRoShiRo1024ss
|
||
* \brief Implementation of the xoroshiro1024** pseudo-random number generator.
|
||
*
|
||
* Generation of pseudo-random uniform deviates using the xoroshiro1024**
|
||
* generator developed in 2019 by David Blackman and Sebastiano Vigna. This is
|
||
* a fast, top-quality generator with a period of 2^1024-1, passing strong
|
||
* statistical test suites—actually, it passes all tests we are aware of.
|
||
*
|
||
* Examples of use:
|
||
*
|
||
* \code
|
||
* XoRoShiRo1024ss X; // initialized automatically
|
||
* // ...
|
||
* double x = X(); // x = random uniform deviate in the range [0,1)
|
||
* uint64 y = X.UI64(); // y = 64-bit unsigned integer random uniform deviate
|
||
* uint32 z = X.UI32(); // z = 32-bit unsigned integer random uniform deviate
|
||
* uint32 t = X.UIN( 100 ); // t = integer uniform deviate in the range [0,99]
|
||
* \endcode
|
||
*
|
||
* <b>References</b>
|
||
*
|
||
* David Blackman and Sebastiano Vigna (2019), <em>Scrambled linear
|
||
* pseudorandom number generators</em> (preprint).
|
||
*
|
||
* See also: http://prng.di.unimi.it/
|
||
*
|
||
* \ingroup random_numbers
|
||
*/
|
||
class PCL_CLASS XoRoShiRo1024ss : public XoShiRoBase
|
||
{
|
||
public:
|
||
|
||
/*!
|
||
* Constructs a %XoRoShiRo1024ss pseudo-random number generator.
|
||
*
|
||
* \param seed 64-bit initialization seed. If this parameter is zero, a
|
||
* unique random seed will be generated automatically. The
|
||
* default value is zero.
|
||
*/
|
||
XoRoShiRo1024ss( uint64 seed = 0 ) noexcept( false )
|
||
{
|
||
Initialize( seed );
|
||
}
|
||
|
||
/*!
|
||
* Returns a double precision uniform random deviate in the [0,1) range.
|
||
*/
|
||
double operator ()() noexcept
|
||
{
|
||
return UI64ToDouble( UI64() );
|
||
}
|
||
|
||
/*!
|
||
* Returns a 64-bit unsigned integer uniform random deviate.
|
||
*/
|
||
uint64 UI64() noexcept
|
||
{
|
||
const int q = m_p;
|
||
const uint64 s0 = m_s[m_p = (m_p + 1) & 15];
|
||
uint64 s15 = m_s[q];
|
||
const uint64 result = RotL( s0*5, 7 ) * 9;
|
||
s15 ^= s0;
|
||
m_s[q] = RotL( s0, 25 ) ^ s15 ^ (s15 << 27);
|
||
m_s[m_p] = RotL( s15, 36 );
|
||
return result;
|
||
}
|
||
|
||
/*!
|
||
* Returns a 32-bit unsigned integer uniform random deviate.
|
||
*/
|
||
uint32 UI32() noexcept
|
||
{
|
||
return uint32( UI64() );
|
||
}
|
||
|
||
/*!
|
||
* Returns a 64-bit unsigned integer uniform random deviate in the range
|
||
* [0,n-1].
|
||
*/
|
||
uint64 UI64N( uint64 n ) noexcept
|
||
{
|
||
return UI64() % n;
|
||
}
|
||
|
||
/*!
|
||
* Returns an unsigned integer uniform random deviate in the range [0,n-1].
|
||
*/
|
||
uint32 UIN( uint32 n ) noexcept
|
||
{
|
||
return UI64() % n;
|
||
}
|
||
|
||
/*!
|
||
* A synonym for UIN().
|
||
*/
|
||
uint32 UI32N( uint32 n ) noexcept
|
||
{
|
||
return UIN( n );
|
||
}
|
||
|
||
/*!
|
||
* Reinitializes this generator with a new \a seed.
|
||
*
|
||
* If the specified \a seed is zero, a unique, high-quality random seed will
|
||
* be generated automatically by calling RandomSeed64().
|
||
*/
|
||
void Initialize( uint64 x )
|
||
{
|
||
if ( x == 0 )
|
||
x = RandomSeed64();
|
||
// Use a SplitMix64 generator to initialize the state space.
|
||
for ( int i = 0; i < 16; ++i )
|
||
m_s[i] = SplitMix64( x );
|
||
m_p = 0;
|
||
}
|
||
|
||
private:
|
||
|
||
uint64 m_s[ 16 ];
|
||
int m_p;
|
||
};
|
||
|
||
// ----------------------------------------------------------------------------
|
||
|
||
/*!
|
||
* \class NormalRandomDeviates
|
||
* \brief Generation of random normal (Gaussian) deviates.
|
||
* \ingroup random_numbers
|
||
*/
|
||
template <class RNG>
|
||
class PCL_CLASS NormalRandomDeviates
|
||
{
|
||
public:
|
||
|
||
/*!
|
||
* Constructs a %NormalRandomDeviates objects using the specified
|
||
* pseudo-random number generator \a R.
|
||
*/
|
||
NormalRandomDeviates( RNG& R ) noexcept( false )
|
||
: m_R( R )
|
||
{
|
||
}
|
||
|
||
/*!
|
||
* Returns a random deviate from a Gaussian distribution with zero mean and
|
||
* unit standard deviation.
|
||
*/
|
||
double operator ()() noexcept
|
||
{
|
||
/*
|
||
* Marsaglia polar method.
|
||
*/
|
||
double x;
|
||
if ( m_first )
|
||
{
|
||
do
|
||
{
|
||
double u1 = m_R();
|
||
double u2 = m_R();
|
||
m_v1 = 2*u1 - 1;
|
||
m_v2 = 2*u2 - 1;
|
||
m_s = m_v1*m_v1 + m_v2*m_v2;
|
||
}
|
||
while ( m_s >= 1 || m_s <= std::numeric_limits<double>::epsilon() );
|
||
|
||
x = m_v1 * Sqrt( -2*Ln( m_s )/m_s );
|
||
}
|
||
else
|
||
x = m_v2 * Sqrt( -2*Ln( m_s )/m_s );
|
||
|
||
m_first = !m_first;
|
||
return x;
|
||
}
|
||
|
||
private:
|
||
|
||
RNG& m_R;
|
||
double m_v1 = 0;
|
||
double m_v2 = 0;
|
||
double m_s = 0;
|
||
bool m_first = true;
|
||
};
|
||
|
||
// ----------------------------------------------------------------------------
|
||
|
||
/*!
|
||
* \class PoissonRandomDeviates
|
||
* \brief Generation of random Poisson deviates.
|
||
* \ingroup random_numbers
|
||
*/
|
||
template <class RNG>
|
||
class PCL_CLASS PoissonRandomDeviates
|
||
{
|
||
public:
|
||
|
||
/*!
|
||
* Constructs a %PoissonRandomDeviates objects using the specified
|
||
* pseudo-random number generator \a R.
|
||
*/
|
||
PoissonRandomDeviates( RNG& R ) noexcept( false )
|
||
: m_R( R )
|
||
{
|
||
}
|
||
|
||
/*!
|
||
* Returns a random Poisson deviate for the specified \a value.
|
||
*/
|
||
int operator ()( double value ) noexcept
|
||
{
|
||
if ( value < 30 )
|
||
{
|
||
/*
|
||
* Implementation of the algorithm by Donald E. Knuth, 1969.
|
||
*
|
||
* This algorithm is slow (unusable) for large values.
|
||
*/
|
||
double p = 1, L = Exp( -value );
|
||
int k = 0;
|
||
do
|
||
{
|
||
++k;
|
||
p *= m_R();
|
||
}
|
||
while ( p > L );
|
||
return k-1;
|
||
}
|
||
|
||
/*
|
||
* Code adapted from 'Random number generation in C++', by John D. Cook:
|
||
*
|
||
* https://www.johndcook.com/blog/cpp_random_number_generation/
|
||
*
|
||
* The algorithm is from "The Computer Generation of Poisson Random
|
||
* Variables" by A. C. Atkinson, Journal of the Royal Statistical
|
||
* Society Series C (Applied Statistics) Vol. 28, No. 1. (1979)
|
||
*
|
||
* This algorithm is slow (unusable) for small values.
|
||
*/
|
||
double c = 0.767 - 3.36/value;
|
||
double beta = Const<double>::pi()/Sqrt( 3*value );
|
||
double alpha = beta*value;
|
||
double k = Ln( c ) - value - Ln( beta );
|
||
for ( ;; )
|
||
{
|
||
double u = m_R();
|
||
double x = (alpha - Ln( (1 - u)/u ))/beta;
|
||
int n = int( Floor( x + 0.5 ) );
|
||
if ( n < 0 )
|
||
continue;
|
||
double v = m_R();
|
||
double y = alpha - beta*x;
|
||
double temp = 1 + Exp( y );
|
||
double lhs = y + Ln( v/temp/temp );
|
||
double rhs = k + n*Ln( value ) - LnFactorial( n );
|
||
if ( lhs <= rhs )
|
||
return n;
|
||
}
|
||
}
|
||
|
||
private:
|
||
|
||
RNG& m_R;
|
||
};
|
||
|
||
// ----------------------------------------------------------------------------
|
||
|
||
/*!
|
||
* \class GammaRandomDeviates
|
||
* \brief Generation of random gamma deviates.
|
||
* \ingroup random_numbers
|
||
*/
|
||
template <class RNG>
|
||
class PCL_CLASS GammaRandomDeviates
|
||
{
|
||
public:
|
||
|
||
/*!
|
||
* Constructs a %GammaRandomDeviates objects using the specified
|
||
* pseudo-random number generator \a R.
|
||
*/
|
||
GammaRandomDeviates( RNG& R, double shape = 1, double scale = 1 ) noexcept( false )
|
||
: m_R( R )
|
||
, m_shape( shape )
|
||
, m_scale( scale )
|
||
, m_normal( R )
|
||
{
|
||
if ( m_shape <= 0 )
|
||
throw Error( "GammaRandomDeviates(): The function shape parameter must be > 0." );
|
||
if ( m_scale <= 0 )
|
||
throw Error( "GammaRandomDeviates(): The scale parameter must be > 0." );
|
||
|
||
m_d = ((m_shape >= 1) ? m_shape : m_shape + 1) - 1.0/3.0;
|
||
m_c = 1/Sqrt( 9*m_d );
|
||
}
|
||
|
||
/*!
|
||
* Returns a random deviate from a Gaussian distribution with zero mean and
|
||
* unit standard deviation.
|
||
*/
|
||
double operator ()() noexcept
|
||
{
|
||
/*
|
||
* Code adapted from 'Random number generation in C++', by John D. Cook:
|
||
* https://www.johndcook.com/blog/cpp_random_number_generation/
|
||
*
|
||
* Implementation based on "A Simple Method for Generating Gamma
|
||
* Variables" by George Marsaglia and Wai Wan Tsang. ACM Transactions on
|
||
* Mathematical Software Vol 26, No 3, September 2000, pages 363-372.
|
||
*/
|
||
for ( ;; )
|
||
{
|
||
double x, v;
|
||
do
|
||
{
|
||
x = m_normal();
|
||
v = 1 + m_c*x;
|
||
}
|
||
while ( v <= 0 );
|
||
v = v*v*v;
|
||
double u = m_R();
|
||
double xsquared = x*x;
|
||
if ( u < 1 - 0.0331*xsquared*xsquared || Ln( u ) < 0.5*xsquared + m_d*(1 - v + Ln( v )) )
|
||
{
|
||
double g = m_scale*m_d*v;
|
||
if ( m_shape < 1 )
|
||
g *= Pow( m_R(), 1/m_shape );
|
||
return g;
|
||
}
|
||
}
|
||
}
|
||
|
||
private:
|
||
|
||
RNG& m_R;
|
||
double m_shape;
|
||
double m_scale;
|
||
double m_d;
|
||
double m_c;
|
||
NormalRandomDeviates<RNG> m_normal;
|
||
};
|
||
|
||
// ----------------------------------------------------------------------------
|
||
|
||
} // pcl
|
||
|
||
#endif // __PCL_Random_h
|
||
|
||
// ----------------------------------------------------------------------------
|
||
// EOF pcl/Random.h - Released 2022-03-12T18:59:29Z
|