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// Random number extensions -*- C++ -*- |
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// Copyright (C) 2012-2013 Free Software Foundation, Inc. |
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// |
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// This file is part of the GNU ISO C++ Library. This library is free |
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// software; you can redistribute it and/or modify it under the |
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// terms of the GNU General Public License as published by the |
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// Free Software Foundation; either version 3, or (at your option) |
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// any later version. |
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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 |
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// GNU General Public License for more details. |
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// Under Section 7 of GPL version 3, you are granted additional |
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// permissions described in the GCC Runtime Library Exception, version |
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// 3.1, as published by the Free Software Foundation. |
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// You should have received a copy of the GNU General Public License and |
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// a copy of the GCC Runtime Library Exception along with this program; |
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// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see |
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// . |
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/** @file ext/random |
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* This file is a GNU extension to the Standard C++ Library. |
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*/ |
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#ifndef _EXT_RANDOM |
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#define _EXT_RANDOM 1 |
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#pragma GCC system_header |
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#if __cplusplus < 201103L |
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# include |
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#else |
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#include |
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#include |
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#include |
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#ifdef __SSE2__ |
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# include |
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#endif |
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#ifdef _GLIBCXX_USE_C99_STDINT_TR1 |
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namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) |
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{ |
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_GLIBCXX_BEGIN_NAMESPACE_VERSION |
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#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ |
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/* Mersenne twister implementation optimized for vector operations. |
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* |
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* Reference: http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT/ |
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*/ |
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template |
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size_t __pos1, size_t __sl1, size_t __sl2, |
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size_t __sr1, size_t __sr2, |
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uint32_t __msk1, uint32_t __msk2, |
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uint32_t __msk3, uint32_t __msk4, |
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uint32_t __parity1, uint32_t __parity2, |
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uint32_t __parity3, uint32_t __parity4> |
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class simd_fast_mersenne_twister_engine |
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{ |
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static_assert(std::is_unsigned<_UIntType>::value, "template argument " |
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"substituting _UIntType not an unsigned integral type"); |
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static_assert(__sr1 < 32, "first right shift too large"); |
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static_assert(__sr2 < 16, "second right shift too large"); |
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static_assert(__sl1 < 32, "first left shift too large"); |
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static_assert(__sl2 < 16, "second left shift too large"); |
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public: |
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typedef _UIntType result_type; |
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private: |
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static constexpr size_t m_w = sizeof(result_type) * 8; |
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static constexpr size_t _M_nstate = __m / 128 + 1; |
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static constexpr size_t _M_nstate32 = _M_nstate * 4; |
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static_assert(std::is_unsigned<_UIntType>::value, "template argument " |
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"substituting _UIntType not an unsigned integral type"); |
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static_assert(__pos1 < _M_nstate, "POS1 not smaller than state size"); |
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static_assert(16 % sizeof(_UIntType) == 0, |
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"UIntType size must divide 16"); |
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public: |
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static constexpr size_t state_size = _M_nstate * (16 |
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/ sizeof(result_type)); |
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static constexpr result_type default_seed = 5489u; |
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// constructors and member function |
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explicit |
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simd_fast_mersenne_twister_engine(result_type __sd = default_seed) |
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{ seed(__sd); } |
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template |
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std::enable_if |
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simd_fast_mersenne_twister_engine>::value> |
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::type> |
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explicit |
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simd_fast_mersenne_twister_engine(_Sseq& __q) |
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{ seed(__q); } |
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void |
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seed(result_type __sd = default_seed); |
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template |
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typename std::enable_if::value>::type |
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seed(_Sseq& __q); |
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static constexpr result_type |
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min() |
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{ return 0; }; |
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static constexpr result_type |
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max() |
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{ return std::numeric_limits::max(); } |
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void |
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discard(unsigned long long __z); |
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result_type |
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operator()() |
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{ |
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if (__builtin_expect(_M_pos >= state_size, 0)) |
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_M_gen_rand(); |
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return _M_stateT[_M_pos++]; |
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} |
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template |
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size_t __pos1_2, size_t __sl1_2, size_t __sl2_2, |
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size_t __sr1_2, size_t __sr2_2, |
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uint32_t __msk1_2, uint32_t __msk2_2, |
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uint32_t __msk3_2, uint32_t __msk4_2, |
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uint32_t __parity1_2, uint32_t __parity2_2, |
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uint32_t __parity3_2, uint32_t __parity4_2> |
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friend bool |
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operator==(const simd_fast_mersenne_twister_engine<_UIntType_2, |
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__m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2, |
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__msk1_2, __msk2_2, __msk3_2, __msk4_2, |
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__parity1_2, __parity2_2, __parity3_2, __parity4_2>& __lhs, |
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const simd_fast_mersenne_twister_engine<_UIntType_2, |
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__m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2, |
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__msk1_2, __msk2_2, __msk3_2, __msk4_2, |
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__parity1_2, __parity2_2, __parity3_2, __parity4_2>& __rhs); |
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template |
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size_t __pos1_2, size_t __sl1_2, size_t __sl2_2, |
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size_t __sr1_2, size_t __sr2_2, |
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uint32_t __msk1_2, uint32_t __msk2_2, |
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uint32_t __msk3_2, uint32_t __msk4_2, |
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uint32_t __parity1_2, uint32_t __parity2_2, |
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uint32_t __parity3_2, uint32_t __parity4_2, |
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typename _CharT, typename _Traits> |
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friend std::basic_ostream<_CharT, _Traits>& |
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operator<<(std::basic_ostream<_CharT, _Traits>& __os, |
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const __gnu_cxx::simd_fast_mersenne_twister_engine |
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<_UIntType_2, |
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__m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2, |
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__msk1_2, __msk2_2, __msk3_2, __msk4_2, |
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__parity1_2, __parity2_2, __parity3_2, __parity4_2>& __x); |
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template |
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size_t __pos1_2, size_t __sl1_2, size_t __sl2_2, |
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size_t __sr1_2, size_t __sr2_2, |
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uint32_t __msk1_2, uint32_t __msk2_2, |
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uint32_t __msk3_2, uint32_t __msk4_2, |
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uint32_t __parity1_2, uint32_t __parity2_2, |
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uint32_t __parity3_2, uint32_t __parity4_2, |
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typename _CharT, typename _Traits> |
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friend std::basic_istream<_CharT, _Traits>& |
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operator>>(std::basic_istream<_CharT, _Traits>& __is, |
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__gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType_2, |
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__m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2, |
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__msk1_2, __msk2_2, __msk3_2, __msk4_2, |
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__parity1_2, __parity2_2, __parity3_2, __parity4_2>& __x); |
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private: |
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union |
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{ |
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#ifdef __SSE2__ |
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__m128i _M_state[_M_nstate]; |
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#endif |
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uint32_t _M_state32[_M_nstate32]; |
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result_type _M_stateT[state_size]; |
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} __attribute__ ((__aligned__ (16))); |
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size_t _M_pos; |
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void _M_gen_rand(void); |
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void _M_period_certification(); |
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}; |
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template |
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size_t __pos1, size_t __sl1, size_t __sl2, |
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size_t __sr1, size_t __sr2, |
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uint32_t __msk1, uint32_t __msk2, |
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uint32_t __msk3, uint32_t __msk4, |
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uint32_t __parity1, uint32_t __parity2, |
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uint32_t __parity3, uint32_t __parity4> |
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inline bool |
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operator!=(const __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType, |
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__m, __pos1, __sl1, __sl2, __sr1, __sr2, __msk1, __msk2, __msk3, |
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__msk4, __parity1, __parity2, __parity3, __parity4>& __lhs, |
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const __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType, |
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__m, __pos1, __sl1, __sl2, __sr1, __sr2, __msk1, __msk2, __msk3, |
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__msk4, __parity1, __parity2, __parity3, __parity4>& __rhs) |
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{ return !(__lhs == __rhs); } |
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/* Definitions for the SIMD-oriented Fast Mersenne Twister as defined |
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* in the C implementation by Daito and Matsumoto, as both a 32-bit |
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* and 64-bit version. |
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*/ |
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typedef simd_fast_mersenne_twister_engine |
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15, 3, 13, 3, |
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0xfdff37ffU, 0xef7f3f7dU, |
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0xff777b7dU, 0x7ff7fb2fU, |
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0x00000001U, 0x00000000U, |
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0x00000000U, 0x5986f054U> |
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sfmt607; |
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typedef simd_fast_mersenne_twister_engine |
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15, 3, 13, 3, |
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0xfdff37ffU, 0xef7f3f7dU, |
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0xff777b7dU, 0x7ff7fb2fU, |
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0x00000001U, 0x00000000U, |
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0x00000000U, 0x5986f054U> |
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sfmt607_64; |
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233 |
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typedef simd_fast_mersenne_twister_engine |
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14, 3, 5, 1, |
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0xf7fefffdU, 0x7fefcfffU, |
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0xaff3ef3fU, 0xb5ffff7fU, |
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0x00000001U, 0x00000000U, |
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0x00000000U, 0x20000000U> |
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sfmt1279; |
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typedef simd_fast_mersenne_twister_engine |
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14, 3, 5, 1, |
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0xf7fefffdU, 0x7fefcfffU, |
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0xaff3ef3fU, 0xb5ffff7fU, |
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0x00000001U, 0x00000000U, |
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0x00000000U, 0x20000000U> |
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sfmt1279_64; |
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249 |
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250 |
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typedef simd_fast_mersenne_twister_engine |
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19, 1, 5, 1, |
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0xbff7ffbfU, 0xfdfffffeU, |
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0xf7ffef7fU, 0xf2f7cbbfU, |
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0x00000001U, 0x00000000U, |
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0x00000000U, 0x41dfa600U> |
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sfmt2281; |
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258 |
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typedef simd_fast_mersenne_twister_engine |
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19, 1, 5, 1, |
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0xbff7ffbfU, 0xfdfffffeU, |
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0xf7ffef7fU, 0xf2f7cbbfU, |
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0x00000001U, 0x00000000U, |
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0x00000000U, 0x41dfa600U> |
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sfmt2281_64; |
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266 |
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267 |
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typedef simd_fast_mersenne_twister_engine |
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20, 1, 7, 1, |
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0x9f7bffffU, 0x9fffff5fU, |
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0x3efffffbU, 0xfffff7bbU, |
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0xa8000001U, 0xaf5390a3U, |
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0xb740b3f8U, 0x6c11486dU> |
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sfmt4253; |
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275 |
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typedef simd_fast_mersenne_twister_engine |
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20, 1, 7, 1, |
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0x9f7bffffU, 0x9fffff5fU, |
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0x3efffffbU, 0xfffff7bbU, |
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0xa8000001U, 0xaf5390a3U, |
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0xb740b3f8U, 0x6c11486dU> |
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sfmt4253_64; |
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283 |
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284 |
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typedef simd_fast_mersenne_twister_engine |
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14, 3, 7, 3, |
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0xeffff7fbU, 0xffffffefU, |
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0xdfdfbfffU, 0x7fffdbfdU, |
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0x00000001U, 0x00000000U, |
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0xe8148000U, 0xd0c7afa3U> |
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sfmt11213; |
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292 |
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typedef simd_fast_mersenne_twister_engine |
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14, 3, 7, 3, |
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0xeffff7fbU, 0xffffffefU, |
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0xdfdfbfffU, 0x7fffdbfdU, |
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0x00000001U, 0x00000000U, |
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0xe8148000U, 0xd0c7afa3U> |
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sfmt11213_64; |
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300 |
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301 |
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typedef simd_fast_mersenne_twister_engine |
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18, 1, 11, 1, |
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0xdfffffefU, 0xddfecb7fU, |
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0xbffaffffU, 0xbffffff6U, |
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306 |
0x00000001U, 0x00000000U, |
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0x00000000U, 0x13c9e684U> |
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308 |
sfmt19937; |
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309 |
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310 |
typedef simd_fast_mersenne_twister_engine |
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18, 1, 11, 1, |
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312 |
0xdfffffefU, 0xddfecb7fU, |
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313 |
0xbffaffffU, 0xbffffff6U, |
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314 |
0x00000001U, 0x00000000U, |
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315 |
0x00000000U, 0x13c9e684U> |
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316 |
sfmt19937_64; |
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317 |
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318 |
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319 |
typedef simd_fast_mersenne_twister_engine |
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5, 3, 9, 3, |
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0xeffffffbU, 0xdfbebfffU, |
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0xbfbf7befU, 0x9ffd7bffU, |
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0x00000001U, 0x00000000U, |
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0xa3ac4000U, 0xecc1327aU> |
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325 |
sfmt44497; |
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326 |
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327 |
typedef simd_fast_mersenne_twister_engine |
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328 |
5, 3, 9, 3, |
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0xeffffffbU, 0xdfbebfffU, |
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330 |
0xbfbf7befU, 0x9ffd7bffU, |
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331 |
0x00000001U, 0x00000000U, |
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332 |
0xa3ac4000U, 0xecc1327aU> |
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333 |
sfmt44497_64; |
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334 |
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335 |
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336 |
typedef simd_fast_mersenne_twister_engine |
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337 |
6, 7, 19, 1, |
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338 |
0xfdbffbffU, 0xbff7ff3fU, |
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339 |
0xfd77efffU, 0xbf9ff3ffU, |
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340 |
0x00000001U, 0x00000000U, |
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341 |
0x00000000U, 0xe9528d85U> |
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342 |
sfmt86243; |
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343 |
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344 |
typedef simd_fast_mersenne_twister_engine |
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345 |
6, 7, 19, 1, |
|
|
346 |
0xfdbffbffU, 0xbff7ff3fU, |
|
|
347 |
0xfd77efffU, 0xbf9ff3ffU, |
|
|
348 |
0x00000001U, 0x00000000U, |
|
|
349 |
0x00000000U, 0xe9528d85U> |
|
|
350 |
sfmt86243_64; |
|
|
351 |
|
|
|
352 |
|
|
|
353 |
typedef simd_fast_mersenne_twister_engine |
|
|
354 |
19, 1, 21, 1, |
|
|
355 |
0xffffbb5fU, 0xfb6ebf95U, |
|
|
356 |
0xfffefffaU, 0xcff77fffU, |
|
|
357 |
0x00000001U, 0x00000000U, |
|
|
358 |
0xcb520000U, 0xc7e91c7dU> |
|
|
359 |
sfmt132049; |
|
|
360 |
|
|
|
361 |
typedef simd_fast_mersenne_twister_engine |
|
|
362 |
19, 1, 21, 1, |
|
|
363 |
0xffffbb5fU, 0xfb6ebf95U, |
|
|
364 |
0xfffefffaU, 0xcff77fffU, |
|
|
365 |
0x00000001U, 0x00000000U, |
|
|
366 |
0xcb520000U, 0xc7e91c7dU> |
|
|
367 |
sfmt132049_64; |
|
|
368 |
|
|
|
369 |
|
|
|
370 |
typedef simd_fast_mersenne_twister_engine |
|
|
371 |
11, 3, 10, 1, |
|
|
372 |
0xbff7bff7U, 0xbfffffffU, |
|
|
373 |
0xbffffa7fU, 0xffddfbfbU, |
|
|
374 |
0xf8000001U, 0x89e80709U, |
|
|
375 |
0x3bd2b64bU, 0x0c64b1e4U> |
|
|
376 |
sfmt216091; |
|
|
377 |
|
|
|
378 |
typedef simd_fast_mersenne_twister_engine |
|
|
379 |
11, 3, 10, 1, |
|
|
380 |
0xbff7bff7U, 0xbfffffffU, |
|
|
381 |
0xbffffa7fU, 0xffddfbfbU, |
|
|
382 |
0xf8000001U, 0x89e80709U, |
|
|
383 |
0x3bd2b64bU, 0x0c64b1e4U> |
|
|
384 |
sfmt216091_64; |
|
|
385 |
|
|
|
386 |
#endif // __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ |
|
|
387 |
|
|
|
388 |
/** |
|
|
389 |
* @brief A beta continuous distribution for random numbers. |
|
|
390 |
* |
|
|
391 |
* The formula for the beta probability density function is: |
|
|
392 |
* @f[ |
|
|
393 |
* p(x|\alpha,\beta) = \frac{1}{B(\alpha,\beta)} |
|
|
394 |
* x^{\alpha - 1} (1 - x)^{\beta - 1} |
|
|
395 |
* @f] |
|
|
396 |
*/ |
|
|
397 |
template |
|
|
398 |
class beta_distribution |
|
|
399 |
{ |
|
|
400 |
static_assert(std::is_floating_point<_RealType>::value, |
|
|
401 |
"template argument not a floating point type"); |
|
|
402 |
|
|
|
403 |
public: |
|
|
404 |
/** The type of the range of the distribution. */ |
|
|
405 |
typedef _RealType result_type; |
|
|
406 |
/** Parameter type. */ |
|
|
407 |
struct param_type |
|
|
408 |
{ |
|
|
409 |
typedef beta_distribution<_RealType> distribution_type; |
|
|
410 |
friend class beta_distribution<_RealType>; |
|
|
411 |
|
|
|
412 |
explicit |
|
|
413 |
param_type(_RealType __alpha_val = _RealType(1), |
|
|
414 |
_RealType __beta_val = _RealType(1)) |
|
|
415 |
: _M_alpha(__alpha_val), _M_beta(__beta_val) |
|
|
416 |
{ |
|
|
417 |
_GLIBCXX_DEBUG_ASSERT(_M_alpha > _RealType(0)); |
|
|
418 |
_GLIBCXX_DEBUG_ASSERT(_M_beta > _RealType(0)); |
|
|
419 |
} |
|
|
420 |
|
|
|
421 |
_RealType |
|
|
422 |
alpha() const |
|
|
423 |
{ return _M_alpha; } |
|
|
424 |
|
|
|
425 |
_RealType |
|
|
426 |
beta() const |
|
|
427 |
{ return _M_beta; } |
|
|
428 |
|
|
|
429 |
friend bool |
|
|
430 |
operator==(const param_type& __p1, const param_type& __p2) |
|
|
431 |
{ return (__p1._M_alpha == __p2._M_alpha |
|
|
432 |
&& __p1._M_beta == __p2._M_beta); } |
|
|
433 |
|
|
|
434 |
private: |
|
|
435 |
void |
|
|
436 |
_M_initialize(); |
|
|
437 |
|
|
|
438 |
_RealType _M_alpha; |
|
|
439 |
_RealType _M_beta; |
|
|
440 |
}; |
|
|
441 |
|
|
|
442 |
public: |
|
|
443 |
/** |
|
|
444 |
* @brief Constructs a beta distribution with parameters |
|
|
445 |
* @f$\alpha@f$ and @f$\beta@f$. |
|
|
446 |
*/ |
|
|
447 |
explicit |
|
|
448 |
beta_distribution(_RealType __alpha_val = _RealType(1), |
|
|
449 |
_RealType __beta_val = _RealType(1)) |
|
|
450 |
: _M_param(__alpha_val, __beta_val) |
|
|
451 |
{ } |
|
|
452 |
|
|
|
453 |
explicit |
|
|
454 |
beta_distribution(const param_type& __p) |
|
|
455 |
: _M_param(__p) |
|
|
456 |
{ } |
|
|
457 |
|
|
|
458 |
/** |
|
|
459 |
* @brief Resets the distribution state. |
|
|
460 |
*/ |
|
|
461 |
void |
|
|
462 |
reset() |
|
|
463 |
{ } |
|
|
464 |
|
|
|
465 |
/** |
|
|
466 |
* @brief Returns the @f$\alpha@f$ of the distribution. |
|
|
467 |
*/ |
|
|
468 |
_RealType |
|
|
469 |
alpha() const |
|
|
470 |
{ return _M_param.alpha(); } |
|
|
471 |
|
|
|
472 |
/** |
|
|
473 |
* @brief Returns the @f$\beta@f$ of the distribution. |
|
|
474 |
*/ |
|
|
475 |
_RealType |
|
|
476 |
beta() const |
|
|
477 |
{ return _M_param.beta(); } |
|
|
478 |
|
|
|
479 |
/** |
|
|
480 |
* @brief Returns the parameter set of the distribution. |
|
|
481 |
*/ |
|
|
482 |
param_type |
|
|
483 |
param() const |
|
|
484 |
{ return _M_param; } |
|
|
485 |
|
|
|
486 |
/** |
|
|
487 |
* @brief Sets the parameter set of the distribution. |
|
|
488 |
* @param __param The new parameter set of the distribution. |
|
|
489 |
*/ |
|
|
490 |
void |
|
|
491 |
param(const param_type& __param) |
|
|
492 |
{ _M_param = __param; } |
|
|
493 |
|
|
|
494 |
/** |
|
|
495 |
* @brief Returns the greatest lower bound value of the distribution. |
|
|
496 |
*/ |
|
|
497 |
result_type |
|
|
498 |
min() const |
|
|
499 |
{ return result_type(0); } |
|
|
500 |
|
|
|
501 |
/** |
|
|
502 |
* @brief Returns the least upper bound value of the distribution. |
|
|
503 |
*/ |
|
|
504 |
result_type |
|
|
505 |
max() const |
|
|
506 |
{ return result_type(1); } |
|
|
507 |
|
|
|
508 |
/** |
|
|
509 |
* @brief Generating functions. |
|
|
510 |
*/ |
|
|
511 |
template |
|
|
512 |
result_type |
|
|
513 |
operator()(_UniformRandomNumberGenerator& __urng) |
|
|
514 |
{ return this->operator()(__urng, _M_param); } |
|
|
515 |
|
|
|
516 |
template |
|
|
517 |
result_type |
|
|
518 |
operator()(_UniformRandomNumberGenerator& __urng, |
|
|
519 |
const param_type& __p); |
|
|
520 |
|
|
|
521 |
template |
|
|
522 |
typename _UniformRandomNumberGenerator> |
|
|
523 |
void |
|
|
524 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
525 |
_UniformRandomNumberGenerator& __urng) |
|
|
526 |
{ this->__generate(__f, __t, __urng, _M_param); } |
|
|
527 |
|
|
|
528 |
template |
|
|
529 |
typename _UniformRandomNumberGenerator> |
|
|
530 |
void |
|
|
531 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
532 |
_UniformRandomNumberGenerator& __urng, |
|
|
533 |
const param_type& __p) |
|
|
534 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
535 |
|
|
|
536 |
template |
|
|
537 |
void |
|
|
538 |
__generate(result_type* __f, result_type* __t, |
|
|
539 |
_UniformRandomNumberGenerator& __urng, |
|
|
540 |
const param_type& __p) |
|
|
541 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
542 |
|
|
|
543 |
/** |
|
|
544 |
* @brief Return true if two beta distributions have the same |
|
|
545 |
* parameters and the sequences that would be generated |
|
|
546 |
* are equal. |
|
|
547 |
*/ |
|
|
548 |
friend bool |
|
|
549 |
operator==(const beta_distribution& __d1, |
|
|
550 |
const beta_distribution& __d2) |
|
|
551 |
{ return __d1._M_param == __d2._M_param; } |
|
|
552 |
|
|
|
553 |
/** |
|
|
554 |
* @brief Inserts a %beta_distribution random number distribution |
|
|
555 |
* @p __x into the output stream @p __os. |
|
|
556 |
* |
|
|
557 |
* @param __os An output stream. |
|
|
558 |
* @param __x A %beta_distribution random number distribution. |
|
|
559 |
* |
|
|
560 |
* @returns The output stream with the state of @p __x inserted or in |
|
|
561 |
* an error state. |
|
|
562 |
*/ |
|
|
563 |
template |
|
|
564 |
friend std::basic_ostream<_CharT, _Traits>& |
|
|
565 |
operator<<(std::basic_ostream<_CharT, _Traits>& __os, |
|
|
566 |
const __gnu_cxx::beta_distribution<_RealType1>& __x); |
|
|
567 |
|
|
|
568 |
/** |
|
|
569 |
* @brief Extracts a %beta_distribution random number distribution |
|
|
570 |
* @p __x from the input stream @p __is. |
|
|
571 |
* |
|
|
572 |
* @param __is An input stream. |
|
|
573 |
* @param __x A %beta_distribution random number generator engine. |
|
|
574 |
* |
|
|
575 |
* @returns The input stream with @p __x extracted or in an error state. |
|
|
576 |
*/ |
|
|
577 |
template |
|
|
578 |
friend std::basic_istream<_CharT, _Traits>& |
|
|
579 |
operator>>(std::basic_istream<_CharT, _Traits>& __is, |
|
|
580 |
__gnu_cxx::beta_distribution<_RealType1>& __x); |
|
|
581 |
|
|
|
582 |
private: |
|
|
583 |
template |
|
|
584 |
typename _UniformRandomNumberGenerator> |
|
|
585 |
void |
|
|
586 |
__generate_impl(_ForwardIterator __f, _ForwardIterator __t, |
|
|
587 |
_UniformRandomNumberGenerator& __urng, |
|
|
588 |
const param_type& __p); |
|
|
589 |
|
|
|
590 |
param_type _M_param; |
|
|
591 |
}; |
|
|
592 |
|
|
|
593 |
/** |
|
|
594 |
* @brief Return true if two beta distributions are different. |
|
|
595 |
*/ |
|
|
596 |
template |
|
|
597 |
inline bool |
|
|
598 |
operator!=(const __gnu_cxx::beta_distribution<_RealType>& __d1, |
|
|
599 |
const __gnu_cxx::beta_distribution<_RealType>& __d2) |
|
|
600 |
{ return !(__d1 == __d2); } |
|
|
601 |
|
|
|
602 |
|
|
|
603 |
/** |
|
|
604 |
* @brief A multi-variate normal continuous distribution for random numbers. |
|
|
605 |
* |
|
|
606 |
* The formula for the normal probability density function is |
|
|
607 |
* @f[ |
|
|
608 |
* p(\overrightarrow{x}|\overrightarrow{\mu },\Sigma) = |
|
|
609 |
* \frac{1}{\sqrt{(2\pi )^k\det(\Sigma))}} |
|
|
610 |
* e^{-\frac{1}{2}(\overrightarrow{x}-\overrightarrow{\mu})^\text{T} |
|
|
611 |
* \Sigma ^{-1}(\overrightarrow{x}-\overrightarrow{\mu})} |
|
|
612 |
* @f] |
|
|
613 |
* |
|
|
614 |
* where @f$\overrightarrow{x}@f$ and @f$\overrightarrow{\mu}@f$ are |
|
|
615 |
* vectors of dimension @f$k@f$ and @f$\Sigma@f$ is the covariance |
|
|
616 |
* matrix (which must be positive-definite). |
|
|
617 |
*/ |
|
|
618 |
template |
|
|
619 |
class normal_mv_distribution |
|
|
620 |
{ |
|
|
621 |
static_assert(std::is_floating_point<_RealType>::value, |
|
|
622 |
"template argument not a floating point type"); |
|
|
623 |
static_assert(_Dimen != 0, "dimension is zero"); |
|
|
624 |
|
|
|
625 |
public: |
|
|
626 |
/** The type of the range of the distribution. */ |
|
|
627 |
typedef std::array<_RealType, _Dimen> result_type; |
|
|
628 |
/** Parameter type. */ |
|
|
629 |
class param_type |
|
|
630 |
{ |
|
|
631 |
static constexpr size_t _M_t_size = _Dimen * (_Dimen + 1) / 2; |
|
|
632 |
|
|
|
633 |
public: |
|
|
634 |
typedef normal_mv_distribution<_Dimen, _RealType> distribution_type; |
|
|
635 |
friend class normal_mv_distribution<_Dimen, _RealType>; |
|
|
636 |
|
|
|
637 |
param_type() |
|
|
638 |
{ |
|
|
639 |
std::fill(_M_mean.begin(), _M_mean.end(), _RealType(0)); |
|
|
640 |
auto __it = _M_t.begin(); |
|
|
641 |
for (size_t __i = 0; __i < _Dimen; ++__i) |
|
|
642 |
{ |
|
|
643 |
std::fill_n(__it, __i, _RealType(0)); |
|
|
644 |
__it += __i; |
|
|
645 |
*__it++ = _RealType(1); |
|
|
646 |
} |
|
|
647 |
} |
|
|
648 |
|
|
|
649 |
template |
|
|
650 |
param_type(_ForwardIterator1 __meanbegin, |
|
|
651 |
_ForwardIterator1 __meanend, |
|
|
652 |
_ForwardIterator2 __varcovbegin, |
|
|
653 |
_ForwardIterator2 __varcovend) |
|
|
654 |
{ |
|
|
655 |
__glibcxx_function_requires(_ForwardIteratorConcept< |
|
|
656 |
_ForwardIterator1>) |
|
|
657 |
__glibcxx_function_requires(_ForwardIteratorConcept< |
|
|
658 |
_ForwardIterator2>) |
|
|
659 |
_GLIBCXX_DEBUG_ASSERT(std::distance(__meanbegin, __meanend) |
|
|
660 |
<= _Dimen); |
|
|
661 |
const auto __dist = std::distance(__varcovbegin, __varcovend); |
|
|
662 |
_GLIBCXX_DEBUG_ASSERT(__dist == _Dimen * _Dimen |
|
|
663 |
|| __dist == _Dimen * (_Dimen + 1) / 2 |
|
|
664 |
|| __dist == _Dimen); |
|
|
665 |
|
|
|
666 |
if (__dist == _Dimen * _Dimen) |
|
|
667 |
_M_init_full(__meanbegin, __meanend, __varcovbegin, __varcovend); |
|
|
668 |
else if (__dist == _Dimen * (_Dimen + 1) / 2) |
|
|
669 |
_M_init_lower(__meanbegin, __meanend, __varcovbegin, __varcovend); |
|
|
670 |
else |
|
|
671 |
_M_init_diagonal(__meanbegin, __meanend, |
|
|
672 |
__varcovbegin, __varcovend); |
|
|
673 |
} |
|
|
674 |
|
|
|
675 |
param_type(std::initializer_list<_RealType> __mean, |
|
|
676 |
std::initializer_list<_RealType> __varcov) |
|
|
677 |
{ |
|
|
678 |
_GLIBCXX_DEBUG_ASSERT(__mean.size() <= _Dimen); |
|
|
679 |
_GLIBCXX_DEBUG_ASSERT(__varcov.size() == _Dimen * _Dimen |
|
|
680 |
|| __varcov.size() == _Dimen * (_Dimen + 1) / 2 |
|
|
681 |
|| __varcov.size() == _Dimen); |
|
|
682 |
|
|
|
683 |
if (__varcov.size() == _Dimen * _Dimen) |
|
|
684 |
_M_init_full(__mean.begin(), __mean.end(), |
|
|
685 |
__varcov.begin(), __varcov.end()); |
|
|
686 |
else if (__varcov.size() == _Dimen * (_Dimen + 1) / 2) |
|
|
687 |
_M_init_lower(__mean.begin(), __mean.end(), |
|
|
688 |
__varcov.begin(), __varcov.end()); |
|
|
689 |
else |
|
|
690 |
_M_init_diagonal(__mean.begin(), __mean.end(), |
|
|
691 |
__varcov.begin(), __varcov.end()); |
|
|
692 |
} |
|
|
693 |
|
|
|
694 |
std::array<_RealType, _Dimen> |
|
|
695 |
mean() const |
|
|
696 |
{ return _M_mean; } |
|
|
697 |
|
|
|
698 |
std::array<_RealType, _M_t_size> |
|
|
699 |
varcov() const |
|
|
700 |
{ return _M_t; } |
|
|
701 |
|
|
|
702 |
friend bool |
|
|
703 |
operator==(const param_type& __p1, const param_type& __p2) |
|
|
704 |
{ return __p1._M_mean == __p2._M_mean && __p1._M_t == __p2._M_t; } |
|
|
705 |
|
|
|
706 |
private: |
|
|
707 |
template |
|
|
708 |
void _M_init_full(_InputIterator1 __meanbegin, |
|
|
709 |
_InputIterator1 __meanend, |
|
|
710 |
_InputIterator2 __varcovbegin, |
|
|
711 |
_InputIterator2 __varcovend); |
|
|
712 |
template |
|
|
713 |
void _M_init_lower(_InputIterator1 __meanbegin, |
|
|
714 |
_InputIterator1 __meanend, |
|
|
715 |
_InputIterator2 __varcovbegin, |
|
|
716 |
_InputIterator2 __varcovend); |
|
|
717 |
template |
|
|
718 |
void _M_init_diagonal(_InputIterator1 __meanbegin, |
|
|
719 |
_InputIterator1 __meanend, |
|
|
720 |
_InputIterator2 __varbegin, |
|
|
721 |
_InputIterator2 __varend); |
|
|
722 |
|
|
|
723 |
std::array<_RealType, _Dimen> _M_mean; |
|
|
724 |
std::array<_RealType, _M_t_size> _M_t; |
|
|
725 |
}; |
|
|
726 |
|
|
|
727 |
public: |
|
|
728 |
normal_mv_distribution() |
|
|
729 |
: _M_param(), _M_nd() |
|
|
730 |
{ } |
|
|
731 |
|
|
|
732 |
template |
|
|
733 |
normal_mv_distribution(_ForwardIterator1 __meanbegin, |
|
|
734 |
_ForwardIterator1 __meanend, |
|
|
735 |
_ForwardIterator2 __varcovbegin, |
|
|
736 |
_ForwardIterator2 __varcovend) |
|
|
737 |
: _M_param(__meanbegin, __meanend, __varcovbegin, __varcovend), |
|
|
738 |
_M_nd() |
|
|
739 |
{ } |
|
|
740 |
|
|
|
741 |
normal_mv_distribution(std::initializer_list<_RealType> __mean, |
|
|
742 |
std::initializer_list<_RealType> __varcov) |
|
|
743 |
: _M_param(__mean, __varcov), _M_nd() |
|
|
744 |
{ } |
|
|
745 |
|
|
|
746 |
explicit |
|
|
747 |
normal_mv_distribution(const param_type& __p) |
|
|
748 |
: _M_param(__p), _M_nd() |
|
|
749 |
{ } |
|
|
750 |
|
|
|
751 |
/** |
|
|
752 |
* @brief Resets the distribution state. |
|
|
753 |
*/ |
|
|
754 |
void |
|
|
755 |
reset() |
|
|
756 |
{ _M_nd.reset(); } |
|
|
757 |
|
|
|
758 |
/** |
|
|
759 |
* @brief Returns the mean of the distribution. |
|
|
760 |
*/ |
|
|
761 |
result_type |
|
|
762 |
mean() const |
|
|
763 |
{ return _M_param.mean(); } |
|
|
764 |
|
|
|
765 |
/** |
|
|
766 |
* @brief Returns the compact form of the variance/covariance |
|
|
767 |
* matrix of the distribution. |
|
|
768 |
*/ |
|
|
769 |
std::array<_RealType, _Dimen * (_Dimen + 1) / 2> |
|
|
770 |
varcov() const |
|
|
771 |
{ return _M_param.varcov(); } |
|
|
772 |
|
|
|
773 |
/** |
|
|
774 |
* @brief Returns the parameter set of the distribution. |
|
|
775 |
*/ |
|
|
776 |
param_type |
|
|
777 |
param() const |
|
|
778 |
{ return _M_param; } |
|
|
779 |
|
|
|
780 |
/** |
|
|
781 |
* @brief Sets the parameter set of the distribution. |
|
|
782 |
* @param __param The new parameter set of the distribution. |
|
|
783 |
*/ |
|
|
784 |
void |
|
|
785 |
param(const param_type& __param) |
|
|
786 |
{ _M_param = __param; } |
|
|
787 |
|
|
|
788 |
/** |
|
|
789 |
* @brief Returns the greatest lower bound value of the distribution. |
|
|
790 |
*/ |
|
|
791 |
result_type |
|
|
792 |
min() const |
|
|
793 |
{ result_type __res; |
|
|
794 |
__res.fill(std::numeric_limits<_RealType>::lowest()); |
|
|
795 |
return __res; } |
|
|
796 |
|
|
|
797 |
/** |
|
|
798 |
* @brief Returns the least upper bound value of the distribution. |
|
|
799 |
*/ |
|
|
800 |
result_type |
|
|
801 |
max() const |
|
|
802 |
{ result_type __res; |
|
|
803 |
__res.fill(std::numeric_limits<_RealType>::max()); |
|
|
804 |
return __res; } |
|
|
805 |
|
|
|
806 |
/** |
|
|
807 |
* @brief Generating functions. |
|
|
808 |
*/ |
|
|
809 |
template |
|
|
810 |
result_type |
|
|
811 |
operator()(_UniformRandomNumberGenerator& __urng) |
|
|
812 |
{ return this->operator()(__urng, _M_param); } |
|
|
813 |
|
|
|
814 |
template |
|
|
815 |
result_type |
|
|
816 |
operator()(_UniformRandomNumberGenerator& __urng, |
|
|
817 |
const param_type& __p); |
|
|
818 |
|
|
|
819 |
template |
|
|
820 |
typename _UniformRandomNumberGenerator> |
|
|
821 |
void |
|
|
822 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
823 |
_UniformRandomNumberGenerator& __urng) |
|
|
824 |
{ return this->__generate_impl(__f, __t, __urng, _M_param); } |
|
|
825 |
|
|
|
826 |
template |
|
|
827 |
typename _UniformRandomNumberGenerator> |
|
|
828 |
void |
|
|
829 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
830 |
_UniformRandomNumberGenerator& __urng, |
|
|
831 |
const param_type& __p) |
|
|
832 |
{ return this->__generate_impl(__f, __t, __urng, __p); } |
|
|
833 |
|
|
|
834 |
/** |
|
|
835 |
* @brief Return true if two multi-variant normal distributions have |
|
|
836 |
* the same parameters and the sequences that would |
|
|
837 |
* be generated are equal. |
|
|
838 |
*/ |
|
|
839 |
template |
|
|
840 |
friend bool |
|
|
841 |
operator==(const |
|
|
842 |
__gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>& |
|
|
843 |
__d1, |
|
|
844 |
const |
|
|
845 |
__gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>& |
|
|
846 |
__d2); |
|
|
847 |
|
|
|
848 |
/** |
|
|
849 |
* @brief Inserts a %normal_mv_distribution random number distribution |
|
|
850 |
* @p __x into the output stream @p __os. |
|
|
851 |
* |
|
|
852 |
* @param __os An output stream. |
|
|
853 |
* @param __x A %normal_mv_distribution random number distribution. |
|
|
854 |
* |
|
|
855 |
* @returns The output stream with the state of @p __x inserted or in |
|
|
856 |
* an error state. |
|
|
857 |
*/ |
|
|
858 |
template |
|
|
859 |
typename _CharT, typename _Traits> |
|
|
860 |
friend std::basic_ostream<_CharT, _Traits>& |
|
|
861 |
operator<<(std::basic_ostream<_CharT, _Traits>& __os, |
|
|
862 |
const |
|
|
863 |
__gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>& |
|
|
864 |
__x); |
|
|
865 |
|
|
|
866 |
/** |
|
|
867 |
* @brief Extracts a %normal_mv_distribution random number distribution |
|
|
868 |
* @p __x from the input stream @p __is. |
|
|
869 |
* |
|
|
870 |
* @param __is An input stream. |
|
|
871 |
* @param __x A %normal_mv_distribution random number generator engine. |
|
|
872 |
* |
|
|
873 |
* @returns The input stream with @p __x extracted or in an error |
|
|
874 |
* state. |
|
|
875 |
*/ |
|
|
876 |
template |
|
|
877 |
typename _CharT, typename _Traits> |
|
|
878 |
friend std::basic_istream<_CharT, _Traits>& |
|
|
879 |
operator>>(std::basic_istream<_CharT, _Traits>& __is, |
|
|
880 |
__gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>& |
|
|
881 |
__x); |
|
|
882 |
|
|
|
883 |
private: |
|
|
884 |
template |
|
|
885 |
typename _UniformRandomNumberGenerator> |
|
|
886 |
void |
|
|
887 |
__generate_impl(_ForwardIterator __f, _ForwardIterator __t, |
|
|
888 |
_UniformRandomNumberGenerator& __urng, |
|
|
889 |
const param_type& __p); |
|
|
890 |
|
|
|
891 |
param_type _M_param; |
|
|
892 |
std::normal_distribution<_RealType> _M_nd; |
|
|
893 |
}; |
|
|
894 |
|
|
|
895 |
/** |
|
|
896 |
* @brief Return true if two multi-variate normal distributions are |
|
|
897 |
* different. |
|
|
898 |
*/ |
|
|
899 |
template |
|
|
900 |
inline bool |
|
|
901 |
operator!=(const __gnu_cxx::normal_mv_distribution<_Dimen, _RealType>& |
|
|
902 |
__d1, |
|
|
903 |
const __gnu_cxx::normal_mv_distribution<_Dimen, _RealType>& |
|
|
904 |
__d2) |
|
|
905 |
{ return !(__d1 == __d2); } |
|
|
906 |
|
|
|
907 |
|
|
|
908 |
/** |
|
|
909 |
* @brief A Rice continuous distribution for random numbers. |
|
|
910 |
* |
|
|
911 |
* The formula for the Rice probability density function is |
|
|
912 |
* @f[ |
|
|
913 |
* p(x|\nu,\sigma) = \frac{x}{\sigma^2} |
|
|
914 |
* \exp\left(-\frac{x^2+\nu^2}{2\sigma^2}\right) |
|
|
915 |
* I_0\left(\frac{x \nu}{\sigma^2}\right) |
|
|
916 |
* @f] |
|
|
917 |
* where @f$I_0(z)@f$ is the modified Bessel function of the first kind |
|
|
918 |
* of order 0 and @f$\nu >= 0@f$ and @f$\sigma > 0@f$. |
|
|
919 |
* |
|
|
920 |
*
|
|
921 |
* Distribution Statistics |
|
|
922 |
* | Mean | @f$\sqrt{\pi/2}L_{1/2}(-\nu^2/2\sigma^2)@f$ | |
|
|
923 |
* | Variance | @f$2\sigma^2 + \nu^2 |
|
|
924 |
* + (\pi\sigma^2/2)L^2_{1/2}(-\nu^2/2\sigma^2)@f$ | |
|
|
925 |
* | Range | @f$[0, \infty)@f$ | |
|
|
926 |
* | |
|
|
927 |
* where @f$L_{1/2}(x)@f$ is the Laguerre polynomial of order 1/2. |
|
|
928 |
*/ |
|
|
929 |
template |
|
|
930 |
class |
|
|
931 |
rice_distribution |
|
|
932 |
{ |
|
|
933 |
static_assert(std::is_floating_point<_RealType>::value, |
|
|
934 |
"template argument not a floating point type"); |
|
|
935 |
public: |
|
|
936 |
/** The type of the range of the distribution. */ |
|
|
937 |
typedef _RealType result_type; |
|
|
938 |
/** Parameter type. */ |
|
|
939 |
struct param_type |
|
|
940 |
{ |
|
|
941 |
typedef rice_distribution distribution_type; |
|
|
942 |
|
|
|
943 |
param_type(result_type __nu_val = result_type(0), |
|
|
944 |
result_type __sigma_val = result_type(1)) |
|
|
945 |
: _M_nu(__nu_val), _M_sigma(__sigma_val) |
|
|
946 |
{ |
|
|
947 |
_GLIBCXX_DEBUG_ASSERT(_M_nu >= result_type(0)); |
|
|
948 |
_GLIBCXX_DEBUG_ASSERT(_M_sigma > result_type(0)); |
|
|
949 |
} |
|
|
950 |
|
|
|
951 |
result_type |
|
|
952 |
nu() const |
|
|
953 |
{ return _M_nu; } |
|
|
954 |
|
|
|
955 |
result_type |
|
|
956 |
sigma() const |
|
|
957 |
{ return _M_sigma; } |
|
|
958 |
|
|
|
959 |
friend bool |
|
|
960 |
operator==(const param_type& __p1, const param_type& __p2) |
|
|
961 |
{ return __p1._M_nu == __p2._M_nu |
|
|
962 |
&& __p1._M_sigma == __p2._M_sigma; } |
|
|
963 |
|
|
|
964 |
private: |
|
|
965 |
void _M_initialize(); |
|
|
966 |
|
|
|
967 |
result_type _M_nu; |
|
|
968 |
result_type _M_sigma; |
|
|
969 |
}; |
|
|
970 |
|
|
|
971 |
/** |
|
|
972 |
* @brief Constructors. |
|
|
973 |
*/ |
|
|
974 |
explicit |
|
|
975 |
rice_distribution(result_type __nu_val = result_type(0), |
|
|
976 |
result_type __sigma_val = result_type(1)) |
|
|
977 |
: _M_param(__nu_val, __sigma_val), |
|
|
978 |
_M_ndx(__nu_val, __sigma_val), |
|
|
979 |
_M_ndy(result_type(0), __sigma_val) |
|
|
980 |
{ } |
|
|
981 |
|
|
|
982 |
explicit |
|
|
983 |
rice_distribution(const param_type& __p) |
|
|
984 |
: _M_param(__p), |
|
|
985 |
_M_ndx(__p.nu(), __p.sigma()), |
|
|
986 |
_M_ndy(result_type(0), __p.sigma()) |
|
|
987 |
{ } |
|
|
988 |
|
|
|
989 |
/** |
|
|
990 |
* @brief Resets the distribution state. |
|
|
991 |
*/ |
|
|
992 |
void |
|
|
993 |
reset() |
|
|
994 |
{ |
|
|
995 |
_M_ndx.reset(); |
|
|
996 |
_M_ndy.reset(); |
|
|
997 |
} |
|
|
998 |
|
|
|
999 |
/** |
|
|
1000 |
* @brief Return the parameters of the distribution. |
|
|
1001 |
*/ |
|
|
1002 |
result_type |
|
|
1003 |
nu() const |
|
|
1004 |
{ return _M_param.nu(); } |
|
|
1005 |
|
|
|
1006 |
result_type |
|
|
1007 |
sigma() const |
|
|
1008 |
{ return _M_param.sigma(); } |
|
|
1009 |
|
|
|
1010 |
/** |
|
|
1011 |
* @brief Returns the parameter set of the distribution. |
|
|
1012 |
*/ |
|
|
1013 |
param_type |
|
|
1014 |
param() const |
|
|
1015 |
{ return _M_param; } |
|
|
1016 |
|
|
|
1017 |
/** |
|
|
1018 |
* @brief Sets the parameter set of the distribution. |
|
|
1019 |
* @param __param The new parameter set of the distribution. |
|
|
1020 |
*/ |
|
|
1021 |
void |
|
|
1022 |
param(const param_type& __param) |
|
|
1023 |
{ _M_param = __param; } |
|
|
1024 |
|
|
|
1025 |
/** |
|
|
1026 |
* @brief Returns the greatest lower bound value of the distribution. |
|
|
1027 |
*/ |
|
|
1028 |
result_type |
|
|
1029 |
min() const |
|
|
1030 |
{ return result_type(0); } |
|
|
1031 |
|
|
|
1032 |
/** |
|
|
1033 |
* @brief Returns the least upper bound value of the distribution. |
|
|
1034 |
*/ |
|
|
1035 |
result_type |
|
|
1036 |
max() const |
|
|
1037 |
{ return std::numeric_limits::max(); } |
|
|
1038 |
|
|
|
1039 |
/** |
|
|
1040 |
* @brief Generating functions. |
|
|
1041 |
*/ |
|
|
1042 |
template |
|
|
1043 |
result_type |
|
|
1044 |
operator()(_UniformRandomNumberGenerator& __urng) |
|
|
1045 |
{ |
|
|
1046 |
result_type __x = this->_M_ndx(__urng); |
|
|
1047 |
result_type __y = this->_M_ndy(__urng); |
|
|
1048 |
#if _GLIBCXX_USE_C99_MATH_TR1 |
|
|
1049 |
return std::hypot(__x, __y); |
|
|
1050 |
#else |
|
|
1051 |
return std::sqrt(__x * __x + __y * __y); |
|
|
1052 |
#endif |
|
|
1053 |
} |
|
|
1054 |
|
|
|
1055 |
template |
|
|
1056 |
result_type |
|
|
1057 |
operator()(_UniformRandomNumberGenerator& __urng, |
|
|
1058 |
const param_type& __p) |
|
|
1059 |
{ |
|
|
1060 |
typename std::normal_distribution::param_type |
|
|
1061 |
__px(__p.nu(), __p.sigma()), __py(result_type(0), __p.sigma()); |
|
|
1062 |
result_type __x = this->_M_ndx(__px, __urng); |
|
|
1063 |
result_type __y = this->_M_ndy(__py, __urng); |
|
|
1064 |
#if _GLIBCXX_USE_C99_MATH_TR1 |
|
|
1065 |
return std::hypot(__x, __y); |
|
|
1066 |
#else |
|
|
1067 |
return std::sqrt(__x * __x + __y * __y); |
|
|
1068 |
#endif |
|
|
1069 |
} |
|
|
1070 |
|
|
|
1071 |
template |
|
|
1072 |
typename _UniformRandomNumberGenerator> |
|
|
1073 |
void |
|
|
1074 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
1075 |
_UniformRandomNumberGenerator& __urng) |
|
|
1076 |
{ this->__generate(__f, __t, __urng, _M_param); } |
|
|
1077 |
|
|
|
1078 |
template |
|
|
1079 |
typename _UniformRandomNumberGenerator> |
|
|
1080 |
void |
|
|
1081 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
1082 |
_UniformRandomNumberGenerator& __urng, |
|
|
1083 |
const param_type& __p) |
|
|
1084 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
1085 |
|
|
|
1086 |
template |
|
|
1087 |
void |
|
|
1088 |
__generate(result_type* __f, result_type* __t, |
|
|
1089 |
_UniformRandomNumberGenerator& __urng, |
|
|
1090 |
const param_type& __p) |
|
|
1091 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
1092 |
|
|
|
1093 |
/** |
|
|
1094 |
* @brief Return true if two Rice distributions have |
|
|
1095 |
* the same parameters and the sequences that would |
|
|
1096 |
* be generated are equal. |
|
|
1097 |
*/ |
|
|
1098 |
friend bool |
|
|
1099 |
operator==(const rice_distribution& __d1, |
|
|
1100 |
const rice_distribution& __d2) |
|
|
1101 |
{ return (__d1._M_param == __d2._M_param |
|
|
1102 |
&& __d1._M_ndx == __d2._M_ndx |
|
|
1103 |
&& __d1._M_ndy == __d2._M_ndy); } |
|
|
1104 |
|
|
|
1105 |
/** |
|
|
1106 |
* @brief Inserts a %rice_distribution random number distribution |
|
|
1107 |
* @p __x into the output stream @p __os. |
|
|
1108 |
* |
|
|
1109 |
* @param __os An output stream. |
|
|
1110 |
* @param __x A %rice_distribution random number distribution. |
|
|
1111 |
* |
|
|
1112 |
* @returns The output stream with the state of @p __x inserted or in |
|
|
1113 |
* an error state. |
|
|
1114 |
*/ |
|
|
1115 |
template |
|
|
1116 |
friend std::basic_ostream<_CharT, _Traits>& |
|
|
1117 |
operator<<(std::basic_ostream<_CharT, _Traits>&, |
|
|
1118 |
const rice_distribution<_RealType1>&); |
|
|
1119 |
|
|
|
1120 |
/** |
|
|
1121 |
* @brief Extracts a %rice_distribution random number distribution |
|
|
1122 |
* @p __x from the input stream @p __is. |
|
|
1123 |
* |
|
|
1124 |
* @param __is An input stream. |
|
|
1125 |
* @param __x A %rice_distribution random number |
|
|
1126 |
* generator engine. |
|
|
1127 |
* |
|
|
1128 |
* @returns The input stream with @p __x extracted or in an error state. |
|
|
1129 |
*/ |
|
|
1130 |
template |
|
|
1131 |
friend std::basic_istream<_CharT, _Traits>& |
|
|
1132 |
operator>>(std::basic_istream<_CharT, _Traits>&, |
|
|
1133 |
rice_distribution<_RealType1>&); |
|
|
1134 |
|
|
|
1135 |
private: |
|
|
1136 |
template |
|
|
1137 |
typename _UniformRandomNumberGenerator> |
|
|
1138 |
void |
|
|
1139 |
__generate_impl(_ForwardIterator __f, _ForwardIterator __t, |
|
|
1140 |
_UniformRandomNumberGenerator& __urng, |
|
|
1141 |
const param_type& __p); |
|
|
1142 |
|
|
|
1143 |
param_type _M_param; |
|
|
1144 |
|
|
|
1145 |
std::normal_distribution _M_ndx; |
|
|
1146 |
std::normal_distribution _M_ndy; |
|
|
1147 |
}; |
|
|
1148 |
|
|
|
1149 |
/** |
|
|
1150 |
* @brief Return true if two Rice distributions are not equal. |
|
|
1151 |
*/ |
|
|
1152 |
template |
|
|
1153 |
inline bool |
|
|
1154 |
operator!=(const rice_distribution<_RealType1>& __d1, |
|
|
1155 |
const rice_distribution<_RealType1>& __d2) |
|
|
1156 |
{ return !(__d1 == __d2); } |
|
|
1157 |
|
|
|
1158 |
|
|
|
1159 |
/** |
|
|
1160 |
* @brief A Nakagami continuous distribution for random numbers. |
|
|
1161 |
* |
|
|
1162 |
* The formula for the Nakagami probability density function is |
|
|
1163 |
* @f[ |
|
|
1164 |
* p(x|\mu,\omega) = \frac{2\mu^\mu}{\Gamma(\mu)\omega^\mu} |
|
|
1165 |
* x^{2\mu-1}e^{-\mu x / \omega} |
|
|
1166 |
* @f] |
|
|
1167 |
* where @f$\Gamma(z)@f$ is the gamma function and @f$\mu >= 0.5@f$ |
|
|
1168 |
* and @f$\omega > 0@f$. |
|
|
1169 |
*/ |
|
|
1170 |
template |
|
|
1171 |
class |
|
|
1172 |
nakagami_distribution |
|
|
1173 |
{ |
|
|
1174 |
static_assert(std::is_floating_point<_RealType>::value, |
|
|
1175 |
"template argument not a floating point type"); |
|
|
1176 |
|
|
|
1177 |
public: |
|
|
1178 |
/** The type of the range of the distribution. */ |
|
|
1179 |
typedef _RealType result_type; |
|
|
1180 |
/** Parameter type. */ |
|
|
1181 |
struct param_type |
|
|
1182 |
{ |
|
|
1183 |
typedef nakagami_distribution distribution_type; |
|
|
1184 |
|
|
|
1185 |
param_type(result_type __mu_val = result_type(1), |
|
|
1186 |
result_type __omega_val = result_type(1)) |
|
|
1187 |
: _M_mu(__mu_val), _M_omega(__omega_val) |
|
|
1188 |
{ |
|
|
1189 |
_GLIBCXX_DEBUG_ASSERT(_M_mu >= result_type(0.5L)); |
|
|
1190 |
_GLIBCXX_DEBUG_ASSERT(_M_omega > result_type(0)); |
|
|
1191 |
} |
|
|
1192 |
|
|
|
1193 |
result_type |
|
|
1194 |
mu() const |
|
|
1195 |
{ return _M_mu; } |
|
|
1196 |
|
|
|
1197 |
result_type |
|
|
1198 |
omega() const |
|
|
1199 |
{ return _M_omega; } |
|
|
1200 |
|
|
|
1201 |
friend bool |
|
|
1202 |
operator==(const param_type& __p1, const param_type& __p2) |
|
|
1203 |
{ return __p1._M_mu == __p2._M_mu |
|
|
1204 |
&& __p1._M_omega == __p2._M_omega; } |
|
|
1205 |
|
|
|
1206 |
private: |
|
|
1207 |
void _M_initialize(); |
|
|
1208 |
|
|
|
1209 |
result_type _M_mu; |
|
|
1210 |
result_type _M_omega; |
|
|
1211 |
}; |
|
|
1212 |
|
|
|
1213 |
/** |
|
|
1214 |
* @brief Constructors. |
|
|
1215 |
*/ |
|
|
1216 |
explicit |
|
|
1217 |
nakagami_distribution(result_type __mu_val = result_type(1), |
|
|
1218 |
result_type __omega_val = result_type(1)) |
|
|
1219 |
: _M_param(__mu_val, __omega_val), |
|
|
1220 |
_M_gd(__mu_val, __omega_val / __mu_val) |
|
|
1221 |
{ } |
|
|
1222 |
|
|
|
1223 |
explicit |
|
|
1224 |
nakagami_distribution(const param_type& __p) |
|
|
1225 |
: _M_param(__p), |
|
|
1226 |
_M_gd(__p.mu(), __p.omega() / __p.mu()) |
|
|
1227 |
{ } |
|
|
1228 |
|
|
|
1229 |
/** |
|
|
1230 |
* @brief Resets the distribution state. |
|
|
1231 |
*/ |
|
|
1232 |
void |
|
|
1233 |
reset() |
|
|
1234 |
{ _M_gd.reset(); } |
|
|
1235 |
|
|
|
1236 |
/** |
|
|
1237 |
* @brief Return the parameters of the distribution. |
|
|
1238 |
*/ |
|
|
1239 |
result_type |
|
|
1240 |
mu() const |
|
|
1241 |
{ return _M_param.mu(); } |
|
|
1242 |
|
|
|
1243 |
result_type |
|
|
1244 |
omega() const |
|
|
1245 |
{ return _M_param.omega(); } |
|
|
1246 |
|
|
|
1247 |
/** |
|
|
1248 |
* @brief Returns the parameter set of the distribution. |
|
|
1249 |
*/ |
|
|
1250 |
param_type |
|
|
1251 |
param() const |
|
|
1252 |
{ return _M_param; } |
|
|
1253 |
|
|
|
1254 |
/** |
|
|
1255 |
* @brief Sets the parameter set of the distribution. |
|
|
1256 |
* @param __param The new parameter set of the distribution. |
|
|
1257 |
*/ |
|
|
1258 |
void |
|
|
1259 |
param(const param_type& __param) |
|
|
1260 |
{ _M_param = __param; } |
|
|
1261 |
|
|
|
1262 |
/** |
|
|
1263 |
* @brief Returns the greatest lower bound value of the distribution. |
|
|
1264 |
*/ |
|
|
1265 |
result_type |
|
|
1266 |
min() const |
|
|
1267 |
{ return result_type(0); } |
|
|
1268 |
|
|
|
1269 |
/** |
|
|
1270 |
* @brief Returns the least upper bound value of the distribution. |
|
|
1271 |
*/ |
|
|
1272 |
result_type |
|
|
1273 |
max() const |
|
|
1274 |
{ return std::numeric_limits::max(); } |
|
|
1275 |
|
|
|
1276 |
/** |
|
|
1277 |
* @brief Generating functions. |
|
|
1278 |
*/ |
|
|
1279 |
template |
|
|
1280 |
result_type |
|
|
1281 |
operator()(_UniformRandomNumberGenerator& __urng) |
|
|
1282 |
{ return std::sqrt(this->_M_gd(__urng)); } |
|
|
1283 |
|
|
|
1284 |
template |
|
|
1285 |
result_type |
|
|
1286 |
operator()(_UniformRandomNumberGenerator& __urng, |
|
|
1287 |
const param_type& __p) |
|
|
1288 |
{ |
|
|
1289 |
typename std::gamma_distribution::param_type |
|
|
1290 |
__pg(__p.mu(), __p.omega() / __p.mu()); |
|
|
1291 |
return std::sqrt(this->_M_gd(__pg, __urng)); |
|
|
1292 |
} |
|
|
1293 |
|
|
|
1294 |
template |
|
|
1295 |
typename _UniformRandomNumberGenerator> |
|
|
1296 |
void |
|
|
1297 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
1298 |
_UniformRandomNumberGenerator& __urng) |
|
|
1299 |
{ this->__generate(__f, __t, __urng, _M_param); } |
|
|
1300 |
|
|
|
1301 |
template |
|
|
1302 |
typename _UniformRandomNumberGenerator> |
|
|
1303 |
void |
|
|
1304 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
1305 |
_UniformRandomNumberGenerator& __urng, |
|
|
1306 |
const param_type& __p) |
|
|
1307 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
1308 |
|
|
|
1309 |
template |
|
|
1310 |
void |
|
|
1311 |
__generate(result_type* __f, result_type* __t, |
|
|
1312 |
_UniformRandomNumberGenerator& __urng, |
|
|
1313 |
const param_type& __p) |
|
|
1314 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
1315 |
|
|
|
1316 |
/** |
|
|
1317 |
* @brief Return true if two Nakagami distributions have |
|
|
1318 |
* the same parameters and the sequences that would |
|
|
1319 |
* be generated are equal. |
|
|
1320 |
*/ |
|
|
1321 |
friend bool |
|
|
1322 |
operator==(const nakagami_distribution& __d1, |
|
|
1323 |
const nakagami_distribution& __d2) |
|
|
1324 |
{ return (__d1._M_param == __d2._M_param |
|
|
1325 |
&& __d1._M_gd == __d2._M_gd); } |
|
|
1326 |
|
|
|
1327 |
/** |
|
|
1328 |
* @brief Inserts a %nakagami_distribution random number distribution |
|
|
1329 |
* @p __x into the output stream @p __os. |
|
|
1330 |
* |
|
|
1331 |
* @param __os An output stream. |
|
|
1332 |
* @param __x A %nakagami_distribution random number distribution. |
|
|
1333 |
* |
|
|
1334 |
* @returns The output stream with the state of @p __x inserted or in |
|
|
1335 |
* an error state. |
|
|
1336 |
*/ |
|
|
1337 |
template |
|
|
1338 |
friend std::basic_ostream<_CharT, _Traits>& |
|
|
1339 |
operator<<(std::basic_ostream<_CharT, _Traits>&, |
|
|
1340 |
const nakagami_distribution<_RealType1>&); |
|
|
1341 |
|
|
|
1342 |
/** |
|
|
1343 |
* @brief Extracts a %nakagami_distribution random number distribution |
|
|
1344 |
* @p __x from the input stream @p __is. |
|
|
1345 |
* |
|
|
1346 |
* @param __is An input stream. |
|
|
1347 |
* @param __x A %nakagami_distribution random number |
|
|
1348 |
* generator engine. |
|
|
1349 |
* |
|
|
1350 |
* @returns The input stream with @p __x extracted or in an error state. |
|
|
1351 |
*/ |
|
|
1352 |
template |
|
|
1353 |
friend std::basic_istream<_CharT, _Traits>& |
|
|
1354 |
operator>>(std::basic_istream<_CharT, _Traits>&, |
|
|
1355 |
nakagami_distribution<_RealType1>&); |
|
|
1356 |
|
|
|
1357 |
private: |
|
|
1358 |
template |
|
|
1359 |
typename _UniformRandomNumberGenerator> |
|
|
1360 |
void |
|
|
1361 |
__generate_impl(_ForwardIterator __f, _ForwardIterator __t, |
|
|
1362 |
_UniformRandomNumberGenerator& __urng, |
|
|
1363 |
const param_type& __p); |
|
|
1364 |
|
|
|
1365 |
param_type _M_param; |
|
|
1366 |
|
|
|
1367 |
std::gamma_distribution _M_gd; |
|
|
1368 |
}; |
|
|
1369 |
|
|
|
1370 |
/** |
|
|
1371 |
* @brief Return true if two Nakagami distributions are not equal. |
|
|
1372 |
*/ |
|
|
1373 |
template |
|
|
1374 |
inline bool |
|
|
1375 |
operator!=(const nakagami_distribution<_RealType>& __d1, |
|
|
1376 |
const nakagami_distribution<_RealType>& __d2) |
|
|
1377 |
{ return !(__d1 == __d2); } |
|
|
1378 |
|
|
|
1379 |
|
|
|
1380 |
/** |
|
|
1381 |
* @brief A Pareto continuous distribution for random numbers. |
|
|
1382 |
* |
|
|
1383 |
* The formula for the Pareto cumulative probability function is |
|
|
1384 |
* @f[ |
|
|
1385 |
* P(x|\alpha,\mu) = 1 - \left(\frac{\mu}{x}\right)^\alpha |
|
|
1386 |
* @f] |
|
|
1387 |
* The formula for the Pareto probability density function is |
|
|
1388 |
* @f[ |
|
|
1389 |
* p(x|\alpha,\mu) = \frac{\alpha + 1}{\mu} |
|
|
1390 |
* \left(\frac{\mu}{x}\right)^{\alpha + 1} |
|
|
1391 |
* @f] |
|
|
1392 |
* where @f$x >= \mu@f$ and @f$\mu > 0@f$, @f$\alpha > 0@f$. |
|
|
1393 |
* |
|
|
1394 |
*
|
|
1395 |
* Distribution Statistics |
|
|
1396 |
* | Mean | @f$\alpha \mu / (\alpha - 1)@f$ |
|
|
1397 |
* for @f$\alpha > 1@f$ | |
|
|
1398 |
* | Variance | @f$\alpha \mu^2 / [(\alpha - 1)^2(\alpha - 2)]@f$ |
|
|
1399 |
* for @f$\alpha > 2@f$ | |
|
|
1400 |
* | Range | @f$[\mu, \infty)@f$ | |
|
|
1401 |
* | |
|
|
1402 |
*/ |
|
|
1403 |
template |
|
|
1404 |
class |
|
|
1405 |
pareto_distribution |
|
|
1406 |
{ |
|
|
1407 |
static_assert(std::is_floating_point<_RealType>::value, |
|
|
1408 |
"template argument not a floating point type"); |
|
|
1409 |
|
|
|
1410 |
public: |
|
|
1411 |
/** The type of the range of the distribution. */ |
|
|
1412 |
typedef _RealType result_type; |
|
|
1413 |
/** Parameter type. */ |
|
|
1414 |
struct param_type |
|
|
1415 |
{ |
|
|
1416 |
typedef pareto_distribution distribution_type; |
|
|
1417 |
|
|
|
1418 |
param_type(result_type __alpha_val = result_type(1), |
|
|
1419 |
result_type __mu_val = result_type(1)) |
|
|
1420 |
: _M_alpha(__alpha_val), _M_mu(__mu_val) |
|
|
1421 |
{ |
|
|
1422 |
_GLIBCXX_DEBUG_ASSERT(_M_alpha > result_type(0)); |
|
|
1423 |
_GLIBCXX_DEBUG_ASSERT(_M_mu > result_type(0)); |
|
|
1424 |
} |
|
|
1425 |
|
|
|
1426 |
result_type |
|
|
1427 |
alpha() const |
|
|
1428 |
{ return _M_alpha; } |
|
|
1429 |
|
|
|
1430 |
result_type |
|
|
1431 |
mu() const |
|
|
1432 |
{ return _M_mu; } |
|
|
1433 |
|
|
|
1434 |
friend bool |
|
|
1435 |
operator==(const param_type& __p1, const param_type& __p2) |
|
|
1436 |
{ return __p1._M_alpha == __p2._M_alpha && __p1._M_mu == __p2._M_mu; } |
|
|
1437 |
|
|
|
1438 |
private: |
|
|
1439 |
void _M_initialize(); |
|
|
1440 |
|
|
|
1441 |
result_type _M_alpha; |
|
|
1442 |
result_type _M_mu; |
|
|
1443 |
}; |
|
|
1444 |
|
|
|
1445 |
/** |
|
|
1446 |
* @brief Constructors. |
|
|
1447 |
*/ |
|
|
1448 |
explicit |
|
|
1449 |
pareto_distribution(result_type __alpha_val = result_type(1), |
|
|
1450 |
result_type __mu_val = result_type(1)) |
|
|
1451 |
: _M_param(__alpha_val, __mu_val), |
|
|
1452 |
_M_ud() |
|
|
1453 |
{ } |
|
|
1454 |
|
|
|
1455 |
explicit |
|
|
1456 |
pareto_distribution(const param_type& __p) |
|
|
1457 |
: _M_param(__p), |
|
|
1458 |
_M_ud() |
|
|
1459 |
{ } |
|
|
1460 |
|
|
|
1461 |
/** |
|
|
1462 |
* @brief Resets the distribution state. |
|
|
1463 |
*/ |
|
|
1464 |
void |
|
|
1465 |
reset() |
|
|
1466 |
{ |
|
|
1467 |
_M_ud.reset(); |
|
|
1468 |
} |
|
|
1469 |
|
|
|
1470 |
/** |
|
|
1471 |
* @brief Return the parameters of the distribution. |
|
|
1472 |
*/ |
|
|
1473 |
result_type |
|
|
1474 |
alpha() const |
|
|
1475 |
{ return _M_param.alpha(); } |
|
|
1476 |
|
|
|
1477 |
result_type |
|
|
1478 |
mu() const |
|
|
1479 |
{ return _M_param.mu(); } |
|
|
1480 |
|
|
|
1481 |
/** |
|
|
1482 |
* @brief Returns the parameter set of the distribution. |
|
|
1483 |
*/ |
|
|
1484 |
param_type |
|
|
1485 |
param() const |
|
|
1486 |
{ return _M_param; } |
|
|
1487 |
|
|
|
1488 |
/** |
|
|
1489 |
* @brief Sets the parameter set of the distribution. |
|
|
1490 |
* @param __param The new parameter set of the distribution. |
|
|
1491 |
*/ |
|
|
1492 |
void |
|
|
1493 |
param(const param_type& __param) |
|
|
1494 |
{ _M_param = __param; } |
|
|
1495 |
|
|
|
1496 |
/** |
|
|
1497 |
* @brief Returns the greatest lower bound value of the distribution. |
|
|
1498 |
*/ |
|
|
1499 |
result_type |
|
|
1500 |
min() const |
|
|
1501 |
{ return this->mu(); } |
|
|
1502 |
|
|
|
1503 |
/** |
|
|
1504 |
* @brief Returns the least upper bound value of the distribution. |
|
|
1505 |
*/ |
|
|
1506 |
result_type |
|
|
1507 |
max() const |
|
|
1508 |
{ return std::numeric_limits::max(); } |
|
|
1509 |
|
|
|
1510 |
/** |
|
|
1511 |
* @brief Generating functions. |
|
|
1512 |
*/ |
|
|
1513 |
template |
|
|
1514 |
result_type |
|
|
1515 |
operator()(_UniformRandomNumberGenerator& __urng) |
|
|
1516 |
{ |
|
|
1517 |
return this->mu() * std::pow(this->_M_ud(__urng), |
|
|
1518 |
-result_type(1) / this->alpha()); |
|
|
1519 |
} |
|
|
1520 |
|
|
|
1521 |
template |
|
|
1522 |
result_type |
|
|
1523 |
operator()(_UniformRandomNumberGenerator& __urng, |
|
|
1524 |
const param_type& __p) |
|
|
1525 |
{ |
|
|
1526 |
return __p.mu() * std::pow(this->_M_ud(__urng), |
|
|
1527 |
-result_type(1) / __p.alpha()); |
|
|
1528 |
} |
|
|
1529 |
|
|
|
1530 |
template |
|
|
1531 |
typename _UniformRandomNumberGenerator> |
|
|
1532 |
void |
|
|
1533 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
1534 |
_UniformRandomNumberGenerator& __urng) |
|
|
1535 |
{ this->__generate(__f, __t, __urng, _M_param); } |
|
|
1536 |
|
|
|
1537 |
template |
|
|
1538 |
typename _UniformRandomNumberGenerator> |
|
|
1539 |
void |
|
|
1540 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
1541 |
_UniformRandomNumberGenerator& __urng, |
|
|
1542 |
const param_type& __p) |
|
|
1543 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
1544 |
|
|
|
1545 |
template |
|
|
1546 |
void |
|
|
1547 |
__generate(result_type* __f, result_type* __t, |
|
|
1548 |
_UniformRandomNumberGenerator& __urng, |
|
|
1549 |
const param_type& __p) |
|
|
1550 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
1551 |
|
|
|
1552 |
/** |
|
|
1553 |
* @brief Return true if two Pareto distributions have |
|
|
1554 |
* the same parameters and the sequences that would |
|
|
1555 |
* be generated are equal. |
|
|
1556 |
*/ |
|
|
1557 |
friend bool |
|
|
1558 |
operator==(const pareto_distribution& __d1, |
|
|
1559 |
const pareto_distribution& __d2) |
|
|
1560 |
{ return (__d1._M_param == __d2._M_param |
|
|
1561 |
&& __d1._M_ud == __d2._M_ud); } |
|
|
1562 |
|
|
|
1563 |
/** |
|
|
1564 |
* @brief Inserts a %pareto_distribution random number distribution |
|
|
1565 |
* @p __x into the output stream @p __os. |
|
|
1566 |
* |
|
|
1567 |
* @param __os An output stream. |
|
|
1568 |
* @param __x A %pareto_distribution random number distribution. |
|
|
1569 |
* |
|
|
1570 |
* @returns The output stream with the state of @p __x inserted or in |
|
|
1571 |
* an error state. |
|
|
1572 |
*/ |
|
|
1573 |
template |
|
|
1574 |
friend std::basic_ostream<_CharT, _Traits>& |
|
|
1575 |
operator<<(std::basic_ostream<_CharT, _Traits>&, |
|
|
1576 |
const pareto_distribution<_RealType1>&); |
|
|
1577 |
|
|
|
1578 |
/** |
|
|
1579 |
* @brief Extracts a %pareto_distribution random number distribution |
|
|
1580 |
* @p __x from the input stream @p __is. |
|
|
1581 |
* |
|
|
1582 |
* @param __is An input stream. |
|
|
1583 |
* @param __x A %pareto_distribution random number |
|
|
1584 |
* generator engine. |
|
|
1585 |
* |
|
|
1586 |
* @returns The input stream with @p __x extracted or in an error state. |
|
|
1587 |
*/ |
|
|
1588 |
template |
|
|
1589 |
friend std::basic_istream<_CharT, _Traits>& |
|
|
1590 |
operator>>(std::basic_istream<_CharT, _Traits>&, |
|
|
1591 |
pareto_distribution<_RealType1>&); |
|
|
1592 |
|
|
|
1593 |
private: |
|
|
1594 |
template |
|
|
1595 |
typename _UniformRandomNumberGenerator> |
|
|
1596 |
void |
|
|
1597 |
__generate_impl(_ForwardIterator __f, _ForwardIterator __t, |
|
|
1598 |
_UniformRandomNumberGenerator& __urng, |
|
|
1599 |
const param_type& __p); |
|
|
1600 |
|
|
|
1601 |
param_type _M_param; |
|
|
1602 |
|
|
|
1603 |
std::uniform_real_distribution _M_ud; |
|
|
1604 |
}; |
|
|
1605 |
|
|
|
1606 |
/** |
|
|
1607 |
* @brief Return true if two Pareto distributions are not equal. |
|
|
1608 |
*/ |
|
|
1609 |
template |
|
|
1610 |
inline bool |
|
|
1611 |
operator!=(const pareto_distribution<_RealType>& __d1, |
|
|
1612 |
const pareto_distribution<_RealType>& __d2) |
|
|
1613 |
{ return !(__d1 == __d2); } |
|
|
1614 |
|
|
|
1615 |
|
|
|
1616 |
/** |
|
|
1617 |
* @brief A K continuous distribution for random numbers. |
|
|
1618 |
* |
|
|
1619 |
* The formula for the K probability density function is |
|
|
1620 |
* @f[ |
|
|
1621 |
* p(x|\lambda, \mu, \nu) = \frac{2}{x} |
|
|
1622 |
* \left(\frac{\lambda\nu x}{\mu}\right)^{\frac{\lambda + \nu}{2}} |
|
|
1623 |
* \frac{1}{\Gamma(\lambda)\Gamma(\nu)} |
|
|
1624 |
* K_{\nu - \lambda}\left(2\sqrt{\frac{\lambda\nu x}{\mu}}\right) |
|
|
1625 |
* @f] |
|
|
1626 |
* where @f$I_0(z)@f$ is the modified Bessel function of the second kind |
|
|
1627 |
* of order @f$\nu - \lambda@f$ and @f$\lambda > 0@f$, @f$\mu > 0@f$ |
|
|
1628 |
* and @f$\nu > 0@f$. |
|
|
1629 |
* |
|
|
1630 |
*
|
|
1631 |
* Distribution Statistics |
|
|
1632 |
* | Mean | @f$\mu@f$ | |
|
|
1633 |
* | Variance | @f$\mu^2\frac{\lambda + \nu + 1}{\lambda\nu}@f$ | |
|
|
1634 |
* | Range | @f$[0, \infty)@f$ | |
|
|
1635 |
* | |
|
|
1636 |
*/ |
|
|
1637 |
template |
|
|
1638 |
class |
|
|
1639 |
k_distribution |
|
|
1640 |
{ |
|
|
1641 |
static_assert(std::is_floating_point<_RealType>::value, |
|
|
1642 |
"template argument not a floating point type"); |
|
|
1643 |
|
|
|
1644 |
public: |
|
|
1645 |
/** The type of the range of the distribution. */ |
|
|
1646 |
typedef _RealType result_type; |
|
|
1647 |
/** Parameter type. */ |
|
|
1648 |
struct param_type |
|
|
1649 |
{ |
|
|
1650 |
typedef k_distribution distribution_type; |
|
|
1651 |
|
|
|
1652 |
param_type(result_type __lambda_val = result_type(1), |
|
|
1653 |
result_type __mu_val = result_type(1), |
|
|
1654 |
result_type __nu_val = result_type(1)) |
|
|
1655 |
: _M_lambda(__lambda_val), _M_mu(__mu_val), _M_nu(__nu_val) |
|
|
1656 |
{ |
|
|
1657 |
_GLIBCXX_DEBUG_ASSERT(_M_lambda > result_type(0)); |
|
|
1658 |
_GLIBCXX_DEBUG_ASSERT(_M_mu > result_type(0)); |
|
|
1659 |
_GLIBCXX_DEBUG_ASSERT(_M_nu > result_type(0)); |
|
|
1660 |
} |
|
|
1661 |
|
|
|
1662 |
result_type |
|
|
1663 |
lambda() const |
|
|
1664 |
{ return _M_lambda; } |
|
|
1665 |
|
|
|
1666 |
result_type |
|
|
1667 |
mu() const |
|
|
1668 |
{ return _M_mu; } |
|
|
1669 |
|
|
|
1670 |
result_type |
|
|
1671 |
nu() const |
|
|
1672 |
{ return _M_nu; } |
|
|
1673 |
|
|
|
1674 |
friend bool |
|
|
1675 |
operator==(const param_type& __p1, const param_type& __p2) |
|
|
1676 |
{ return __p1._M_lambda == __p2._M_lambda |
|
|
1677 |
&& __p1._M_mu == __p2._M_mu |
|
|
1678 |
&& __p1._M_nu == __p2._M_nu; } |
|
|
1679 |
|
|
|
1680 |
private: |
|
|
1681 |
void _M_initialize(); |
|
|
1682 |
|
|
|
1683 |
result_type _M_lambda; |
|
|
1684 |
result_type _M_mu; |
|
|
1685 |
result_type _M_nu; |
|
|
1686 |
}; |
|
|
1687 |
|
|
|
1688 |
/** |
|
|
1689 |
* @brief Constructors. |
|
|
1690 |
*/ |
|
|
1691 |
explicit |
|
|
1692 |
k_distribution(result_type __lambda_val = result_type(1), |
|
|
1693 |
result_type __mu_val = result_type(1), |
|
|
1694 |
result_type __nu_val = result_type(1)) |
|
|
1695 |
: _M_param(__lambda_val, __mu_val, __nu_val), |
|
|
1696 |
_M_gd1(__lambda_val, result_type(1) / __lambda_val), |
|
|
1697 |
_M_gd2(__nu_val, __mu_val / __nu_val) |
|
|
1698 |
{ } |
|
|
1699 |
|
|
|
1700 |
explicit |
|
|
1701 |
k_distribution(const param_type& __p) |
|
|
1702 |
: _M_param(__p), |
|
|
1703 |
_M_gd1(__p.lambda(), result_type(1) / __p.lambda()), |
|
|
1704 |
_M_gd2(__p.nu(), __p.mu() / __p.nu()) |
|
|
1705 |
{ } |
|
|
1706 |
|
|
|
1707 |
/** |
|
|
1708 |
* @brief Resets the distribution state. |
|
|
1709 |
*/ |
|
|
1710 |
void |
|
|
1711 |
reset() |
|
|
1712 |
{ |
|
|
1713 |
_M_gd1.reset(); |
|
|
1714 |
_M_gd2.reset(); |
|
|
1715 |
} |
|
|
1716 |
|
|
|
1717 |
/** |
|
|
1718 |
* @brief Return the parameters of the distribution. |
|
|
1719 |
*/ |
|
|
1720 |
result_type |
|
|
1721 |
lambda() const |
|
|
1722 |
{ return _M_param.lambda(); } |
|
|
1723 |
|
|
|
1724 |
result_type |
|
|
1725 |
mu() const |
|
|
1726 |
{ return _M_param.mu(); } |
|
|
1727 |
|
|
|
1728 |
result_type |
|
|
1729 |
nu() const |
|
|
1730 |
{ return _M_param.nu(); } |
|
|
1731 |
|
|
|
1732 |
/** |
|
|
1733 |
* @brief Returns the parameter set of the distribution. |
|
|
1734 |
*/ |
|
|
1735 |
param_type |
|
|
1736 |
param() const |
|
|
1737 |
{ return _M_param; } |
|
|
1738 |
|
|
|
1739 |
/** |
|
|
1740 |
* @brief Sets the parameter set of the distribution. |
|
|
1741 |
* @param __param The new parameter set of the distribution. |
|
|
1742 |
*/ |
|
|
1743 |
void |
|
|
1744 |
param(const param_type& __param) |
|
|
1745 |
{ _M_param = __param; } |
|
|
1746 |
|
|
|
1747 |
/** |
|
|
1748 |
* @brief Returns the greatest lower bound value of the distribution. |
|
|
1749 |
*/ |
|
|
1750 |
result_type |
|
|
1751 |
min() const |
|
|
1752 |
{ return result_type(0); } |
|
|
1753 |
|
|
|
1754 |
/** |
|
|
1755 |
* @brief Returns the least upper bound value of the distribution. |
|
|
1756 |
*/ |
|
|
1757 |
result_type |
|
|
1758 |
max() const |
|
|
1759 |
{ return std::numeric_limits::max(); } |
|
|
1760 |
|
|
|
1761 |
/** |
|
|
1762 |
* @brief Generating functions. |
|
|
1763 |
*/ |
|
|
1764 |
template |
|
|
1765 |
result_type |
|
|
1766 |
operator()(_UniformRandomNumberGenerator&); |
|
|
1767 |
|
|
|
1768 |
template |
|
|
1769 |
result_type |
|
|
1770 |
operator()(_UniformRandomNumberGenerator&, const param_type&); |
|
|
1771 |
|
|
|
1772 |
template |
|
|
1773 |
typename _UniformRandomNumberGenerator> |
|
|
1774 |
void |
|
|
1775 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
1776 |
_UniformRandomNumberGenerator& __urng) |
|
|
1777 |
{ this->__generate(__f, __t, __urng, _M_param); } |
|
|
1778 |
|
|
|
1779 |
template |
|
|
1780 |
typename _UniformRandomNumberGenerator> |
|
|
1781 |
void |
|
|
1782 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
1783 |
_UniformRandomNumberGenerator& __urng, |
|
|
1784 |
const param_type& __p) |
|
|
1785 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
1786 |
|
|
|
1787 |
template |
|
|
1788 |
void |
|
|
1789 |
__generate(result_type* __f, result_type* __t, |
|
|
1790 |
_UniformRandomNumberGenerator& __urng, |
|
|
1791 |
const param_type& __p) |
|
|
1792 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
1793 |
|
|
|
1794 |
/** |
|
|
1795 |
* @brief Return true if two K distributions have |
|
|
1796 |
* the same parameters and the sequences that would |
|
|
1797 |
* be generated are equal. |
|
|
1798 |
*/ |
|
|
1799 |
friend bool |
|
|
1800 |
operator==(const k_distribution& __d1, |
|
|
1801 |
const k_distribution& __d2) |
|
|
1802 |
{ return (__d1._M_param == __d2._M_param |
|
|
1803 |
&& __d1._M_gd1 == __d2._M_gd1 |
|
|
1804 |
&& __d1._M_gd2 == __d2._M_gd2); } |
|
|
1805 |
|
|
|
1806 |
/** |
|
|
1807 |
* @brief Inserts a %k_distribution random number distribution |
|
|
1808 |
* @p __x into the output stream @p __os. |
|
|
1809 |
* |
|
|
1810 |
* @param __os An output stream. |
|
|
1811 |
* @param __x A %k_distribution random number distribution. |
|
|
1812 |
* |
|
|
1813 |
* @returns The output stream with the state of @p __x inserted or in |
|
|
1814 |
* an error state. |
|
|
1815 |
*/ |
|
|
1816 |
template |
|
|
1817 |
friend std::basic_ostream<_CharT, _Traits>& |
|
|
1818 |
operator<<(std::basic_ostream<_CharT, _Traits>&, |
|
|
1819 |
const k_distribution<_RealType1>&); |
|
|
1820 |
|
|
|
1821 |
/** |
|
|
1822 |
* @brief Extracts a %k_distribution random number distribution |
|
|
1823 |
* @p __x from the input stream @p __is. |
|
|
1824 |
* |
|
|
1825 |
* @param __is An input stream. |
|
|
1826 |
* @param __x A %k_distribution random number |
|
|
1827 |
* generator engine. |
|
|
1828 |
* |
|
|
1829 |
* @returns The input stream with @p __x extracted or in an error state. |
|
|
1830 |
*/ |
|
|
1831 |
template |
|
|
1832 |
friend std::basic_istream<_CharT, _Traits>& |
|
|
1833 |
operator>>(std::basic_istream<_CharT, _Traits>&, |
|
|
1834 |
k_distribution<_RealType1>&); |
|
|
1835 |
|
|
|
1836 |
private: |
|
|
1837 |
template |
|
|
1838 |
typename _UniformRandomNumberGenerator> |
|
|
1839 |
void |
|
|
1840 |
__generate_impl(_ForwardIterator __f, _ForwardIterator __t, |
|
|
1841 |
_UniformRandomNumberGenerator& __urng, |
|
|
1842 |
const param_type& __p); |
|
|
1843 |
|
|
|
1844 |
param_type _M_param; |
|
|
1845 |
|
|
|
1846 |
std::gamma_distribution _M_gd1; |
|
|
1847 |
std::gamma_distribution _M_gd2; |
|
|
1848 |
}; |
|
|
1849 |
|
|
|
1850 |
/** |
|
|
1851 |
* @brief Return true if two K distributions are not equal. |
|
|
1852 |
*/ |
|
|
1853 |
template |
|
|
1854 |
inline bool |
|
|
1855 |
operator!=(const k_distribution<_RealType>& __d1, |
|
|
1856 |
const k_distribution<_RealType>& __d2) |
|
|
1857 |
{ return !(__d1 == __d2); } |
|
|
1858 |
|
|
|
1859 |
|
|
|
1860 |
/** |
|
|
1861 |
* @brief An arcsine continuous distribution for random numbers. |
|
|
1862 |
* |
|
|
1863 |
* The formula for the arcsine probability density function is |
|
|
1864 |
* @f[ |
|
|
1865 |
* p(x|a,b) = \frac{1}{\pi \sqrt{(x - a)(b - x)}} |
|
|
1866 |
* @f] |
|
|
1867 |
* where @f$x >= a@f$ and @f$x <= b@f$. |
|
|
1868 |
* |
|
|
1869 |
*
|
|
1870 |
* Distribution Statistics |
|
|
1871 |
* | Mean | @f$ (a + b) / 2 @f$ | |
|
|
1872 |
* | Variance | @f$ (b - a)^2 / 8 @f$ | |
|
|
1873 |
* | Range | @f$[a, b]@f$ | |
|
|
1874 |
* | |
|
|
1875 |
*/ |
|
|
1876 |
template |
|
|
1877 |
class |
|
|
1878 |
arcsine_distribution |
|
|
1879 |
{ |
|
|
1880 |
static_assert(std::is_floating_point<_RealType>::value, |
|
|
1881 |
"template argument not a floating point type"); |
|
|
1882 |
|
|
|
1883 |
public: |
|
|
1884 |
/** The type of the range of the distribution. */ |
|
|
1885 |
typedef _RealType result_type; |
|
|
1886 |
/** Parameter type. */ |
|
|
1887 |
struct param_type |
|
|
1888 |
{ |
|
|
1889 |
typedef arcsine_distribution distribution_type; |
|
|
1890 |
|
|
|
1891 |
param_type(result_type __a = result_type(0), |
|
|
1892 |
result_type __b = result_type(1)) |
|
|
1893 |
: _M_a(__a), _M_b(__b) |
|
|
1894 |
{ |
|
|
1895 |
_GLIBCXX_DEBUG_ASSERT(_M_a <= _M_b); |
|
|
1896 |
} |
|
|
1897 |
|
|
|
1898 |
result_type |
|
|
1899 |
a() const |
|
|
1900 |
{ return _M_a; } |
|
|
1901 |
|
|
|
1902 |
result_type |
|
|
1903 |
b() const |
|
|
1904 |
{ return _M_b; } |
|
|
1905 |
|
|
|
1906 |
friend bool |
|
|
1907 |
operator==(const param_type& __p1, const param_type& __p2) |
|
|
1908 |
{ return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; } |
|
|
1909 |
|
|
|
1910 |
private: |
|
|
1911 |
void _M_initialize(); |
|
|
1912 |
|
|
|
1913 |
result_type _M_a; |
|
|
1914 |
result_type _M_b; |
|
|
1915 |
}; |
|
|
1916 |
|
|
|
1917 |
/** |
|
|
1918 |
* @brief Constructors. |
|
|
1919 |
*/ |
|
|
1920 |
explicit |
|
|
1921 |
arcsine_distribution(result_type __a = result_type(0), |
|
|
1922 |
result_type __b = result_type(1)) |
|
|
1923 |
: _M_param(__a, __b), |
|
|
1924 |
_M_ud(-1.5707963267948966192313216916397514L, |
|
|
1925 |
+1.5707963267948966192313216916397514L) |
|
|
1926 |
{ } |
|
|
1927 |
|
|
|
1928 |
explicit |
|
|
1929 |
arcsine_distribution(const param_type& __p) |
|
|
1930 |
: _M_param(__p), |
|
|
1931 |
_M_ud(-1.5707963267948966192313216916397514L, |
|
|
1932 |
+1.5707963267948966192313216916397514L) |
|
|
1933 |
{ } |
|
|
1934 |
|
|
|
1935 |
/** |
|
|
1936 |
* @brief Resets the distribution state. |
|
|
1937 |
*/ |
|
|
1938 |
void |
|
|
1939 |
reset() |
|
|
1940 |
{ _M_ud.reset(); } |
|
|
1941 |
|
|
|
1942 |
/** |
|
|
1943 |
* @brief Return the parameters of the distribution. |
|
|
1944 |
*/ |
|
|
1945 |
result_type |
|
|
1946 |
a() const |
|
|
1947 |
{ return _M_param.a(); } |
|
|
1948 |
|
|
|
1949 |
result_type |
|
|
1950 |
b() const |
|
|
1951 |
{ return _M_param.b(); } |
|
|
1952 |
|
|
|
1953 |
/** |
|
|
1954 |
* @brief Returns the parameter set of the distribution. |
|
|
1955 |
*/ |
|
|
1956 |
param_type |
|
|
1957 |
param() const |
|
|
1958 |
{ return _M_param; } |
|
|
1959 |
|
|
|
1960 |
/** |
|
|
1961 |
* @brief Sets the parameter set of the distribution. |
|
|
1962 |
* @param __param The new parameter set of the distribution. |
|
|
1963 |
*/ |
|
|
1964 |
void |
|
|
1965 |
param(const param_type& __param) |
|
|
1966 |
{ _M_param = __param; } |
|
|
1967 |
|
|
|
1968 |
/** |
|
|
1969 |
* @brief Returns the greatest lower bound value of the distribution. |
|
|
1970 |
*/ |
|
|
1971 |
result_type |
|
|
1972 |
min() const |
|
|
1973 |
{ return this->a(); } |
|
|
1974 |
|
|
|
1975 |
/** |
|
|
1976 |
* @brief Returns the least upper bound value of the distribution. |
|
|
1977 |
*/ |
|
|
1978 |
result_type |
|
|
1979 |
max() const |
|
|
1980 |
{ return this->b(); } |
|
|
1981 |
|
|
|
1982 |
/** |
|
|
1983 |
* @brief Generating functions. |
|
|
1984 |
*/ |
|
|
1985 |
template |
|
|
1986 |
result_type |
|
|
1987 |
operator()(_UniformRandomNumberGenerator& __urng) |
|
|
1988 |
{ |
|
|
1989 |
result_type __x = std::sin(this->_M_ud(__urng)); |
|
|
1990 |
return (__x * (this->b() - this->a()) |
|
|
1991 |
+ this->a() + this->b()) / result_type(2); |
|
|
1992 |
} |
|
|
1993 |
|
|
|
1994 |
template |
|
|
1995 |
result_type |
|
|
1996 |
operator()(_UniformRandomNumberGenerator& __urng, |
|
|
1997 |
const param_type& __p) |
|
|
1998 |
{ |
|
|
1999 |
result_type __x = std::sin(this->_M_ud(__urng)); |
|
|
2000 |
return (__x * (__p.b() - __p.a()) |
|
|
2001 |
+ __p.a() + __p.b()) / result_type(2); |
|
|
2002 |
} |
|
|
2003 |
|
|
|
2004 |
template |
|
|
2005 |
typename _UniformRandomNumberGenerator> |
|
|
2006 |
void |
|
|
2007 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
2008 |
_UniformRandomNumberGenerator& __urng) |
|
|
2009 |
{ this->__generate(__f, __t, __urng, _M_param); } |
|
|
2010 |
|
|
|
2011 |
template |
|
|
2012 |
typename _UniformRandomNumberGenerator> |
|
|
2013 |
void |
|
|
2014 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
2015 |
_UniformRandomNumberGenerator& __urng, |
|
|
2016 |
const param_type& __p) |
|
|
2017 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
2018 |
|
|
|
2019 |
template |
|
|
2020 |
void |
|
|
2021 |
__generate(result_type* __f, result_type* __t, |
|
|
2022 |
_UniformRandomNumberGenerator& __urng, |
|
|
2023 |
const param_type& __p) |
|
|
2024 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
2025 |
|
|
|
2026 |
/** |
|
|
2027 |
* @brief Return true if two arcsine distributions have |
|
|
2028 |
* the same parameters and the sequences that would |
|
|
2029 |
* be generated are equal. |
|
|
2030 |
*/ |
|
|
2031 |
friend bool |
|
|
2032 |
operator==(const arcsine_distribution& __d1, |
|
|
2033 |
const arcsine_distribution& __d2) |
|
|
2034 |
{ return (__d1._M_param == __d2._M_param |
|
|
2035 |
&& __d1._M_ud == __d2._M_ud); } |
|
|
2036 |
|
|
|
2037 |
/** |
|
|
2038 |
* @brief Inserts a %arcsine_distribution random number distribution |
|
|
2039 |
* @p __x into the output stream @p __os. |
|
|
2040 |
* |
|
|
2041 |
* @param __os An output stream. |
|
|
2042 |
* @param __x A %arcsine_distribution random number distribution. |
|
|
2043 |
* |
|
|
2044 |
* @returns The output stream with the state of @p __x inserted or in |
|
|
2045 |
* an error state. |
|
|
2046 |
*/ |
|
|
2047 |
template |
|
|
2048 |
friend std::basic_ostream<_CharT, _Traits>& |
|
|
2049 |
operator<<(std::basic_ostream<_CharT, _Traits>&, |
|
|
2050 |
const arcsine_distribution<_RealType1>&); |
|
|
2051 |
|
|
|
2052 |
/** |
|
|
2053 |
* @brief Extracts a %arcsine_distribution random number distribution |
|
|
2054 |
* @p __x from the input stream @p __is. |
|
|
2055 |
* |
|
|
2056 |
* @param __is An input stream. |
|
|
2057 |
* @param __x A %arcsine_distribution random number |
|
|
2058 |
* generator engine. |
|
|
2059 |
* |
|
|
2060 |
* @returns The input stream with @p __x extracted or in an error state. |
|
|
2061 |
*/ |
|
|
2062 |
template |
|
|
2063 |
friend std::basic_istream<_CharT, _Traits>& |
|
|
2064 |
operator>>(std::basic_istream<_CharT, _Traits>&, |
|
|
2065 |
arcsine_distribution<_RealType1>&); |
|
|
2066 |
|
|
|
2067 |
private: |
|
|
2068 |
template |
|
|
2069 |
typename _UniformRandomNumberGenerator> |
|
|
2070 |
void |
|
|
2071 |
__generate_impl(_ForwardIterator __f, _ForwardIterator __t, |
|
|
2072 |
_UniformRandomNumberGenerator& __urng, |
|
|
2073 |
const param_type& __p); |
|
|
2074 |
|
|
|
2075 |
param_type _M_param; |
|
|
2076 |
|
|
|
2077 |
std::uniform_real_distribution _M_ud; |
|
|
2078 |
}; |
|
|
2079 |
|
|
|
2080 |
/** |
|
|
2081 |
* @brief Return true if two arcsine distributions are not equal. |
|
|
2082 |
*/ |
|
|
2083 |
template |
|
|
2084 |
inline bool |
|
|
2085 |
operator!=(const arcsine_distribution<_RealType>& __d1, |
|
|
2086 |
const arcsine_distribution<_RealType>& __d2) |
|
|
2087 |
{ return !(__d1 == __d2); } |
|
|
2088 |
|
|
|
2089 |
|
|
|
2090 |
/** |
|
|
2091 |
* @brief A Hoyt continuous distribution for random numbers. |
|
|
2092 |
* |
|
|
2093 |
* The formula for the Hoyt probability density function is |
|
|
2094 |
* @f[ |
|
|
2095 |
* p(x|q,\omega) = \frac{(1 + q^2)x}{q\omega} |
|
|
2096 |
* \exp\left(-\frac{(1 + q^2)^2 x^2}{4 q^2 \omega}\right) |
|
|
2097 |
* I_0\left(\frac{(1 - q^4) x^2}{4 q^2 \omega}\right) |
|
|
2098 |
* @f] |
|
|
2099 |
* where @f$I_0(z)@f$ is the modified Bessel function of the first kind |
|
|
2100 |
* of order 0 and @f$0 < q < 1@f$. |
|
|
2101 |
* |
|
|
2102 |
*
|
|
2103 |
* Distribution Statistics |
|
|
2104 |
* | Mean | @f$ \sqrt{\frac{2}{\pi}} \sqrt{\frac{\omega}{1 + q^2}} |
|
|
2105 |
* E(1 - q^2) @f$ | |
|
|
2106 |
* | Variance | @f$ \omega \left(1 - \frac{2E^2(1 - q^2)} |
|
|
2107 |
* {\pi (1 + q^2)}\right) @f$ | |
|
|
2108 |
* | Range | @f$[0, \infty)@f$ | |
|
|
2109 |
* | |
|
|
2110 |
* where @f$E(x)@f$ is the elliptic function of the second kind. |
|
|
2111 |
*/ |
|
|
2112 |
template |
|
|
2113 |
class |
|
|
2114 |
hoyt_distribution |
|
|
2115 |
{ |
|
|
2116 |
static_assert(std::is_floating_point<_RealType>::value, |
|
|
2117 |
"template argument not a floating point type"); |
|
|
2118 |
|
|
|
2119 |
public: |
|
|
2120 |
/** The type of the range of the distribution. */ |
|
|
2121 |
typedef _RealType result_type; |
|
|
2122 |
/** Parameter type. */ |
|
|
2123 |
struct param_type |
|
|
2124 |
{ |
|
|
2125 |
typedef hoyt_distribution distribution_type; |
|
|
2126 |
|
|
|
2127 |
param_type(result_type __q = result_type(0.5L), |
|
|
2128 |
result_type __omega = result_type(1)) |
|
|
2129 |
: _M_q(__q), _M_omega(__omega) |
|
|
2130 |
{ |
|
|
2131 |
_GLIBCXX_DEBUG_ASSERT(_M_q > result_type(0)); |
|
|
2132 |
_GLIBCXX_DEBUG_ASSERT(_M_q < result_type(1)); |
|
|
2133 |
} |
|
|
2134 |
|
|
|
2135 |
result_type |
|
|
2136 |
q() const |
|
|
2137 |
{ return _M_q; } |
|
|
2138 |
|
|
|
2139 |
result_type |
|
|
2140 |
omega() const |
|
|
2141 |
{ return _M_omega; } |
|
|
2142 |
|
|
|
2143 |
friend bool |
|
|
2144 |
operator==(const param_type& __p1, const param_type& __p2) |
|
|
2145 |
{ return __p1._M_q == __p2._M_q |
|
|
2146 |
&& __p1._M_omega == __p2._M_omega; } |
|
|
2147 |
|
|
|
2148 |
private: |
|
|
2149 |
void _M_initialize(); |
|
|
2150 |
|
|
|
2151 |
result_type _M_q; |
|
|
2152 |
result_type _M_omega; |
|
|
2153 |
}; |
|
|
2154 |
|
|
|
2155 |
/** |
|
|
2156 |
* @brief Constructors. |
|
|
2157 |
*/ |
|
|
2158 |
explicit |
|
|
2159 |
hoyt_distribution(result_type __q = result_type(0.5L), |
|
|
2160 |
result_type __omega = result_type(1)) |
|
|
2161 |
: _M_param(__q, __omega), |
|
|
2162 |
_M_ad(result_type(0.5L) * (result_type(1) + __q * __q), |
|
|
2163 |
result_type(0.5L) * (result_type(1) + __q * __q) |
|
|
2164 |
/ (__q * __q)), |
|
|
2165 |
_M_ed(result_type(1)) |
|
|
2166 |
{ } |
|
|
2167 |
|
|
|
2168 |
explicit |
|
|
2169 |
hoyt_distribution(const param_type& __p) |
|
|
2170 |
: _M_param(__p), |
|
|
2171 |
_M_ad(result_type(0.5L) * (result_type(1) + __p.q() * __p.q()), |
|
|
2172 |
result_type(0.5L) * (result_type(1) + __p.q() * __p.q()) |
|
|
2173 |
/ (__p.q() * __p.q())), |
|
|
2174 |
_M_ed(result_type(1)) |
|
|
2175 |
{ } |
|
|
2176 |
|
|
|
2177 |
/** |
|
|
2178 |
* @brief Resets the distribution state. |
|
|
2179 |
*/ |
|
|
2180 |
void |
|
|
2181 |
reset() |
|
|
2182 |
{ |
|
|
2183 |
_M_ad.reset(); |
|
|
2184 |
_M_ed.reset(); |
|
|
2185 |
} |
|
|
2186 |
|
|
|
2187 |
/** |
|
|
2188 |
* @brief Return the parameters of the distribution. |
|
|
2189 |
*/ |
|
|
2190 |
result_type |
|
|
2191 |
q() const |
|
|
2192 |
{ return _M_param.q(); } |
|
|
2193 |
|
|
|
2194 |
result_type |
|
|
2195 |
omega() const |
|
|
2196 |
{ return _M_param.omega(); } |
|
|
2197 |
|
|
|
2198 |
/** |
|
|
2199 |
* @brief Returns the parameter set of the distribution. |
|
|
2200 |
*/ |
|
|
2201 |
param_type |
|
|
2202 |
param() const |
|
|
2203 |
{ return _M_param; } |
|
|
2204 |
|
|
|
2205 |
/** |
|
|
2206 |
* @brief Sets the parameter set of the distribution. |
|
|
2207 |
* @param __param The new parameter set of the distribution. |
|
|
2208 |
*/ |
|
|
2209 |
void |
|
|
2210 |
param(const param_type& __param) |
|
|
2211 |
{ _M_param = __param; } |
|
|
2212 |
|
|
|
2213 |
/** |
|
|
2214 |
* @brief Returns the greatest lower bound value of the distribution. |
|
|
2215 |
*/ |
|
|
2216 |
result_type |
|
|
2217 |
min() const |
|
|
2218 |
{ return result_type(0); } |
|
|
2219 |
|
|
|
2220 |
/** |
|
|
2221 |
* @brief Returns the least upper bound value of the distribution. |
|
|
2222 |
*/ |
|
|
2223 |
result_type |
|
|
2224 |
max() const |
|
|
2225 |
{ return std::numeric_limits::max(); } |
|
|
2226 |
|
|
|
2227 |
/** |
|
|
2228 |
* @brief Generating functions. |
|
|
2229 |
*/ |
|
|
2230 |
template |
|
|
2231 |
result_type |
|
|
2232 |
operator()(_UniformRandomNumberGenerator& __urng); |
|
|
2233 |
|
|
|
2234 |
template |
|
|
2235 |
result_type |
|
|
2236 |
operator()(_UniformRandomNumberGenerator& __urng, |
|
|
2237 |
const param_type& __p); |
|
|
2238 |
|
|
|
2239 |
template |
|
|
2240 |
typename _UniformRandomNumberGenerator> |
|
|
2241 |
void |
|
|
2242 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
2243 |
_UniformRandomNumberGenerator& __urng) |
|
|
2244 |
{ this->__generate(__f, __t, __urng, _M_param); } |
|
|
2245 |
|
|
|
2246 |
template |
|
|
2247 |
typename _UniformRandomNumberGenerator> |
|
|
2248 |
void |
|
|
2249 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
2250 |
_UniformRandomNumberGenerator& __urng, |
|
|
2251 |
const param_type& __p) |
|
|
2252 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
2253 |
|
|
|
2254 |
template |
|
|
2255 |
void |
|
|
2256 |
__generate(result_type* __f, result_type* __t, |
|
|
2257 |
_UniformRandomNumberGenerator& __urng, |
|
|
2258 |
const param_type& __p) |
|
|
2259 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
2260 |
|
|
|
2261 |
/** |
|
|
2262 |
* @brief Return true if two Hoyt distributions have |
|
|
2263 |
* the same parameters and the sequences that would |
|
|
2264 |
* be generated are equal. |
|
|
2265 |
*/ |
|
|
2266 |
friend bool |
|
|
2267 |
operator==(const hoyt_distribution& __d1, |
|
|
2268 |
const hoyt_distribution& __d2) |
|
|
2269 |
{ return (__d1._M_param == __d2._M_param |
|
|
2270 |
&& __d1._M_ad == __d2._M_ad |
|
|
2271 |
&& __d1._M_ed == __d2._M_ed); } |
|
|
2272 |
|
|
|
2273 |
/** |
|
|
2274 |
* @brief Inserts a %hoyt_distribution random number distribution |
|
|
2275 |
* @p __x into the output stream @p __os. |
|
|
2276 |
* |
|
|
2277 |
* @param __os An output stream. |
|
|
2278 |
* @param __x A %hoyt_distribution random number distribution. |
|
|
2279 |
* |
|
|
2280 |
* @returns The output stream with the state of @p __x inserted or in |
|
|
2281 |
* an error state. |
|
|
2282 |
*/ |
|
|
2283 |
template |
|
|
2284 |
friend std::basic_ostream<_CharT, _Traits>& |
|
|
2285 |
operator<<(std::basic_ostream<_CharT, _Traits>&, |
|
|
2286 |
const hoyt_distribution<_RealType1>&); |
|
|
2287 |
|
|
|
2288 |
/** |
|
|
2289 |
* @brief Extracts a %hoyt_distribution random number distribution |
|
|
2290 |
* @p __x from the input stream @p __is. |
|
|
2291 |
* |
|
|
2292 |
* @param __is An input stream. |
|
|
2293 |
* @param __x A %hoyt_distribution random number |
|
|
2294 |
* generator engine. |
|
|
2295 |
* |
|
|
2296 |
* @returns The input stream with @p __x extracted or in an error state. |
|
|
2297 |
*/ |
|
|
2298 |
template |
|
|
2299 |
friend std::basic_istream<_CharT, _Traits>& |
|
|
2300 |
operator>>(std::basic_istream<_CharT, _Traits>&, |
|
|
2301 |
hoyt_distribution<_RealType1>&); |
|
|
2302 |
|
|
|
2303 |
private: |
|
|
2304 |
template |
|
|
2305 |
typename _UniformRandomNumberGenerator> |
|
|
2306 |
void |
|
|
2307 |
__generate_impl(_ForwardIterator __f, _ForwardIterator __t, |
|
|
2308 |
_UniformRandomNumberGenerator& __urng, |
|
|
2309 |
const param_type& __p); |
|
|
2310 |
|
|
|
2311 |
param_type _M_param; |
|
|
2312 |
|
|
|
2313 |
__gnu_cxx::arcsine_distribution _M_ad; |
|
|
2314 |
std::exponential_distribution _M_ed; |
|
|
2315 |
}; |
|
|
2316 |
|
|
|
2317 |
/** |
|
|
2318 |
* @brief Return true if two Hoyt distributions are not equal. |
|
|
2319 |
*/ |
|
|
2320 |
template |
|
|
2321 |
inline bool |
|
|
2322 |
operator!=(const hoyt_distribution<_RealType>& __d1, |
|
|
2323 |
const hoyt_distribution<_RealType>& __d2) |
|
|
2324 |
{ return !(__d1 == __d2); } |
|
|
2325 |
|
|
|
2326 |
|
|
|
2327 |
/** |
|
|
2328 |
* @brief A triangular distribution for random numbers. |
|
|
2329 |
* |
|
|
2330 |
* The formula for the triangular probability density function is |
|
|
2331 |
* @f[ |
|
|
2332 |
* / 0 for x < a |
|
|
2333 |
* p(x|a,b,c) = | \frac{2(x-a)}{(c-a)(b-a)} for a <= x <= b |
|
|
2334 |
* | \frac{2(c-x)}{(c-a)(c-b)} for b < x <= c |
|
|
2335 |
* \ 0 for c < x |
|
|
2336 |
* @f] |
|
|
2337 |
* |
|
|
2338 |
*
|
|
2339 |
* Distribution Statistics |
|
|
2340 |
* | Mean | @f$ \frac{a+b+c}{2} @f$ | |
|
|
2341 |
* | Variance | @f$ \frac{a^2+b^2+c^2-ab-ac-bc} |
|
|
2342 |
* {18}@f$ | |
|
|
2343 |
* | Range | @f$[a, c]@f$ | |
|
|
2344 |
* | |
|
|
2345 |
*/ |
|
|
2346 |
template |
|
|
2347 |
class triangular_distribution |
|
|
2348 |
{ |
|
|
2349 |
static_assert(std::is_floating_point<_RealType>::value, |
|
|
2350 |
"template argument not a floating point type"); |
|
|
2351 |
|
|
|
2352 |
public: |
|
|
2353 |
/** The type of the range of the distribution. */ |
|
|
2354 |
typedef _RealType result_type; |
|
|
2355 |
/** Parameter type. */ |
|
|
2356 |
struct param_type |
|
|
2357 |
{ |
|
|
2358 |
friend class triangular_distribution<_RealType>; |
|
|
2359 |
|
|
|
2360 |
explicit |
|
|
2361 |
param_type(_RealType __a = _RealType(0), |
|
|
2362 |
_RealType __b = _RealType(0.5), |
|
|
2363 |
_RealType __c = _RealType(1)) |
|
|
2364 |
: _M_a(__a), _M_b(__b), _M_c(__c) |
|
|
2365 |
{ |
|
|
2366 |
_GLIBCXX_DEBUG_ASSERT(_M_a <= _M_b); |
|
|
2367 |
_GLIBCXX_DEBUG_ASSERT(_M_b <= _M_c); |
|
|
2368 |
_GLIBCXX_DEBUG_ASSERT(_M_a < _M_c); |
|
|
2369 |
|
|
|
2370 |
_M_r_ab = (_M_b - _M_a) / (_M_c - _M_a); |
|
|
2371 |
_M_f_ab_ac = (_M_b - _M_a) * (_M_c - _M_a); |
|
|
2372 |
_M_f_bc_ac = (_M_c - _M_b) * (_M_c - _M_a); |
|
|
2373 |
} |
|
|
2374 |
|
|
|
2375 |
_RealType |
|
|
2376 |
a() const |
|
|
2377 |
{ return _M_a; } |
|
|
2378 |
|
|
|
2379 |
_RealType |
|
|
2380 |
b() const |
|
|
2381 |
{ return _M_b; } |
|
|
2382 |
|
|
|
2383 |
_RealType |
|
|
2384 |
c() const |
|
|
2385 |
{ return _M_c; } |
|
|
2386 |
|
|
|
2387 |
friend bool |
|
|
2388 |
operator==(const param_type& __p1, const param_type& __p2) |
|
|
2389 |
{ return (__p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b |
|
|
2390 |
&& __p1._M_c == __p2._M_c); } |
|
|
2391 |
|
|
|
2392 |
private: |
|
|
2393 |
|
|
|
2394 |
_RealType _M_a; |
|
|
2395 |
_RealType _M_b; |
|
|
2396 |
_RealType _M_c; |
|
|
2397 |
_RealType _M_r_ab; |
|
|
2398 |
_RealType _M_f_ab_ac; |
|
|
2399 |
_RealType _M_f_bc_ac; |
|
|
2400 |
}; |
|
|
2401 |
|
|
|
2402 |
/** |
|
|
2403 |
* @brief Constructs a triangle distribution with parameters |
|
|
2404 |
* @f$ a @f$, @f$ b @f$ and @f$ c @f$. |
|
|
2405 |
*/ |
|
|
2406 |
explicit |
|
|
2407 |
triangular_distribution(result_type __a = result_type(0), |
|
|
2408 |
result_type __b = result_type(0.5), |
|
|
2409 |
result_type __c = result_type(1)) |
|
|
2410 |
: _M_param(__a, __b, __c) |
|
|
2411 |
{ } |
|
|
2412 |
|
|
|
2413 |
explicit |
|
|
2414 |
triangular_distribution(const param_type& __p) |
|
|
2415 |
: _M_param(__p) |
|
|
2416 |
{ } |
|
|
2417 |
|
|
|
2418 |
/** |
|
|
2419 |
* @brief Resets the distribution state. |
|
|
2420 |
*/ |
|
|
2421 |
void |
|
|
2422 |
reset() |
|
|
2423 |
{ } |
|
|
2424 |
|
|
|
2425 |
/** |
|
|
2426 |
* @brief Returns the @f$ a @f$ of the distribution. |
|
|
2427 |
*/ |
|
|
2428 |
result_type |
|
|
2429 |
a() const |
|
|
2430 |
{ return _M_param.a(); } |
|
|
2431 |
|
|
|
2432 |
/** |
|
|
2433 |
* @brief Returns the @f$ b @f$ of the distribution. |
|
|
2434 |
*/ |
|
|
2435 |
result_type |
|
|
2436 |
b() const |
|
|
2437 |
{ return _M_param.b(); } |
|
|
2438 |
|
|
|
2439 |
/** |
|
|
2440 |
* @brief Returns the @f$ c @f$ of the distribution. |
|
|
2441 |
*/ |
|
|
2442 |
result_type |
|
|
2443 |
c() const |
|
|
2444 |
{ return _M_param.c(); } |
|
|
2445 |
|
|
|
2446 |
/** |
|
|
2447 |
* @brief Returns the parameter set of the distribution. |
|
|
2448 |
*/ |
|
|
2449 |
param_type |
|
|
2450 |
param() const |
|
|
2451 |
{ return _M_param; } |
|
|
2452 |
|
|
|
2453 |
/** |
|
|
2454 |
* @brief Sets the parameter set of the distribution. |
|
|
2455 |
* @param __param The new parameter set of the distribution. |
|
|
2456 |
*/ |
|
|
2457 |
void |
|
|
2458 |
param(const param_type& __param) |
|
|
2459 |
{ _M_param = __param; } |
|
|
2460 |
|
|
|
2461 |
/** |
|
|
2462 |
* @brief Returns the greatest lower bound value of the distribution. |
|
|
2463 |
*/ |
|
|
2464 |
result_type |
|
|
2465 |
min() const |
|
|
2466 |
{ return _M_param._M_a; } |
|
|
2467 |
|
|
|
2468 |
/** |
|
|
2469 |
* @brief Returns the least upper bound value of the distribution. |
|
|
2470 |
*/ |
|
|
2471 |
result_type |
|
|
2472 |
max() const |
|
|
2473 |
{ return _M_param._M_c; } |
|
|
2474 |
|
|
|
2475 |
/** |
|
|
2476 |
* @brief Generating functions. |
|
|
2477 |
*/ |
|
|
2478 |
template |
|
|
2479 |
result_type |
|
|
2480 |
operator()(_UniformRandomNumberGenerator& __urng) |
|
|
2481 |
{ return this->operator()(__urng, _M_param); } |
|
|
2482 |
|
|
|
2483 |
template |
|
|
2484 |
result_type |
|
|
2485 |
operator()(_UniformRandomNumberGenerator& __urng, |
|
|
2486 |
const param_type& __p) |
|
|
2487 |
{ |
|
|
2488 |
std::__detail::_Adaptor<_UniformRandomNumberGenerator, result_type> |
|
|
2489 |
__aurng(__urng); |
|
|
2490 |
result_type __rnd = __aurng(); |
|
|
2491 |
if (__rnd <= __p._M_r_ab) |
|
|
2492 |
return __p.a() + std::sqrt(__rnd * __p._M_f_ab_ac); |
|
|
2493 |
else |
|
|
2494 |
return __p.c() - std::sqrt((result_type(1) - __rnd) |
|
|
2495 |
* __p._M_f_bc_ac); |
|
|
2496 |
} |
|
|
2497 |
|
|
|
2498 |
template |
|
|
2499 |
typename _UniformRandomNumberGenerator> |
|
|
2500 |
void |
|
|
2501 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
2502 |
_UniformRandomNumberGenerator& __urng) |
|
|
2503 |
{ this->__generate(__f, __t, __urng, _M_param); } |
|
|
2504 |
|
|
|
2505 |
template |
|
|
2506 |
typename _UniformRandomNumberGenerator> |
|
|
2507 |
void |
|
|
2508 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
2509 |
_UniformRandomNumberGenerator& __urng, |
|
|
2510 |
const param_type& __p) |
|
|
2511 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
2512 |
|
|
|
2513 |
template |
|
|
2514 |
void |
|
|
2515 |
__generate(result_type* __f, result_type* __t, |
|
|
2516 |
_UniformRandomNumberGenerator& __urng, |
|
|
2517 |
const param_type& __p) |
|
|
2518 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
2519 |
|
|
|
2520 |
/** |
|
|
2521 |
* @brief Return true if two triangle distributions have the same |
|
|
2522 |
* parameters and the sequences that would be generated |
|
|
2523 |
* are equal. |
|
|
2524 |
*/ |
|
|
2525 |
friend bool |
|
|
2526 |
operator==(const triangular_distribution& __d1, |
|
|
2527 |
const triangular_distribution& __d2) |
|
|
2528 |
{ return __d1._M_param == __d2._M_param; } |
|
|
2529 |
|
|
|
2530 |
/** |
|
|
2531 |
* @brief Inserts a %triangular_distribution random number distribution |
|
|
2532 |
* @p __x into the output stream @p __os. |
|
|
2533 |
* |
|
|
2534 |
* @param __os An output stream. |
|
|
2535 |
* @param __x A %triangular_distribution random number distribution. |
|
|
2536 |
* |
|
|
2537 |
* @returns The output stream with the state of @p __x inserted or in |
|
|
2538 |
* an error state. |
|
|
2539 |
*/ |
|
|
2540 |
template |
|
|
2541 |
friend std::basic_ostream<_CharT, _Traits>& |
|
|
2542 |
operator<<(std::basic_ostream<_CharT, _Traits>& __os, |
|
|
2543 |
const __gnu_cxx::triangular_distribution<_RealType1>& __x); |
|
|
2544 |
|
|
|
2545 |
/** |
|
|
2546 |
* @brief Extracts a %triangular_distribution random number distribution |
|
|
2547 |
* @p __x from the input stream @p __is. |
|
|
2548 |
* |
|
|
2549 |
* @param __is An input stream. |
|
|
2550 |
* @param __x A %triangular_distribution random number generator engine. |
|
|
2551 |
* |
|
|
2552 |
* @returns The input stream with @p __x extracted or in an error state. |
|
|
2553 |
*/ |
|
|
2554 |
template |
|
|
2555 |
friend std::basic_istream<_CharT, _Traits>& |
|
|
2556 |
operator>>(std::basic_istream<_CharT, _Traits>& __is, |
|
|
2557 |
__gnu_cxx::triangular_distribution<_RealType1>& __x); |
|
|
2558 |
|
|
|
2559 |
private: |
|
|
2560 |
template |
|
|
2561 |
typename _UniformRandomNumberGenerator> |
|
|
2562 |
void |
|
|
2563 |
__generate_impl(_ForwardIterator __f, _ForwardIterator __t, |
|
|
2564 |
_UniformRandomNumberGenerator& __urng, |
|
|
2565 |
const param_type& __p); |
|
|
2566 |
|
|
|
2567 |
param_type _M_param; |
|
|
2568 |
}; |
|
|
2569 |
|
|
|
2570 |
/** |
|
|
2571 |
* @brief Return true if two triangle distributions are different. |
|
|
2572 |
*/ |
|
|
2573 |
template |
|
|
2574 |
inline bool |
|
|
2575 |
operator!=(const __gnu_cxx::triangular_distribution<_RealType>& __d1, |
|
|
2576 |
const __gnu_cxx::triangular_distribution<_RealType>& __d2) |
|
|
2577 |
{ return !(__d1 == __d2); } |
|
|
2578 |
|
|
|
2579 |
|
|
|
2580 |
/** |
|
|
2581 |
* @brief A von Mises distribution for random numbers. |
|
|
2582 |
* |
|
|
2583 |
* The formula for the von Mises probability density function is |
|
|
2584 |
* @f[ |
|
|
2585 |
* p(x|\mu,\kappa) = \frac{e^{\kappa \cos(x-\mu)}} |
|
|
2586 |
* {2\pi I_0(\kappa)} |
|
|
2587 |
* @f] |
|
|
2588 |
* |
|
|
2589 |
* The generating functions use the method according to: |
|
|
2590 |
* |
|
|
2591 |
* D. J. Best and N. I. Fisher, 1979. "Efficient Simulation of the |
|
|
2592 |
* von Mises Distribution", Journal of the Royal Statistical Society. |
|
|
2593 |
* Series C (Applied Statistics), Vol. 28, No. 2, pp. 152-157. |
|
|
2594 |
* |
|
|
2595 |
*
|
|
2596 |
* Distribution Statistics |
|
|
2597 |
* | Mean | @f$ \mu @f$ | |
|
|
2598 |
* | Variance | @f$ 1-I_1(\kappa)/I_0(\kappa) @f$ | |
|
|
2599 |
* | Range | @f$[-\pi, \pi]@f$ | |
|
|
2600 |
* | |
|
|
2601 |
*/ |
|
|
2602 |
template |
|
|
2603 |
class von_mises_distribution |
|
|
2604 |
{ |
|
|
2605 |
static_assert(std::is_floating_point<_RealType>::value, |
|
|
2606 |
"template argument not a floating point type"); |
|
|
2607 |
|
|
|
2608 |
public: |
|
|
2609 |
/** The type of the range of the distribution. */ |
|
|
2610 |
typedef _RealType result_type; |
|
|
2611 |
/** Parameter type. */ |
|
|
2612 |
struct param_type |
|
|
2613 |
{ |
|
|
2614 |
friend class von_mises_distribution<_RealType>; |
|
|
2615 |
|
|
|
2616 |
explicit |
|
|
2617 |
param_type(_RealType __mu = _RealType(0), |
|
|
2618 |
_RealType __kappa = _RealType(1)) |
|
|
2619 |
: _M_mu(__mu), _M_kappa(__kappa) |
|
|
2620 |
{ |
|
|
2621 |
const _RealType __pi = __gnu_cxx::__math_constants<_RealType>::__pi; |
|
|
2622 |
_GLIBCXX_DEBUG_ASSERT(_M_mu >= -__pi && _M_mu <= __pi); |
|
|
2623 |
_GLIBCXX_DEBUG_ASSERT(_M_kappa >= _RealType(0)); |
|
|
2624 |
|
|
|
2625 |
auto __tau = std::sqrt(_RealType(4) * _M_kappa * _M_kappa |
|
|
2626 |
+ _RealType(1)) + _RealType(1); |
|
|
2627 |
auto __rho = ((__tau - std::sqrt(_RealType(2) * __tau)) |
|
|
2628 |
/ (_RealType(2) * _M_kappa)); |
|
|
2629 |
_M_r = (_RealType(1) + __rho * __rho) / (_RealType(2) * __rho); |
|
|
2630 |
} |
|
|
2631 |
|
|
|
2632 |
_RealType |
|
|
2633 |
mu() const |
|
|
2634 |
{ return _M_mu; } |
|
|
2635 |
|
|
|
2636 |
_RealType |
|
|
2637 |
kappa() const |
|
|
2638 |
{ return _M_kappa; } |
|
|
2639 |
|
|
|
2640 |
friend bool |
|
|
2641 |
operator==(const param_type& __p1, const param_type& __p2) |
|
|
2642 |
{ return (__p1._M_mu == __p2._M_mu |
|
|
2643 |
&& __p1._M_kappa == __p2._M_kappa); } |
|
|
2644 |
|
|
|
2645 |
private: |
|
|
2646 |
_RealType _M_mu; |
|
|
2647 |
_RealType _M_kappa; |
|
|
2648 |
_RealType _M_r; |
|
|
2649 |
}; |
|
|
2650 |
|
|
|
2651 |
/** |
|
|
2652 |
* @brief Constructs a von Mises distribution with parameters |
|
|
2653 |
* @f$\mu@f$ and @f$\kappa@f$. |
|
|
2654 |
*/ |
|
|
2655 |
explicit |
|
|
2656 |
von_mises_distribution(result_type __mu = result_type(0), |
|
|
2657 |
result_type __kappa = result_type(1)) |
|
|
2658 |
: _M_param(__mu, __kappa) |
|
|
2659 |
{ } |
|
|
2660 |
|
|
|
2661 |
explicit |
|
|
2662 |
von_mises_distribution(const param_type& __p) |
|
|
2663 |
: _M_param(__p) |
|
|
2664 |
{ } |
|
|
2665 |
|
|
|
2666 |
/** |
|
|
2667 |
* @brief Resets the distribution state. |
|
|
2668 |
*/ |
|
|
2669 |
void |
|
|
2670 |
reset() |
|
|
2671 |
{ } |
|
|
2672 |
|
|
|
2673 |
/** |
|
|
2674 |
* @brief Returns the @f$ \mu @f$ of the distribution. |
|
|
2675 |
*/ |
|
|
2676 |
result_type |
|
|
2677 |
mu() const |
|
|
2678 |
{ return _M_param.mu(); } |
|
|
2679 |
|
|
|
2680 |
/** |
|
|
2681 |
* @brief Returns the @f$ \kappa @f$ of the distribution. |
|
|
2682 |
*/ |
|
|
2683 |
result_type |
|
|
2684 |
kappa() const |
|
|
2685 |
{ return _M_param.kappa(); } |
|
|
2686 |
|
|
|
2687 |
/** |
|
|
2688 |
* @brief Returns the parameter set of the distribution. |
|
|
2689 |
*/ |
|
|
2690 |
param_type |
|
|
2691 |
param() const |
|
|
2692 |
{ return _M_param; } |
|
|
2693 |
|
|
|
2694 |
/** |
|
|
2695 |
* @brief Sets the parameter set of the distribution. |
|
|
2696 |
* @param __param The new parameter set of the distribution. |
|
|
2697 |
*/ |
|
|
2698 |
void |
|
|
2699 |
param(const param_type& __param) |
|
|
2700 |
{ _M_param = __param; } |
|
|
2701 |
|
|
|
2702 |
/** |
|
|
2703 |
* @brief Returns the greatest lower bound value of the distribution. |
|
|
2704 |
*/ |
|
|
2705 |
result_type |
|
|
2706 |
min() const |
|
|
2707 |
{ |
|
|
2708 |
return -__gnu_cxx::__math_constants::__pi; |
|
|
2709 |
} |
|
|
2710 |
|
|
|
2711 |
/** |
|
|
2712 |
* @brief Returns the least upper bound value of the distribution. |
|
|
2713 |
*/ |
|
|
2714 |
result_type |
|
|
2715 |
max() const |
|
|
2716 |
{ |
|
|
2717 |
return __gnu_cxx::__math_constants::__pi; |
|
|
2718 |
} |
|
|
2719 |
|
|
|
2720 |
/** |
|
|
2721 |
* @brief Generating functions. |
|
|
2722 |
*/ |
|
|
2723 |
template |
|
|
2724 |
result_type |
|
|
2725 |
operator()(_UniformRandomNumberGenerator& __urng) |
|
|
2726 |
{ return this->operator()(__urng, _M_param); } |
|
|
2727 |
|
|
|
2728 |
template |
|
|
2729 |
result_type |
|
|
2730 |
operator()(_UniformRandomNumberGenerator& __urng, |
|
|
2731 |
const param_type& __p) |
|
|
2732 |
{ |
|
|
2733 |
const result_type __pi |
|
|
2734 |
= __gnu_cxx::__math_constants::__pi; |
|
|
2735 |
std::__detail::_Adaptor<_UniformRandomNumberGenerator, result_type> |
|
|
2736 |
__aurng(__urng); |
|
|
2737 |
|
|
|
2738 |
result_type __f; |
|
|
2739 |
while (1) |
|
|
2740 |
{ |
|
|
2741 |
result_type __rnd = std::cos(__pi * __aurng()); |
|
|
2742 |
__f = (result_type(1) + __p._M_r * __rnd) / (__p._M_r + __rnd); |
|
|
2743 |
result_type __c = __p._M_kappa * (__p._M_r - __f); |
|
|
2744 |
|
|
|
2745 |
result_type __rnd2 = __aurng(); |
|
|
2746 |
if (__c * (result_type(2) - __c) > __rnd2) |
|
|
2747 |
break; |
|
|
2748 |
if (std::log(__c / __rnd2) >= __c - result_type(1)) |
|
|
2749 |
break; |
|
|
2750 |
} |
|
|
2751 |
|
|
|
2752 |
result_type __res = std::acos(__f); |
|
|
2753 |
#if _GLIBCXX_USE_C99_MATH_TR1 |
|
|
2754 |
__res = std::copysign(__res, __aurng() - result_type(0.5)); |
|
|
2755 |
#else |
|
|
2756 |
if (__aurng() < result_type(0.5)) |
|
|
2757 |
__res = -__res; |
|
|
2758 |
#endif |
|
|
2759 |
__res += __p._M_mu; |
|
|
2760 |
if (__res > __pi) |
|
|
2761 |
__res -= result_type(2) * __pi; |
|
|
2762 |
else if (__res < -__pi) |
|
|
2763 |
__res += result_type(2) * __pi; |
|
|
2764 |
return __res; |
|
|
2765 |
} |
|
|
2766 |
|
|
|
2767 |
template |
|
|
2768 |
typename _UniformRandomNumberGenerator> |
|
|
2769 |
void |
|
|
2770 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
2771 |
_UniformRandomNumberGenerator& __urng) |
|
|
2772 |
{ this->__generate(__f, __t, __urng, _M_param); } |
|
|
2773 |
|
|
|
2774 |
template |
|
|
2775 |
typename _UniformRandomNumberGenerator> |
|
|
2776 |
void |
|
|
2777 |
__generate(_ForwardIterator __f, _ForwardIterator __t, |
|
|
2778 |
_UniformRandomNumberGenerator& __urng, |
|
|
2779 |
const param_type& __p) |
|
|
2780 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
2781 |
|
|
|
2782 |
template |
|
|
2783 |
void |
|
|
2784 |
__generate(result_type* __f, result_type* __t, |
|
|
2785 |
_UniformRandomNumberGenerator& __urng, |
|
|
2786 |
const param_type& __p) |
|
|
2787 |
{ this->__generate_impl(__f, __t, __urng, __p); } |
|
|
2788 |
|
|
|
2789 |
/** |
|
|
2790 |
* @brief Return true if two von Mises distributions have the same |
|
|
2791 |
* parameters and the sequences that would be generated |
|
|
2792 |
* are equal. |
|
|
2793 |
*/ |
|
|
2794 |
friend bool |
|
|
2795 |
operator==(const von_mises_distribution& __d1, |
|
|
2796 |
const von_mises_distribution& __d2) |
|
|
2797 |
{ return __d1._M_param == __d2._M_param; } |
|
|
2798 |
|
|
|
2799 |
/** |
|
|
2800 |
* @brief Inserts a %von_mises_distribution random number distribution |
|
|
2801 |
* @p __x into the output stream @p __os. |
|
|
2802 |
* |
|
|
2803 |
* @param __os An output stream. |
|
|
2804 |
* @param __x A %von_mises_distribution random number distribution. |
|
|
2805 |
* |
|
|
2806 |
* @returns The output stream with the state of @p __x inserted or in |
|
|
2807 |
* an error state. |
|
|
2808 |
*/ |
|
|
2809 |
template |
|
|
2810 |
friend std::basic_ostream<_CharT, _Traits>& |
|
|
2811 |
operator<<(std::basic_ostream<_CharT, _Traits>& __os, |
|
|
2812 |
const __gnu_cxx::von_mises_distribution<_RealType1>& __x); |
|
|
2813 |
|
|
|
2814 |
/** |
|
|
2815 |
* @brief Extracts a %von_mises_distribution random number distribution |
|
|
2816 |
* @p __x from the input stream @p __is. |
|
|
2817 |
* |
|
|
2818 |
* @param __is An input stream. |
|
|
2819 |
* @param __x A %von_mises_distribution random number generator engine. |
|
|
2820 |
* |
|
|
2821 |
* @returns The input stream with @p __x extracted or in an error state. |
|
|
2822 |
*/ |
|
|
2823 |
template |
|
|
2824 |
friend std::basic_istream<_CharT, _Traits>& |
|
|
2825 |
operator>>(std::basic_istream<_CharT, _Traits>& __is, |
|
|
2826 |
__gnu_cxx::von_mises_distribution<_RealType1>& __x); |
|
|
2827 |
|
|
|
2828 |
private: |
|
|
2829 |
template |
|
|
2830 |
typename _UniformRandomNumberGenerator> |
|
|
2831 |
void |
|
|
2832 |
__generate_impl(_ForwardIterator __f, _ForwardIterator __t, |
|
|
2833 |
_UniformRandomNumberGenerator& __urng, |
|
|
2834 |
const param_type& __p); |
|
|
2835 |
|
|
|
2836 |
param_type _M_param; |
|
|
2837 |
}; |
|
|
2838 |
|
|
|
2839 |
/** |
|
|
2840 |
* @brief Return true if two von Mises distributions are different. |
|
|
2841 |
*/ |
|
|
2842 |
template |
|
|
2843 |
inline bool |
|
|
2844 |
operator!=(const __gnu_cxx::von_mises_distribution<_RealType>& __d1, |
|
|
2845 |
const __gnu_cxx::von_mises_distribution<_RealType>& __d2) |
|
|
2846 |
{ return !(__d1 == __d2); } |
|
|
2847 |
|
|
|
2848 |
_GLIBCXX_END_NAMESPACE_VERSION |
|
|
2849 |
} // namespace __gnu_cxx |
|
|
2850 |
|
|
|
2851 |
#include "ext/opt_random.h" |
|
|
2852 |
#include "random.tcc" |
|
|
2853 |
|
|
|
2854 |
#endif // _GLIBCXX_USE_C99_STDINT_TR1 |
|
|
2855 |
|
|
|
2856 |
#endif // C++11 |
|
|
2857 |
|
|
|
2858 |
#endif // _EXT_RANDOM |