Concepts¶
Introduction & Motivations¶
Purpose:
The purpose of this little class is too facilitate the writing and maintenance of Metropolis MonteCarlo algorithms, with several advantages :
- Easy to add new moves and measures.
- For complex MC algorithms, with 6 or 7 different moves, it helps to clearly separate the code for each move.
- Parallelism is automatic.
- The random generator is a simple parameter, it can be chosen dynamically.
Principle
The mc_generic class is a generic version of the algorithms, with moves and measures. The user :
- writes move classes, modelling the Move concept.
- writes measure classes, modelling the Measure concepts.
- register them in a mc_generic object MC
- call MC.warmup_and_accumulate(…) … and that is (almost) it !
The Move concept¶
Elements Comment
- mc_sign_type attempt()
First part of the Move.
Returns the probability to accept the move. If :
- the move is \(x\rightarrow x'\), proposed with proba \(T_{x\rightarrow x'}\)
- the probability of the \(x\) config is denoted \(p_x\)
- then attempt should return the Metropolis ratio:
\[\frac{p_{x'} T_{x'\rightarrow x}}{p_x T_{x\rightarrow x'}}\]with the sign. (The sign will be separated from the absolute value and kept by the MonteCarlo class). In other words: attempt() = move_sign * move_rate with abs(move_sign) = 1
- mc_sign_type accept()
- Called iif the Move is accepted.
- Returns a number r such that \(|r| =1\)
- There is a possibility to update the sign here as well, so that the final sign is: move_sign * accept()
- CAREFUL that we need the ratio new_sign / old_sign here just like we needed a ratio in attempt()
- void reject()
- Called iif the Move is rejected (for cleaning).
The Measure concept¶
Elements Comment
- void accumulate(std::complex<double> sign)
- Accumulation with the sign
- void collect_results ( boost::mpi::communicator const & c)
- Collects the results over the communicator, and finalize the calculation (compute average, error).