mirror of
https://github.com/triqs/dft_tools
synced 2024-11-01 19:53:45 +01:00
edd1ff4529
A first general restructuration of the doc according to the pattern [tour|tutorial|reference]. In the reference part, objects are documented per topic. In each topic, [definition|c++|python|hdf5] (not yet implemented)
76 lines
3.0 KiB
ReStructuredText
76 lines
3.0 KiB
ReStructuredText
.. _montecarloloop:
|
|
|
|
The Monte Carlo loop
|
|
--------------------
|
|
|
|
Introduction
|
|
************
|
|
|
|
The ``mc_generic`` class is an implementation of the Monte Carlo loop. Its
|
|
goal is to propose and then accept or reject changes to a configuration
|
|
according to this loop:
|
|
|
|
.. image:: loop.png
|
|
:width: 700
|
|
:align: center
|
|
|
|
As shown in the figure, after a first initialization, the loop starts by
|
|
proposing an update. In the following, we generically refer to this proposal as
|
|
a proposed **move**. The move proposes a modification of the state of the
|
|
system, which we call the **configuration** of the system. After having
|
|
computed the transition probabilities between this proposed configuration and
|
|
the old one, as well as their probability density, we compute an acceptance
|
|
probability for the move. Based on this probability, the move is either
|
|
**accepted** or **rejected**. If it is rejected, nothing happens and we remain
|
|
in the same configuration. If it is accepted, the configuration is updated.
|
|
|
|
This procedure is the heart of the Monte Carlo algorithm and is repeated
|
|
at every Monte Carlo **step** (meaning one loop). Measurements are not
|
|
made at every step, to allow for some decorrelation between measured
|
|
configurations. Thus, measurements are made every :math:`L` steps. We
|
|
say that these :math:`L` steps form a **cycle** and :math:`L` is the
|
|
length of a cycle.
|
|
|
|
At the very beginning of the simulation, one usually allows for :math:`W`
|
|
**warmup** (thermalization) cycles. This means that there will be no measurements
|
|
during these first :math:`W` cycles. After that, we define :math:`N`, the
|
|
number of cycles that will be done until the end of the simulation.
|
|
|
|
At the end of the simulation, the code will have done:
|
|
|
|
* :math:`N` measurements
|
|
* :math:`N + W` cycles
|
|
* :math:`(N + W) \times L` steps
|
|
|
|
|
|
C++ variable names
|
|
******************
|
|
|
|
In the C++ examples, these variables will be called:
|
|
|
|
* ``n_cycles`` :math:`= N`
|
|
* ``length_cycle`` :math:`= L`
|
|
* ``n_warmup_cycle`` :math:`= W`
|
|
|
|
You will also have to use these names if you will construct an ``mc_generic``
|
|
instance from a dictonary (see full reference below).
|
|
|
|
Monte Carlo loop and connection with moves and measures
|
|
*******************************************************
|
|
|
|
We will cover this in more details, but let us already mention here that the
|
|
``mc_generic`` class only implements the Monte Carlo loop. It doesn't need (and
|
|
in fact doesn't) know anything about what the configuration is or what the
|
|
moves and measurements really do. All it does, is to use external classes which
|
|
take care of making the moves. It just expects back a Metropolis ratio so that
|
|
it can decide wether the move should be accepted or rejected. Once this choice
|
|
is made, it tells the external class which again does we is needed if the move
|
|
is accepted or rejected. The same is true for measurements which are external
|
|
classes called by the loop. This will become clearer with an example in the
|
|
following section.
|
|
|
|
.. note::
|
|
|
|
Above, we described the Metropolis algorithm. A different accept/reject
|
|
scheme could be used but the mechanism remains the same.
|