XXX-CIRC:  Do a circularly-coupled Markov chain simulation.

There is a version of this program for each 'mc' application (eg,
net-circ).  Version "xxx" does a circularly-coupled Markov chain
simulation with multiple starting points, either sequentially or in
parallel, using the xxx-gen, xxx-genp, xxx-mc, and xxx-tbl programs.

Usage:

    xxx-circ [ -p ] log-file n-chains n-iters max-stages [ seed ]

Runs and reruns <n-chains> Monte Carlo simulations of type <xxx>
(eg, dist, net, gp, mix), using the specifications in <log-file>,
coupling them so as to produce a circular chain if coalesence occurs.
The (up to) n-chains simulations done in each stage will be run in
parallel (assuming enough processors) if the -p option is given.

Each chain uses a different random number seed (derived from the
optional seed argument, which defaults to 1), and is started initially
from a state generated using the xxx-gen program.  After <n-iters>
iterations of this first stage simulation, using the xxx-mc program,
the final state of each simulation is compared to the initial state of
the next simulation in order (wrapping from last to first), and the
simulation as a whole is stopped if all these comparisons come out
equal.  Otherwise, another stage is done, in which simulations are
rerun (if necessary) with their initial state being the final state of
the previous simulation, and with the random number seed again set to
its initial value.  A new run is not done for those chains whose
initial state would be the same as before, since the new run would be
indentical to the old run.  This process of rerunning simulations
continues until all chains have coalesed or until <max-stages>
simulation runs have been done for each chain (as necessary).  In each
stage after the first, the runs are done using xxx-mc with the -c
option (see xxx-mc.doc), so that they will terminate early if
coalescence occurs in the middle of a run.

Details of which simulations were run, and of how many iterations each
took (before possible coalescence), are written to standard output.  A
one-line summary is written to standard error.

The states from runs in the final stage are appended to the original
<log-file>, to produce the circular chain.  This is the log file that
should be used when estimating expectations of functions of state.

Separate log files are also produced for every simulaton run of every
chain, called <log-file>.<stage>.<chain>, where <stage> and <chain>
are integers from 0 on up.  Some of these files may be links to runs
from earlier stages, when the initial state did not change, leading to
the run being the same as the previous one.  Log files tracing the
simulations from each initial state are also produced, called
<log-file>:<chain>, where <chain> is an integer from 0 on up
identifing the chain where the initial state was first used.

The exit value is 1 if <max-stages> was reached without coalescence
occuring, and is zero (indicating success) if coalescence did occur.

            Copyright (c) 2000 by Radford M. Neal