<s>
The	O
Wang	B-Algorithm
and	I-Algorithm
Landau	I-Algorithm
algorithm	I-Algorithm
,	O
proposed	O
by	O
Fugao	O
Wang	O
and	O
David	O
P	O
.	O
Landau	O
,	O
is	O
a	O
Monte	B-Algorithm
Carlo	I-Algorithm
method	I-Algorithm
designed	O
to	O
estimate	O
the	O
density	O
of	O
states	O
of	O
a	O
system	O
.	O
</s>
<s>
The	O
Wang	B-Algorithm
and	I-Algorithm
Landau	I-Algorithm
algorithm	I-Algorithm
is	O
an	O
important	O
method	O
to	O
obtain	O
the	O
density	O
of	O
states	O
required	O
to	O
perform	O
a	O
multicanonical	B-Algorithm
simulation	I-Algorithm
.	O
</s>
<s>
The	O
Wang	B-Algorithm
and	I-Algorithm
Landau	I-Algorithm
algorithm	I-Algorithm
is	O
used	O
to	O
obtain	O
an	O
estimate	O
for	O
the	O
density	O
of	O
states	O
of	O
a	O
system	O
characterized	O
by	O
a	O
cost	O
function	O
.	O
</s>
<s>
It	O
uses	O
a	O
non-Markovian	O
stochastic	O
process	O
which	O
asymptotically	O
converges	O
to	O
a	O
multicanonical	B-Algorithm
ensemble	I-Algorithm
.	O
</s>
<s>
to	O
a	O
Metropolis	B-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
algorithm	I-Algorithm
with	O
sampling	O
distribution	O
inverse	O
to	O
the	O
density	O
of	O
states	O
)	O
The	O
major	O
consequence	O
is	O
that	O
this	O
sampling	O
distribution	O
leads	O
to	O
a	O
simulation	O
where	O
the	O
energy	O
barriers	O
are	O
invisible	O
.	O
</s>
<s>
This	O
means	O
that	O
the	O
algorithm	O
visits	O
all	O
the	O
accessible	O
states	O
(	O
favorable	O
and	O
less	O
favorable	O
)	O
much	O
faster	O
than	O
a	O
Metropolis	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
The	O
algorithm	O
then	O
performs	O
a	O
multicanonical	B-Algorithm
ensemble	I-Algorithm
simulation	O
:	O
a	O
Metropolis	B-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
random	O
walk	O
in	O
the	O
phase	O
space	O
of	O
the	O
system	O
with	O
a	O
probability	O
distribution	O
given	O
by	O
and	O
a	O
probability	O
of	O
proposing	O
a	O
new	O
state	O
given	O
by	O
a	O
probability	O
distribution	O
.	O
</s>
<s>
Like	O
in	O
the	O
Metropolis	B-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
algorithm	I-Algorithm
,	O
a	O
proposal-acceptance	O
step	O
is	O
performed	O
,	O
and	O
consists	O
in	O
(	O
see	O
Metropolis	B-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
algorithm	I-Algorithm
overview	O
)	O
:	O
</s>
<s>
This	O
is	O
the	O
crucial	O
step	O
of	O
the	O
algorithm	O
,	O
and	O
it	O
is	O
what	O
makes	O
the	O
Wang	B-Algorithm
and	I-Algorithm
Landau	I-Algorithm
algorithm	I-Algorithm
non-Markovian	O
:	O
the	O
stochastic	O
process	O
now	O
depends	O
on	O
the	O
history	O
of	O
the	O
process	O
.	O
</s>
<s>
The	O
following	O
is	O
a	O
sample	O
code	O
of	O
the	O
Wang	O
–	O
Landau	O
algorithm	O
in	O
Python	B-Language
,	O
where	O
we	O
assume	O
that	O
a	O
symmetric	O
proposal	O
distribution	O
g	O
is	O
used	O
:	O
</s>
