def test_mcmc():
seed = 42
np.random.seed(seed)
EPS = 1e-2
size = int(2e1)
beta = 2
pair_pot = lambda x: -beta * d_tor(x, size=size)
n_iter = int(1e3)
init_val = np.random.rand(size) * size - size / 2
torify = lambda x: x - size * np.floor((x / size + .5))
propose = lambda x: torify(x + np.random.randn(size))
#energy decrease factor
decrease_factor = 2
#size of rolling window for moving averages
window = 50
trace = mcmc(pair_pot, n_iter, init_val, propose, np.random.get_state())
#correct shape
assert trace.shape == (n_iter, ) + init_val.shape
#values should change
assert_array_less(EPS, trace.var(axis=0))
#energy must decrease
energy_trace = [energy(conf, pair_pot) for conf in trace]
assert np.mean(energy_trace[:window]) - np.mean(
energy_trace[-window:]) > np.std(
energy_trace[-window:]) * decrease_factor
def test_torify():
seed = 42
np.random.seed(seed)
size = np.array([20, 2])
x = np.expand_dims(((np.random.rand(10, 2) - .5) * size), -1)
x = np.repeat(x, 200 + 1, -1)
x_tor = torify(x, size=size)
assert_array_less(np.max(np.abs(x_tor), (0, 2)), size / 2)
def test_mcmc_dyn_dim2():
seed = 42
np.random.seed(seed)
state = np.random.get_state()
EPS = 1e-2
size = np.array([int(2e1), 2])
n_part = int(size[0] / 2)
beta = 2
steps = 20
pair_pot = lambda x: -beta / (steps + 1) * d_tor(x, size=size)
n_iter = int(2e3)
var = 1
states = [
state for state, _ in [[np.random.get_state(),
np.random.rand()] for _ in range(n_part)]
]
init_start_pts = np.expand_dims(((np.random.rand(n_part, 2) - .5) * size),
-1)
init_start_pts = np.repeat(init_start_pts, steps + 1, -1)
init_bridges = np.array([[bridge(var, steps) for _ in range(2)]
for _ in range(n_part)])
init_val = init_start_pts + init_bridges
propose = lambda x: torify(
np.repeat(
np.expand_dims(x[:, :, 0] + np.random.randn(*(x[:, :, 0].shape)),
-1), steps + 1, -1) + np.array(
[[bridge(var, steps) for _ in range(2)]
for _ in range(x.shape[0])]), size)
#energy decrease factor
decrease_factor = 2
#size of rolling window for moving averages
window = 50
trace = mcmc(pair_pot, n_iter, init_val, propose, state)
#correct shape
assert trace.shape == (n_iter, ) + init_val.shape
#values should change
assert_array_less(EPS, trace.var(axis=0))
#energy must decrease
energy_trace = [energy(conf, pair_pot) for conf in trace]
assert np.mean(energy_trace[:window]) - np.mean(
energy_trace[-window:]) > np.std(
energy_trace[-window:]) * decrease_factor
def test_mcmc_dyn():
seed = 42
np.random.seed(seed)
state = np.random.get_state()
EPS = 1e-2
size = int(2e1)
beta = 2
steps = 20
pair_pot = lambda x: -beta / (steps + 1) * d_tor(x, size=size)
n_iter = int(3e3)
var = 1
states = [
state for state, _ in [[np.random.get_state(),
np.random.rand()]
for _ in range(int(size / 2))]
]
init_start_pts = np.repeat(
(np.random.rand(int(size / 2)) - .5)[np.newaxis] * size, steps + 1,
0).transpose()
init_bridges = np.array([bridge(var, steps, state) for state in states])
init_val = init_start_pts + init_bridges
torify = lambda x: x - size * np.floor((x / size + .5))
propose = lambda x: torify(
np.repeat(
(x[:, 0] + np.random.randn(x.shape[0]))[np.newaxis], steps + 1, 0).
transpose() + np.array([bridge(var, steps)
for _ in range(x.shape[0])]))
#energy decrease factor
decrease_factor = 2
#size of rolling window for moving averages
window = 50
trace = mcmc(pair_pot, n_iter, init_val, propose, state)
#correct shape
assert trace.shape == (n_iter, ) + init_val.shape
#values should change
assert_array_less(EPS, trace.var(axis=0))
#energy must decrease
energy_trace = [energy(conf, pair_pot) for conf in trace]
assert np.mean(energy_trace[:window]) - np.mean(
energy_trace[-window:]) > np.std(
energy_trace[-window:]) * decrease_factor
def jellium_strip(size=np.array([20, 2]),
n_part=10,
beta=2,
steps_mcmc=int(1e4),
steps_bridge=200,
state=None):
"""Wigner's jellium on strip-shaped torus
# Arguments
size: strip size
beta: inverse temperature
n_part: number of particles
steps_mcmc: number of steps of the MCMC simulator
steps_bridge: number of time steps for the bridges
state = state for random number generator
# Result
trace of MCMC simulating the jellium
"""
if state == None:
state = np.random.get_state()
np.random.set_state(state)
pair_pot = lambda x: beta / (steps_bridge + 1) * green_strip(x, size=size)
var = 1
#init val
init_start_pts = np.expand_dims(((np.random.rand(n_part, 2) - .5) * size),
-1)
init_start_pts = np.repeat(init_start_pts, steps_bridge + 1, -1)
init_bridges = np.array([[bridge(var, steps_bridge) for _ in range(2)]
for _ in range(n_part)])
init_val = init_start_pts + init_bridges
#proposal
propose = lambda x: torify(
np.repeat(
np.expand_dims(x[:, :, 0] + np.random.randn(*(x[:, :, 0].shape)),
-1), steps_bridge + 1, -1) + np.array(
[[bridge(var, steps_bridge) for _ in range(2)]
for _ in range(x.shape[0])]), size)
return mcmc(pair_pot, steps_mcmc, init_val, propose, state)