def test_update_covariance(self):
"""Check proposal covariance is updated."""
constraints = hs.MockedConstraints()
distribution = pr.ConstrainedDistribution(constraints)
x = distribution.get_example()
cov = np.identity(2)
sampler = sr.MetroSampler(distribution, x, cov, 200, 0, 0)
samples, _, _ = sampler.sample(200, 1)
samples = np.append(samples[:-1], x.reshape(1, len(x)), 0)
x_mean = np.mean(samples, 0)
x2_sum = np.zeros(cov.shape)
for val in samples:
x2_sum += np.outer(val, val)
nlen = samples.shape[0]
fact = float(nlen - 1.0)
x_covariance = (x2_sum - float(nlen) * np.outer(x_mean, x_mean)) / fact
sd = sampler.sd
eps = sampler.eps
delta = sd * eps * np.identity(x_covariance.shape[0])
covariance = sd * x_covariance + delta
assert (abs(covariance[0, 0] - sampler.covariance[0, 0])) <= 1.0e-5
assert (abs(covariance[1, 0] - sampler.covariance[1, 0])) <= 1.0e-5
assert (abs(covariance[1, 1] - sampler.covariance[1, 1])) <= 1.0e-5
def test_get_example(self):
"""Test get_example method."""
constraints = hp.MockedConstraints()
distribution = sp.ConstrainedDistribution(constraints)
x = distribution.get_example()
assert x[0] == .2
assert x[1] == .5
def test_prob_invalid_x(self):
"""Test prob method with a state of incompatible size."""
constraints = hp.MockedConstraints()
distribution = sp.ConstrainedDistribution(constraints)
x = np.array([.1, .1, .1])
with pytest.raises(ValueError):
distribution.prob(x)
def test_prob_valid_x_size_feasible(self):
"""Test prob method with a feasible state."""
constraints = hp.MockedConstraints()
distribution = sp.ConstrainedDistribution(constraints)
x = np.array([.2, .9])
valid = distribution.prob(x)
assert abs(valid - 1.0) <= 1.0e-5
def test_running_mean(self):
"""Check correctness of the running mean computation."""
constraints = hs.MockedConstraints()
distribution = pr.ConstrainedDistribution(constraints)
x = distribution.get_example()
cov = np.identity(2)
sampler = sr.MetroSampler(distribution, x, cov, 0, 0, 0)
samples, _, _ = sampler.sample(200, 1)
samples = np.append(samples[:-1], x.reshape(1, len(x)), 0)
x_mean = np.mean(samples, 0)
assert abs(x_mean[0] - sampler.x_mean[0]) <= 1.0e-5
assert abs(x_mean[1] - sampler.x_mean[1]) <= 1.0e-5
def generate_samples():
# Create distribution and initial covariance matrix for proposal
constraints = sc.Constraint('./Data/mixture.txt')
posterior = sp.ConstrainedDistribution(constraints)
covariance = np.identity(2)
# Sampler's parameters
t0 = 1000
tb = 50000
# Generate samples
x0 = posterior.get_example()
sampler = sr.MetroSampler(posterior, x0, covariance, 200, t0, tb, 0.1)
vals, accepted, total = sampler.sample(4000, 200)
# Generate scatter plot
plt.scatter(vals[:, 0], vals[:, 1], s = 0.2)
plt.show()
def test_running_covariance(self):
"""Check correctness of the running covariance computation."""
constraints = hs.MockedConstraints()
distribution = pr.ConstrainedDistribution(constraints)
x = distribution.get_example()
cov = np.identity(2)
sampler = sr.MetroSampler(distribution, x, cov, 0, 0, 0)
samples, _, _ = sampler.sample(200, 1)
samples = np.append(samples[:-1], x.reshape(1, len(x)), 0)
x_mean = np.mean(samples, 0)
x2_sum = np.zeros(cov.shape)
for val in samples:
x2_sum += np.outer(val, val)
nlen = samples.shape[0]
fact = float(nlen - 1.0)
x_covariance = (x2_sum - float(nlen) * np.outer(x_mean, x_mean)) / fact
assert abs(x_covariance[0, 0] - sampler.x_covariance[0, 0]) <= 1.0e-5
assert abs(x_covariance[1, 1] - sampler.x_covariance[1, 1]) <= 1.0e-5
assert abs(x_covariance[0, 1] - sampler.x_covariance[0, 1]) <= 1.0e-5
def gendist():
# Arguments descriptions
descA = 'Generate samples from high-dimensional uniform distribution'
descI = 'path to file with constraints specification'
descO = 'path to file where sample will be saved'
descS = 'number of samples to generate'
# Initialize parser and parse arguments
parser = argparse.ArgumentParser(description=descA)
parser.add_argument('inpfile', help=descI)
parser.add_argument('outfile', help=descO)
parser.add_argument('samples', help=descS, type=int)
args = parser.parse_args()
# Check that constraints file exists
input_file = args.inpfile
if not os.path.isfile(input_file):
print 'Error: the specified input file does not exist !!!'
exit(0)
# Check that output file can be written
try:
with open(args.outfile, 'w') as f:
pass
except IOError as err:
print 'Cannot write to output file: ', err.errno, ',', err.strerror
exit(0)
# Create constrained distribution
constraints = cons.Constraint(input_file)
posterior = post.ConstrainedDistribution(constraints)
# Initial state of Markov chain and initial covariance matrix
x0 = posterior.get_example()
cov0 = np.identity(x0.shape[0])
# Initialize sampler parameters
t0 = 1000
tb = 10000
ratio = .0
gamma = .1
steps = 0
# Tune the sampler step size
print "Adjusting the step size...\n"
while steps < 8 and (ratio < .20 or ratio > .35):
sampler = samp.MetroSampler(posterior, x0, cov0, 200, t0, tb, gamma)
vals, accepted, total = sampler.sample(2000, 10)
print 'With gamma = %f, the number of accepted and total ' \
'samples is %d %d' % (gamma, accepted, total)
ratio = float(accepted) / float(total)
gamma = adjust_gamma(ratio, gamma)
steps += 1
# Start sampling
print '\nThe optimal step size is gamma = %f' % gamma, '. Start sampling...'
sampler = samp.MetroSampler(posterior, x0, cov0, 200, t0, tb * 5, gamma)
vals, accepted, total = sampler.sample(args.samples, 200)
# Store samples to file
print 'Sampling completed. The number of accepted and total ' \
'samples is: %d %d' % (accepted, total), '. Storing data to file..'
np.savetxt(args.outfile, vals, delimiter=' ', fmt='%1.4e')