def qho(self, dim = 4, sites = 10, spacing = 1.):
"""checks that QHO can be initialised and all functions run"""
passed = True
shape = (sites,)*dim
raw_lattice = np.arange(sites**dim).reshape(shape)
self.pot = QHO()
self.x = Periodic_Lattice(raw_lattice)
self.p = np.asarray(shape)
idx_list = [(0,)*dim, (sites,)*dim, (sites-1,)*dim]
passed = self._TestFns("QHO Potential", passed, self.x, self.p, idx_list)
return passed
if __name__ == '__main__':
# utils.logs.logging.root.setLevel(utils.logs.logging.DEBUG)
dim = 1
n = 10
spacing = 1.
step_size = [0.01, .1]
n_steps = [1, 500]
samples = 5
step_sample = np.linspace(n_steps[0], n_steps[1], samples, True,
dtype=int),
step_sizes = np.linspace(step_size[0], step_size[1], samples, True)
for pot in [SHO(), KG(), QHO()]:
x_nd = np.random.random((n, ) * dim)
p0 = np.random.random((n, ) * dim)
x0 = Periodic_Lattice(x_nd)
dynamics = Leap_Frog(duE=pot.duE,
n_steps=n_steps[-1],
step_size=step_size[-1])
test = Constant_Energy(pot, dynamics)
utils.newTest(test.id)
test.run(p0, x0, step_sample, step_sizes)
test = Reversibility(pot, dynamics)
utils.newTest(test.id)
#!/usr/bin/env python
import numpy as np
from scipy.stats import norm
from common import hmc_sample_1d
from hmc.potentials import Quantum_Harmonic_Oscillator as QHO
file_name = __file__
pot = QHO()
dim = 1; n = 100
x0 = np.random.random((n,)*dim)
n_burn_in, n_samples = 15, 100
theory_label = r'$|\psi_0(x)|^2 = \sqrt{\frac{\omega}{\pi}}e^{-\omega x^2}$ for $\omega=\sqrt{\frac{5}{4}}$'
def theory(x, samples):
"""The actual PDF curve
As per the paper by Creutz and Fredman
Required Inputs
x :: np.array :: 1D array of x-axis
samples :: np.array :: 1D array of HMC samples
"""
w = np.sqrt(1.25) # w = 1/(sigma)^2
sigma = 1./np.sqrt(2*w)
c = np.sqrt(w / np.pi) # this is the theory
theory = np.exp(-x**2*1.1)*c
return theory
#
def fitted(x, samples):