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import numpy as np
from math import pi
import time
from compyle.config import get_config
from compyle.api import declare, annotate
from compyle.parallel import Elementwise, Reduction
from compyle.array import get_backend, wrap
import compyle.array as carr
@annotate
def calculate_energy(i, vx, vy, vz, pe, num_particles):
ke = 0.5 * (vx[i] * vx[i] + vy[i] * vy[i] + vz[i] * vz[i])
return pe[i] + ke
@annotate
def calculate_kinetic_energy(i, vx, vy, vz):
return 0.5 * (vx[i] * vx[i] + vy[i] * vy[i] + vz[i] * vz[i])
@annotate
def calculate_force(i, x, y, z, fx, fy, fz, pe, num_particles):
force_cutoff = 3.
force_cutoff2 = force_cutoff * force_cutoff
for j in range(num_particles):
if i == j:
continue
xij = x[i] - x[j]
yij = y[i] - y[j]
zij = z[i] - z[j]
rij2 = xij * xij + yij * yij + zij * zij
if rij2 > force_cutoff2:
continue
irij2 = 1.0 / rij2
irij6 = irij2 * irij2 * irij2
irij12 = irij6 * irij6
pe[i] += (2 * (irij12 - irij6))
f_base = 24 * irij2 * (2 * irij12 - irij6)
fx[i] += f_base * xij
fy[i] += f_base * yij
fz[i] += f_base * zij
@annotate
def step_method1(i, x, y, z, vx, vy, vz, fx, fy, fz, pe, xmin, xmax,
ymin, ymax, zmin, zmax, m, dt, num_particles):
integrate_step1(i, m, dt, x, y, z, vx, vy, vz, fx, fy, fz)
boundary_condition(i, x, y, z, vx, vy, vz, fx, fy, fz, pe, xmin, xmax,
ymin, ymax, zmin, zmax)
@annotate
def step_method2(i, x, y, z, vx, vy, vz, fx, fy, fz, pe, xmin, xmax,
ymin, ymax, zmin, zmax, m, dt, num_particles):
calculate_force(i, x, y, z, fx, fy, fz, pe, num_particles)
integrate_step2(i, m, dt, x, y, z, vx, vy, vz, fx, fy, fz)
@annotate
def integrate_step1(i, m, dt, x, y, z, vx, vy, vz, fx, fy, fz):
x[i] += vx[i] * dt + 0.5 * fx[i] * dt * dt
y[i] += vy[i] * dt + 0.5 * fy[i] * dt * dt
z[i] += vz[i] * dt + 0.5 * fz[i] * dt * dt
vx[i] += 0.5 * fx[i] * dt
vy[i] += 0.5 * fy[i] * dt
vz[i] += 0.5 * fz[i] * dt
@annotate
def integrate_step2(i, m, dt, x, y, z, vx, vy, vz, fx, fy, fz):
vx[i] += 0.5 * fx[i] * dt
vy[i] += 0.5 * fy[i] * dt
vz[i] += 0.5 * fz[i] * dt
@annotate
def boundary_condition(i, x, y, z, vx, vy, vz, fx, fy, fz, pe,
xmin, xmax, ymin, ymax, zmin, zmax):
xwidth = xmax - xmin
ywidth = ymax - ymin
zwidth = zmax - zmin
stiffness = 50.
pe[i] = 0.
if x[i] < 0.5:
fx[i] = stiffness * (0.5 - x[i])
pe[i] += 0.5 * stiffness * (0.5 - x[i]) * (0.5 - x[i])
elif x[i] > xwidth - 0.5:
fx[i] = stiffness * (xwidth - 0.5 - x[i])
pe[i] += 0.5 * stiffness * (xwidth - 0.5 - x[i]) * (xwidth - 0.5 - x[i])
else:
fx[i] = 0.
if y[i] < 0.5:
fy[i] = stiffness * (0.5 - y[i])
pe[i] += 0.5 * stiffness * (0.5 - y[i]) * (0.5 - y[i])
elif y[i] > ywidth - 0.5:
fy[i] = stiffness * (ywidth - 0.5 - y[i])
pe[i] += 0.5 * stiffness * (ywidth - 0.5 - y[i]) * (ywidth - 0.5 - y[i])
else:
fy[i] = 0.
if z[i] < 0.5:
fz[i] = stiffness * (0.5 - z[i])
pe[i] += 0.5 * stiffness * (0.5 - z[i]) * (0.5 - z[i])
elif z[i] > zwidth - 0.5:
fz[i] = stiffness * (zwidth - 0.5 - z[i])
pe[i] += 0.5 * stiffness * (zwidth - 0.5 - z[i]) * (zwidth - 0.5 - z[i])
else:
fz[i] = 0.
class MDSolverBase(object):
def __init__(self, num_particles, x=None, y=None, z=None,
vx=None, vy=None, vz=None,
xmax=100., ymax=100., zmax=100., dx=2., init_T=0.,
backend=None):
self.backend = get_backend(backend)
self.num_particles = num_particles
self.xmin, self.xmax = 0., xmax
self.ymin, self.ymax = 0., ymax
self.zmin, self.zmax = 0., zmax
self.log_data = []
self.m = 1.
if x is None and y is None and z is None:
self.x, self.y, self.z = self.setup_positions(num_particles, dx)
if vx is None and vy is None and vz is None:
self.vx, self.vy, self.vz = self.setup_velocities(
init_T, num_particles)
self.fx = carr.zeros_like(self.x, backend=self.backend)
self.fy = carr.zeros_like(self.y, backend=self.backend)
self.fz = carr.zeros_like(self.z, backend=self.backend)
self.pe = carr.zeros_like(self.x, backend=self.backend)
self.energy_calc = Reduction("a+b", map_func=calculate_energy,
backend=self.backend)
self.kinetic_energy_calc = Reduction(
"a+b",
map_func=calculate_kinetic_energy,
backend=self.backend)
def setup_velocities(self, T, num_particles):
np.random.seed(123)
vx = np.random.uniform(0, 1., size=num_particles).astype(np.float64)
vy = np.random.uniform(0, 1., size=num_particles).astype(np.float64)
vz = np.random.uniform(0, 1., size=num_particles).astype(np.float64)
T_current = np.average(vx ** 2 + vy ** 2 + vz ** 2)
scaling_factor = (T / T_current) ** 0.5
vx = vx * scaling_factor
vy = vy * scaling_factor
vz = vz * scaling_factor
return wrap(vx, vy, vz, backend=self.backend)
def setup_positions(self, num_particles, dx):
ndim = np.ceil(num_particles ** (1 / 3.))
dim_length = ndim * dx
self.xmax = 3 * (1 + round(dim_length * 1.5 / 3.))
self.ymax = 3 * (1 + round(dim_length * 1.5 / 3.))
self.zmax = 3 * (1 + round(dim_length * 1.5 / 3.))
xmin_eff = ((self.xmax - self.xmin) - dim_length) / 2.
xmax_eff = ((self.xmax - self.xmin) + dim_length) / 2.
x, y, z = np.mgrid[xmin_eff:xmax_eff:dx, xmin_eff:xmax_eff:dx,
xmin_eff:xmax_eff:dx]
x = x.ravel().astype(np.float64)[:num_particles]
y = y.ravel().astype(np.float64)[:num_particles]
z = z.ravel().astype(np.float64)[:num_particles]
return wrap(x, y, z, backend=self.backend)
def post_step(self, step, log_output=False):
energy = self.energy_calc(self.vx, self.vy, self.vz, self.pe,
self.num_particles)
if log_output:
self.log_data.append([step, carr.sum(self.pe),
self.kinetic_energy_calc(self.vx, self.vy, self.vz)])
print("Energy at time step =", step, "is", energy)
def write_log(self, fname):
np.savetxt(fname, np.array(self.log_data),
header="timestep\tpotential_energy\tkinetic_energy")
def pull(self):
self.x.pull()
self.y.pull()
self.z.pull()
def plot(self):
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.set_xlim(self.xmin, self.xmax)
ax.set_ylim(self.ymin, self.ymax)
ax.set_zlim(self.zmin, self.zmax)
ax.scatter(self.x.data, self.y.data, self.z.data)
plt.show()
class MDSolver(MDSolverBase):
def __init__(self, num_particles, x=None, y=None, z=None,
vx=None, vy=None, vz=None,
xmax=100., ymax=100., zmax=100., dx=2., init_T=0.,
backend=None):
super().__init__(num_particles, x=x, y=y, z=z, vx=vx, vy=vy, vz=vz,
xmax=xmax, ymax=ymax, zmax=zmax, dx=dx, init_T=init_T,
backend=backend)
self.init_forces = Elementwise(calculate_force, backend=self.backend)
self.step1 = Elementwise(step_method1, backend=self.backend)
self.step2 = Elementwise(step_method2, backend=self.backend)
def solve(self, t, dt, log_output=False):
num_steps = int(t // dt)
self.init_forces(self.x, self.y, self.z, self.fx, self.fy, self.fz,
self.pe, self.num_particles)
for i in range(num_steps):
self.step1(self.x, self.y, self.z, self.vx, self.vy, self.vz,
self.fx, self.fy, self.fz,
self.pe, self.xmin, self.xmax, self.ymin, self.ymax,
self.zmin, self.zmax, self.m, dt, self.num_particles)
self.step2(self.x, self.y, self.z, self.vx, self.vy, self.vz,
self.fx, self.fy, self.fz,
self.pe, self.xmin, self.xmax, self.ymin, self.ymax,
self.zmin, self.zmax, self.m, dt, self.num_particles)
if i % 100 == 0:
self.post_step(i, log_output=log_output)
if __name__ == '__main__':
from compyle.utils import ArgumentParser
p = ArgumentParser()
p.add_argument(
'--show', action='store_true', dest='show',
default=False, help='Show plot'
)
p.add_argument('-n', action='store', type=int, dest='n',
default=100, help='Number of particles')
p.add_argument('--tf', action='store', type=float, dest='t',
default=40., help='Final time')
p.add_argument('--dt', action='store', type=float, dest='dt',
default=0.02, help='Time step')
o = p.parse_args()
solver = MDSolver(o.n, backend=o.backend)
start = time.time()
solver.solve(o.t, o.dt)
end = time.time()
print("Time taken for N = %i is %g secs" % (o.n, (end - start)))
if o.show:
solver.pull()
solver.plot()
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