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add: task 3 and 4, 

cleanup: moved non task specific code to seperate file
This commit is contained in:
Daniel Kapla 2022-04-11 12:14:40 +02:00
parent cdf9e3104f
commit 1ff5c11866
4 changed files with 363 additions and 100 deletions
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137
Exercise_02/molecular_dynamics.py Normal file
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#!/usr/bin/env python
import numpy as np
from jax import numpy as jnp, jit, grad
# toy moleculat dynamic system parameters (constants)
De = 1.6 # [eV (electronvolt)]
alpha = 3.028 # [A^-1]
re = 1.411 # [A]
mass = 18.998403 # atomic mass of a single particle
def dump(file, position, velocity, box_size, mode = "w", comment = ""):
"""
Dumps `position` and `velocity` to `file` with meta data.
First writes a header to `file` in `mode` file write mode defines as three
lines.
`<nr of particles [int]>`
`<comment (ignored)>`
`<box side lenght [float]>`
then each line (nr of particles many) have the form `x y z vx vy vx`.
"""
header = [str(position.shape[0]), comment, str(box_size)]
data = np.hstack((position, velocity))
np.savetxt(file, data, comments = "", header = "\n".join(header))
def load(file):
"""
Loads a state from `file` and returns the `position` and `velocity` system
states as two `numpy` arrays.
As a side effect the config object as agumented with `file` header info.
"""
if isinstance(file, str):
with open(file) as handle:
return load(handle)
# read header
nr_particles = int(file.readline().strip())
file.readline() # ignore comment line
box_size = float(file.readline().strip())
# read the state data, each line constains `x y z vx vy vz`
data = np.loadtxt(file, max_rows = nr_particles)
return np.hsplit(data, 2), box_size
def iter_load(file):
"""
Iterator yielding similar to `load` entries from `file` in the same format.
"""
if isinstance(file, str):
with open(file) as handle:
yield from iter_load(handle)
else:
while True:
# read header
line = file.readline().strip()
if not line:
return
nr_particles = int(line)
file.readline() # ignore comment line
line = file.readline().strip()
if not line:
return
box_size = float(line)
# read the state data, each line constains `x y z vx vy vz`
data = np.loadtxt(file, max_rows = nr_particles)
if not data.shape[0] == nr_particles:
return
yield np.hsplit(data, 2), box_size
def print_prog_bar(index, max_index):
"""
Simple progress bar. Just for convenience.
"""
if (index % 100) and (max_index != index + 1):
return
progress = (30 * (index + 1)) // max_index
print(f"\r{(index + 1)}/{max_index} - " \
f"[{'':=>{(progress)}}{'': >{(30 - progress)}}]",
end = "\n" if max_index == index + 1 else "",
flush = True)
@jit
def energy(position, box_size):
"""
Computes the potential energy of a system of particles with `position` using
Morses potential.
"""
# enforce expected shape
# (`scipy.optimize.minimize` drops shape information)
if len(position.shape) == 1:
position = position.reshape((position.shape[0] // 3, 3))
# compute all pairwise position differences (all!)
diff = position[:, jnp.newaxis, :] - position
# extract only one of two distance combinations of non-equal particles
lower_tri = jnp.tril_indices(position.shape[0], k = -1)
diff = diff[lower_tri[0], lower_tri[1], :]
# fold space in all directions. The `max_dist` is the maximum distance
# in the folded space untill the distance through the folded space
# border is smaller than inside the box. 3-axis parallel fold
max_dist = box_size / 2.0
diff = jnp.mod(diff + max_dist, box_size) - max_dist
# Compute distances
dist = jnp.linalg.norm(diff, axis = 1)
# calc inbetween exp(.) expression
ex = jnp.exp(-alpha * (dist - re))
# evaluate Morse potential
return De * jnp.sum(ex * (ex - 2.0))
@jit
def force(position, box_size):
"""
Computes the forces acting on each particle in `position` as the negative
gradient of the potential energy.
"""
return -grad(energy)(position, box_size)
@jit
def kinetic(velocity):
"""
Computes the kenetic energy given a systems `velocity` state.
"""
return (mass / 2.0) * jnp.linalg.norm(velocity, axis = 1).sum()
@jit
def step(position, velocity, acceleration, box_size, step_size):
"""
Performs a single Newton time step with `step_size` given system state
through the current particle `position`, `velocity` and `acceleration`.
"""
# update position with a second order Taylor expantion
position += step_size * velocity + (0.5 * step_size**2) * acceleration
# compute new particle acceleration through Newton’s second law of motion
acceleration_next = force(position, box_size) / mass
# update velocity with a finite mean approximation
velocity += (0.5 * step_size) * (acceleration + acceleration_next)
# updated state
return position, velocity, acceleration_next

183
Exercise_02/task02.py
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#!/usr/bin/env python
from optparse import OptionParser # to parse script parameters
import scipy
import numpy as np # static objects like constants (and outside functions)
from jax import numpy as jnp # tracable objects like particle positions
from jax import jit, grad, vmap
################################################################################
### parse script parameters ###
################################################################################
from optparse import OptionParser
# Parte script parameters
arg_parser = OptionParser()
usage = "usage: %prog [options] [<NR_PARTICLES>] [<BOX_SIZE>] [<TEMPERATURE>]"
arg_parser = OptionParser(usage = usage)
arg_parser.add_option("-M", "--particles", action = "store", type = int,
dest = "nr_particles", help = "Nr. of particles", default = 1000)
dest = "nr_particles", default = -1,
help = "Nr. of particles (required!)")
arg_parser.add_option("-L", "--box_size", action = "store", type = float,
dest = "box_size", help = "side box_size [A (angstrom)] of the simulation cube",
default = 15.0)
arg_parser.add_option("-T", "--temp", action = "store", type = float,
dest = "temp", help = "temperature [K] to generate initial conditions",
default = 300.0)
arg_parser.add_option("-f", "--file", action = "store", type = str,
dest = "path", help = "output file path",
default = "task02.xyz")
arg_parser.add_option("-p", "--plot", action = "store", type = str,
dest = "plot", help = "output file path for a plot of the configuration " \
"(default: no plot generated)",
default = None)
arg_parser.add_option("-v", action = "store_true", dest = "verbose",
default = False, help = "turn verbosity mode on (default: off a.k.a. silent)")
dest = "box_size", default = -1.0,
help = "side box_size [A (angstrom)] of the simulation cube (required!)")
arg_parser.add_option("-T", "--temperature", action = "store", type = float,
dest = "temperature", default = -1.0,
help = "temperature [K] to generate initial conditions (required!)")
arg_parser.add_option("-o", "--output", action = "store", type = str,
dest = "output", default = "task02.xyz",
help = "output file path (default: 'task02.xyz')")
arg_parser.add_option("-v", action = "store_true",
dest = "verbose", default = False,
help = "turn verbosity mode on (default: off a.k.a. silent)")
# Parse command line arguments (as def. above) or store defaults to `config`
config, args = arg_parser.parse_args()
# overwrite options with positional arguments if supplied
try:
if len(args) > 0:
config.nr_particles = int(args[0])
if len(args) > 1:
config.box_size = float(args[1])
if len(args) > 2:
config.temperature = float(args[2])
except ValueError as expression:
arg_parser.print_help()
print(f"Error: {expression}")
exit(-1)
else:
# quick and dirty validation
if not config.nr_particles > 0 \
or not config.box_size > 0.0 \
or not config.temperature > 0.0:
arg_parser.print_help()
print("Error: missing or illegal argument")
exit(-1)
# toy moleculat dynamic system parameters
De = 1.6 # [eV (electronvolt)]
alpha = 3.028 # [A^-1]
re = 1.411 # [A]
mass = 18.998403 # atomic mass of a single particle
def dump(position, velocity, box_size = config.box_size, \
path = config.path, mode = "w", comment = ""):
"""
Dumps `position` and `velocity` to `path` with meta data.
First writes a header to `path` in `mode` file write mode defines as three
lines.
`<nr of particles [int]>`
`<comment (ignored)>`
`<box side lenght [float]>`
then each line (nr of particles many) have the form `x y z vx vy vx`.
"""
with open(path, mode) as file:
# write headers
print(position.shape[0], comment, box_size, sep = "\n", file = file)
# store position and velocity for with `x y z vx vy vz` entries per line`
for (x, y, z), (vx, vy, vz) in zip(position, velocity):
print(x, y, z, vx, vy, vz, file = file)
@jit
def energy(position):
"""
Computes the potential energy of a system of particles with `position` using
Morses potential.
"""
# enforce expected shape
# (`scipy.optimize.minimize` drops shape information)
position = position.reshape((config.nr_particles, 3))
# compute all pairwise position differences (all!)
diff = position[:, jnp.newaxis, :] - position
# extract only one of two distance combinations of non-equal particles
lower_tri = jnp.tril_indices(config.nr_particles, k = -1)
diff = diff[lower_tri[0], lower_tri[1], :]
# fold space in all directions. The `max_dist` is the maximum distance
# in the folded space untill the distance through the folded space
# border is smaller than inside the box. 3-axis parallel fold
max_dist = config.box_size / 2
diff = jnp.mod(diff + max_dist, 2 * max_dist) - max_dist
# Compute distances
dist = jnp.linalg.norm(diff, axis = 1)
# calc inbetween exp(.) expression
ex = jnp.exp(-alpha * (dist - re))
# evaluate Morse potential
return De * jnp.sum(ex * (ex - 2.0))
@jit
def force(position):
"""
Computes the forces acting on each particle in `position` as the gradient of
the potential energy. (a.k.a. the derivative (gradient) of `energy`)
"""
return grad(energy)(position)
################################################################################
### task 2 / generation of initial conditions ###
################################################################################
# note, load module _after_ processing script parameters (no need to load all
# of the heavy numeric modules if only usage or alike is needed)
import numpy as np
import scipy
from jax import jit, grad
from molecular_dynamics import dump, energy, force, mass
# Sample random positions in a 3D cube (TODO: make this not just uniform :-})
position = np.random.uniform(0.0, config.box_size, (config.nr_particles, 3))
# Sample particle velocities
sd = np.sqrt(scipy.constants.Boltzmann * config.temp / mass)
sd = np.sqrt(scipy.constants.Boltzmann * config.temperature / mass)
velocity = np.random.normal(0.0, sd, (config.nr_particles, 3))
# center velocities
velocity -= velocity.mean(axis = 0)
# remember energy before optimizing for a low energy state
initial_energy = energy(position)
initial_energy = energy(position, config.box_size)
forces = force(position, config.box_size)
initial_mean_forces = forces.mean(axis = 0)
initial_mean_fnorm = np.linalg.norm(forces, axis = 1).mean()
# optimize energy to find low energy system state using Conjugate-Gradients
optim = scipy.optimize.minimize(energy, x0 = position, jac = force, method = "CG")
optim = scipy.optimize.minimize(energy, # objective func.
jac = jit(grad(energy)), # jacobian
x0 = position, # initial position
args = (config.box_size, ), # further args
method = "CG")
# extract (and reshape) optimization result
position = optim.x.reshape((config.nr_particles, 3))
# ensure all particles are in the box
position = np.mod(position, config.box_size)
# recompute stats after optimizing for low energy state
final_energy = energy(position)
mean_forces = force(position).mean(axis = 0)
final_energy = energy(position, config.box_size)
forces = force(position, config.box_size)
final_mean_forces = forces.mean(axis = 0)
final_mean_fnorm = np.linalg.norm(forces, axis = 1).mean()
# store state snapshot to file (default target file defined by script args)
dump(position, velocity)
dump(config.output, position, velocity, config.box_size)
# report stats (if requested by `-v` script argument)
if config.verbose:
print("Initial Energy: {:.4e}".format(initial_energy))
print("Final Energy: {:.4e}".format(final_energy))
print("Mean Forces: {:.4e} {:.4e} {:.4e}".format(*mean_forces))
print(f"Initial Energy: {initial_energy:.4e}")
print( "Initial Mean Forces: {:.4e} {:.4e} {:.4e}".format(*initial_mean_forces))
print(f"Initial Mean ||Forces||: {initial_mean_fnorm:.4e}")
print(f"Final Energy: {final_energy:.4e}")
print( "Final Mean Forces: {:.4e} {:.4e} {:.4e}".format(*final_mean_forces))
print(f"Final Mean ||Forces||: {final_mean_fnorm:.4e}")
print(f"Done: saved inital state to '{config.output}'")
# if a plot path is provided
if not config.plot is None:
from mpl_toolkits import mplot3d
import matplotlib.pyplot as plt
# new plot with 3D axis
plt.figure()
ax = plt.axes(projection = "3d")
# create 3D position scatter plot
ax.scatter(position[:, 0], position[:, 1], position[:, 2])
# and save to file
plt.savefig(config.plot)
# # if a plot path is provided
# if not config.plot is None:
# from mpl_toolkits import mplot3d
# import matplotlib.pyplot as plt
# # new plot with 3D axis
# plt.figure()
# ax = plt.axes(projection = "3d")
# # create 3D position scatter plot
# ax.scatter(position[:, 0], position[:, 1], position[:, 2])
# # and save to file
# plt.savefig(config.plot)

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Exercise_02/task03.py Normal file
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#!/usr/bin/env python
################################################################################
### parse script parameters ###
################################################################################
from optparse import OptionParser
usage = "usage: %prog [options] [<INPUT>] [<STEP_SIZE>] [<ITERATIONS>]"
arg_parser = OptionParser(usage = usage)
arg_parser.add_option("-i", "--input", action = "store", type = str,
dest = "input", default = None,
help = "input file path (required!)")
arg_parser.add_option("-t", "--step_size", action = "store", type = float,
dest = "step_size", default = -1.0,
help = "time step size (Delta t) for integration (required!)")
arg_parser.add_option("-N", "--iterations", action = "store", type = int,
dest = "iterations", default = -1,
help = "Number of time steps used for Newton's equation integration (required!)")
arg_parser.add_option("-o", "--output", action = "store", type = str,
dest = "output", default = "task03.xyz",
help = "output file path (default: 'task03.xyz')")
arg_parser.add_option("-v", action = "store_true",
dest = "verbose", default = False,
help = "turn verbosity mode on (default: off a.k.a. silent)")
# Parse command line arguments (as def. above) or store defaults to `config`
config, args = arg_parser.parse_args()
# overwrite options with positional arguments if supplied
try:
if len(args) > 0:
config.input = args[0]
if len(args) > 1:
config.step_size = float(args[1])
if len(args) > 2:
config.iterations = int(args[2])
except ValueError as expression:
arg_parser.print_help()
print(f"Error: {expression}")
exit(-1)
else:
# quick and dirty validation
if not config.step_size > 0.0 \
or not config.iterations > 0 \
or config.input is None:
arg_parser.print_help()
print("Error: missing or illegal argument")
exit(-1)
################################################################################
### task 3 / trajectory generation ###
################################################################################
# note, load module _after_ processing script parameters (no need to load all
# of the heavy numeric modules if only usage or alike is needed)
from molecular_dynamics import load, dump, force, mass, step, print_prog_bar
# load initial state from file
(position, velocity), box_size = load(config.input)
# compute initial acceleration using Newton’s second law of motion
acceleration = force(position, box_size) / mass
# iterate time steps for system time evolution
with open(config.output, "w") as output:
# store initial state to file
dump(output, position, velocity, box_size)
# perform iterations many time steps
for iteration in range(1, config.iterations):
# perform a single time step
position, velocity, acceleration = step(position, velocity, acceleration,
box_size, config.step_size)
# dump current state to file
dump(output, position, velocity, box_size)
# if verbosity turned on, print a progress bar
if config.verbose:
print_prog_bar(iteration, config.iterations)
# report output file path
print(f"Done: trajectories saved to '{config.output}'")

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Exercise_02/task04.py Normal file
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#!/usr/bin/env python
################################################################################
### parse script parameters ###
################################################################################
from optparse import OptionParser
usage = "usage: %prog [options] [<INPUT>]"
arg_parser = OptionParser(usage = usage)
arg_parser.add_option("-i", "--input", action = "store", type = str,
dest = "input", default = None,
help = "input file path (required!)")
arg_parser.add_option("-a", "--animate", action = "store_true",
dest = "animate", default = False,
help = "creates an trajectory animation of the states in the input file")
# Parse command line arguments (as def. above) or store defaults to `config`
config, args = arg_parser.parse_args()
# overwrite options with positional arguments if supplied
try:
if len(args) > 0:
config.input = args[0]
except ValueError as expression:
arg_parser.print_help()
print(f"Error: {expression}")
exit(-1)
else:
# quick and dirty validation
if config.input is None:
arg_parser.print_help()
print("Error: missing or illegal argument")
exit(-1)
################################################################################
### task 3 / trajectory generation ###
################################################################################
# note, load module _after_ processing script parameters (no need to load all
# of the heavy numeric modules if only usage or alike is needed)
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits import mplot3d
from molecular_dynamics import iter_load, energy, kinetic
if config.animate:
# new plot with 3D axis
fig = plt.figure()
ax = fig.add_subplot(111, projection = "3d")
count = 0
for (position, velocity), box_size in iter_load(config.input):
count += 1
e_pot = energy(position, box_size)
e_kin = kinetic(velocity)
print(f"{count: >3} - {e_pot:10.5e} {e_kin:10.5e} {(e_pot + e_kin):10.5e}")
if config.animate:
ax.cla()
plt.title(f"time step {count}")
plt.xlim([0, box_size])
plt.ylim([0, box_size])
ax.set_zlim([0, box_size])
# create 3D position scatter plot
position = np.mod(position, box_size)
ax.scatter(position[:, 0], position[:, 1], position[:, 2])
# # and save to file
# plt.savefig(config.plot)
plt.pause(0.01)