Random walking an ensemble of particles, best leveraging of NumPy?Optimizing numpy gmean calculationEfficient...
Find longest word in a string: are any of these algorithms good?
Should I tell my boss the work he did was worthless
An alternative proof of an application of Hahn-Banach
Was Luke Skywalker the leader of the Rebel forces on Hoth?
weren't playing vs didn't play
Does the nature of the Apocalypse in The Umbrella Academy change from the first to the last episode?
If I receive an SOS signal, what is the proper response?
finite abelian groups tensor product.
Can I pump my MTB tire to max (55 psi / 380 kPa) without the tube inside bursting?
Do I really need to have a scientific explanation for my premise?
Examples of a statistic that is not independent of sample's distribution?
Is "conspicuously missing" or "conspicuously" the subject of this sentence?
They call me Inspector Morse
Recommendation letter by significant other if you worked with them professionally?
How do I express some one as a black person?
Intuition behind counterexample of Euler's sum of powers conjecture
Hotkey (or other quick way) to insert a keyframe for only one component of a vector-valued property?
Accepted offer letter, position changed
PTIJ: wiping amalek’s memory?
When traveling to Europe from North America, do I need to purchase a different power strip?
Declaring and defining template, and specialising them
Could you please stop shuffling the deck and play already?
When a wind turbine does not produce enough electricity how does the power company compensate for the loss?
How does one describe somebody who is bi-racial?
Random walking an ensemble of particles, best leveraging of NumPy?
Optimizing numpy gmean calculationEfficient numpy cosine distance calculationStable partition in NumpyGroupby in NumPyK-Mean with NumpySpeed up a function using NumPyNumPy eliminate double loopInstantiating a kind of NumPy arraySlicing a big NumPy arraySudoku solver using NumPy
$begingroup$
I've implemented the example given to me in this answer in the script below.
begin{align*}
xbig(tfrac{1}{2}Delta tbig) &= x(0) + tfrac{1}{2}Delta t, p(0)/m
\
p(Delta t) &= p(0)exp(-gamma Delta t) + sqrt{1-exp(-2gamma Delta t)} sqrt{m k_B T} , R
\
x(Delta t) &= xbig(tfrac{1}{2}Delta tbig) + tfrac{1}{2}Delta t, p(Delta t)/m
end{align*}
Every nsubsteps I save a snapshot of the positions of an ensemble of nparticles particles in 3D, then plot $r^2$ versus time; the envelope should increase roughly linearly with time.
I will adjust the size of the group to maximize speed. There's overhead instantiating numpy arrays which is a penalty doing one particle at a time, but if the arrays are too big I get hit by something that might be cache swapping.
I will like to keep the feature of only saving results every 1/n of the iterations so I don't build unnecessarily long lists.
Question If I want to ramp this up to do simulations for much longer times, or simulate many more particles, am I missing a substantially faster way to do this calculation?
import numpy as np
import matplotlib.pyplot as plt
from numpy import random
pi = np.pi
kB = 1.381E-23
T = 293.
eta_air = 18.5E-06 # viscocity of air Pa-s (kg m^-1 s^-1)
eta_water = 1.0E-03 # viscocity of water Pa-s (kg m^-1 s^-1)
rho = 1000. # kg/m^3 porous carbon
R = 0.5 * 2.5E-06 # meters, PM2.5 radius
m = (4./3) * pi * rho * R**3 # kg
mkBT = m * kB * T
gamma = 6 * pi * eta_air * R / m
nsteps = 10000
nsubsteps = 100
dt = 0.000001
tsteps = dt * nsubsteps * np.arange(nsteps)
nparticles = 10
ndims = 3 # keep it real
A = np.exp(-gamma * dt)
B = np.sqrt(1 - np.exp(-2*gamma*dt)) * np.sqrt(mkBT)
C = 0.5 * dt / m
print "np.exp(-gamma * dt) should be of order unity: ", np.exp(-gamma * dt)
x, p = np.zeros((2, nparticles, ndims))
xs = []
for i in range(nsteps):
rans = random.normal(0, 1, (nsubsteps, nparticles, ndims))
for j in range(nsubsteps):
xh = x + 0.5 * dt * p / m
p = p * A + B * rans[j]
x = xh + C * p
xs.append(x) # save only every nsubstepth (is that a word?)
x = np.moveaxis(np.array(xs), 0, 2)
rsqs = (x**2).sum(axis=1)
if True:
plt.figure()
plt.ylabel('r^2 (um^2)', fontsize=16)
plt.xlabel('time (sec)', fontsize=16)
for thing in rsqs:
plt.plot(tsteps, 1E+12 * thing)
plt.title('random walk of spherical PM2.5 particles in air', fontsize=18)
plt.show()
python python-2.x numpy simulation physics
asked Mar 6 at 14:30
uhohuhoh
1907
$endgroup$
add a comment |
$begingroup$
I've implemented the example given to me in this answer in the script below.
begin{align*}
xbig(tfrac{1}{2}Delta tbig) &= x(0) + tfrac{1}{2}Delta t, p(0)/m
\
p(Delta t) &= p(0)exp(-gamma Delta t) + sqrt{1-exp(-2gamma Delta t)} sqrt{m k_B T} , R
\
x(Delta t) &= xbig(tfrac{1}{2}Delta tbig) + tfrac{1}{2}Delta t, p(Delta t)/m
end{align*}
Every nsubsteps I save a snapshot of the positions of an ensemble of nparticles particles in 3D, then plot $r^2$ versus time; the envelope should increase roughly linearly with time.
I will adjust the size of the group to maximize speed. There's overhead instantiating numpy arrays which is a penalty doing one particle at a time, but if the arrays are too big I get hit by something that might be cache swapping.
I will like to keep the feature of only saving results every 1/n of the iterations so I don't build unnecessarily long lists.
Question If I want to ramp this up to do simulations for much longer times, or simulate many more particles, am I missing a substantially faster way to do this calculation?
import numpy as np
import matplotlib.pyplot as plt
from numpy import random
pi = np.pi
kB = 1.381E-23
T = 293.
eta_air = 18.5E-06 # viscocity of air Pa-s (kg m^-1 s^-1)
eta_water = 1.0E-03 # viscocity of water Pa-s (kg m^-1 s^-1)
rho = 1000. # kg/m^3 porous carbon
R = 0.5 * 2.5E-06 # meters, PM2.5 radius
m = (4./3) * pi * rho * R**3 # kg
mkBT = m * kB * T
gamma = 6 * pi * eta_air * R / m
nsteps = 10000
nsubsteps = 100
dt = 0.000001
tsteps = dt * nsubsteps * np.arange(nsteps)
nparticles = 10
ndims = 3 # keep it real
A = np.exp(-gamma * dt)
B = np.sqrt(1 - np.exp(-2*gamma*dt)) * np.sqrt(mkBT)
C = 0.5 * dt / m
print "np.exp(-gamma * dt) should be of order unity: ", np.exp(-gamma * dt)
x, p = np.zeros((2, nparticles, ndims))
xs = []
for i in range(nsteps):
rans = random.normal(0, 1, (nsubsteps, nparticles, ndims))
for j in range(nsubsteps):
xh = x + 0.5 * dt * p / m
p = p * A + B * rans[j]
x = xh + C * p
xs.append(x) # save only every nsubstepth (is that a word?)
x = np.moveaxis(np.array(xs), 0, 2)
rsqs = (x**2).sum(axis=1)
if True:
plt.figure()
plt.ylabel('r^2 (um^2)', fontsize=16)
plt.xlabel('time (sec)', fontsize=16)
for thing in rsqs:
plt.plot(tsteps, 1E+12 * thing)
plt.title('random walk of spherical PM2.5 particles in air', fontsize=18)
plt.show()
python python-2.x numpy simulation physics
asked Mar 6 at 14:30
uhohuhoh
1907
$endgroup$
2
$begingroup$
It's definitely worth making the switch regardless if it is faster, since python2.x EOL is less then a year away ;) pythonclock.org
$endgroup$
– Ludisposed
Mar 6 at 14:51
$begingroup$
@Ludisposed yes I know (blush). I'm lookiing/hoping for a case that forces me to take the plunge.
$endgroup$
– uhoh
Mar 6 at 14:52
add a comment |
$begingroup$
I've implemented the example given to me in this answer in the script below.
begin{align*}
xbig(tfrac{1}{2}Delta tbig) &= x(0) + tfrac{1}{2}Delta t, p(0)/m
\
p(Delta t) &= p(0)exp(-gamma Delta t) + sqrt{1-exp(-2gamma Delta t)} sqrt{m k_B T} , R
\
x(Delta t) &= xbig(tfrac{1}{2}Delta tbig) + tfrac{1}{2}Delta t, p(Delta t)/m
end{align*}
Every nsubsteps I save a snapshot of the positions of an ensemble of nparticles particles in 3D, then plot $r^2$ versus time; the envelope should increase roughly linearly with time.
I will adjust the size of the group to maximize speed. There's overhead instantiating numpy arrays which is a penalty doing one particle at a time, but if the arrays are too big I get hit by something that might be cache swapping.
I will like to keep the feature of only saving results every 1/n of the iterations so I don't build unnecessarily long lists.
Question If I want to ramp this up to do simulations for much longer times, or simulate many more particles, am I missing a substantially faster way to do this calculation?
import numpy as np
import matplotlib.pyplot as plt
from numpy import random
pi = np.pi
kB = 1.381E-23
T = 293.
eta_air = 18.5E-06 # viscocity of air Pa-s (kg m^-1 s^-1)
eta_water = 1.0E-03 # viscocity of water Pa-s (kg m^-1 s^-1)
rho = 1000. # kg/m^3 porous carbon
R = 0.5 * 2.5E-06 # meters, PM2.5 radius
m = (4./3) * pi * rho * R**3 # kg
mkBT = m * kB * T
gamma = 6 * pi * eta_air * R / m
nsteps = 10000
nsubsteps = 100
dt = 0.000001
tsteps = dt * nsubsteps * np.arange(nsteps)
nparticles = 10
ndims = 3 # keep it real
A = np.exp(-gamma * dt)
B = np.sqrt(1 - np.exp(-2*gamma*dt)) * np.sqrt(mkBT)
C = 0.5 * dt / m
print "np.exp(-gamma * dt) should be of order unity: ", np.exp(-gamma * dt)
x, p = np.zeros((2, nparticles, ndims))
xs = []
for i in range(nsteps):
rans = random.normal(0, 1, (nsubsteps, nparticles, ndims))
for j in range(nsubsteps):
xh = x + 0.5 * dt * p / m
p = p * A + B * rans[j]
x = xh + C * p
xs.append(x) # save only every nsubstepth (is that a word?)
x = np.moveaxis(np.array(xs), 0, 2)
rsqs = (x**2).sum(axis=1)
if True:
plt.figure()
plt.ylabel('r^2 (um^2)', fontsize=16)
plt.xlabel('time (sec)', fontsize=16)
for thing in rsqs:
plt.plot(tsteps, 1E+12 * thing)
plt.title('random walk of spherical PM2.5 particles in air', fontsize=18)
plt.show()
python python-2.x numpy simulation physics
asked Mar 6 at 14:30
uhohuhoh
1907
$endgroup$
I've implemented the example given to me in this answer in the script below.
begin{align*}
xbig(tfrac{1}{2}Delta tbig) &= x(0) + tfrac{1}{2}Delta t, p(0)/m
\
p(Delta t) &= p(0)exp(-gamma Delta t) + sqrt{1-exp(-2gamma Delta t)} sqrt{m k_B T} , R
\
x(Delta t) &= xbig(tfrac{1}{2}Delta tbig) + tfrac{1}{2}Delta t, p(Delta t)/m
end{align*}
Every nsubsteps I save a snapshot of the positions of an ensemble of nparticles particles in 3D, then plot $r^2$ versus time; the envelope should increase roughly linearly with time.
I will adjust the size of the group to maximize speed. There's overhead instantiating numpy arrays which is a penalty doing one particle at a time, but if the arrays are too big I get hit by something that might be cache swapping.
I will like to keep the feature of only saving results every 1/n of the iterations so I don't build unnecessarily long lists.
Question If I want to ramp this up to do simulations for much longer times, or simulate many more particles, am I missing a substantially faster way to do this calculation?
import numpy as np
import matplotlib.pyplot as plt
from numpy import random
pi = np.pi
kB = 1.381E-23
T = 293.
eta_air = 18.5E-06 # viscocity of air Pa-s (kg m^-1 s^-1)
eta_water = 1.0E-03 # viscocity of water Pa-s (kg m^-1 s^-1)
rho = 1000. # kg/m^3 porous carbon
R = 0.5 * 2.5E-06 # meters, PM2.5 radius
m = (4./3) * pi * rho * R**3 # kg
mkBT = m * kB * T
gamma = 6 * pi * eta_air * R / m
nsteps = 10000
nsubsteps = 100
dt = 0.000001
tsteps = dt * nsubsteps * np.arange(nsteps)
nparticles = 10
ndims = 3 # keep it real
A = np.exp(-gamma * dt)
B = np.sqrt(1 - np.exp(-2*gamma*dt)) * np.sqrt(mkBT)
C = 0.5 * dt / m
print "np.exp(-gamma * dt) should be of order unity: ", np.exp(-gamma * dt)
x, p = np.zeros((2, nparticles, ndims))
xs = []
for i in range(nsteps):
rans = random.normal(0, 1, (nsubsteps, nparticles, ndims))
for j in range(nsubsteps):
xh = x + 0.5 * dt * p / m
p = p * A + B * rans[j]
x = xh + C * p
xs.append(x) # save only every nsubstepth (is that a word?)
x = np.moveaxis(np.array(xs), 0, 2)
rsqs = (x**2).sum(axis=1)
if True:
plt.figure()
plt.ylabel('r^2 (um^2)', fontsize=16)
plt.xlabel('time (sec)', fontsize=16)
for thing in rsqs:
plt.plot(tsteps, 1E+12 * thing)
plt.title('random walk of spherical PM2.5 particles in air', fontsize=18)
plt.show()
python python-2.x numpy simulation physics
python python-2.x numpy simulation physics
asked Mar 6 at 14:30
uhohuhoh
1907
asked Mar 6 at 14:30
uhohuhoh
1907
edited 9 mins ago
uhoh
asked Mar 6 at 14:30
uhohuhoh
1907
asked Mar 6 at 14:30
uhohuhoh
1907
asked Mar 6 at 14:30
uhohuhoh
1907
1907
2
$begingroup$
It's definitely worth making the switch regardless if it is faster, since python2.x EOL is less then a year away ;) pythonclock.org
$endgroup$
– Ludisposed
Mar 6 at 14:51
$begingroup$
@Ludisposed yes I know (blush). I'm lookiing/hoping for a case that forces me to take the plunge.
$endgroup$
– uhoh
Mar 6 at 14:52
add a comment |
2
$begingroup$
It's definitely worth making the switch regardless if it is faster, since python2.x EOL is less then a year away ;) pythonclock.org
$endgroup$
– Ludisposed
Mar 6 at 14:51
$begingroup$
@Ludisposed yes I know (blush). I'm lookiing/hoping for a case that forces me to take the plunge.
$endgroup$
– uhoh
Mar 6 at 14:52
2
2
$begingroup$
It's definitely worth making the switch regardless if it is faster, since python2.x EOL is less then a year away ;) pythonclock.org
$endgroup$
– Ludisposed
Mar 6 at 14:51
$begingroup$
It's definitely worth making the switch regardless if it is faster, since python2.x EOL is less then a year away ;) pythonclock.org
$endgroup$
– Ludisposed
Mar 6 at 14:51
$begingroup$
@Ludisposed yes I know (blush). I'm lookiing/hoping for a case that forces me to take the plunge.
$endgroup$
– uhoh
Mar 6 at 14:52
$begingroup$
@Ludisposed yes I know (blush). I'm lookiing/hoping for a case that forces me to take the plunge.
$endgroup$
– uhoh
Mar 6 at 14:52
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["\$", "\$"]]);
});
});
}, "mathjax-editing");
StackExchange.ifUsing("editor", function () {
StackExchange.using("externalEditor", function () {
StackExchange.using("snippets", function () {
StackExchange.snippets.init();
});
});
}, "code-snippets");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "196"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcodereview.stackexchange.com%2fquestions%2f214843%2frandom-walking-an-ensemble-of-particles-best-leveraging-of-numpy%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Code Review Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcodereview.stackexchange.com%2fquestions%2f214843%2frandom-walking-an-ensemble-of-particles-best-leveraging-of-numpy%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
$begingroup$
It's definitely worth making the switch regardless if it is faster, since python2.x EOL is less then a year away ;) pythonclock.org
$endgroup$
– Ludisposed
Mar 6 at 14:51
$begingroup$
@Ludisposed yes I know (blush). I'm lookiing/hoping for a case that forces me to take the plunge.
$endgroup$
– uhoh
Mar 6 at 14:52