# Lorenz -- another Q

Hi,

Given the Lorenz code shared yesterday, is there a way
to generate a log file of the x,y,z points generated?

--Prahas

In case you deleted the code:

import numpy as np
from scipy import integrate

from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.colors import cnames
from matplotlib import animation

# orig value of N_traj was 20 -- very cool this way.

N_trajectories = 1

def lorentz_deriv((x, y, z), t0, sigma=10., beta=8./3, rho=28.0):
"""Compute the time-derivative of a Lorentz system."""
return [sigma * (y - x), x * (rho - z) - y, x * y - beta * z]

# Choose random starting points, uniformly distributed from -15 to 15

np.random.seed(1)

# changing from -15,30 to 10,5 below starts the drawing in the middle,
# rather than getting the long line from below....

# x0 = -15 + 30 * np.random.random((N_trajectories, 3))

x0 = 10 + 5 * np.random.random((N_trajectories, 3))

# Solve for the trajectories

# orig values: 0,4,1000
# 3rd value -- lower it, it gets choppier.
# 2nd value -- increase it -- more points, but speedier.

# change middle num from 4 to 15 -- this adds points!!!!!!!!

t = np.linspace(0, 40, 3000)
x_t = np.asarray([integrate.odeint(lorentz_deriv, x0i, t)
for x0i in x0])

# Set up figure & 3D axis for animation
fig = plt.figure()
ax = fig.add_axes([0, 0, 1, 1], projection='3d')

# changing off to on below adds axises. slows it down but you
# can fix that with interval value in the animation call

ax.axis('on')

# choose a different color for each trajectory
colors = plt.cm.jet(np.linspace(0, 1, N_trajectories))

# set up lines and points -- this is a correction from
# the orig jake code. the next four lines...

lines = [ax.plot([], [], [], '-', c=c)[0]
for c in colors]
pts = [ax.plot([], [], [], 'o', c=c)[0]
for c in colors]

# prepare the axes limits
ax.set_xlim((-25, 25))
ax.set_ylim((-35, 35))
ax.set_zlim((5, 55))

# set point-of-view: specified by (altitude degrees, azimuth degrees)
ax.view_init(30, 0)

# initialization function: plot the background of each frame
def init():
for line, pt in zip(lines, pts):
line.set_data([], [])
line.set_3d_properties([])

pt.set_data([], [])
pt.set_3d_properties([])
return lines + pts

# animation function. This will be called sequentially with the frame number
def animate(i):
# we'll step two time-steps per frame. This leads to nice results.

i = (2 * i) % x_t.shape[1]

for line, pt, xi in zip(lines, pts, x_t):
x, y, z = xi[:i].T
line.set_data(x, y)
line.set_3d_properties(z)

pt.set_data(x[-1:], y[-1:])
pt.set_3d_properties(z[-1:])

# changed 0.3 to 0.05 below -- this slows the rotation of the view.
# changed 30 to 20 below
# changing 20 to (20 + (.1 * i)) rotates on the Z axis. trippy.

ax.view_init(10, 0.1 * i)
# ax.view_init(10, 100)
fig.canvas.draw()
return lines + pts

# instantiate the animator. I've deleted the blit switch (for Mac)
# enlarging frames=500 works now -- it failed before because I didn't give it
# enough data -- by changing the t=np.linspace line above I generate
more points.
# interval larger slows it down
# changed inteval from 30 to 200, frames from 500 to 3000

anim = animation.FuncAnimation(fig, animate, init_func=init,
frames=3000, interval=200)

# Save as mp4. This requires mplayer or ffmpeg to be installed. COMPLEX!!!!!
# Instead, use a screen record program: Quicktime on the Mac; MS
Expression Encoder on PC.
# anim.save('PDNlorentz_attractor.mp4', fps=15, extra_args=['-vcodec',
'libx264'])

plt.show()

Prahas,

If I read it correctly, it looks like all of your x,y,z values are stored in x_t (and computed before plotting). See numpy.savetxt — NumPy v1.26 Manual
to output these to a file, if so desired.

-Sterling

···

On Mar 11, 2015, at 8:07AM, Prahas David Nafissian <prahas.music@...287...> wrote:

Hi,

Given the Lorenz code shared yesterday, is there a way
to generate a log file of the x,y,z points generated?

--Prahas

In case you deleted the code:

import numpy as np
from scipy import integrate

from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.colors import cnames
from matplotlib import animation

# orig value of N_traj was 20 -- very cool this way.

N_trajectories = 1

def lorentz_deriv((x, y, z), t0, sigma=10., beta=8./3, rho=28.0):
"""Compute the time-derivative of a Lorentz system."""
return [sigma * (y - x), x * (rho - z) - y, x * y - beta * z]

# Choose random starting points, uniformly distributed from -15 to 15

np.random.seed(1)

# changing from -15,30 to 10,5 below starts the drawing in the middle,
# rather than getting the long line from below....

# x0 = -15 + 30 * np.random.random((N_trajectories, 3))

x0 = 10 + 5 * np.random.random((N_trajectories, 3))

# Solve for the trajectories

# orig values: 0,4,1000
# 3rd value -- lower it, it gets choppier.
# 2nd value -- increase it -- more points, but speedier.

# change middle num from 4 to 15 -- this adds points!!!!!!!!

t = np.linspace(0, 40, 3000)
x_t = np.asarray([integrate.odeint(lorentz_deriv, x0i, t)
for x0i in x0])

# Set up figure & 3D axis for animation
fig = plt.figure()
ax = fig.add_axes([0, 0, 1, 1], projection='3d')

# changing off to on below adds axises. slows it down but you
# can fix that with interval value in the animation call

ax.axis('on')

# choose a different color for each trajectory
colors = plt.cm.jet(np.linspace(0, 1, N_trajectories))

# set up lines and points -- this is a correction from
# the orig jake code. the next four lines...

lines = [ax.plot(, , , '-', c=c)[0]
for c in colors]
pts = [ax.plot(, , , 'o', c=c)[0]
for c in colors]

# prepare the axes limits
ax.set_xlim((-25, 25))
ax.set_ylim((-35, 35))
ax.set_zlim((5, 55))

# set point-of-view: specified by (altitude degrees, azimuth degrees)
ax.view_init(30, 0)

# initialization function: plot the background of each frame
def init():
for line, pt in zip(lines, pts):
line.set_data(, )
line.set_3d_properties()

pt.set_data(, )
pt.set_3d_properties()
return lines + pts

# animation function. This will be called sequentially with the frame number
def animate(i):
# we'll step two time-steps per frame. This leads to nice results.

i = (2 * i) % x_t.shape[1]

for line, pt, xi in zip(lines, pts, x_t):
x, y, z = xi[:i].T
line.set_data(x, y)
line.set_3d_properties(z)

pt.set_data(x[-1:], y[-1:])
pt.set_3d_properties(z[-1:])

# changed 0.3 to 0.05 below -- this slows the rotation of the view.
# changed 30 to 20 below
# changing 20 to (20 + (.1 * i)) rotates on the Z axis. trippy.

ax.view_init(10, 0.1 * i)
# ax.view_init(10, 100)
fig.canvas.draw()
return lines + pts

# instantiate the animator. I've deleted the blit switch (for Mac)
# enlarging frames=500 works now -- it failed before because I didn't give it
# enough data -- by changing the t=np.linspace line above I generate
more points.
# interval larger slows it down
# changed inteval from 30 to 200, frames from 500 to 3000

anim = animation.FuncAnimation(fig, animate, init_func=init,
frames=3000, interval=200)

# Save as mp4. This requires mplayer or ffmpeg to be installed. COMPLEX!!!!!
# Instead, use a screen record program: Quicktime on the Mac; MS
Expression Encoder on PC.
# anim.save('PDNlorentz_attractor.mp4', fps=15, extra_args=['-vcodec',
'libx264'])

plt.show()

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Hello,

Solved the write issue.

I tried numpy savetxt but it chokes on 3D arrays.

So I'm doing this:

x_t.tofile('test3.txt',sep=" ",format="%f")

Only issue -- no end-of-lines. But I can write a quick
Pascal program to fix this...

Once again, thanks!

What 3D array? There shouldn’t be any 3D arrays. I suspect that x_t is only accidentally 3d by having a shape like (N, M, 1) or (1, N, M).

Ben Root

···

On Wed, Mar 11, 2015 at 5:05 PM, Prahas David Nafissian <prahas.music@…287…> wrote:

Hello,

Solved the write issue.

I tried numpy savetxt but it chokes on 3D arrays.

So I’m doing this:

x_t.tofile(‘test3.txt’,sep=" “,format=”%f")

Only issue – no end-of-lines. But I can write a quick

Pascal program to fix this…

Once again, thanks!

Dive into the World of Parallel Programming The Go Parallel Website, sponsored

by Intel and developed in partnership with Slashdot Media, is your hub for all

things parallel software development, from weekly thought leadership blogs to

news, videos, case studies, tutorials and more. Take a look and join the

conversation now. http://goparallel.sourceforge.net/

Matplotlib-users mailing list

Matplotlib-users@lists.sourceforge.net

https://lists.sourceforge.net/lists/listinfo/matplotlib-users

Sometimes a simple text file really does the trick… However, you might consider saving yourself some future pain by learning some non-text based storage formats. In the past, I used text files all the time, and they quickly became limiting, as you’ve noticed.

I personally like HDF files. There are libraries for these files on all OSs using many programming languages. Python has at least two: PyTables and h5py. I’ve personally used PyTables and find it very user-friendly. Pandas also has capabilities for interacting with HDF files (via PyTables).

If you are only going to be using Numpy, there are also binary formats such as .npy, .npz, and memmaps. See `numpy.save`, `numpy.savez`, and `numpy.memmap`. I don’t have much experience here, so I can’t say much on these formats…

Good luck.

Ryan

···

On Wed, Mar 11, 2015 at 5:15 PM, Benjamin Root <ben.root@…1304…> wrote:

What 3D array? There shouldn’t be any 3D arrays. I suspect that x_t is only accidentally 3d by having a shape like (N, M, 1) or (1, N, M).

Ben Root

Dive into the World of Parallel Programming The Go Parallel Website, sponsored

by Intel and developed in partnership with Slashdot Media, is your hub for all

things parallel software development, from weekly thought leadership blogs to

news, videos, case studies, tutorials and more. Take a look and join the

conversation now. http://goparallel.sourceforge.net/

Matplotlib-users mailing list

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On Wed, Mar 11, 2015 at 5:05 PM, Prahas David Nafissian <prahas.music@…287…> wrote:

Hello,

Solved the write issue.

I tried numpy savetxt but it chokes on 3D arrays.

So I’m doing this:

x_t.tofile(‘test3.txt’,sep=" “,format=”%f")

Only issue – no end-of-lines. But I can write a quick

Pascal program to fix this…

Once again, thanks!

Dive into the World of Parallel Programming The Go Parallel Website, sponsored

by Intel and developed in partnership with Slashdot Media, is your hub for all

things parallel software development, from weekly thought leadership blogs to

news, videos, case studies, tutorials and more. Take a look and join the

conversation now. http://goparallel.sourceforge.net/

Matplotlib-users mailing list

Matplotlib-users@lists.sourceforge.net

https://lists.sourceforge.net/lists/listinfo/matplotlib-users