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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Example usage for pyJHTDB.
Step1:  I'm going to create a 2D grid of points, and then get the values of the velocity at those points.
Note that the points must be in single precision if they are to be used for any getData call.
Step2:  Since the dataset I'm gonna use is the isotropic turbulence dataset, it doesn't really matter what value I choose for the z coordinates, if it's fixed.
Not for this simple example anyway.
The next step is to generate a libJHTDB object, connect it to the database, and use it to read the data that we need.
I'm using 4th order Lagrange interpolation (that's the sinterp = 4 line), and for now we need to specify the actual number corresponding to that (you can find all the different codes in turblib.h from the C package).
Step3:  Now we have the velocity stored in u, and we're gonna compute the energy and make a nice plot of it.
Step4:  Next, get some trajectories.
Step5:  Now, plot trajectories. Not spectactular because they're not that long, but this is the way a simple plot would work for long trajectories as well.
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Python Code:
%matplotlib inline
import numpy as np
import pyJHTDB
Explanation: Example usage for pyJHTDB.
End of explanation
t = np.linspace(0, 1, 64)
x = np.zeros((t.shape[0], t.shape[0], 3), np.float32)
x[:, :, 0] = t[np.newaxis, :]
x[:, :, 1] = t[:, np.newaxis]
x[:, :, 2] = .0
Explanation: I'm going to create a 2D grid of points, and then get the values of the velocity at those points.
Note that the points must be in single precision if they are to be used for any getData call.
End of explanation
lJHTDB = pyJHTDB.libJHTDB()
lJHTDB.initialize()
#Add token
auth_token  = "edu.jhu.pha.turbulence.testing-201311"  #Replace with your own token here
lJHTDB.add_token(auth_token)
import pyJHTDB.dbinfo
T = pyJHTDB.dbinfo.isotropic1024coarse['time'][-1]
time = np.random.random()*T
u = lJHTDB.getData(
               time,
               x,
               sinterp = 4,
               getFunction='getVelocity')
ubox = lJHTDB.getBoxFilter(
               time,
               x,
               field = 'velocity',
               filter_width = 5*(2*np.pi / 1024))
lJHTDB.finalize()
Explanation: Since the dataset I'm gonna use is the isotropic turbulence dataset, it doesn't really matter what value I choose for the z coordinates, if it's fixed.
Not for this simple example anyway.
The next step is to generate a libJHTDB object, connect it to the database, and use it to read the data that we need.
I'm using 4th order Lagrange interpolation (that's the sinterp = 4 line), and for now we need to specify the actual number corresponding to that (you can find all the different codes in turblib.h from the C package).
End of explanation
e = np.sum(u**2, axis = 2)
ebox = np.sum(ubox**2, axis = 2)
import matplotlib.pyplot as plt
fig = plt.figure(figsize = (10, 5))
a = fig.add_subplot(121)
a.set_axis_off()
a.imshow(e,
         extent = [t[0], t[-1] - t[0], t[0], t[-1] - t[0]],
         interpolation = 'none')
a = fig.add_subplot(122)
a.imshow(ebox,
         extent = [t[0], t[-1] - t[0], t[0], t[-1] - t[0]],
         interpolation = 'none')
Explanation: Now we have the velocity stored in u, and we're gonna compute the energy and make a nice plot of it.
End of explanation
lJHTDB.initialize()
x, t = lJHTDB.getPosition(
    starttime = 0.1,
    endtime = 0.2,
    dt = 0.001,
    point_coords = 2*np.pi * np.random.random((20, 3)),
    steps_to_keep = 50)
lJHTDB.finalize()
Explanation: Next, get some trajectories.
End of explanation
fig = plt.figure(figsize = (10, 5))
a = fig.add_subplot(111)
a.plot(x[:, 0], x[:, 1])
Explanation: Now, plot trajectories. Not spectactular because they're not that long, but this is the way a simple plot would work for long trajectories as well.
End of explanation
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