def trajectory_plot(time, data, averaging_time=1.):
"""
TODO
"""
data = np.array(data)
x, x_average, _ = cal.subtract_moving_average(time, data[:, 0],
averaging_time)
y, y_average, time = cal.subtract_moving_average(time, data[:, 1],
averaging_time)
trajectory = np.stack((x, y), axis=1)
trajectory_averaged = np.stack((x_average, y_average), axis=1)
fig = plt.figure()
titles = ['x', 'y']
for i in range(2):
ax = fig.add_subplot(1, 2, i + 1)
ax.set_title(
'Trajectory of a trapped particle \n in {} direction'.format(
titles[i]))
ax.grid(True)
ax.set_xlabel('Time [s]')
ax.set_ylabel('Direction {} '.format(titles[i]) + r'[$\mu m$]')
ax.scatter(time,
trajectory[:, i] + trajectory_averaged[:, i],
s=4,
label=r'original')
ax.scatter(time, trajectory_averaged[:, i], s=4, label=r'averaged')
ax.legend(loc='best')
fig.tight_layout()
plt.show()
return None
def calibration_plots(time, data, averaging_time=1., temp=293.):
"""
TODO (Taken from the calibration.py)
"""
data = np.array(data)
x = cal.subtract_moving_average(time, data[:, 0], averaging_time)[0]
y = cal.subtract_moving_average(time, data[:, 1], averaging_time)[0]
trajectory, phi, var = cal.center_and_rotate(x, y)
k = cal.KB * temp / var * 1e12
def scatter_plot(data, trajectory, phi):
fig, (ax1, ax2) = plt.subplots(1, 2)
ax1.set_title('Original data')
ax1.grid(True)
ax1.set_xlabel('Direction x ' + r'[$\mu m$]')
ax1.set_ylabel('Direction y ' + r'[$\mu m$]')
ax1.scatter(data[:, 0], data[:, 1], s=4)
ax1.set_aspect('equal')
ax2.set_title('Centered data, phi = {:.2f} rad'.format(phi, ))
ax2.grid(True)
ax2.set_xlabel('Direction x ' + r'[$\mu m$]')
ax2.set_ylabel('Direction y ' + r'[$\mu m$]')
ax2.scatter(trajectory[:, 0], trajectory[:, 1], s=4)
ax2.set_aspect('equal')
fig.tight_layout()
plt.show()
return None
def histogram_plot(trajectory, var):
fig = plt.figure()
titles = ['x', 'y']
for i in range(2):
ax = fig.add_subplot(1, 2, i + 1)
ax.set_xlabel(('Direction {} ' + r'[$\mu m$]').format(titles[i]))
ax.set_ylabel('Bin height')
hist, bin_edges = np.histogram(trajectory[:, i],
bins=int(
np.sqrt(len(trajectory[:, i]))),
density=True)
ax.set_title('k_{} = {:.2e}J/m^2'.format(titles[i], k[i]))
bin_centres = (bin_edges[:-1] + bin_edges[1:]) / 2.
ax.scatter(bin_centres, hist, s=4)
x_model = np.linspace(min(bin_centres), max(bin_centres), 100)
prefactor = 1. / np.sqrt(2. * np.pi * var[i])
ax.plot(x_model,
prefactor * np.exp(-x_model**2. / (2. * var[i])),
label=r'fit')
ax.legend(loc='best')
fig.tight_layout()
plt.show()
return None
scatter_plot(data, trajectory, phi)
histogram_plot(trajectory, var)
return None
def trajectory_plot(time, data, averaging_time=1.):
"""
Creates a pair of plots showing the particle's trajectory components (x(t),y(t)). Time-averaged data is overlaid onto the raw data points.
Parameters
----------
time : list of floats
times of recorded points
data : ndarray of floats
x- and y-positions of particle at each point in time
averaging_time : float
time interval over which data is averaged
"""
data = np.array(data)
x, x_average, _ = cal.subtract_moving_average(
time, data[:, 0], averaging_time)
y, y_average, time = cal.subtract_moving_average(
time, data[:, 1], averaging_time)
trajectory = np.stack((x, y), axis=1)
trajectory_averaged = np.stack((x_average, y_average), axis=1)
fig = plt.figure()
titles = ['x', 'y']
for i in range(2):
ax = fig.add_subplot(1, 2, i+1)
ax.set_title('Trajectory of a trapped particle \n in {} direction'.format(titles[i]))
ax.grid(True)
ax.set_xlabel('Time [s]')
ax.set_ylabel('Direction {} '.format(titles[i]) + r'[$\mu m$]')
ax.scatter(
time, trajectory[:, i] + trajectory_averaged[:, i],
s=4, label=r'original'
)
ax.scatter(time, trajectory_averaged[:, i], s=4, label=r'averaged')
ax.legend(loc='best')
fig.tight_layout()
plt.show()
return None
def calibration_plots(time, data, averaging_time=1., temp=293.):
"""
Creates sets of scatter (y(x)) and histogram (#points(r)) plots for the particle's position. The first plot of each set shows raw data; in the second one, trap drift is averaged out and the trapping potential's axes aligned with the coordinate system.
Parameters
----------
time : list of floats
times of recorded points
data : ndarray of floats
x- and y-positions of particle at each point in time
averaging_time : float
time interval over which data is averaged
temp : float
temperature of system in Kelvin
"""
data = np.array(data)
x = cal.subtract_moving_average(time, data[:, 0], averaging_time)[0]
y = cal.subtract_moving_average(time, data[:, 1], averaging_time)[0]
trajectory, phi, var = cal.center_and_rotate(x, y)
k = cal.KB*temp/var*1e12
def scatter_plot(data, trajectory, phi):
fig, (ax1, ax2) = plt.subplots(1, 2)
ax1.set_title('Original data')
ax1.grid(True)
ax1.set_xlabel('Direction x ' + r'[$\mu m$]')
ax1.set_ylabel('Direction y ' + r'[$\mu m$]')
ax1.scatter(data[:, 0], data[:, 1], s=4)
ax1.set_aspect('equal')
ax2.set_title('Centered data, phi = {:.2f} rad'.format(phi,))
ax2.grid(True)
ax2.set_xlabel('Direction x ' + r'[$\mu m$]')
ax2.set_ylabel('Direction y ' + r'[$\mu m$]')
ax2.scatter(trajectory[:, 0], trajectory[:, 1], s=4)
ax2.set_aspect('equal')
fig.tight_layout()
plt.show()
return None
def histogram_plot(trajectory, var):
fig = plt.figure()
titles = ['x', 'y']
for i in range(2):
ax = fig.add_subplot(1, 2, i+1)
ax.set_xlabel(('Direction {} ' + r'[$\mu m$]').format(titles[i]))
ax.set_ylabel('Bin height')
hist, bin_edges = np.histogram(trajectory[:, i], bins=int(
np.sqrt(len(trajectory[:, i]))), density=True)
ax.set_title('k_{} = {:.2e}J/m^2'.format(titles[i], k[i]))
bin_centres = (bin_edges[:-1] + bin_edges[1:])/2.
ax.scatter(bin_centres, hist, s=4)
x_model = np.linspace(min(bin_centres), max(bin_centres), 100)
prefactor = 1./np.sqrt(2.*np.pi*var[i])
ax.plot(x_model, prefactor*np.exp(-x_model **
2./(2.*var[i])), label=r'fit')
ax.legend(loc='best')
fig.tight_layout()
plt.show()
return None
scatter_plot(data, trajectory, phi)
histogram_plot(trajectory, var)
return None
def test_moving_average(self):
trajectory = gen.generate([self.kx, self.ky], phi = self.phi)
t = gen.generate_time()
x, _, _ = cal.subtract_moving_average(t, trajectory[:, 0], 1)
y, _, _ = cal.subtract_moving_average(t, trajectory[:, 1], 1)
self.assertTrue(np.allclose(np.mean(x), 0, atol = 1e-4) and np.allclose(np.mean(y), 0, atol = 1e-4))