def core_density_plot(data,
out_file=None,
show=True,
retrieve=False,
color='k'):
nbody = Bodies()
nbody.copy(data)
core_density = np.zeros(nbody.m.shape[0])
distances = np.zeros(nbody.m.shape)
for i in range(nbody.m.shape[0]):
total_mass = np.sum(nbody.m[i])
center = center_of_mass(nbody.r[i], nbody.m[i])
distances[i] = nbody[i].sort_by_radius(center=center)
confined_mass = 0
j = 0
while confined_mass <= total_mass * 0.1:
confined_mass += nbody.m[i, j]
j += 1
core_density[i] = 3 * confined_mass / 4 / np.pi / distances[i, j]**3
plt.semilogy(nbody.t, core_density, color=color)
plt.xlabel('Time, s')
plt.ylabel('Core density, kg m$^{-3}$')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return core_density
def potential_energy_plot_other(data,
out_file=None,
show=True,
retrieve=False,
color='b'):
nbody = Bodies()
nbody.copy(data)
all_potential_energy = np.zeros(nbody.m.shape[0])
for j in range(nbody.m.shape[1]):
if j % 10 == 0:
print j
for k in range(j):
distances = np.sqrt(
np.sum(np.power(nbody.r[:, j, :] - nbody.r[:, k, :], 2),
axis=1))
all_potential_energy -= constants.G * nbody.m[:,
j] * nbody.m[:,
k] / distances
plt.plot(nbody.t, all_potential_energy, color=color)
plt.xlabel('Time, s')
plt.ylabel('Potential energy')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return all_potential_energy
def center_of_mass_plot(data,
out_file=None,
show=True,
retrieve=False,
color='k'):
nbody = Bodies()
nbody.copy(data)
centers_of_mass = np.zeros((nbody.m.shape[0], 3))
for i in range(nbody.m.shape[0]):
centers_of_mass[i] = center_of_mass(nbody.r[i], nbody.m[i])
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(centers_of_mass[:, 0],
centers_of_mass[:, 1],
zs=centers_of_mass[:, 2],
c=color,
depthshade=False)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return center_of_mass
def half_mass_radius_center_off_plot(data,
out_file=None,
show=True,
retrieve=False,
color='k'):
nbody = Bodies()
nbody.copy(data)
half_mass_radius = np.zeros(nbody.m.shape[0])
distances = np.zeros(nbody.m.shape)
for i in range(nbody.m.shape[0]):
total_mass = np.sum(nbody.m[i])
distances[i] = nbody[i].sort_by_radius()
confined_mass = 0
j = 0
while confined_mass <= total_mass * 0.5:
confined_mass += nbody.m[i, j]
j += 1
half_mass_radius[i] = distances[i, j]
plt.plot(nbody.t, half_mass_radius, color=color)
plt.xlabel('Time, s')
plt.ylabel('Half mass radius, m')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return half_mass_radius
def half_mass_radius_center_off_plot(data, out_file=None, show=True, retrieve=False, color='k'):
nbody = Bodies()
nbody.copy(data)
half_mass_radius = np.zeros(nbody.m.shape[0])
distances = np.zeros(nbody.m.shape)
for i in range(nbody.m.shape[0]):
total_mass = np.sum(nbody.m[i])
distances[i] = nbody[i].sort_by_radius()
confined_mass = 0
j = 0
while confined_mass <= total_mass * 0.5:
confined_mass += nbody.m[i, j]
j += 1
half_mass_radius[i] = distances[i, j]
plt.plot(nbody.t, half_mass_radius, color=color)
plt.xlabel('Time, s')
plt.ylabel('Half mass radius, m')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return half_mass_radius
def total_energy_plot(data,
out_file=None,
show=True,
show_ratio=False,
color='0.5'):
nbody = Bodies()
nbody.copy(data)
all_kinetic_energy = kinetic_energy_plot(data,
out_file=None,
show=False,
retrieve=True)
all_potential_energy = potential_energy_plot_other(data,
out_file=None,
show=False,
retrieve=True)
if show_ratio is True:
plt.clf()
plt.plot(nbody.t,
all_kinetic_energy / all_potential_energy,
color=color)
else:
plt.plot(nbody.t,
all_kinetic_energy + all_potential_energy,
color=color)
plt.ylabel('Energy')
plt.xlabel('Time, s')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
def potential_energy_center_off_plot(data, out_file=None, show=True, retrieve=False, color='b'):
nbody = Bodies()
nbody.copy(data)
all_potential_energy = np.zeros(nbody.m.shape[0])
potential_energy = np.zeros(nbody.m.shape[1])
distances = np.zeros(nbody.m.shape)
for i in range(nbody.m.shape[0]):
#distances[i] = np.sqrt(np.sum(nbody.r[i, :, :] ** 2, axis=1))
# Turiu zvaigzdziu atstumus iki centro
distances[i] = nbody[i].sort_by_radius()
confined_mass = 0
for j in range(nbody.m.shape[1]):
potential_energy[j] = -constants.G * confined_mass * nbody.m[i, j] / distances[i, j]
confined_mass += nbody.m[i, j]
all_potential_energy[i] = np.sum(potential_energy)
plt.plot(nbody.t, all_potential_energy, color=color)
plt.xlabel('Time')
plt.ylabel('Potential energy')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return all_potential_energy
def core_density_plot(data, out_file=None, show=True, retrieve=False, color='k'):
nbody = Bodies()
nbody.copy(data)
core_density = np.zeros(nbody.m.shape[0])
distances = np.zeros(nbody.m.shape)
for i in range(nbody.m.shape[0]):
total_mass = np.sum(nbody.m[i])
center = center_of_mass(nbody.r[i], nbody.m[i])
distances[i] = nbody[i].sort_by_radius(center=center)
confined_mass = 0
j = 0
while confined_mass <= total_mass * 0.1:
confined_mass += nbody.m[i, j]
j += 1
core_density[i] = 3 * confined_mass / 4 / np.pi / distances[i, j]**3
plt.semilogy(nbody.t, core_density, color=color)
plt.xlabel('Time, s')
plt.ylabel('Core density, kg m$^{-3}$')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return core_density
def potential_energy_center_off_plot(data,
out_file=None,
show=True,
retrieve=False,
color='b'):
nbody = Bodies()
nbody.copy(data)
all_potential_energy = np.zeros(nbody.m.shape[0])
potential_energy = np.zeros(nbody.m.shape[1])
distances = np.zeros(nbody.m.shape)
for i in range(nbody.m.shape[0]):
#distances[i] = np.sqrt(np.sum(nbody.r[i, :, :] ** 2, axis=1))
# Turiu zvaigzdziu atstumus iki centro
distances[i] = nbody[i].sort_by_radius()
confined_mass = 0
for j in range(nbody.m.shape[1]):
potential_energy[j] = -constants.G * confined_mass * nbody.m[
i, j] / distances[i, j]
confined_mass += nbody.m[i, j]
all_potential_energy[i] = np.sum(potential_energy)
plt.plot(nbody.t, all_potential_energy, color=color)
plt.xlabel('Time')
plt.ylabel('Potential energy')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return all_potential_energy
def mean_distance_plot(data,
out_file=None,
show=True,
retrieve=False,
color='k'):
nbody = Bodies()
nbody.copy(data)
mean_distance = np.zeros(nbody.m.shape[0])
#mass = np.sum(nbody[0].m)
#rad = np.zeros(nbody.m.shape[0])
for i in range(nbody.m.shape[0]):
center = center_of_mass(nbody.r[i], nbody.m[i])
mean_distance[i] = np.mean(np.sqrt(
np.sum((nbody.r[i, :, :] - center)**2, axis=1)),
axis=0)
#rad[i] = analytic_collapse.radius_at_t(nbody.t[i], 1e14, 3./4./np.pi*mass/1e14**3)
plt.plot(nbody.t, mean_distance, color=color)
#plt.plot(nbody.t, rad, color='b')
plt.xlabel('Time, s')
plt.ylabel('Mean distance, m')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return mean_distance
def mean_distance_center_off_plot(data, out_file=None, show=True, retrieve=False, color='k'):
nbody = Bodies()
nbody.copy(data)
mean_distance = np.zeros(nbody.m.shape[0])
for i in range(nbody.m.shape[0]):
mean_distance[i] = np.mean(np.sqrt(np.sum(nbody.r[i, :, :] ** 2, axis=1)), axis=0)
plt.plot(nbody.t, mean_distance, color=color)
plt.xlabel('Time, s')
plt.ylabel('Mean distance, m')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return mean_distance
def total_energy_plot(data, out_file=None, show=True, show_ratio=False, color='0.5'):
nbody = Bodies()
nbody.copy(data)
all_kinetic_energy = kinetic_energy_plot(data, out_file=None, show=False, retrieve=True)
all_potential_energy = potential_energy_plot_other(data, out_file=None, show=False, retrieve=True)
if show_ratio is True:
plt.clf()
plt.plot(nbody.t, all_kinetic_energy / all_potential_energy, color=color)
else:
plt.plot(nbody.t, all_kinetic_energy + all_potential_energy, color=color)
plt.ylabel('Energy')
plt.xlabel('Time, s')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
def kinetic_energy_plot(data, out_file=None, show=True, retrieve=False, color='r'):
nbody = Bodies()
nbody.copy(data)
all_kinetic_energy = np.zeros(nbody.m.shape[0])
for i in range(nbody.m.shape[0]):
all_kinetic_energy[i] = np.sum(np.sum(nbody.v[i] ** 2, axis=1) * nbody.m[i] / 2.)
plt.plot(nbody.t, all_kinetic_energy, color=color)
plt.xlabel('Time, s')
plt.ylabel('Kinetic energy')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return all_kinetic_energy
def lagrange_radius_plot(data, out_file=None, show=True):
nbody = Bodies()
nbody.copy(data)
lag_radii_10 = np.zeros(nbody.m.shape[0])
lag_radii_25 = np.zeros(nbody.m.shape[0])
lag_radii_50 = np.zeros(nbody.m.shape[0])
lag_radii_80 = np.zeros(nbody.m.shape[0])
distances = np.zeros(nbody.m.shape)
for i in range(nbody.m.shape[0]):
total_mass = np.sum(nbody.m[i])
center = center_of_mass(nbody.r[i], nbody.m[i])
distances[i] = nbody[i].sort_by_radius(center=center)
confined_mass = 0
j = 0
while confined_mass <= total_mass * 0.1:
confined_mass += nbody.m[i, j]
j += 1
lag_radii_10[i] = distances[i, j]
while confined_mass <= total_mass * 0.25:
confined_mass += nbody.m[i, j]
j += 1
lag_radii_25[i] = distances[i, j]
while confined_mass <= total_mass * 0.5:
confined_mass += nbody.m[i, j]
j += 1
lag_radii_50[i] = distances[i, j]
while confined_mass <= total_mass * 0.8:
confined_mass += nbody.m[i, j]
j += 1
lag_radii_80[i] = distances[i, j]
plt.plot(nbody.t, lag_radii_10, color='r', label='10% mass radii')
plt.plot(nbody.t, lag_radii_25, color='b', label='25% mass radii')
plt.plot(nbody.t, lag_radii_50, color='g', label='50% mass radii')
plt.plot(nbody.t, lag_radii_80, color='k', label='80% mass radii')
plt.xlabel('Time, s')
plt.ylabel('Lagrange radii, m')
plt.xlim((0, nbody.t[-1]))
plt.legend(frameon=False, loc=0)
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
def center_of_mass_plot(data, out_file=None, show=True, retrieve=False, color='k'):
nbody = Bodies()
nbody.copy(data)
centers_of_mass = np.zeros((nbody.m.shape[0], 3))
for i in range(nbody.m.shape[0]):
centers_of_mass[i] = center_of_mass(nbody.r[i], nbody.m[i])
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(centers_of_mass[:, 0], centers_of_mass[:, 1], zs=centers_of_mass[:, 2], c=color, depthshade=False)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return center_of_mass
def lagrange_radius_plot(data, out_file=None, show=True):
nbody = Bodies()
nbody.copy(data)
lag_radii_10 = np.zeros(nbody.m.shape[0])
lag_radii_25 = np.zeros(nbody.m.shape[0])
lag_radii_50 = np.zeros(nbody.m.shape[0])
lag_radii_80 = np.zeros(nbody.m.shape[0])
distances = np.zeros(nbody.m.shape)
for i in range(nbody.m.shape[0]):
total_mass = np.sum(nbody.m[i])
center = center_of_mass(nbody.r[i], nbody.m[i])
distances[i] = nbody[i].sort_by_radius(center=center)
confined_mass = 0
j = 0
while confined_mass <= total_mass * 0.1:
confined_mass += nbody.m[i, j]
j += 1
lag_radii_10[i] = distances[i, j]
while confined_mass <= total_mass * 0.25:
confined_mass += nbody.m[i, j]
j += 1
lag_radii_25[i] = distances[i, j]
while confined_mass <= total_mass * 0.5:
confined_mass += nbody.m[i, j]
j += 1
lag_radii_50[i] = distances[i, j]
while confined_mass <= total_mass * 0.8:
confined_mass += nbody.m[i, j]
j += 1
lag_radii_80[i] = distances[i, j]
plt.plot(nbody.t, lag_radii_10, color='r', label='10% mass radii')
plt.plot(nbody.t, lag_radii_25, color='b', label='25% mass radii')
plt.plot(nbody.t, lag_radii_50, color='g', label='50% mass radii')
plt.plot(nbody.t, lag_radii_80, color='k', label='80% mass radii')
plt.xlabel('Time, s')
plt.ylabel('Lagrange radii, m')
plt.xlim((0, nbody.t[-1]))
plt.legend(frameon=False, loc=0)
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
def potential_energy_plot_other(data, out_file=None, show=True, retrieve=False, color='b'):
nbody = Bodies()
nbody.copy(data)
all_potential_energy = np.zeros(nbody.m.shape[0])
for j in range(nbody.m.shape[1]):
if j % 10 == 0:
print j
for k in range(j):
distances = np.sqrt(np.sum(np.power(nbody.r[:, j, :] - nbody.r[:, k, :], 2), axis=1))
all_potential_energy -= constants.G*nbody.m[:, j]*nbody.m[:, k]/distances
plt.plot(nbody.t, all_potential_energy, color=color)
plt.xlabel('Time, s')
plt.ylabel('Potential energy')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return all_potential_energy
def mean_distance_plot(data, out_file=None, show=True, retrieve=False, color='k'):
nbody = Bodies()
nbody.copy(data)
mean_distance = np.zeros(nbody.m.shape[0])
#mass = np.sum(nbody[0].m)
#rad = np.zeros(nbody.m.shape[0])
for i in range(nbody.m.shape[0]):
center = center_of_mass(nbody.r[i], nbody.m[i])
mean_distance[i] = np.mean(np.sqrt(np.sum((nbody.r[i, :, :] - center) ** 2, axis=1)), axis=0)
#rad[i] = analytic_collapse.radius_at_t(nbody.t[i], 1e14, 3./4./np.pi*mass/1e14**3)
plt.plot(nbody.t, mean_distance, color=color)
#plt.plot(nbody.t, rad, color='b')
plt.xlabel('Time, s')
plt.ylabel('Mean distance, m')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return mean_distance
def kinetic_energy_plot(data,
out_file=None,
show=True,
retrieve=False,
color='r'):
nbody = Bodies()
nbody.copy(data)
all_kinetic_energy = np.zeros(nbody.m.shape[0])
for i in range(nbody.m.shape[0]):
all_kinetic_energy[i] = np.sum(
np.sum(nbody.v[i]**2, axis=1) * nbody.m[i] / 2.)
plt.plot(nbody.t, all_kinetic_energy, color=color)
plt.xlabel('Time, s')
plt.ylabel('Kinetic energy')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return all_kinetic_energy
def mean_distance_center_off_plot(data,
out_file=None,
show=True,
retrieve=False,
color='k'):
nbody = Bodies()
nbody.copy(data)
mean_distance = np.zeros(nbody.m.shape[0])
for i in range(nbody.m.shape[0]):
mean_distance[i] = np.mean(np.sqrt(np.sum(nbody.r[i, :, :]**2,
axis=1)),
axis=0)
plt.plot(nbody.t, mean_distance, color=color)
plt.xlabel('Time, s')
plt.ylabel('Mean distance, m')
plt.xlim((0, nbody.t[-1]))
if out_file is not None:
plt.savefig(out_file)
if show is True:
plt.show()
if retrieve is True:
return mean_distance
