density_norm = m / vol_mass
dens_norm = g.scratch_array()
dens_norm[mask_mass] = density_norm
'''
# analytical potential of a spheroid at y surface
phi_anal = g.scratch_y_plane_array()
for i in range(g.nx):
for j in range(g.nz):
spheroid_V = ap.Ana_Mac_pot(a1, a3, g.x[i], g.y[8], g.z[j], density)
phi_anal[i, j] = spheroid_V.potential
'''
lmax = 30
center = (0, 0, 0)
# m = multipole.Multipole(g, dens, lmax, 0.3*g.dr, center=center)
m = multipole.Multipole(g, dens_norm, lmax, 0.3 * g.dr, center=center)
phi = m.Phi()
'''
phi = m.PhiY(8)
plt.imshow(np.log10(np.abs(np.transpose(phi))), origin="lower",
interpolation="nearest",
extent=[g.xlim[0], g.xlim[1],
g.zlim[0], g.zlim[1]])
plt.colorbar()
ax = plt.gca()
ax.set_aspect("equal")
plt.savefig("lmax=0.png")
diff = comdf.comp_diff(phi_anal, phi)
"""
"""
center = (0, 0)
n_moments = 0
m = multipole.Multipole(g, n_moments, 2*g.dr, center=center)
m.compute_expansion(dens)
phi = g.scratch_array()
for i in range(g.nr):
for j in range(g.nz):
phi[i, j] = m.phi_point(g.r[i], g.z[j])
"""
# test brute force version Multipole
center = (0, 0)
n_moments = 0
m = multipole.Multipole(g, n_moments, center=center)
m.compute_expansion(dens)
phi = m.phi()
phi_norm = np.sqrt(np.sum(phi**2 / phi.size))
L2normerr = L2.L2_diff(phi_anal, phi, g.scratch_array())
# L2normerr = L2.L2_diff(phi_anal, phi, g)
# normalized L2 norm error
L2normerr = L2normerr / phi_norm
print("lmax=", n_moments)
print(L2normerr)
"""
plt.imshow(np.log10(np.abs(np.transpose(phi_mac))), origin="lower",
interpolation="nearest",
extent=[g.rlim[0], g.rlim[1],
g.zlim[0], g.zlim[1]])
plt.colorbar()
ax = plt.gca()
ax.set_aspect("equal")
plt.savefig("anal_phi.png")
"""
# create a multipole object
center = (0.0, 0.0)
n_moments = 1
m = multipole.Multipole(g, n_moments, 1.2 * g.dr, center=center)
# calculate the multipole
for l in range(n_moments):
m.compute_expansion(dens, l)
"""
phi = g.scratch_array()
for i in range(g.nr):
for j in range(g.nz):
phi[i, j] = m.phi(g.r[i], g.z[j])
"""
# evaluate eq.20 at the surface
# the surface coodinates satisfy:
# r_surface = r_grid_center - dr/2
phi = g.scratch_array()
for i in range(g.nr):
plt.colorbar()
ax = plt.gca()
ax.set_aspect("equal")
plt.savefig("lmax=0.png")
L2normerr = L2.L2_diff(V_cube, phi, g.scratch_array())
print("resolution", nx)
print("lmax =", n_moments)
print(L2normerr)
"""
# test brute force codes
n_moments = 0
# center = (a/2, b/2, c/2)
center = (0.5, 0.5, 0.5)
# multipole expansion with concentric sphere
moment = multipole.Multipole(g, dens, n_moments, 2 * g.dr, center=center)
'''
# with azumuthal
for l in range(n_moments):
for m in range(-l, l+1):
moment.compute_expansion(dens, l, m)
'''
phi = g.y_plane_array()
for i in range(g.nx):
for j in range(g.nz):
phi[i, j] = moment.phi(g.x[i], g.y[0], g.z[j])
# phi[i, j] = moment.phi_point(g.x[i], g.y[0], g.z[j])
plt.imshow(np.log10(np.abs(np.transpose(phi))),