ll = np.array(dim * [grid.min()]) - 3 * dx
ur = np.array(dim * [grid.max()]) + 3 * dx
virtual_grid_shape = np.abs(ur-ll) / dx + 1
# The (i,j,...) indices of the grid points, taking `ll` as origin.
int_grid = np.round((grid - ll) / dx).astype(np.int)
# Initial conditions
th, phi, r = cart2sph(grid[:, 0], grid[:, 1], grid[:, 2])
u = np.cos(phi + np.pi / 2)
# Let's keep a copy of the initial conditions
initial_u = u.copy()
# Build interpolation and differential matrix.
E = build_interp_matrix(int_grid, cp, dx, p, ll, virtual_grid_shape)
L = build_diff_matrix(int_grid, dx, virtual_grid_shape)
M = build_linear_diagonal_splitting(L, E)
# Compute eigenvalues
t = time()
print "Computing eigenvalues..."
Evals, Evecs = splinalg.eigs(-M, k=32, which="SM")
sorted_indices = np.argsort(Evals)
print "...took", time() -t
xp, yp, zp = s.parametric_grid(65)
_, phi_plot, _ = cart2sph(xp, yp, zp)
Eplot = build_interp_matrix(int_grid,
np.column_stack((xp.ravel(),
yp.ravel(),
zp.ravel())),
dx, p, ll, virtual_grid_shape)
ll = np.array(dim * [grid.min()]) - 3 * dx
ur = np.array(dim * [grid.max()]) + 3 * dx
virtual_grid_shape = np.abs(ur - ll) / dx + 1
# The (i,j,...) indices of the grid points, taking `ll` as origin.
int_grid = np.round((grid - ll) / dx).astype(np.int)
# Initial conditions
th, phi, r = cart2sph(grid[:, 0], grid[:, 1], grid[:, 2])
u = np.cos(phi + np.pi / 2)
# Let's keep a copy of the initial conditions
initial_u = u.copy()
# Build interpolation and differential matrix.
E = build_interp_matrix(int_grid, cp, dx, p, ll, virtual_grid_shape)
L = build_diff_matrix(int_grid, dx, virtual_grid_shape)
xp, yp, zp = s.parametric_grid(65)
_, phi_plot, _ = cart2sph(xp, yp, zp)
Eplot = build_interp_matrix(
int_grid, np.column_stack((xp.ravel(), yp.ravel(), zp.ravel())), dx, p, ll,
virtual_grid_shape)
if PLOT:
# Plotting code. Build a pipeline to be able to change the data later.
src = mlab.pipeline.grid_source(xp,
yp,
zp,
scalars=(Eplot * u).reshape(xp.shape))
normals = mlab.pipeline.poly_data_normals(src)
surf = mlab.pipeline.surface(normals)