# from enthought.mayavi import mlab
from cp.surfaces.coordinate_transform import cart2sph
def uexactfn(t,cp):
th,phi,r = cart2sph(cp[:,0],cp[:,1],cp[:,2])
return np.exp(-2*t)*np.cos(phi + np.pi / 2)
if __name__ == '__main__':
MBlocklist = [10,20,40,80]
error = []
dx = []
comm = MPI.COMM_WORLD
surface = Sphere(center=np.array([0.0, 0.0, 0.0]))
# exact solution
rez = 30
xx, yy, zz = surface.parametric_grid(rez)
th, phi, r = cart2sph(xx,yy,zz)
exactu = np.cos(phi + np.pi / 2).ravel()
points = np.array([xx.ravel(),yy.ravel(),zz.ravel()]).T
vsize = xx.ravel().shape[0]
vAssigned = vsize // comm.size + int(comm.rank < (vsize % comm.size))
vstart = comm.exscan(vAssigned)
if comm.rank == 0:
vstart = 0
for MBlock in MBlocklist:
"""Solves the heat equation on a true sphere."""
import numpy as np
try:
from mayavi import mlab
except ImportError:
from enthought.mayavi import mlab
from cp.surfaces import Sphere
from cp.build_matrices import build_interp_matrix, build_diff_matrix
from cp.surfaces.coordinate_transform import cart2sph
PLOT = False
s = Sphere()
p = 3
diff_stencil_arm = 1
dim = 3
# As a byproduct of finding the banded grid, we already have its
# closest points, so we don't really have to call s.closest_point()
cp, distance, grid, dx = s.grid(num_blocks_per_dim=41,
levels=1,
p=p,
diff_stencil_arm=diff_stencil_arm)
cp2, distance2, _, _ = s.closest_point(grid)
assert np.allclose(cp, cp2)
assert np.allclose(distance, distance2)
# Corners of the virtual grid, superset of `grid`
ll = np.array(dim * [grid.min()]) - 3 * dx
from time import time
import numpy as np
import scipy.sparse.linalg as splinalg
try:
from mayavi import mlab
except ImportError:
from enthought.mayavi import mlab
from cp.surfaces import Sphere
from cp.build_matrices import build_interp_matrix, build_diff_matrix, build_linear_diagonal_splitting
from cp.surfaces.coordinate_transform import cart2sph
PLOT = True
s = Sphere()
p = 3
diff_stencil_arm = 1
dim = 3
# As a byproduct of finding the banded grid, we already have its
# closest points, so we don't really have to call s.closest_point()
cp, distance, grid, dx = s.grid(num_blocks_per_dim=41,
levels=1,
p=p,
diff_stencil_arm=diff_stencil_arm)
cp2, distance2, _, _ = s.closest_point(grid)
assert np.allclose(cp, cp2)
assert np.allclose(distance, distance2)
# grid
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()
# Let's build the matrices. TODO: I think it would be nicer to use
# `grid` instead of `int_grid`. It is a simple change.
E = build_interp_matrix(int_grid, cp, dx, p, ll, virtual_grid_shape)
# TODO: being able to select different laplacian operators. Currently
# it uses the second order laplacian for 2D and 3D. We could probably
# use stencils.py, and give the stencil as a parameter
L = build_diff_matrix(int_grid, dx, virtual_grid_shape)
# Points in the surface of the sphere, used por plotting
xp, yp, zp = Sphere().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)
mlab.colorbar()
def setUp(self):
self.surface = Sphere()
"""Controlled patterns using the Grey-Scott reaction-diffusion equations
and a forcing term."""
import numpy as np
from scipy.sparse import eye
import matplotlib.pyplot as plt
try:
from mayavi import mlab
except ImportError:
from enthought.mayavi import mlab
from cp.surfaces import Sphere
from cp.build_matrices import build_interp_matrix, build_diff_matrix
PLOT = True
s = Sphere()
p = 3
diff_stencil_arm = 1
dim = 3
# As a byproduct of finding the banded grid, we already have its
# closest points, so we don't really have to call s.closest_point()
cp, distance, grid, dx = s.grid(num_blocks_per_dim=41,
levels=2,
p=p,
diff_stencil_arm=diff_stencil_arm)
# Corners of the virtual grid, superset of `grid`
# TODO: Hide this inside grid
ll = np.array(dim * [grid.min()]) - 3 * dx
ur = np.array(dim * [grid.max()]) + 3 * dx
"""Controlled patterns using the Grey-Scott reaction-diffusion equations
and a forcing term."""
import numpy as np
from scipy.sparse import eye
import matplotlib.pyplot as plt
try:
from mayavi import mlab
except ImportError:
from enthought.mayavi import mlab
from cp.surfaces import Sphere
from cp.build_matrices import build_interp_matrix, build_diff_matrix
PLOT = True
s = Sphere()
p = 3
diff_stencil_arm = 1
dim = 3
# As a byproduct of finding the banded grid, we already have its
# closest points, so we don't really have to call s.closest_point()
cp, distance, grid, dx = s.grid(num_blocks_per_dim=41,
levels=2,
p=p,
diff_stencil_arm=diff_stencil_arm)
# Corners of the virtual grid, superset of `grid`
# TODO: Hide this inside grid
ll = np.array(dim * [grid.min()]) - 3 * dx
ur = np.array(dim * [grid.max()]) + 3 * dx
from cp.surfaces.coordinate_transform import cart2sph
def initialu(cp):
th,phi,r = cart2sph(cp[:,0],cp[:,1],cp[:,2])
return np.cos(phi + np.pi / 2)
if __name__ == '__main__':
MBlocklist = [10,20,40,80]
Tf = 0.5
error = []
dx = []
comm = MPI.COMM_WORLD
surface = Sphere(center=np.array([0.0, 0.0, 0.0]))
# exact solution
rez = 30
xx, yy, zz = surface.parametric_grid(rez)
th, phi, r = cart2sph(xx,yy,zz)
exactu = np.cos(phi + np.pi / 2).ravel()
points = np.array([xx.ravel(),yy.ravel(),zz.ravel()]).T
vsize = xx.ravel().shape[0]
vAssigned = vsize // comm.size + int(comm.rank < (vsize % comm.size))
vstart = comm.exscan(vAssigned)
if comm.rank == 0:
vstart = 0
for MBlock in MBlocklist:
