def closest_point(self, xx):
x,y,z = xx.T
# no boundaries for now
if self.axis == 'x':
th, r, zz = cart2pol(y,z,x)
cpzzr, dist, _, _ = self.curve.closest_point(np.column_stack((zz, r)))
cpzz, cpr = cpzzr.T
cpy, cpz, cpx = pol2cart(th, cpr, cpzz)
elif self.axis == 'y':
th, r, zz = cart2pol(z,x,y)
cprzz, dist, _, _ = self.curve.closest_point(np.column_stack((r, zz)))
cpr, cpzz = cprzz.T
cpz, cpx, cpy = pol2cart(th, cpr, cpzz)
cpxx = np.column_stack((cpx, cpy, cpz))
return cpxx, dist, np.zeros(xx.ndim), {}
def uexactfn(t,cp):
k1 = 2
k2 = 4
k3 = 6
th, r = cart2pol(cp[:,0],cp[:,1])
return np.exp(-k1**2*t)*np.cos(k1*th) + np.exp(-k2**2*t)*np.sin(k2*th)\
+ np.exp(-k3**2*t)*np.cos(k3*th)
def uexactfn(t, cp):
k1 = 2
k2 = 4
k3 = 6
th, r = cart2pol(cp[:, 0], cp[:, 1])
return np.exp(-k1**2*t)*np.cos(k1*th) + np.exp(-k2**2*t)*np.sin(k2*th)\
+ np.exp(-k3**2*t)*np.cos(k3*th)
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
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, r = cart2pol(grid[:, 0], grid[:, 1])
u = np.cos(th + 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 = s.parametric_grid(65)
th_plot, _ = cart2pol(xp, yp)
Eplot = build_interp_matrix(int_grid,
np.column_stack((xp.ravel(),
yp.ravel())),
dx, p, ll, virtual_grid_shape)
def uexactfn(t,cp):
k = 2
th, r = cart2pol(cp[:,0],cp[:,1])
return np.exp(-k**2*t)*np.cos(k*th)
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
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, r = cart2pol(grid[:, 0], grid[:, 1])
u = np.cos(th + 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 = s.parametric_grid(65)
th_plot, _ = cart2pol(xp, yp)
Eplot = build_interp_matrix(int_grid, np.column_stack(
(xp.ravel(), yp.ravel())), dx, p, ll, virtual_grid_shape)
# choose a Closest Point Method algorithm
cpm = 0
