def test_poisson(self):
cases = []
# 1D
cases.append(((1, ), np.array([[2]])))
cases.append(((2, ), np.array([[2, -1], [-1, 2]])))
cases.append(((4, ),
np.array([[2, -1, 0, 0], [-1, 2, -1, 0], [0, -1, 2, -1],
[0, 0, -1, 2]])))
# 2D
cases.append(((1, 1), np.array([[4]])))
cases.append(((2, 1), np.array([[4, -1], [-1, 4]])))
cases.append(((1, 2), np.array([[4, -1], [-1, 4]])))
cases.append(((1, 3), np.array([[4, -1, 0], [-1, 4, -1], [0, -1, 4]])))
cases.append(((2, 2),
np.array([[4, -1, -1, 0], [-1, 4, 0, -1], [-1, 0, 4, -1],
[0, -1, -1, 4]])))
# 3D
cases.append(((2, 2, 1),
np.array([[6, -1, -1, 0], [-1, 6, 0, -1], [-1, 0, 6, -1],
[0, -1, -1, 6]])))
cases.append(((2, 2, 2),
np.array([[6, -1, -1, 0, -1, 0, 0, 0],
[-1, 6, 0, -1, 0, -1, 0, 0],
[-1, 0, 6, -1, 0, 0, -1, 0],
[0, -1, -1, 6, 0, 0, 0, -1],
[-1, 0, 0, 0, 6, -1, -1, 0],
[0, -1, 0, 0, -1, 6, 0, -1],
[0, 0, -1, 0, -1, 0, 6, -1],
[0, 0, 0, -1, 0, -1, -1, 6]])))
for grid, expected in cases:
assert_equal(poisson(grid).toarray(), expected)
def test_poisson(self):
cases = []
# 1D
cases.append(((1,), np.array([[2]])))
cases.append(((2,), np.array([[2, -1],
[-1, 2]])))
cases.append(((4,), np.array([[2, -1, 0, 0],
[-1, 2, -1, 0],
[0, -1, 2, -1],
[0, 0, -1, 2]])))
# 2D
cases.append(((1, 1), np.array([[4]])))
cases.append(((2, 1), np.array([[4, -1],
[-1, 4]])))
cases.append(((1, 2), np.array([[4, -1],
[-1, 4]])))
cases.append(((1, 3), np.array([[4, -1, 0],
[-1, 4, -1],
[0, -1, 4]])))
cases.append(((2, 2), np.array([[4, -1, -1, 0],
[-1, 4, 0, -1],
[-1, 0, 4, -1],
[0, -1, -1, 4]])))
# 3D
cases.append(((2, 2, 1), np.array([[6, -1, -1, 0],
[-1, 6, 0, -1],
[-1, 0, 6, -1],
[0, -1, -1, 6]])))
cases.append(((2, 2, 2), np.array([[6, -1, -1, 0, -1, 0, 0, 0],
[-1, 6, 0, -1, 0, -1, 0, 0],
[-1, 0, 6, -1, 0, 0, -1, 0],
[0, -1, -1, 6, 0, 0, 0, -1],
[-1, 0, 0, 0, 6, -1, -1, 0],
[0, -1, 0, 0, -1, 6, 0, -1],
[0, 0, -1, 0, -1, 0, 6, -1],
[0, 0, 0, -1, 0, -1, -1, 6]])))
for grid, expected in cases:
assert_equal(poisson(grid).toarray(), expected)
def normalConstraints(A_8U, N0_32F, alpha_th=20, w_sil=1e+10):
h, w = A_8U.shape
L = laplacian.poisson((h, w))
L_lil = L.tolil()
A_flat = A_8U.flatten()
sil_ids = np.where(A_flat < alpha_th)
for sil_id in sil_ids:
L_lil[sil_id, sil_id] = w_sil
A = L_lil.tocsr()
N0_flat = N0_32F.reshape(h * w, 3)
N0_flat[A_flat > alpha_th, :] = 0.0
b_all = w_sil * N0_flat
b = np.zeros(b_all.shape)
b[A_flat < alpha_th, :] = b_all[A_flat < alpha_th, :]
return A, b
def normalConstraints(A_8U, N0_32F, alpha_th=20, w_sil=1e+10):
h, w = A_8U.shape
L = laplacian.poisson((h, w))
L_lil = L.tolil()
A_flat = A_8U.flatten()
sil_ids = np.where(A_flat < alpha_th)
for sil_id in sil_ids:
L_lil[sil_id, sil_id] = w_sil
A = L_lil.tocsr()
N0_flat = N0_32F.reshape(h * w, 3)
N0_flat[A_flat > alpha_th, :] = 0.0
b_all = w_sil * N0_flat
b = np.zeros(b_all.shape)
b[A_flat < alpha_th, :] = b_all[A_flat < alpha_th, :]
return A, b
import numpy as np
from pyamg import smoothed_aggregation_solver
from pyamg.gallery import stencil_grid
from pyamg.gallery.diffusion import diffusion_stencil_2d
n = 100
X, Y = np.meshgrid(np.linspace(0, 1, n), np.linspace(0, 1, n))
stencil = diffusion_stencil_2d(type='FE', epsilon=0.001, theta=np.pi / 3)
A = stencil_grid(stencil, (n, n), format='csr')
from pyamg.gallery.laplacian import poisson
A = poisson((n, n), format='csr')
b = np.random.rand(A.shape[0])
ml = smoothed_aggregation_solver(A,
B=X.reshape(n * n, 1),
strength='symmetric',
aggregate='standard',
smooth=('jacobi', {
'omega': 4.0 / 3.0,
'degree': 2
}),
presmoother=('jacobi', {
'omega': 4.0 / 3.0
}),
postsmoother=('jacobi', {
'omega': 4.0 / 3.0
}),
max_levels=10,
max_coarse=5,
keep=False)