def test_1d(self):
stencil = array([1, 2, 3])
result = stencil_grid(stencil, (3, )).todense()
expected = matrix([[2, 3, 0], [1, 2, 3], [0, 1, 2]])
assert_equal(result, expected)
stencil = array([1, 2, 3, 4, 5])
result = stencil_grid(stencil, (5, )).todense()
expected = matrix([[3, 4, 5, 0, 0], [2, 3, 4, 5, 0], [1, 2, 3, 4, 5],
[0, 1, 2, 3, 4], [0, 0, 1, 2, 3]])
assert_equal(result, expected)
def test_poisson3d_7pt(self):
stencil = array([[[0, 0, 0],
[0, -1, 0],
[0, 0, 0]],
[[0, -1, 0],
[-1, 6, -1],
[0, -1, 0]],
[[0, 0, 0],
[0, -1, 0],
[0, 0, 0]]])
cases = []
cases.append(((1, 1, 1), matrix([[6]])))
cases.append(((2, 1, 1), matrix([[6, -1],
[-1, 6]])))
cases.append(((2, 2, 1), matrix([[6, -1, -1, 0],
[-1, 6, 0, -1],
[-1, 0, 6, -1],
[0, -1, -1, 6]])))
cases.append(((2, 2, 2), matrix([[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:
result = stencil_grid(stencil, grid).todense()
assert_equal(result, expected)
def test_poisson3d_7pt(self):
stencil = np.array([[[0, 0, 0],
[0, -1, 0],
[0, 0, 0]],
[[0, -1, 0],
[-1, 6, -1],
[0, -1, 0]],
[[0, 0, 0],
[0, -1, 0],
[0, 0, 0]]])
cases = []
cases.append(((1, 1, 1), np.array([[6]])))
cases.append(((2, 1, 1), np.array([[6, -1],
[-1, 6]])))
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:
result = stencil_grid(stencil, grid).toarray()
assert_equal(result, expected)
def test_1d(self):
stencil = array([1, 2, 3])
result = stencil_grid(stencil, (3,)).todense()
expected = matrix([[2, 3, 0],
[1, 2, 3],
[0, 1, 2]])
assert_equal(result, expected)
stencil = array([1, 2, 3, 4, 5])
result = stencil_grid(stencil, (5,)).todense()
expected = matrix([[3, 4, 5, 0, 0],
[2, 3, 4, 5, 0],
[1, 2, 3, 4, 5],
[0, 1, 2, 3, 4],
[0, 0, 1, 2, 3]])
assert_equal(result, expected)
def test_2d(self):
stencil = array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
result = stencil_grid(stencil, (2, 3)).todense()
expected = matrix([[5, 6, 0, 8, 9, 0], [4, 5, 6, 7, 8, 9],
[0, 4, 5, 0, 7, 8], [2, 3, 0, 5, 6, 0],
[1, 2, 3, 4, 5, 6], [0, 1, 2, 0, 4, 5]])
assert_equal(result, expected)
def test_2d(self):
stencil = array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
result = stencil_grid(stencil, (2, 3)).todense()
expected = matrix([[5, 6, 0, 8, 9, 0],
[4, 5, 6, 7, 8, 9],
[0, 4, 5, 0, 7, 8],
[2, 3, 0, 5, 6, 0],
[1, 2, 3, 4, 5, 6],
[0, 1, 2, 0, 4, 5]])
assert_equal(result, expected)
def test_poisson1d(self):
stencil = array([-1, 2, -1])
cases = []
cases.append(((1, ), matrix([[2]])))
cases.append(((2, ), matrix([[2, -1], [-1, 2]])))
cases.append(((4, ),
matrix([[2, -1, 0, 0], [-1, 2, -1, 0], [0, -1, 2, -1],
[0, 0, -1, 2]])))
for grid, expected in cases:
result = stencil_grid(stencil, grid).todense()
assert_equal(result, expected)
def test_poisson1d(self):
stencil = array([-1, 2, -1])
cases = []
cases.append(((1,), matrix([[2]])))
cases.append(((2,), matrix([[2, -1],
[-1, 2]])))
cases.append(((4,), matrix([[2, -1, 0, 0],
[-1, 2, -1, 0],
[0, -1, 2, -1],
[0, 0, -1, 2]])))
for grid, expected in cases:
result = stencil_grid(stencil, grid).todense()
assert_equal(result, expected)
def test_poisson2d_9pt(self):
stencil = array([[-1, -1, -1], [-1, 8, -1], [-1, -1, -1]])
cases = []
cases.append(((1, 1), matrix([[8]])))
cases.append(((2, 1), matrix([[8, -1], [-1, 8]])))
cases.append(((1, 2), matrix([[8, -1], [-1, 8]])))
cases.append(((1, 3), matrix([[8, -1, 0], [-1, 8, -1], [0, -1, 8]])))
cases.append(((2, 2),
matrix([[8, -1, -1, -1], [-1, 8, -1, -1],
[-1, -1, 8, -1], [-1, -1, -1, 8]])))
for grid, expected in cases:
result = stencil_grid(stencil, grid).todense()
assert_equal(result, expected)
def test_poisson2d_5pt(self):
stencil = np.array([[0, -1, 0], [-1, 4, -1], [0, -1, 0]])
cases = []
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]])))
for grid, expected in cases:
result = stencil_grid(stencil, grid).toarray()
assert_equal(result, expected)
def test_poisson2d_9pt(self):
stencil = array([[-1, -1, -1],
[-1, 8, -1],
[-1, -1, -1]])
cases = []
cases.append(((1, 1), matrix([[8]])))
cases.append(((2, 1), matrix([[8, -1],
[-1, 8]])))
cases.append(((1, 2), matrix([[8, -1],
[-1, 8]])))
cases.append(((1, 3), matrix([[8, -1, 0],
[-1, 8, -1],
[0, -1, 8]])))
cases.append(((2, 2), matrix([[8, -1, -1, -1],
[-1, 8, -1, -1],
[-1, -1, 8, -1],
[-1, -1, -1, 8]])))
for grid, expected in cases:
result = stencil_grid(stencil, grid).todense()
assert_equal(result, expected)
from copy import deepcopy
# ------------------------------------------------------------------------- #
# ------------------------------------------------------------------------- #
SOC = 'evol'
SOC_drop = 4.0
SA = 1 # Use SA type coarsening or CR
pow_G = 1
epsilon = 0.1
theta = 3.0 * math.pi / 16.0
N = 40
n = N * N
grid_dims = [N, N]
stencil = diffusion_stencil_2d(epsilon, theta)
A = stencil_grid(stencil, grid_dims, format='csr')
[d, d, A] = symmetric_rescaling(A)
A = csr_matrix(A)
B = np.kron(np.ones((A.shape[0] / 1, 1), dtype=A.dtype), np.eye(1))
tol = 1e-12 # Drop tolerance for singular values
if SA:
if SOC == 'evol':
C = evolution_strength_of_connection(A, B, epsilon=SOC_drop, k=2)
else:
SOC = 'symm'
C = symmetric_strength_of_connection(A, theta=SOC_drop)
AggOp, Cpts = standard_aggregation(C)
else:
splitting = CR(A, method='habituated')