def cmscr1d_img_pb(img: np.array,
alpha0: float, alpha1: float,
alpha2: float, alpha3: float,
beta: float, deriv='mesh') \
-> (np.array, np.array, float, float, bool):
"""Computes the L2-H1 mass conserving flow with source for a 1D image
sequence with spatio-temporal and convective regularisation with periodic
spatial boundary.
Args:
img (np.array): 1D image sequence of shape (m, n), where m is the
number of time steps and n is the number of pixels.
alpha0 (float): The spatial regularisation parameter for v.
alpha1 (float): The temporal regularisation parameter for v.
alpha2 (float): The spatial regularisation parameter for k.
alpha3 (float): The temporal regularisation parameter for k.
beta (float): The convective regularisation parameter.
deriv (str): Specifies how to approximate pertial derivatives.
When set to 'mesh' it uses FEniCS built in function.
Returns:
v (np.array): A velocity array of shape (m, n).
k (np.array): A source array of shape (m, n).
res (float): The residual.
fun (float): The function value.
converged (bool): True if Newton's method converged.
"""
# Check for valid arguments.
valid = {'mesh'}
if deriv not in valid:
raise ValueError("Argument 'deriv' must be one of %r." % valid)
# Create mesh.
m, n = img.shape
mesh = UnitSquareMesh(m - 1, n - 1)
# Define function space.
V = dh.create_function_space(mesh, 'periodic')
W = dh.create_vector_function_space(mesh, 'periodic')
# Convert array to function.
f = Function(V)
f.vector()[:] = dh.img2funvec_pb(img)
# Compute partial derivatives.
ft, fx = f.dx(0), f.dx(1)
# Compute velocity.
v, k, res, fun, converged = cmscr1d_weak_solution(W, f, ft, fx, alpha0,
alpha1, alpha2, alpha3,
beta)
# Convert back to array and return.
v = dh.funvec2img(v.vector().get_local(), m, n)
k = dh.funvec2img(k.vector().get_local(), m, n)
return v, k, res, fun, converged
def cm1d_img_pb(img: np.array,
alpha0: float,
alpha1: float,
deriv='mesh') -> np.array:
"""Computes the L2-H1 mass conserving flow for a 1D image sequence with
periodic spatial boundary.
Allows to specify how to approximate partial derivatives of f numerically.
Note that the last column of img is ignored.
Args:
img (np.array): 1D image sequence of shape (m, n), where m is the
number of time steps and n is the number of pixels.
alpha0 (float): Spatial regularisation parameter.
alpha1 (float): Temporal regularisation parameter.
deriv (str): Specifies how to approximate pertial derivatives.
When set to 'mesh' it uses FEniCS built in function.
Returns:
v (np.array): A velocity array of shape (m, n).
res (float): The residual.
func (float): The value of the functional.
"""
# Check for valid arguments.
valid = {'mesh'}
if deriv not in valid:
raise ValueError("Argument 'deriv' must be one of %r." % valid)
# Create mesh.
m, n = img.shape
mesh = UnitSquareMesh(m - 1, n - 1)
# Define function space.
V = dh.create_function_space(mesh, 'periodic')
# Convert array to function.
f = Function(V)
f.vector()[:] = dh.img2funvec_pb(img)
# Compute partial derivatives.
ft, fx = f.dx(0), f.dx(1)
# Compute velocity.
v, res, fun = cm1d_weak_solution(V, f, ft, fx, alpha0, alpha1)
# Convert to array and return.
return dh.funvec2img_pb(v.vector().get_local(), m, n), res, fun
def test_img2funvec_pb(self):
m, n = 3, 4
img = np.ones((m, n))
v = dh.img2funvec_pb(img)
np.testing.assert_allclose(v, np.ones(m * (n - 1)))
def test_img2fun_fun2img_pb(self):
m, n = 7, 13
img = np.random.rand(m, n)
v = dh.img2funvec_pb(img)
np.testing.assert_allclose(
dh.funvec2img_pb(v, m, n)[:, 1:], img[:, 1:])