def test_checkpointing(controlspace_t):
mesh = fd.UnitSquareMesh(5, 5)
if controlspace_t == fs.BsplineControlSpace:
bbox = [(-1, 2), (-1, 2)]
orders = [2, 2]
levels = [4, 4]
Q = fs.BsplineControlSpace(mesh, bbox, orders, levels)
elif controlspace_t == fs.FeMultiGridControlSpace:
Q = fs.FeMultiGridControlSpace(mesh, refinements=1, order=2)
else:
Q = controlspace_t(mesh)
inner = fs.H1InnerProduct(Q)
q = fs.ControlVector(Q, inner)
p = fs.ControlVector(Q, inner)
from firedrake.petsc import PETSc
rand = PETSc.Random().create(mesh.comm)
rand.setInterval((1, 2))
q.vec_wo().setRandom(rand)
Q.store(q)
Q.load(p)
assert q.norm() > 0
assert abs(q.norm()-p.norm()) < 1e-14
p.axpy(-1, q)
assert p.norm() < 1e-14
def run_L2tracking_optimization(write_output=False):
""" Test template for fsz.LevelsetFunctional."""
# tool for developing new tests, allows storing shape iterates
if write_output:
out = fd.File("domain.pvd")
def cb(*args):
out.write(Q.mesh_m.coordinates)
cb()
else:
cb = None
# setup problem
mesh = fd.UnitSquareMesh(30, 30)
Q = fs.FeControlSpace(mesh)
inner = fs.ElasticityInnerProduct(Q)
q = fs.ControlVector(Q, inner)
# setup PDE constraint
mesh_m = Q.mesh_m
e = PoissonSolver(mesh_m)
# create PDEconstrained objective functional
J_ = L2trackingObjective(e, Q, cb=cb)
J = fs.ReducedObjective(J_, e)
# ROL parameters
params_dict = {
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 10
}
},
'Step': {
'Type': 'Line Search',
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
},
},
'Status Test': {
'Gradient Tolerance': 1e-4,
'Step Tolerance': 1e-5,
'Iteration Limit': 15
}
}
# assemble and solve ROL optimization problem
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
# verify that the norm of the gradient at optimum is small enough
state = solver.getAlgorithmState()
assert (state.gnorm < 1e-4)
def test_equality_constraint(pytestconfig):
mesh = fs.DiskMesh(0.05, radius=2.)
Q = fs.FeControlSpace(mesh)
inner = fs.ElasticityInnerProduct(Q, direct_solve=True)
mesh_m = Q.mesh_m
(x, y) = fd.SpatialCoordinate(mesh_m)
q = fs.ControlVector(Q, inner)
if pytestconfig.getoption("verbose"):
out = fd.File("domain.pvd")
def cb(*args):
out.write(Q.mesh_m.coordinates)
else:
cb = None
f = (pow(2 * x, 2)) + pow(y - 0.1, 2) - 1.2
J = fsz.LevelsetFunctional(f, Q, cb=cb)
vol = fsz.LevelsetFunctional(fd.Constant(1.0), Q)
e = fs.EqualityConstraint([vol])
emul = ROL.StdVector(1)
params_dict = {
'Step': {
'Type': 'Augmented Lagrangian',
'Augmented Lagrangian': {
'Subproblem Step Type': 'Line Search',
'Penalty Parameter Growth Factor': 2.,
'Initial Penalty Parameter': 1.,
'Subproblem Iteration Limit': 20,
},
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
},
},
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 5
}
},
'Status Test': {
'Gradient Tolerance': 1e-4,
'Step Tolerance': 1e-10,
'Iteration Limit': 10
}
}
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q, econ=e, emul=emul)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
state = solver.getAlgorithmState()
assert (state.gnorm < 1e-4)
assert (state.cnorm < 1e-6)
def test_TimeTracking():
""" Main test."""
# setup problem
mesh = fd.UnitSquareMesh(20, 20)
Q = fs.FeControlSpace(mesh)
inner = fs.LaplaceInnerProduct(Q, fixed_bids=[1, 2, 3, 4])
q = fs.ControlVector(Q, inner)
# create PDEconstrained objective functional
J = TimeTracking(Q)
# ROL parameters
params_dict = {
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 25
}
},
'Step': {
'Type': 'Trust Region'
},
'Status Test': {
'Gradient Tolerance': 1e-3,
'Step Tolerance': 1e-8,
'Iteration Limit': 20
}
}
# assemble and solve ROL optimization problem
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
# verify that the norm of the gradient at optimum is small enough
state = solver.getAlgorithmState()
assert (state.gnorm < 1e-3)
# mesh = fd.UnitSquareMesh(n, n)
mesh = fd.Mesh("UnitSquareCrossed.msh")
mesh = fd.MeshHierarchy(mesh, 1)[-1]
Q = fs.FeMultiGridControlSpace(mesh, refinements=3, order=2)
inner = fs.LaplaceInnerProduct(Q)
mesh_m = Q.mesh_m
V_m = fd.FunctionSpace(mesh_m, "CG", 1)
f_m = fd.Function(V_m)
(x, y) = fd.SpatialCoordinate(mesh_m)
f = (pow(x - 0.5, 2)) + pow(y - 0.5, 2) - 2.
out = fd.File("domain.pvd")
J = fsz.LevelsetFunctional(f, Q, cb=lambda: out.write(mesh_m.coordinates))
q = fs.ControlVector(Q, inner)
params_dict = {
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 5
}
},
'Step': {
'Type': 'Line Search',
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
}
def test_levelset(dim, inner_t, controlspace_t, use_extension, pytestconfig):
verbose = pytestconfig.getoption("verbose")
""" Test template for fsz.LevelsetFunctional."""
clscale = 0.1 if dim == 2 else 0.2
# make the mesh a bit coarser if we are using a multigrid control space as
# we are refining anyway
if controlspace_t == fs.FeMultiGridControlSpace:
clscale *= 4
if dim == 2:
mesh = fs.DiskMesh(clscale)
elif dim == 3:
mesh = fs.SphereMesh(clscale)
else:
raise NotImplementedError
if controlspace_t == fs.BsplineControlSpace:
if dim == 2:
bbox = [(-2, 2), (-2, 2)]
orders = [2, 2]
levels = [4, 4]
else:
bbox = [(-3, 3), (-3, 3), (-3, 3)]
orders = [2, 2, 2]
levels = [3, 3, 3]
Q = fs.BsplineControlSpace(mesh, bbox, orders, levels)
elif controlspace_t == fs.FeMultiGridControlSpace:
Q = fs.FeMultiGridControlSpace(mesh, refinements=1, order=2)
else:
Q = controlspace_t(mesh)
inner = inner_t(Q)
# if running with -v or --verbose, then export the shapes
if verbose:
out = fd.File("domain.pvd")
def cb(*args):
out.write(Q.mesh_m.coordinates)
cb()
else:
cb = None
# levelset test case
if dim == 2:
(x, y) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x, 2)) + pow(1.3 * y, 2) - 1.
elif dim == 3:
(x, y, z) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x, 2)) + pow(0.8 * y, 2) + pow(1.3 * z, 2) - 1.
else:
raise NotImplementedError
J = fsz.LevelsetFunctional(f, Q, cb=cb, scale=0.1)
if use_extension == "w_ext":
ext = fs.ElasticityExtension(Q.V_r)
if use_extension == "w_ext_fixed_dim":
ext = fs.ElasticityExtension(Q.V_r, fixed_dims=[0])
else:
ext = None
q = fs.ControlVector(Q, inner, boundary_extension=ext)
# these tolerances are not very stringent, but solutions are correct with
# tighter tolerances, the combination
# FeMultiGridControlSpace-ElasticityInnerProduct fails because the mesh
# self-intersects (one should probably be more careful with the opt params)
grad_tol = 1e-1
itlim = 15
itlimsub = 15
# Volume constraint
vol = fsz.LevelsetFunctional(fd.Constant(1.0), Q, scale=1)
initial_vol = vol.value(q, None)
econ = fs.EqualityConstraint([vol], target_value=[initial_vol])
emul = ROL.StdVector(1)
# ROL parameters
params_dict = {
'Step': {
'Type': 'Augmented Lagrangian',
'Augmented Lagrangian': {
'Subproblem Step Type': 'Line Search',
'Penalty Parameter Growth Factor': 1.05,
'Print Intermediate Optimization History': True,
'Subproblem Iteration Limit': itlimsub
},
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
},
},
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 50
}
},
'Status Test': {
'Gradient Tolerance': grad_tol,
'Step Tolerance': 1e-10,
'Iteration Limit': itlim
}
}
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q, econ=econ, emul=emul)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
# verify that the norm of the gradient at optimum is small enough
# and that the volume has not changed too much
state = solver.getAlgorithmState()
assert (state.gnorm < grad_tol)
assert abs(vol.value(q, None) - initial_vol) < 1e-2
Q = fs.FeMultiGridControlSpace(mesh, refinements=4, order=2)
# Q = fs.FeControlSpace(mesh)
# inner = fs.SurfaceInnerProduct(Q)
inner = fs.ElasticityInnerProduct(Q)
extension = fs.ElasticityExtension(Q.V_r, direct_solve=True)
mesh_m = Q.mesh_m
if dim == 2:
(x, y) = fd.SpatialCoordinate(mesh_m)
f = (pow(x, 2)) + pow(0.5 * y, 2) - 1.
else:
(x, y, z) = fd.SpatialCoordinate(mesh_m)
f = (pow(x - 0.5, 2)) + pow(y - 0.5, 2) + pow(z - 0.5, 2) - 2.
q = fs.ControlVector(Q, inner, boundary_extension=extension)
out = fd.File("domain.pvd")
J = fsz.LevelsetFunctional(f, Q, cb=lambda: out.write(mesh_m.coordinates))
J.cb()
g = q.clone()
J.update(q, None, 1)
J.gradient(g, q, None)
g.scale(-0.3)
J.update(g, None, 1)
J.checkGradient(q, g, 9, 1)
params_dict = {
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 25
def test_regularization(controlspace_t, use_extension):
n = 10
mesh = fd.UnitSquareMesh(n, n)
if controlspace_t == fs.FeMultiGridControlSpace:
Q = fs.FeMultiGridControlSpace(mesh, refinements=1, order=2)
else:
Q = controlspace_t(mesh)
if use_extension:
inner = fs.SurfaceInnerProduct(Q)
ext = fs.ElasticityExtension(Q.V_r)
else:
inner = fs.LaplaceInnerProduct(Q)
ext = None
q = fs.ControlVector(Q, inner, boundary_extension=ext)
X = fd.SpatialCoordinate(mesh)
q.fun.interpolate(0.5 * X)
lower_bound = Q.T.copy(deepcopy=True)
lower_bound.interpolate(fd.Constant((-0.0, -0.0)))
upper_bound = Q.T.copy(deepcopy=True)
upper_bound.interpolate(fd.Constant((+1.3, +0.9)))
J1 = fsz.MoYoBoxConstraint(1, [1, 2, 3, 4],
Q,
lower_bound=lower_bound,
upper_bound=upper_bound)
J2 = fsz.MoYoSpectralConstraint(1, fd.Constant(0.2), Q)
J3 = fsz.DeformationRegularization(Q,
l2_reg=.1,
sym_grad_reg=1.,
skew_grad_reg=.5)
if isinstance(Q, fs.FeMultiGridControlSpace):
J4 = fsz.CoarseDeformationRegularization(Q,
l2_reg=.1,
sym_grad_reg=1.,
skew_grad_reg=.5)
Js = 0.1 * J1 + J2 + 2. * (J3 + J4)
else:
Js = 0.1 * J1 + J2 + 2. * J3
g = q.clone()
def run_taylor_test(J):
J.update(q, None, 1)
J.gradient(g, q, None)
return J.checkGradient(q, g, 7, 1)
def check_result(test_result):
for i in range(len(test_result) - 1):
assert test_result[i + 1][3] <= test_result[i][3] * 0.11
check_result(run_taylor_test(J1))
check_result(run_taylor_test(J2))
check_result(run_taylor_test(J3))
if isinstance(Q, fs.FeMultiGridControlSpace):
check_result(run_taylor_test(J4))
check_result(run_taylor_test(Js))
out = fd.File("output/%s.pvd" % label)
if args.spectral:
Js = fsz.MoYoSpectralConstraint(1e3, fd.Constant(0.5), Q)
J = J + Js
if args.tikhonov > 0:
Jt = args.tikhonov * fsz.CoarseDeformationRegularization(extension, Q)
J = J + Jt
if args.smooth:
control_constraint = fs.InteriorControlConstraint(Q.V_r_coarse,
form=extension)
else:
dirichlet_extension = None
control_constraint = None
q = fs.ControlVector(Q, innerp, control_constraint=control_constraint)
vol = fsz.LevelsetFunctional(fd.Constant(10.0), Q)
if args.problem == "pipe":
econ_unscaled = fs.EqualityConstraint([vol])
def wrap(f):
return fs.DeformationCheckObjective(
f,
delta_threshold=0.25 if args.dim == 2 else 0.25, # noqa
strict=False)
scale = 1e1
J = wrap(scale * J)
volweight = 0.1 if args.dim == 2 else 1.
vol = wrap(volweight * scale**0.5 * vol)
econ = fs.EqualityConstraint([vol])
def test_box_constraint(pytestconfig):
n = 5
mesh = fd.UnitSquareMesh(n, n)
T = mesh.coordinates.copy(deepcopy=True)
(x, y) = fd.SpatialCoordinate(mesh)
T.interpolate(T + fd.Constant((1, 0)) * x * y)
mesh = fd.Mesh(T)
Q = fs.FeControlSpace(mesh)
inner = fs.LaplaceInnerProduct(Q, fixed_bids=[1])
mesh_m = Q.mesh_m
q = fs.ControlVector(Q, inner)
if pytestconfig.getoption("verbose"):
out = fd.File("domain.pvd")
def cb():
out.write(mesh_m.coordinates)
else:
def cb():
pass
lower_bound = Q.T.copy(deepcopy=True)
lower_bound.interpolate(fd.Constant((-0.0, -0.0)))
upper_bound = Q.T.copy(deepcopy=True)
upper_bound.interpolate(fd.Constant((+1.3, +0.9)))
J = fsz.MoYoBoxConstraint(1, [2],
Q,
lower_bound=lower_bound,
upper_bound=upper_bound,
cb=cb,
quadrature_degree=100)
g = q.clone()
J.gradient(g, q, None)
taylor_result = J.checkGradient(q, g, 9, 1)
for i in range(len(taylor_result) - 1):
if taylor_result[i][3] > 1e-7:
assert taylor_result[i + 1][3] <= taylor_result[i][3] * 0.11
params_dict = {
'Step': {
'Type': 'Line Search',
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
}
},
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 2
}
},
'Status Test': {
'Gradient Tolerance': 1e-10,
'Step Tolerance': 1e-10,
'Iteration Limit': 150
}
}
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
Tvec = Q.T.vector()
nodes = fd.DirichletBC(Q.V_r, fd.Constant((0.0, 0.0)), [2]).nodes
assert np.all(Tvec[nodes, 0] <= 1.3 + 1e-4)
assert np.all(Tvec[nodes, 1] <= 0.9 + 1e-4)
def test_objective_plus_box_constraint(pytestconfig):
n = 10
mesh = fd.UnitSquareMesh(n, n)
T = mesh.coordinates.copy(deepcopy=True)
(x, y) = fd.SpatialCoordinate(mesh)
T.interpolate(T + fd.Constant((0, 0)))
mesh = fd.Mesh(T)
Q = fs.FeControlSpace(mesh)
inner = fs.LaplaceInnerProduct(Q)
mesh_m = Q.mesh_m
q = fs.ControlVector(Q, inner)
if pytestconfig.getoption("verbose"):
out = fd.File("domain.pvd")
def cb():
out.write(mesh_m.coordinates)
else:
def cb():
pass
lower_bound = Q.T.copy(deepcopy=True)
lower_bound.interpolate(fd.Constant((-0.2, -0.2)))
upper_bound = Q.T.copy(deepcopy=True)
upper_bound.interpolate(fd.Constant((+1.2, +1.2)))
# levelset test case
(x, y) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x - 0.5, 2)) + pow(y - 0.5, 2) - 4.
J1 = fsz.LevelsetFunctional(f, Q, cb=cb, quadrature_degree=10)
J2 = fsz.MoYoBoxConstraint(10., [1, 2, 3, 4],
Q,
lower_bound=lower_bound,
upper_bound=upper_bound,
cb=cb,
quadrature_degree=10)
J3 = fsz.MoYoSpectralConstraint(100,
fd.Constant(0.6),
Q,
cb=cb,
quadrature_degree=100)
J = 0.1 * J1 + J2 + J3
g = q.clone()
J.gradient(g, q, None)
taylor_result = J.checkGradient(q, g, 9, 1)
for i in range(len(taylor_result) - 1):
if taylor_result[i][3] > 1e-6 and taylor_result[i][3] < 1e-3:
assert taylor_result[i + 1][3] <= taylor_result[i][3] * 0.15
params_dict = {
'Step': {
'Type': 'Line Search',
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
}
},
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 2
}
},
'Status Test': {
'Gradient Tolerance': 1e-10,
'Step Tolerance': 1e-10,
'Iteration Limit': 10
}
}
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
Tvec = Q.T.vector()
nodes = fd.DirichletBC(Q.V_r, fd.Constant((0.0, 0.0)), [2]).nodes
assert np.all(Tvec[nodes, 0] <= 1.2 + 1e-1)
assert np.all(Tvec[nodes, 1] <= 1.2 + 1e-1)
def test_spectral_constraint(pytestconfig):
n = 5
mesh = fd.UnitSquareMesh(n, n)
T = fd.Function(fd.VectorFunctionSpace(
mesh, "CG",
1)).interpolate(fd.SpatialCoordinate(mesh) - fd.Constant((0.5, 0.5)))
mesh = fd.Mesh(T)
Q = fs.FeControlSpace(mesh)
inner = fs.LaplaceInnerProduct(Q)
mesh_m = Q.mesh_m
q = fs.ControlVector(Q, inner)
if pytestconfig.getoption("verbose"):
out = fd.File("domain.pvd")
def cb():
out.write(mesh_m.coordinates)
else:
def cb():
pass
J = fsz.MoYoSpectralConstraint(0.5, fd.Constant(0.1), Q, cb=cb)
q.fun += Q.T
g = q.clone()
J.update(q, None, -1)
J.gradient(g, q, None)
cb()
taylor_result = J.checkGradient(q, g, 7, 1)
for i in range(len(taylor_result) - 1):
assert taylor_result[i + 1][3] <= taylor_result[i][3] * 0.11
params_dict = {
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 2
}
},
'Step': {
'Type': 'Line Search',
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
}
},
'Status Test': {
'Gradient Tolerance': 1e-10,
'Step Tolerance': 1e-10,
'Iteration Limit': 150
}
}
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
Tvec = Q.T.vector()[:, :]
for i in range(Tvec.shape[0]):
assert abs(Tvec[i, 0]) < 0.55 + 1e-4
assert abs(Tvec[i, 1]) < 0.55 + 1e-4
assert np.any(np.abs(Tvec) > 0.55 - 1e-4)
mu_cr = mu_base / args.alpha
inner = CauchyRiemannAugmentation(mu_cr, inner)
mesh_m = Q.mesh_m
(x, y) = fd.SpatialCoordinate(mesh_m)
a = 0.8
b = 2.0
expr = (fd.sqrt((x - a)**2 + b * y**2) - 1) \
* (fd.sqrt((x + a)**2 + b * y**2) - 1) \
* (fd.sqrt(b * x**2 + (y - a)**2) - 1) \
* (fd.sqrt(b * x**2 + (y + a)**2) - 1) - 0.001
J = 0.1 * fsz.LevelsetFunctional(expr, Q, quadrature_degree=5)
q = fs.ControlVector(Q, inner)
params_dict = {
"General": {
"Secant": {
"Type": "Limited-Memory BFGS",
"Maximum Storage": 1
}
},
"Step": {
"Type": "Line Search",
"Line Search": {
"Descent Method": {
"Type": "Quasi-Newton Step"
}
}
if not os.path.exists(directory):
os.makedirs(directory, exist_ok=True)
out = fd.File(directory + "u.pvd")
vol = fsz.LevelsetFunctional(fd.Constant(1.0), Q)
baryx = fsz.LevelsetFunctional(x, Q)
baryy = fsz.LevelsetFunctional(y, Q)
econ = fs.EqualityConstraint([vol, baryx, baryy])
emul = ROL.StdVector(3)
econ_val = ROL.StdVector(3)
Je = fsz.EnergyObjective(e, Q, cb=None)
Jr = fs.ReducedObjective(Je, e)
# J = 2e-4 * Jr
J = 1e-2 * Jr
q = fs.ControlVector(Q, inner)
params_dict = {
"General": {
"Secant": {
"Type": "Limited-Memory BFGS",
"Maximum Storage": 5
}
},
"Step": {
"Type": "Augmented Lagrangian",
"Line Search": {
"Descent Method": {
"Type": "Quasi-Newton Step"
}
},
def test_periodic(dim, inner_t, use_extension, pytestconfig):
verbose = pytestconfig.getoption("verbose")
""" Test template for PeriodicControlSpace."""
if dim == 2:
mesh = fd.PeriodicUnitSquareMesh(30, 30)
elif dim == 3:
mesh = fd.PeriodicUnitCubeMesh(20, 20, 20)
else:
raise NotImplementedError
Q = fs.FeControlSpace(mesh)
inner = inner_t(Q)
# levelset test case
V = fd.FunctionSpace(Q.mesh_m, "DG", 0)
sigma = fd.Function(V)
if dim == 2:
x, y = fd.SpatialCoordinate(Q.mesh_m)
g = fd.sin(y * np.pi) # truncate at bdry
f = fd.cos(2 * np.pi * x) * g
perturbation = 0.05 * fd.sin(x * np.pi) * g**2
sigma.interpolate(g * fd.cos(2 * np.pi * x * (1 + perturbation)))
elif dim == 3:
x, y, z = fd.SpatialCoordinate(Q.mesh_m)
g = fd.sin(y * np.pi) * fd.sin(z * np.pi) # truncate at bdry
f = fd.cos(2 * np.pi * x) * g
perturbation = 0.05 * fd.sin(x * np.pi) * g**2
sigma.interpolate(g * fd.cos(2 * np.pi * x * (1 + perturbation)))
else:
raise NotImplementedError
class LevelsetFct(fs.ShapeObjective):
def __init__(self, sigma, f, *args, **kwargs):
super().__init__(*args, **kwargs)
self.sigma = sigma # initial
self.f = f # target
Vdet = fd.FunctionSpace(Q.mesh_r, "DG", 0)
self.detDT = fd.Function(Vdet)
def value_form(self):
# volume integral
self.detDT.interpolate(fd.det(fd.grad(self.Q.T)))
if min(self.detDT.vector()) > 0.05:
integrand = (self.sigma - self.f)**2
else:
integrand = np.nan * (self.sigma - self.f)**2
return integrand * fd.dx(metadata={"quadrature_degree": 1})
# if running with -v or --verbose, then export the shapes
if verbose:
out = fd.File("sigma.pvd")
def cb(*args):
out.write(sigma)
else:
cb = None
J = LevelsetFct(sigma, f, Q, cb=cb)
if use_extension == "w_ext":
ext = fs.ElasticityExtension(Q.V_r)
if use_extension == "w_ext_fixed_dim":
ext = fs.ElasticityExtension(Q.V_r, fixed_dims=[0])
else:
ext = None
q = fs.ControlVector(Q, inner, boundary_extension=ext)
"""
move mesh a bit to check that we are not doing the
taylor test in T=id
"""
g = q.clone()
J.gradient(g, q, None)
q.plus(g)
J.update(q, None, 1)
""" Start taylor test """
J.gradient(g, q, None)
res = J.checkGradient(q, g, 5, 1)
errors = [l[-1] for l in res]
assert (errors[-1] < 0.11 * errors[-2])
q.scale(0)
""" End taylor test """
# ROL parameters
grad_tol = 1e-4
params_dict = {
'Step': {
'Type': 'Trust Region'
},
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 25
}
},
'Status Test': {
'Gradient Tolerance': grad_tol,
'Step Tolerance': 1e-10,
'Iteration Limit': 40
}
}
# assemble and solve ROL optimization problem
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
# verify that the norm of the gradient at optimum is small enough
state = solver.getAlgorithmState()
assert (state.gnorm < grad_tol)
def test_levelset(dim, inner_t, controlspace_t, use_extension, pytestconfig):
verbose = pytestconfig.getoption("verbose")
""" Test template for fsz.LevelsetFunctional."""
clscale = 0.1 if dim == 2 else 0.2
# make the mesh a bit coarser if we are using a multigrid control space as
# we are refining anyway
if controlspace_t == fs.FeMultiGridControlSpace:
clscale *= 2
if dim == 2:
mesh = fs.DiskMesh(clscale)
elif dim == 3:
mesh = fs.SphereMesh(clscale)
else:
raise NotImplementedError
if controlspace_t == fs.BsplineControlSpace:
if dim == 2:
bbox = [(-2, 2), (-2, 2)]
orders = [2, 2]
levels = [4, 4]
else:
bbox = [(-3, 3), (-3, 3), (-3, 3)]
orders = [2, 2, 2]
levels = [3, 3, 3]
Q = fs.BsplineControlSpace(mesh, bbox, orders, levels)
elif controlspace_t == fs.FeMultiGridControlSpace:
Q = fs.FeMultiGridControlSpace(mesh, refinements=1, order=2)
else:
Q = controlspace_t(mesh)
inner = inner_t(Q)
# if running with -v or --verbose, then export the shapes
if verbose:
out = fd.File("domain.pvd")
def cb(*args):
out.write(Q.mesh_m.coordinates)
cb()
else:
cb = None
# levelset test case
if dim == 2:
(x, y) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x, 2)) + pow(1.3 * y, 2) - 1.
elif dim == 3:
(x, y, z) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x, 2)) + pow(0.8 * y, 2) + pow(1.3 * z, 2) - 1.
else:
raise NotImplementedError
J = fsz.LevelsetFunctional(f, Q, cb=cb, scale=0.1)
if use_extension == "w_ext":
ext = fs.ElasticityExtension(Q.V_r)
if use_extension == "w_ext_fixed_dim":
ext = fs.ElasticityExtension(Q.V_r, fixed_dims=[0])
else:
ext = None
q = fs.ControlVector(Q, inner, boundary_extension=ext)
"""
move mesh a bit to check that we are not doing the
taylor test in T=id
"""
g = q.clone()
J.gradient(g, q, None)
q.plus(g)
J.update(q, None, 1)
""" Start taylor test """
J.gradient(g, q, None)
res = J.checkGradient(q, g, 5, 1)
errors = [l[-1] for l in res]
assert (errors[-1] < 0.11 * errors[-2])
q.scale(0)
""" End taylor test """
grad_tol = 1e-6 if dim == 2 else 1e-4
# ROL parameters
params_dict = {
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 50
}
},
'Step': {
'Type': 'Line Search',
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
}
},
'Status Test': {
'Gradient Tolerance': grad_tol,
'Step Tolerance': 1e-10,
'Iteration Limit': 150
}
}
# assemble and solve ROL optimization problem
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
# verify that the norm of the gradient at optimum is small enough
state = solver.getAlgorithmState()
assert (state.gnorm < grad_tol)
