def solve(self):
"""
Solve the optimization problem and return the optimized
parameters.
"""
bnd = self.bounds
econs = self.constraints[0][0]
emuls = self.constraints[0][1]
icons = self.constraints[1][0]
imuls = self.constraints[1][1]
if len(icons) > 0:
zeros = [i.clone() for i in imuls]
ibnds = [ROL.Bounds(z, isLower=True) for z in zeros]
else:
ibnds = []
rolproblem = ROL.OptimizationProblem(self.rolobjective,
self.rolvector,
bnd=bnd,
econs=econs,
emuls=emuls,
icons=icons,
imuls=imuls,
ibnds=ibnds)
x = self.rolvector
params = ROL.ParameterList(self.params_dict, "Parameters")
self.solver = ROL.OptimizationSolver(rolproblem, params)
self.solver.solve()
return self.problem.reduced_functional.controls.delist(x.dat)
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 run_HS13(Vec, params_dict):
obj = HS13_Obj()
x = Vec(2)
d = Vec(2)
HS13_initial_guess(x)
l = Vec(1)
l[0] = 1.0
icon = HS13_Icon()
ilower = Vec(1)
HS13_Ibnds(ilower)
ibnd = ROL.Bounds(ilower, isLower=True)
lower = Vec(2)
HS13_Bnd(lower)
bnd = ROL.Bounds(lower, isLower=True)
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(obj,
x,
bnd=bnd,
icons=[icon],
imuls=[l],
ibnds=[ibnd])
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
print(x[0], x[1])
assert HS13_minimum(x)
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 run_U(algo):
obj = MyObj()
paramsDict["Step"]["Type"] = algo
params = ROL.ParameterList(paramsDict, "Parameters")
x = NumpyVector(2)
optimProblem = ROL.OptimizationProblem(obj, x)
solver = ROL.OptimizationSolver(optimProblem, params)
solver.solve()
print(x.data)
assert round(x[0] - 1.0, 6) == 0.0
assert round(x[1], 6) == 0.0
def test_create_bounds_seperately():
obj = MyObj()
paramsDict["Step"]["Type"] = "Trust Region"
params = ROL.ParameterList(paramsDict, "Parameters")
x = NumpyVector(2)
bnd = createBounds()
bnd.test()
optimProblem = ROL.OptimizationProblem(obj, x, bnd=bnd)
solver = ROL.OptimizationSolver(optimProblem, params)
solver.solve()
assert round(x[0] - 0.7, 6) == 0.0
assert round(x[1], 6) == 0.0
def run_HS4(Vec, params_dict):
obj = HS4_Obj()
x = Vec(2)
HS4_initial_guess(x)
lower = Vec(2)
upper = Vec(2)
HS4_Bnd(lower, upper)
bnd = ROL.Bounds(lower, upper, 1.0)
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(obj, x, bnd=bnd)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
print(x[0], x[1])
assert HS4_minimum(x)
def run_E(algo):
obj = MyObj2()
paramsDict["Step"]["Type"] = algo
params = ROL.ParameterList(paramsDict, "Parameters")
x = NumpyVector(2)
x[0] = 0.5 * 0.5**2
x[1] = 0.5 * 0.5**2
l = NumpyVector(1)
con = EqConstraint()
optimProblem = ROL.OptimizationProblem(obj, x, econ=con, emul=l)
solver = ROL.OptimizationSolver(optimProblem, params)
solver.solve()
assert round(x[0] - 0.707106, 5) == 0.0
assert round(x[1] - 0.707106, 5) == 0.0
def run_HS28(Vec, params_dict):
obj = HS28_Obj()
x = Vec(3)
HS28_initial_guess(x)
# obj.checkGradient(x)
# obj.checkHessVec(x)
HS28_initial_guess(x)
l = Vec(1)
l[0] = 0.0
con = HS28_Econ()
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(obj, x, econs=[con], emuls=[l])
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
print(x[0], x[1], x[2])
assert HS28_minimum(x)
def run_B(algo):
obj = MyObj()
paramsDict["Step"]["Type"] = algo
params = ROL.ParameterList(paramsDict, "Parameters")
x = NumpyVector(2)
x_lo = NumpyVector(2)
x_lo[0] = -1
x_lo[1] = -1
x_up = NumpyVector(2)
x_up[0] = +0.7
x_up[1] = +0.7
bnd = ROL.Bounds(x_lo, x_up, 1.0)
optimProblem = ROL.OptimizationProblem(obj, x, bnd=bnd)
solver = ROL.OptimizationSolver(optimProblem, params)
solver.solve()
assert round(x[0] - 0.7, 6) == 0.0
assert round(x[1], 6) == 0.0
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)
def run_HS29(Vec, params_dict):
params = ROL.ParameterList(params_dict, "Parameters")
obj = HS29_Obj()
x = Vec(3)
x[0] = 1.
x[1] = 2.
x[2] = .1
d = Vec(3)
d[0] = 1
d[1] = -1
d[2] = 1.
v = Vec(3)
v[0] = 1
v[1] = -1
v[2] = 1.
# obj.checkGradient(x)
# obj.checkHessVec(x, d, 4, 1)
HS29_initial_guess(x)
l = Vec(1)
l[0] = 0.0
con = HS29_Icon()
jv = Vec(1)
jv[0] = 1.
# con.checkApplyJacobian(x, d, jv, 4, 1)
# con.checkAdjointConsistencyJacobian(jv, d, x)
# con.checkApplyAdjointHessian(x, jv, d, v, 5, 1)
ilower = Vec(1)
HS29_Ibnds(ilower)
ibnd = ROL.Bounds(ilower, isLower=True)
problem = ROL.OptimizationProblem(obj,
x,
icons=[con],
imuls=[l],
ibnds=[ibnd])
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
print(x[0], x[1], x[2])
assert HS29_minimum(x)
def rol_minimize(fun,
x0,
method=None,
jac=None,
hess=None,
hessp=None,
bounds=None,
constraints=(),
tol=None,
options={},
x_grad=None):
obj = ROLObj(fun, jac, hess, hessp)
if x_grad is not None:
print("Testing objective", flush=True)
xg = get_rol_numpy_vector(x_grad)
d = get_rol_numpy_vector(np.random.normal(0, 1, (x_grad.shape[0])))
obj.checkGradient(xg, d, 12, 1)
obj.checkHessVec(xg, d, 12, 1)
use_bfgs = False
if hess is None and hessp is None:
use_bfgs = True
if type(hess) == BFGS:
use_bfgs = True
for constr in constraints:
if (type(constr) != LinearConstraint
and (type(constr.hess) == BFGS or constr.hess is None)):
use_bfgs = True
constr.hess = None
assert method == 'rol-trust-constr' or method == None
if 'step-type' in options:
rol_method = options['step-type']
del options['step-type']
else:
rol_method = 'Augmented Lagrangian'
params = get_rol_parameters(rol_method, use_bfgs, options)
x = get_rol_numpy_vector(x0)
bnd, econ, emul, icon, imul, ibnd = get_constraints(
constraints, bounds, x_grad)
optimProblem = ROL.OptimizationProblem(obj,
x,
bnd=bnd,
econs=econ,
emuls=emul,
icons=icon,
imuls=imul,
ibnds=ibnd)
solver = ROL.OptimizationSolver(optimProblem, params)
solver.solve(options.get('verbose', 0))
state = solver.getAlgorithmState()
success = state.statusFlag.name == 'EXITSTATUS_CONVERGED'
res = OptimizeResult(
x=rol_vector_to_numpy(x),
fun=state.value,
cnorm=state.cnorm,
gnorm=state.gnorm,
snorm=state.snorm,
success=success,
nit=state.iter,
nfev=state.nfval,
ngev=state.ngrad,
constr_nfev=state.ncval,
status=state.statusFlag.name,
message=f'Optimization terminated early {state.statusFlag.name}')
return res
def test_create_problem_seperately():
paramsDict["Step"]["Type"] = "Trust Region"
params = ROL.ParameterList(paramsDict, "Parameters")
problem = get_problem()
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
'Gradient Tolerance': 1e-15,
'Relative Gradient Tolerance': 1e-10,
'Step Tolerance': 1e-16,
'Relative Step Tolerance': 1e-10,
'Iteration Limit': 30
}
}
params = ROL.ParameterList(paramsDict, "Parameters")
bound_constraint = ROL.Bounds(lower, upper, 1.0)
optimProblem = ROL.OptimizationProblem(obj,
x,
bnd=bound_constraint,
econ=volConstr,
emul=l_initializacao)
solver = ROL.OptimizationSolver(optimProblem, params)
solver.solve()
print("aqui mudouuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu")
q.assign(0.1)
interm = obj.resposta()
del x
interm = FeVector(interm.vector(), dot_product)
params2 = ROL.ParameterList(paramsDict2, "Parameters")
bound_constraint = ROL.Bounds(lower, upper, 1.0)
optimProblem = ROL.OptimizationProblem(obj,
interm,
bnd=bound_constraint,
econ=volConstr,
emul=l_initializacao)
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_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 *= 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
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)
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'
}
}
},
'Status Test': {
'Gradient Tolerance': 1e-5,
'Step Tolerance': 1e-6,
'Iteration Limit': 40
}
}
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
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)