def transpose_operators(operators):
out = [None, None]
for i in range(2):
op = operators[i]
if op is None:
out[i] = None
elif isinstance(op, dolfin.cpp.GenericMatrix):
out[i] = op.__class__()
dolfin.assemble(dolfin.adjoint(op.form), tensor=out[i])
if hasattr(op, 'bcs'):
adjoint_bcs = [utils.homogenize(bc) for bc in op.bcs if isinstance(bc, dolfin.cpp.DirichletBC)] + [bc for bc in op.bcs if not isinstance(bc, dolfin.DirichletBC)]
[bc.apply(out[i]) for bc in adjoint_bcs]
elif isinstance(op, dolfin.Form) or isinstance(op, ufl.form.Form):
out[i] = dolfin.adjoint(op)
if hasattr(op, 'bcs'):
out[i].bcs = [utils.homogenize(bc) for bc in op.bcs if isinstance(bc, dolfin.cpp.DirichletBC)] + [bc for bc in op.bcs if not isinstance(bc, dolfin.DirichletBC)]
elif isinstance(op, AdjointKrylovMatrix):
pass
else:
print "op.__class__: ", op.__class__
raise libadjoint.exceptions.LibadjointErrorNotImplemented("Don't know how to transpose anything else!")
return out
def basic_solve(self, var, b):
if isinstance(self.data, IdentityMatrix):
x=b.duplicate()
x.axpy(1.0, b)
if isinstance(x.data, ufl.Form):
x = Vector(backend.Function(x.fn_space, backend.assemble(x.data)))
else:
if var.type in ['ADJ_TLM', 'ADJ_ADJOINT', 'ADJ_SOA']:
dirichlet_bcs = [utils.homogenize(bc) for bc in self.bcs if isinstance(bc, backend.DirichletBC)]
other_bcs = [bc for bc in self.bcs if not isinstance(bc, backend.DirichletBC)]
bcs = dirichlet_bcs + other_bcs
else:
bcs = self.bcs
test = self.test_function()
#FIXME: This is a hack, the test and trial function should carry
# the MultiMeshFunctionSpace as an attribute
if hasattr(test, '_V_multi'):
x = Vector(backend.MultiMeshFunction(test._V_multi))
else:
x = Vector(backend.Function(test.function_space()))
#print "b.data is a %s in the solution of %s" % (b.data.__class__, var)
if b.data is None and not hasattr(b, 'nonlinear_form'):
# This means we didn't get any contribution on the RHS of the adjoint system. This could be that the
# simulation ran further ahead than when the functional was evaluated, or it could be that the
# functional is set up incorrectly.
backend.warning("Warning: got zero RHS for the solve associated with variable %s" % var)
elif isinstance(b.data, backend.Function):
assembled_lhs = self.assemble_data()
[bc.apply(assembled_lhs) for bc in bcs]
assembled_rhs = compatibility.assembled_rhs(b)
[bc.apply(assembled_rhs) for bc in bcs]
wrap_solve(assembled_lhs, x.data, assembled_rhs, self.solver_parameters)
else:
if hasattr(b, 'nonlinear_form'): # was a nonlinear solve
x = compatibility.assign_function_to_vector(x, b.nonlinear_u, function_space = test.function_space())
F = backend.replace(b.nonlinear_form, {b.nonlinear_u: x.data})
J = backend.replace(b.nonlinear_J, {b.nonlinear_u: x.data})
try:
compatibility.solve(F == 0, x.data, b.nonlinear_bcs, J=J, solver_parameters=self.solver_parameters)
except RuntimeError as rte:
x.data.vector()[:] = float("nan")
else:
assembled_lhs = self.assemble_data()
[bc.apply(assembled_lhs) for bc in bcs]
assembled_rhs = wrap_assemble(b.data, test)
[bc.apply(assembled_rhs) for bc in bcs]
wrap_solve(assembled_lhs, x.data, assembled_rhs, self.solver_parameters)
return x
def diag_assembly_cb(dependencies, values, hermitian, coefficient, context):
"""This callback must conform to the libadjoint Python block assembly
interface. It returns either the form or its transpose, depending on
the value of the logical hermitian."""
assert coefficient == 1
value_coeffs = [v.data for v in values]
expressions.update_expressions(frozen_expressions)
constant.update_constants(frozen_constants)
eq_l = backend.replace(eq_lhs, dict(zip(diag_coeffs, value_coeffs)))
kwargs = {"cache": eq_l in caching.assembled_fwd_forms} # should we cache our matrices on the way backwards?
if hermitian:
# Homogenise the adjoint boundary conditions. This creates the adjoint
# solution associated with the lifted discrete system that is actually solved.
adjoint_bcs = [utils.homogenize(bc) for bc in eq_bcs if isinstance(bc, backend.DirichletBC)] + [
bc for bc in eq_bcs if not isinstance(bc, backend.DirichletBC)
]
if len(adjoint_bcs) == 0:
adjoint_bcs = None
else:
adjoint_bcs = misc.uniq(adjoint_bcs)
kwargs["bcs"] = adjoint_bcs
kwargs["solver_parameters"] = solver_parameters
kwargs["adjoint"] = True
if initial_guess:
kwargs["initial_guess"] = value_coeffs[dependencies.index(initial_guess_var)]
if replace_map:
kwargs["replace_map"] = dict(zip(diag_coeffs, value_coeffs))
return (
matrix_class(
backend.adjoint(eq_l, reordered_arguments=ufl.algorithms.extract_arguments(eq_l)), **kwargs
),
adjlinalg.Vector(None, fn_space=u.function_space()),
)
else:
kwargs["bcs"] = misc.uniq(eq_bcs)
kwargs["solver_parameters"] = solver_parameters
kwargs["adjoint"] = False
if initial_guess:
kwargs["initial_guess"] = value_coeffs[dependencies.index(initial_guess_var)]
if replace_map:
kwargs["replace_map"] = dict(zip(diag_coeffs, value_coeffs))
return (matrix_class(eq_l, **kwargs), adjlinalg.Vector(None, fn_space=u.function_space()))
def caching_solve(self, var, b):
if isinstance(self.data, IdentityMatrix):
output = b.duplicate()
output.axpy(1.0, b)
if isinstance(output.data, ufl.Form):
output = Vector(backend.Function(output.fn_space, backend.assemble(output.data)))
elif b.data is None:
backend.warning("Warning: got zero RHS for the solve associated with variable %s" % var)
output = Vector(backend.Function(self.test_function().function_space()))
else:
dirichlet_bcs = [utils.homogenize(bc) for bc in self.bcs if isinstance(bc, backend.DirichletBC)]
other_bcs = [bc for bc in self.bcs if not isinstance(bc, backend.DirichletBC)]
bcs = dirichlet_bcs + other_bcs
output = Vector(backend.Function(self.test_function().function_space()))
#print "b.data is a %s in the solution of %s" % (b.data.__class__, var)
if backend.parameters["adjoint"]["symmetric_bcs"] and backend.__version__ > '1.2.0':
assembler = backend.SystemAssembler(self.data, b.data, bcs)
assembled_rhs = backend.Vector()
assembler.assemble(assembled_rhs)
elif isinstance(b.data, ufl.Form):
assembled_rhs = wrap_assemble(b.data, self.test_function())
else:
if backend.__name__ == "dolfin":
assembled_rhs = b.data.vector()
else:
assembled_rhs = b.data
[bc.apply(assembled_rhs) for bc in bcs]
if not var in caching.lu_solvers:
if backend.parameters["adjoint"]["debug_cache"]:
backend.info_red("Got a cache miss for %s" % var)
if backend.parameters["adjoint"]["symmetric_bcs"] and backend.__version__ > '1.2.0':
assembled_lhs = backend.Matrix()
assembler.assemble(assembled_lhs)
else:
assembled_lhs = self.assemble_data()
[bc.apply(assembled_lhs) for bc in bcs]
caching.lu_solvers[var] = compatibility.LUSolver(assembled_lhs, "mumps")
caching.lu_solvers[var].parameters["reuse_factorization"] = True
else:
if backend.parameters["adjoint"]["debug_cache"]:
backend.info_green("Got a cache hit for %s" % var)
caching.lu_solvers[var].solve(output.data.vector(), assembled_rhs)
return output
def pixel_to_ray_vec(self, pts):
""" given a pixel, calculate a line that all points will be projected to the pixel
through the camera
Params:
pts - 2 by n array, points in image coordinates
Return:
d - 3 by n array, direction vector for each pixel
C - 3 by 1 array, camera center in world frame, pencil of point representation.
"""
pts_homo = homogenize(pts)
pts_norm = np.matmul(self.K_inv, pts_homo)
d = np.matmul(self.R.T, pts_norm)
d = d / np.sign(d[0, :]) / np.linalg.norm(d, axis=0)
C = self.C_world_inhomo
return d, C
def solve(self, var, b):
if reuse_factorization is False:
return adjlinalg.Matrix.solve(self, var, b)
if var.type in ['ADJ_TLM', 'ADJ_ADJOINT']:
bcs = [utils.homogenize(bc) for bc in self.bcs if isinstance(bc, dolfin.DirichletBC)] + [bc for bc in self.bcs if not isinstance(bc, dolfin.DirichletBC)]
else:
bcs = self.bcs
if var.type in ['ADJ_FORWARD', 'ADJ_TLM']:
solver = lu_solvers[idx]
if solver is None:
A = assembly.assemble(self.data); [bc.apply(A) for bc in bcs]
lu_solvers[idx] = LUSolver(A)
lu_solvers[idx].parameters["reuse_factorization"] = True
solver = lu_solvers[idx]
else:
if adj_lu_solvers[idx] is None:
A = assembly.assemble(self.data); [bc.apply(A) for bc in bcs]
adj_lu_solvers[idx] = LUSolver(A)
adj_lu_solvers[idx].parameters["reuse_factorization"] = True
solver = adj_lu_solvers[idx]
x = adjlinalg.Vector(dolfin.Function(self.test_function().function_space()))
if b.data is None:
# This means we didn't get any contribution on the RHS of the adjoint system. This could be that the
# simulation ran further ahead than when the functional was evaluated, or it could be that the
# functional is set up incorrectly.
dolfin.info_red("Warning: got zero RHS for the solve associated with variable %s" % var)
else:
if isinstance(b.data, dolfin.Function):
b_vec = b.data.vector().copy()
else:
b_vec = dolfin.assemble(b.data)
[bc.apply(b_vec) for bc in bcs]
solver.solve(x.data.vector(), b_vec, annotate=False)
return x
def derivative_assembly(self, dependencies, values, variable, hermitian):
replace_map = {}
for i in range(len(self.deps)):
if self.deps[i] == self.ic_var: continue
j = dependencies.index(self.deps[i])
replace_map[self.coeffs[i]] = values[j].data
diff_var = values[dependencies.index(variable)].data
current_form = backend.replace(self.form, replace_map)
deriv = backend.derivative(current_form, diff_var)
if hermitian:
deriv = backend.adjoint(deriv)
bcs = [utils.homogenize(bc) for bc in self.bcs if isinstance(bc, backend.DirichletBC)] + [bc for bc in self.bcs if not isinstance(bc, backend.DirichletBC)]
else:
bcs = self.bcs
return adjlinalg.Matrix(deriv, bcs=bcs)
def solve(selfmat, var, b):
if selfmat.adjoint:
operators = transpose_operators(selfmat.operators)
else:
operators = selfmat.operators
# Fetch/construct the solver
if var.type in ['ADJ_FORWARD', 'ADJ_TLM']:
solver = petsc_krylov_solvers[idx]
need_to_set_operator = self._need_to_reset_operator
else:
if adj_petsc_krylov_solvers[idx] is None:
need_to_set_operator = True
adj_petsc_krylov_solvers[idx] = PETScKrylovSolver(*solver_parameters)
adj_ksp = adj_petsc_krylov_solvers[idx].ksp()
fwd_ksp = petsc_krylov_solvers[idx].ksp()
adj_ksp.setOptionsPrefix(fwd_ksp.getOptionsPrefix())
adj_ksp.setType(fwd_ksp.getType())
adj_ksp.pc.setType(fwd_ksp.pc.getType())
adj_ksp.setFromOptions()
else:
need_to_set_operator = self._need_to_reset_operator
solver = adj_petsc_krylov_solvers[idx]
# FIXME: work around DOLFIN bug #583
try:
solver.parameters.convergence_norm_type
except:
solver.parameters.convergence_norm_type = "preconditioned"
# end FIXME
solver.parameters.update(parameters)
self._need_to_reset_operator = False
if selfmat.adjoint:
(nsp_, tnsp_) = (tnsp, nsp)
else:
(nsp_, tnsp_) = (nsp, tnsp)
x = dolfin.Function(fn_space)
if selfmat.initial_guess is not None and var.type == 'ADJ_FORWARD':
x.vector()[:] = selfmat.initial_guess.vector()
if b.data is None:
dolfin.info_red("Warning: got zero RHS for the solve associated with variable %s" % var)
return adjlinalg.Vector(x)
if var.type in ['ADJ_TLM', 'ADJ_ADJOINT']:
selfmat.bcs = [utils.homogenize(bc) for bc in selfmat.bcs if isinstance(bc, dolfin.cpp.DirichletBC)] + [bc for bc in selfmat.bcs if not isinstance(bc, dolfin.cpp.DirichletBC)]
# This is really hideous. Sorry.
if isinstance(b.data, dolfin.Function):
rhs = b.data.vector().copy()
[bc.apply(rhs) for bc in selfmat.bcs]
if need_to_set_operator:
if assemble_system: # if we called assemble_system, rather than assemble
v = dolfin.TestFunction(fn_space)
(A, rhstmp) = dolfin.assemble_system(operators[0], dolfin.inner(b.data, v)*dolfin.dx, selfmat.bcs)
if has_preconditioner:
(P, rhstmp) = dolfin.assemble_system(operators[1], dolfin.inner(b.data, v)*dolfin.dx, selfmat.bcs)
solver.set_operators(A, P)
else:
solver.set_operator(A)
else: # we called assemble
A = dolfin.assemble(operators[0])
[bc.apply(A) for bc in selfmat.bcs]
if has_preconditioner:
P = dolfin.assemble(operators[1])
[bc.apply(P) for bc in selfmat.bcs]
solver.set_operators(A, P)
else:
solver.set_operator(A)
else:
if assemble_system: # if we called assemble_system, rather than assemble
(A, rhs) = dolfin.assemble_system(operators[0], b.data, selfmat.bcs)
if need_to_set_operator:
if has_preconditioner:
(P, rhstmp) = dolfin.assemble_system(operators[1], b.data, selfmat.bcs)
solver.set_operators(A, P)
else:
solver.set_operator(A)
else: # we called assemble
A = dolfin.assemble(operators[0])
rhs = dolfin.assemble(b.data)
[bc.apply(A) for bc in selfmat.bcs]
[bc.apply(rhs) for bc in selfmat.bcs]
if need_to_set_operator:
if has_preconditioner:
P = dolfin.assemble(operators[1])
[bc.apply(P) for bc in selfmat.bcs]
solver.set_operators(A, P)
else:
solver.set_operator(A)
if need_to_set_operator:
print "|A|: %.6e" % A.norm("frobenius")
# Set the nullspace for the linear operator
if nsp_ is not None and need_to_set_operator:
dolfin.as_backend_type(A).set_nullspace(nsp_)
# (Possibly override the user in) orthogonalize
# the right-hand-side
if tnsp_ is not None:
tnsp_.orthogonalize(rhs)
print "%s: |b|: %.6e" % (var, rhs.norm("l2"))
solver.solve(x.vector(), rhs)
return adjlinalg.Vector(x)
def solve(self, var, b):
if self.adjoint:
operators = transpose_operators(self.operators)
else:
operators = self.operators
solver = dolfin.LinearSolver(*solver_parameters)
solver.parameters.update(parameters)
x = dolfin.Function(fn_space)
if self.initial_guess is not None and var.type == 'ADJ_FORWARD':
x.vector()[:] = self.initial_guess.vector()
if b.data is None:
dolfin.info_red("Warning: got zero RHS for the solve associated with variable %s" % var)
return adjlinalg.Vector(x)
if var.type in ['ADJ_TLM', 'ADJ_ADJOINT']:
self.bcs = [utils.homogenize(bc) for bc in self.bcs if isinstance(bc, dolfin.cpp.DirichletBC)] + [bc for bc in self.bcs if not isinstance(bc, dolfin.cpp.DirichletBC)]
# This is really hideous. Sorry.
if isinstance(b.data, dolfin.Function):
rhs = b.data.vector().copy()
[bc.apply(rhs) for bc in self.bcs]
if assemble_system: # if we called assemble_system, rather than assemble
v = dolfin.TestFunction(fn_space)
(A, rhstmp) = dolfin.assemble_system(operators[0], dolfin.inner(b.data, v)*dolfin.dx, self.bcs)
if has_preconditioner:
(P, rhstmp) = dolfin.assemble_system(operators[1], dolfin.inner(b.data, v)*dolfin.dx, self.bcs)
solver.set_operators(A, P)
else:
solver.set_operator(A)
else: # we called assemble
A = dolfin.assemble(operators[0])
[bc.apply(A) for bc in self.bcs]
# Set nullspace
if nsp:
dolfin.as_backend_type(A).set_nullspace(nsp)
nsp.orthogonalize(b);
if has_preconditioner:
P = dolfin.assemble(operators[1])
[bc.apply(P) for bc in self.bcs]
solver.set_operators(A, P)
else:
solver.set_operator(A)
else:
if assemble_system: # if we called assemble_system, rather than assemble
(A, rhs) = dolfin.assemble_system(operators[0], b.data, self.bcs)
if has_preconditioner:
(P, rhstmp) = dolfin.assemble_system(operators[1], b.data, self.bcs)
solver.set_operators(A, P)
else:
solver.set_operator(A)
else: # we called assemble
A = dolfin.assemble(operators[0])
rhs = dolfin.assemble(b.data)
[bc.apply(A) for bc in self.bcs]
[bc.apply(rhs) for bc in self.bcs]
# Set nullspace
if nsp:
dolfin.as_backend_type(A).set_nullspace(nsp)
nsp.orthogonalize(rhs);
if has_preconditioner:
P = dolfin.assemble(operators[1])
[bc.apply(P) for bc in self.bcs]
solver.set_operators(A, P)
else:
solver.set_operator(A)
solver.solve(x.vector(), rhs)
return adjlinalg.Vector(x)
def solve(self, var, b):
if self.adjoint:
operators = transpose_operators(self.operators)
else:
operators = self.operators
# Fetch/construct the solver
if var.type in ['ADJ_FORWARD', 'ADJ_TLM']:
solver = krylov_solvers[idx]
need_to_set_operator = False
else:
if adj_krylov_solvers[idx] is None:
need_to_set_operator = True
adj_krylov_solvers[idx] = KrylovSolver(*solver_parameters)
else:
need_to_set_operator = False
solver = adj_krylov_solvers[idx]
solver.parameters.update(parameters)
if self.adjoint:
(nsp_, tnsp_) = (tnsp, nsp)
else:
(nsp_, tnsp_) = (nsp, tnsp)
x = dolfin.Function(fn_space)
if self.initial_guess is not None and var.type == 'ADJ_FORWARD':
x.vector()[:] = self.initial_guess.vector()
if b.data is None:
dolfin.info_red("Warning: got zero RHS for the solve associated with variable %s" % var)
return adjlinalg.Vector(x)
if var.type in ['ADJ_TLM', 'ADJ_ADJOINT']:
self.bcs = [utils.homogenize(bc) for bc in self.bcs if isinstance(bc, dolfin.cpp.DirichletBC)] + [bc for bc in self.bcs if not isinstance(bc, dolfin.cpp.DirichletBC)]
# This is really hideous. Sorry.
if isinstance(b.data, dolfin.Function):
rhs = b.data.vector().copy()
[bc.apply(rhs) for bc in self.bcs]
if need_to_set_operator:
if assemble_system: # if we called assemble_system, rather than assemble
v = dolfin.TestFunction(fn_space)
(A, rhstmp) = dolfin.assemble_system(operators[0], dolfin.inner(b.data, v)*dolfin.dx, self.bcs)
if has_preconditioner:
(P, rhstmp) = dolfin.assemble_system(operators[1], dolfin.inner(b.data, v)*dolfin.dx, self.bcs)
solver.set_operators(A, P)
else:
solver.set_operator(A)
else: # we called assemble
A = dolfin.assemble(operators[0])
[bc.apply(A) for bc in self.bcs]
if has_preconditioner:
P = dolfin.assemble(operators[1])
[bc.apply(P) for bc in self.bcs]
solver.set_operators(A, P)
else:
solver.set_operator(A)
else:
if assemble_system: # if we called assemble_system, rather than assemble
(A, rhs) = dolfin.assemble_system(operators[0], b.data, self.bcs)
if need_to_set_operator:
if has_preconditioner:
(P, rhstmp) = dolfin.assemble_system(operators[1], b.data, self.bcs)
solver.set_operators(A, P)
else:
solver.set_operator(A)
else: # we called assemble
A = dolfin.assemble(operators[0])
rhs = dolfin.assemble(b.data)
[bc.apply(A) for bc in self.bcs]
[bc.apply(rhs) for bc in self.bcs]
if need_to_set_operator:
if has_preconditioner:
P = dolfin.assemble(operators[1])
[bc.apply(P) for bc in self.bcs]
solver.set_operators(A, P)
else:
solver.set_operator(A)
# Set the nullspace for the linear operator
if nsp_ is not None and need_to_set_operator:
dolfin.as_backend_type(A).set_nullspace(nsp_)
# (Possibly override the user in) orthogonalize
# the right-hand-side
if tnsp_ is not None:
tnsp_.orthogonalize(rhs)
solver.solve(x.vector(), rhs)
return adjlinalg.Vector(x)
def get_image_coordinate(self, X):
""" get the image coordinate of world point X """
x_homo = np.matmul(self.P, homogenize(X))
x = dehomogenize(x_homo)
return x