def matrix_eval(self):
A_array = assemble(a).array()
A_array[[0, 1, min_dof_0_2pi, max_dof_0_2pi], :] = A_array[[min_dof_0_2pi, max_dof_0_2pi, 0, 1], :]
A_array[:, [0, 1, min_dof_0_2pi, max_dof_0_2pi]] = A_array[:, [min_dof_0_2pi, max_dof_0_2pi, 0, 1]]
A = Matrix(*A_array.shape)
A[:, :] = A_array
return A
def jacobian_eval(self, solution):
self._solution_from_dense_to_sparse(solution)
jacobian_array = assemble(j).array()
jacobian_array[[0, 1, min_dof_0_2pi, max_dof_0_2pi], :] = jacobian_array[[min_dof_0_2pi, max_dof_0_2pi, 0, 1], :]
jacobian_array[:, [0, 1, min_dof_0_2pi, max_dof_0_2pi]] = jacobian_array[:, [min_dof_0_2pi, max_dof_0_2pi, 0, 1]]
jacobian = Matrix(*jacobian_array.shape)
jacobian[:, :] = jacobian_array
return jacobian
def jacobian_eval(self, t, solution, solution_dot, solution_dot_coefficient):
self._solution_from_dense_to_sparse(solution, u)
self._solution_from_dense_to_sparse(solution_dot, u_dot)
jacobian_array = assemble(Constant(solution_dot_coefficient)*j_u_dot + j_u).array()
jacobian_array[[0, 1, min_dof_0_2pi, max_dof_0_2pi], :] = jacobian_array[[min_dof_0_2pi, max_dof_0_2pi, 0, 1], :]
jacobian_array[:, [0, 1, min_dof_0_2pi, max_dof_0_2pi]] = jacobian_array[:, [min_dof_0_2pi, max_dof_0_2pi, 0, 1]]
jacobian = Matrix(*jacobian_array.shape)
jacobian[:, :] = jacobian_array
return jacobian
def _test_eigen_solver_dense(sparse_LHS, sparse_RHS):
from rbnics.backends.online.numpy import EigenSolver, Matrix
# Extract constrained matrices from sparse eigensolver
LHS = Matrix(*sparse_LHS.array().shape)
RHS = Matrix(*sparse_RHS.array().shape)
LHS[:, :] = sparse_LHS.array()
RHS[:, :] = sparse_RHS.array()
# Solve the eigenproblem
solver = EigenSolver(None, LHS, RHS)
solver.set_parameters({
"problem_type": "gen_non_hermitian",
"spectrum": "smallest real",
})
solver.solve(1)
r, c = solver.get_eigenvalue(0)
assert abs(c) < 1.e-10
assert r > 0., "r = " + str(r) + " is not positive"
print("Dense inf-sup constant: ", sqrt(r))
return (sqrt(r), LHS, RHS)