https://github.com/landreman/stellopt_scenarios/tree/master/2DOF_circularCrossSection_varyAxis_targetIotaAndQuasisymmetry
See that website for a detailed description of the problem and plots
of the objective function landscape.
"""
vmec = Vmec(os.path.join(os.path.dirname(__file__), 'inputs', 'input.2DOF_circularCrossSection_varyAxis_targetIotaAndQuasisymmetry'))
# Define parameter space:
vmec.boundary.all_fixed()
vmec.boundary.set_fixed("rc(0,1)", False)
vmec.boundary.set_fixed("zs(0,1)", False)
# Define objective function:
boozer = Boozer(vmec, mpol=32, ntor=16)
qs = Quasisymmetry(boozer,
1.0, # Radius to target
1, 0, # (M, N) you want in |B|
normalization="symmetric",
weight="stellopt_ornl")
# Objective function is 100 * (iota - (-0.41))^2 + 1 * (qs - 0)^2
prob = LeastSquaresProblem([(vmec.iota_axis, -0.41, 100),
(qs, 0, 1)])
least_squares_serial_solve(prob)
print("Final values before shifting and scaling:", prob.dofs.f())
print("Final residuals:", prob.f())
print("Final state vector:", prob.x)
print("Final iota on axis:", vmec.iota_axis())
surf.set_fixed("Delta(0,0)") # toroidally-averaged minor radius
# Define objective function:
boozer = Boozer(vmec, mpol=32, ntor=16)
qs = Quasisymmetry(
boozer,
1.0, # Radius to target
1,
0, # (M, N) you want in |B|
normalization="symmetric",
weight="stellopt")
# Objective function is 100 * (iota - (-0.41))^2 + 1 * (qs - 0)^2
prob = LeastSquaresProblem([(vmec.iota_axis, -0.41, 100), (qs, 0, 1)])
residuals = prob.f()
vals = prob.dofs.f()
if mpi.proc0_world:
print("Initial values before shifting and scaling: ", vals[:10])
print("Initial residuals after shifting and scaling:", residuals[:10])
print("size of residuals:", len(residuals))
print("Initial objective function:", prob.objective())
print("Parameter space:")
for name in prob.dofs.names:
print(name)
print("Initial state vector:", prob.x)
print("Initial iota on axis:", vmec.iota_axis())
#exit(0)
least_squares_mpi_solve(prob, mpi, grad=True)