volume_weight = 1
term1 = (spec.volume, desired_volume, volume_weight)
desired_iota = 0.41
iota_weight = 1
term2 = (vmec.iota_axis, desired_iota, iota_weight)
prob = LeastSquaresProblem([term1, term2])
# Solve the minimization problem:
least_squares_mpi_solve(prob, mpi=mpi, grad=True)
# Evaluate quantities on all processes, in case communication is
# required:
final_objective = prob.objective()
vmec_volume = vmec.volume()
spec_volume = spec.volume()
surf_volume = surf.volume()
vmec_iota = vmec.iota_axis()
spec_iota = spec.iota()
if mpi.proc0_world:
logging.info("At the optimum,")
logging.info(f" objective function = {final_objective}")
logging.info(f" rc(m=1,n=1) = {surf.get_rc(1, 1)}")
logging.info(f" zs(m=1,n=1) = {surf.get_zs(1, 1)}")
logging.info(f" volume, according to VMEC = {vmec_volume}")
logging.info(f" volume, according to SPEC = {spec_volume}")
logging.info(f" volume, according to Surface = {surf_volume}")
logging.info(f" iota on axis, from VMEC = {vmec_iota}")
logging.info(f" iota at mid-radius, from SPEC = {spec_iota}")
# combined to form a nonlinear-least-squares problem.
desired_volume = 0.15
volume_weight = 1
term1 = (equil.volume, desired_volume, volume_weight)
desired_iota = 0.41
iota_weight = 1
term2 = (equil.iota_axis, desired_iota, iota_weight)
prob = LeastSquaresProblem([term1, term2])
# Solve the minimization problem:
least_squares_mpi_solve(prob, mpi, grad=True)
objective = prob.objective()
if mpi.proc0_world:
print("At the optimum,")
print(" rc(m=1,n=1) = ", surf.get_rc(1, 1))
print(" zs(m=1,n=1) = ", surf.get_zs(1, 1))
print(" volume, according to VMEC = ", equil.volume())
print(" volume, according to Surface = ", surf.volume())
print(" iota on axis = ", equil.iota_axis())
print(" objective function = ", objective)
assert np.abs(surf.get_rc(1, 1) - 0.0313066948) < 1.0e-3
assert np.abs(surf.get_zs(1, 1) - (-0.031232391)) < 1.0e-3
assert np.abs(equil.volume() - 0.178091) < 1.0e-3
assert np.abs(surf.volume() - 0.178091) < 1.0e-3
assert np.abs(equil.iota_axis() - 0.4114567) < 1.0e-4
assert prob.objective() < 1.0e-2