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