plt.savefig('Results/ReimanInitialPoincare.png', dpi=500)
plt.savefig('Results/ReimanInitialPoincare.pdf')
p.plot_iota()
plt.tight_layout()
plt.savefig('Results/ReimanInitialIota.png')
# exit()
## Optimization
prob = LeastSquaresProblem([(obj.residue1, 0, 1)])
# Set degrees of freedom for the optimization
obj.all_fixed()
obj.set_fixed('epsilon', False)
# Run optimization problem
# nIterations = 10
print('Starting optimization...')
least_squares_serial_solve(
prob, bounds=[-0.037, 0.021], xtol=1e-12, ftol=1e-12,
gtol=1e-12) #, method='lm', max_nfev=nIterations)
print('Optimization finished...')
## Create final Poincare Plot
solFinal = [obj.residue()]
p = obj.poincare(nPpts=350, nPtrj=8, Rbegin=1.19, Rend=1.23)
p.plot(s=1.5)
[
plt.scatter(fSol[1],
fSol[2],
s=35,
marker="x",
label=f"Periods = {fSol[3]:.0f}, Residue = {fSol[0]:.4f}")
for fSol in solFinal
]
# Curve itself.
obj = CurveLength(curve)
print('Initial curve length: ', obj.J())
# Each target function is then equipped with a shift and weight, to
# become a term in a least-squares objective function.
# A list of terms are combined to form a nonlinear-least-squares
# problem.
prob = LeastSquaresProblem([(obj, 0.0, 1.0)])
# At the initial condition, get the Jacobian two ways: analytic
# derivatives and finite differencing. The difference should be small.
fd_jac = prob.dofs.fd_jac()
jac = prob.dofs.jac()
print('finite difference Jacobian:')
print(fd_jac)
print('Analytic Jacobian:')
print(jac)
print('Difference:')
print(fd_jac - jac)
# Solve the minimization problem:
least_squares_serial_solve(prob)
print('At the optimum, x: ', prob.x)
print(' Final curve dofs: ', curve.get_dofs())
print(' Final curve length: ', obj.J())
print(' Expected final length: ', 2 * np.pi * x0[0])
print(' objective function: ', prob.objective())
# Each Target is then equipped with a shift and weight, to become a
# term in a least-squares objective function. A list of terms are
# 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, desired_iota, iota_weight)
prob = LeastSquaresProblem([term1, term2])
# Solve the minimization problem:
least_squares_serial_solve(prob, grad=True)
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())
print(" objective function = ", prob.objective())
# The tests here are based on values from the VMEC version in
# https://github.com/landreman/stellopt_scenarios/tree/master/2DOF_vmecOnly_targetIotaAndVolume
# Due to this and the fact that we don't yet have iota on axis from SPEC, the tolerances are wide.
assert np.abs(surf.get_rc(1, 1) - 0.0313066948) < 0.001
assert np.abs(surf.get_zs(1, 1) - (-0.031232391)) < 0.001
assert np.abs(equil.volume() - 0.178091) < 0.001
plt.tight_layout()
plt.savefig('Results/DommaschkInitialIota.png')
## Optimization
prob = LeastSquaresProblem([(obj.residue1, 0, 1), (obj.residue2, 0, 1),
(obj.residue3, 0, 1)])
# Set degrees of freedom for the optimization
obj.all_fixed()
obj.set_fixed('bc(5,10)', False)
obj.set_dofs([5, 2, 5, 4, 5, 10, 1.4, 1.4, 19.25, 0, -1e4])
# Run optimization problem
nIterations = 400
print('Starting optimization...')
least_squares_serial_solve(prob,
xtol=1e-9,
ftol=1e-9,
gtol=1e-9,
method='lm',
max_nfev=nIterations)
print('Optimization finished...')
## Create final Poincare Plot
solFinal = []
# residueInputs = [[1.1884,8],[1.124,9],[1.075,11],[1.150,8]]
residueInputs = [[1.1884, 8], [1.124, 9], [1.075, 11]]
[
solFinal.append(obj.residue(resIn[0], resIn[1]))
for resIn in residueInputs
]
p = obj.poincare(nPpts=500, nPtrj=50, Rbegin=0.98, Rend=1.18)
p.plot(s=1.5)
[
