



```python
import simsopt
import numpy as np
import scipy.optimize as optimize

# Define the objective function
def objective(x):
    # Calculate the flux and its gradient
    A, dA = A_and_dA_vjp(x)
    # Calculate the curve length penalty and its gradient
    curve_length_penalty, d_curve_length_penalty = curve_length_penalty_and_gradient(x)
    # Calculate the coil-to-coil distance penalty and its gradient
    coil_to_coil_distance_penalty, d_coil_to_coil_distance_penalty = coil_to_coil_distance_penalty_and_gradient(x)
    # Combine the terms to form the objective function
    obj = A**2 + curve_length_penalty + coil_to_coil_distance_penalty
    # Calculate the gradient of the objective function
    dobj = 2*A*dA + d_curve_length_penalty + d_coil_to_coil_distance_penalty
    return obj, dobj

# Initialize the boundary magnetic surface
boundary_surface = test_curves_and_surface()

# Create equally spaced curves and multifilament grid
curves, multifilament_grid = relax_and_split(boundary_surface)

# Apply stellarator and rotation symmetries
multifilament_grid = apply_stellarator_and_rotation_symmetries(multifilament_grid)

# Define the Biot-Savart law
def B_and_dB_vjp(x):
    A, dA = A_vjp(x)
    B = _A_impl(x)
    dB = dA
    return B, dB

# Perform a Taylor test
test_biotsavart_gradient_symmetric_and_divergence_free()

# Run the optimization using L-BFGS-B
x0 = np.zeros(multifilament_grid.shape)
res = optimize.minimize(objective, x0, method='L-BFGS-B', jac=True)

# Save the output in VTK format
save_output_in_vtk_format(res.x)
```



This code defines the objective function, initializes the boundary magnetic surface, creates equally spaced curves and multifilament grid, applies stellarator and rotation symmetries, defines the Biot-Savart law, performs a Taylor test, runs the optimization using L-BFGS-B, and saves the output in VTK format. Source: assistant
EOT: true