desc.objectives.VacuumBoundaryError

class desc.objectives.VacuumBoundaryError(eq, field, target=None, bounds=None, weight=1, normalize=True, normalize_target=True, loss_function=None, deriv_mode='auto', eval_grid=None, field_grid=None, field_fixed=False, name='Vacuum boundary error', jac_chunk_size=None, *, bs_chunk_size=None, **kwargs)Source

Target for free boundary conditions on LCFS for vacuum equilibrium.

Computes the residuals of the following:

𝐁ₒᵤₜ ⋅ 𝐧 = 0 𝐁ₒᵤₜ² - 𝐁ᵢₙ² = 0

Where 𝐁ᵢₙ is the total field inside the LCFS (from fixed boundary calculation) 𝐁ₒᵤₜ is the total field outside the LCFS (from coils), and 𝐧 is the outward surface normal. All residuals are weighted by the local area element ||𝐞_θ × 𝐞_ζ|| Δθ Δζ

(Technically for vacuum equilibria the second condition is redundant with the first, but including it makes things more robust).

Parameters:

• eq (Equilibrium) – Equilibrium that will be optimized to satisfy the Objective.

• field (MagneticField) – External field produced by coils or other sources outside the plasma.

• eval_grid (Grid, optional) – Collocation grid containing the nodes to evaluate error at. Should be at rho=1. Defaults to LinearGrid(M=eq.M_grid, N=eq.N_grid)

• field_grid (Grid, optional) – Grid used to discretize field. Defaults to the default grid for given field.

• field_fixed (bool) – Whether to assume the field is fixed. For free boundary solve, should be fixed. For single stage optimization, should be False (default).

• bs_chunk_size (int or None) – Size to split Biot-Savart computation into chunks of evaluation points. If no chunking should be done or the chunk size is the full input then supply None.

• target ({float, ndarray}, optional) – Target value(s) of the objective. Only used if bounds is None. Must be broadcastable to Objective.dim_f. Defaults to target=0.

• bounds (tuple of {float, ndarray}, optional) – Lower and upper bounds on the objective. Overrides target. Both bounds must be broadcastable to Objective.dim_f. Defaults to target=0.

• weight ({float, ndarray}, optional) – Weighting to apply to the Objective, relative to other Objectives. Must be broadcastable to Objective.dim_f.

• normalize (bool, optional) – Whether to compute the error in physical units or non-dimensionalize.

• normalize_target (bool, optional) – Whether target and bounds should be normalized before comparing to computed values. If normalize is True and the target is in physical units, this should also be set to True.

• loss_function ({None, 'mean', 'min', 'max','sum'}, optional) – Loss function to apply to the objective values once computed. This loss function is called on the raw compute value, before any shifting, scaling, or normalization.

• deriv_mode ({"auto", "fwd", "rev"}) – Specify how to compute Jacobian matrix, either forward mode or reverse mode AD. auto selects forward or reverse mode based on the size of the input and output of the objective. Has no effect on self.grad or self.hess which always use reverse mode and forward over reverse mode respectively.

• name (str, optional) – Name of the objective.

• jac_chunk_size (int or auto, optional) – Will calculate the Jacobian jac_chunk_size columns at a time, instead of all at once. The memory usage of the Jacobian calculation is roughly memory usage = m0+m1*jac_chunk_size: the smaller the chunk size, the less memory the Jacobian calculation will require (with some baseline memory usage). The time it takes to compute the Jacobian is roughly t = t0+t1/jac_chunk_size so the larger the jac_chunk_size, the faster the calculation takes, at the cost of requiring more memory. If None, it will use the largest size i.e obj.dim_x. Can also help with Hessian computation memory, as Hessian is essentially jacfwd(jacrev(f)), and each of these operations may be chunked. Defaults to chunk_size=None. Note: When running on a CPU (not a GPU) on a HPC cluster, DESC is unable to accurately estimate the available device memory, so the auto chunk_size option will yield a larger chunk size than may be needed. It is recommended to manually choose a chunk_size if an OOM error is experienced in this case.

Methods

build([use_jit, verbose])	Build constant arrays.
compute(eq_params, *field_params[, constants])	Compute boundary force error.
compute_scalar(*args, **kwargs)	Compute the scalar form of the objective.
compute_scaled(*args, **kwargs)	Compute and apply weighting and normalization.
compute_scaled_error(*args, **kwargs)	Compute and apply the target/bounds, weighting, and normalization.
compute_unscaled(*args, **kwargs)	Compute the raw value of the objective.
copy([deepcopy])	Return a (deep)copy of this object.
equiv(other)	Compare equivalence between DESC objects.
grad(*args, **kwargs)	Compute gradient vector of self.compute_scalar wrt x.
hess(*args, **kwargs)	Compute Hessian matrix of self.compute_scalar wrt x.
jac_scaled(*args, **kwargs)	Compute Jacobian matrix of self.compute_scaled wrt x.
jac_scaled_error(*args, **kwargs)	Compute Jacobian matrix of self.compute_scaled_error wrt x.
jac_unscaled(*args, **kwargs)	Compute Jacobian matrix of self.compute_unscaled wrt x.
jvp_scaled(v, x[, constants])	Compute Jacobian-vector product of self.compute_scaled.
jvp_scaled_error(v, x[, constants])	Compute Jacobian-vector product of self.compute_scaled_error.
jvp_unscaled(v, x[, constants])	Compute Jacobian-vector product of self.compute_unscaled.
load(load_from[, file_format])	Initialize from file.
print_value(args[, args0])	Print the value of the objective and return a dict of values.
save(file_name[, file_format, file_mode])	Save the object.
xs(*things)	Return a tuple of args required by this objective from optimizable things.

Attributes

bounds	Lower and upper bounds of the objective.
built	Whether the transforms have been precomputed (or not).
constants	Constant parameters such as transforms and profiles.
dim_f	Number of objective equations.
fixed	Whether the objective fixes individual parameters (or linear combo).
linear	Whether the objective is a linear function (or nonlinear).
name	Name of objective (str).
normalization	normalizing scale factor.
scalar	Whether default "compute" method is a scalar or vector.
target	Target value(s) of the objective.
things	Optimizable things that this objective is tied to.
weight	Weighting to apply to the Objective, relative to other Objectives.