desc.objectives.Omnigenity

class desc.objectives.Omnigenity(eq, field, target=None, bounds=None, weight=1, normalize=True, normalize_target=True, loss_function=None, deriv_mode='auto', eq_grid=None, field_grid=None, M_booz=None, N_booz=None, eta_weight=1, eq_fixed=False, field_fixed=False, name='omnigenity', jac_chunk_size=None)Source

Omnigenity error.

Errors are relative to a target field that is perfectly omnigenous, and are computed on a collocation grid in (ρ,η,α) coordinates.

This objective assumes that the collocation point (θ=0,ζ=0) lies on the contour of maximum field strength ||B||=B_max.

Parameters:

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

  • field (OmnigenousField) – Omnigenous magnetic field to be optimized to satisfy the Objective.

  • eq_grid (Grid, optional) – Collocation grid containing the nodes to evaluate at for equilibrium data. Defaults to a linearly space grid on the rho=1 surface. Must be without stellarator symmetry.

  • field_grid (Grid, optional) – Collocation grid containing the nodes to evaluate at for omnigenous field data. The grid nodes are given in the usual (ρ,θ,ζ) coordinates (with θ ∈ [0, 2π), ζ ∈ [0, 2π/NFP)), but θ is mapped to η and ζ is mapped to α. Defaults to a linearly space grid on the rho=1 surface. Must be without stellarator symmetry.

  • M_booz (int, optional) – Poloidal resolution of Boozer transformation. Default = 2 * eq.M.

  • N_booz (int, optional) – Toroidal resolution of Boozer transformation. Default = 2 * eq.N.

  • eta_weight (float, optional) – Magnitude of relative weight as a function of η: w(η) = (eta_weight + 1) / 2 + (eta_weight - 1) / 2 * cos(η) Default value of 1 weights all nodes equally.

  • eq_fixed (bool, optional) – Whether the Equilibrium eq is fixed or not. If True, the equilibrium is fixed and its values are precomputed, which saves on computation time during optimization and only field is allowed to change. If False, the equilibrium is allowed to change during the optimization and its associated data are re-computed at every iteration (Default).

  • field_fixed (bool, optional) – Whether the OmnigenousField field is fixed or not. If True, the field is fixed and its values are precomputed, which saves on computation time during optimization and only eq is allowed to change. If False, the field is allowed to change during the optimization and its associated data are re-computed at every iteration (Default).

  • 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([params_1, params_2, constants])

Compute omnigenity errors.

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.