Evaluating the fitted field

Once a fit has been written with write_gg_fit, load it back with read_gg_fit and evaluate the field, the vector potential, and the field-expansion coefficients anywhere.

using GeneralizedGradients
fit, meta = read_gg_fit("gg_fit_result.h5")

read_gg_fit returns a two-tuple. fit is a GGCoefs struct with the GG coefficient dictionaries a, b, bs (plus z_base, m_max, rms_plane, g_ref, origin, dz_grid), and meta is a NamedTuple of the associated fit-control metadata n_planes_add, core_weight, outer_plane_weight. Both are passed together to the evaluation functions below.

Field and vector potential

The GG coefficients are stored only at the grid planes fit.z_base. Evaluate at a specific plane index ip:

B, A, dA = field_and_potential_evaluate(fit, ip, x, y)

or at an arbitrary longitudinal position s (Hermite-interpolated between the straddling planes):

B, A, dA = field_and_potential_evaluate_at(fit, x, y, s)

Here B is the field 3-vector [Bx, By, Bs], A is the vector potential, and dA[i, j] = ∂A_i/∂u_j with u = (x, y, s). The transverse coordinates x, y are absolute; fit.origin is subtracted internally.

Note

On a curved reference frame (g_ref ≠ 0) the returned B is exactly the Frenet–Serret curl of A, which is a useful self-consistency check.

Field-expansion coefficients

To get the coefficients C_{c,i,j} of xⁱ yʲ in each field component:

CBx, CBy, CBs = field_coefficients_at_plane(fit, ip)   # at grid plane ip
CBx, CBy, CBs = field_coefficients_at_s(fit, s)        # at arbitrary s

Generalized-gradient coefficients

To get the GG coefficients themselves as scalar dictionaries:

a, b, bs = gg_coefficients_at_plane(fit, ip)   # at grid plane ip
a, b, bs = gg_coefficients_at_s(fit, s)        # at arbitrary s

a and b are keyed by (n, m) with a(n,m) = dᵐaₙ/dsᵐ; bs is keyed by m with bs(m) = dᵐb_s/dsᵐ.

See the API Reference (sidebar) for the full signatures and return types.