Magnetic axis limits and new variables

desc/backend.py

@@ -201,7 +201,7 @@
             val = body_fun(i, val)
         return val
 
-    def cond(pred, true_fun, false_fun, operand):
+    def cond(pred, true_fun, false_fun, *operand):
         """Conditionally apply true_fun or false_fun.
 
         This version is for the numpy backend, for jax backend see jax.lax.cond
@@ -227,9 +227,9 @@
 
         """
         if pred:
-            return true_fun(operand)
+            return true_fun(*operand)
         else:
-            return false_fun(operand)
+            return false_fun(*operand)
 
     def switch(index, branches, operand):
         """Apply exactly one of branches given by index.

desc/compute/__init__.py

@@ -5,11 +5,11 @@
 Parameters
 ----------
 params : dict of ndarray
-    Parameters from the equilibrium, such as R_lmn, Z_lmn, i_l, p_l, etc
+    Parameters from the equilibrium, such as R_lmn, Z_lmn, i_l, p_l, etc.
 transforms : dict of Transform
-    Transforms for R, Z, lambda, etc
+    Transforms for R, Z, lambda, etc.
 profiles : dict of Profile
-    Profile objects for pressure, iota, current, etc
+    Profile objects for pressure, iota, current, etc.
 data : dict of ndarray
     Data computed so far, generally output from other compute functions
 kwargs : dict
@@ -59,8 +59,8 @@
 # import the compute module.
 def _build_data_index():
 
-    for p in data_index.keys():
-        for key in data_index[p].keys():
+    for p in data_index:
+        for key in data_index[p]:
             full = {
                 "data": get_data_deps(key, p, has_axis=False),
                 "transforms": get_derivs(key, p, has_axis=False),

desc/compute/_basis_vectors.py

@@ -26,10 +26,10 @@
     transforms={},
     profiles=[],
     coordinates="rtz",
-    data=["B"],
+    data=["B", "|B|"],
 )
 def _b(params, transforms, profiles, data, **kwargs):
-    data["b"] = (data["B"].T / jnp.linalg.norm(data["B"], axis=-1)).T
+    data["b"] = (data["B"].T / data["|B|"]).T
     return data
 
 
@@ -47,6 +47,8 @@
     data=["e_theta/sqrt(g)", "e_zeta"],
 )
 def _e_sup_rho(params, transforms, profiles, data, **kwargs):
+    # At the magnetic axis, this function returns the multivalued map whose
+    # image is the set { 𝐞^ρ | ρ=0 }.
     data["e^rho"] = cross(data["e_theta/sqrt(g)"], data["e_zeta"])
     return data
 
@@ -196,8 +198,14 @@
     profiles=[],
     coordinates="rtz",
     data=["e_rho", "e_zeta"],
+    parameterization=[
+        "desc.equilibrium.equilibrium.Equilibrium",
+        "desc.geometry.core.Surface",
+    ],
 )
 def _e_sup_theta_times_sqrt_g(params, transforms, profiles, data, **kwargs):
+    # At the magnetic axis, this function returns the multivalued map whose
+    # image is the set { 𝐞^θ √g | ρ=0 }.
     data["e^theta*sqrt(g)"] = cross(data["e_zeta"], data["e_rho"])
     return data
 
@@ -299,6 +307,8 @@
     data=["e_rho", "e_theta/sqrt(g)"],
 )
 def _e_sup_zeta(params, transforms, profiles, data, **kwargs):
+    # At the magnetic axis, this function returns the multivalued map whose
+    # image is the set { 𝐞^ζ | ρ=0 }.
     data["e^zeta"] = cross(data["e_rho"], data["e_theta/sqrt(g)"])
     return data
 
@@ -453,6 +463,8 @@
     data=["R", "R_r", "Z_r", "omega_r"],
 )
 def _e_sub_rho(params, transforms, profiles, data, **kwargs):
+    # At the magnetic axis, this function returns the multivalued map whose
+    # image is the set { 𝐞ᵨ | ρ=0 }.
     data["e_rho"] = jnp.array([data["R_r"], data["R"] * data["omega_r"], data["Z_r"]]).T
     return data
 
@@ -1386,6 +1398,8 @@
     axis_limit_data=["e_theta_r", "sqrt(g)_r"],
 )
 def _e_sub_theta_over_sqrt_g(params, transforms, profiles, data, **kwargs):
+    # At the magnetic axis, this function returns the multivalued map whose
+    # image is the set { 𝐞_θ / √g | ρ=0 }.
     data["e_theta/sqrt(g)"] = transforms["grid"].replace_at_axis(
         (data["e_theta"].T / data["sqrt(g)"]).T,
         lambda: (data["e_theta_r"].T / data["sqrt(g)_r"]).T,
@@ -1426,6 +1440,8 @@
     data=["R", "R_r", "R_rt", "R_t", "Z_rt", "omega_r", "omega_rt", "omega_t"],
 )
 def _e_sub_theta_r(params, transforms, profiles, data, **kwargs):
+    # At the magnetic axis, this function returns the multivalued map whose
+    # image is the set { ∂ᵨ 𝐞_θ | ρ=0 }
     data["e_theta_r"] = jnp.array(
         [
             -data["R"] * data["omega_t"] * data["omega_r"] + data["R_rt"],
@@ -3428,16 +3444,22 @@
     profiles=[],
     coordinates="rtz",
     data=["e_theta", "e_zeta", "|e_theta x e_zeta|"],
+    axis_limit_data=["e_theta_r", "|e_theta x e_zeta|_r"],
     parameterization=[
         "desc.equilibrium.equilibrium.Equilibrium",
         "desc.geometry.core.Surface",
     ],
 )
 def _n_rho(params, transforms, profiles, data, **kwargs):
-    # equal to e^rho / |e^rho| but works correctly for surfaces as well that don't have
-    # contravariant basis defined
-    data["n_rho"] = (
-        cross(data["e_theta"], data["e_zeta"]) / data["|e_theta x e_zeta|"][:, None]
+    # Equal to 𝐞^ρ / ‖𝐞^ρ‖ but works correctly for surfaces as well that don't
+    # have contravariant basis defined.
+    data["n_rho"] = transforms["grid"].replace_at_axis(
+        (cross(data["e_theta"], data["e_zeta"]).T / data["|e_theta x e_zeta|"]).T,
+        # At the magnetic axis, this function returns the multivalued map whose
+        # image is the set { 𝐞^ρ / ‖𝐞^ρ‖ | ρ=0 }.
+        lambda: (
+            cross(data["e_theta_r"], data["e_zeta"]).T / data["|e_theta x e_zeta|_r"]
+        ).T,
     )
     return data
 
@@ -3460,9 +3482,11 @@
     ],
 )
 def _n_theta(params, transforms, profiles, data, **kwargs):
+    # Equal to 𝐞^θ / ‖𝐞^θ‖ but works correctly for surfaces as well that don't
+    # have contravariant basis defined.
     data["n_theta"] = (
-        cross(data["e_zeta"], data["e_rho"]) / data["|e_zeta x e_rho|"][:, None]
-    )
+        cross(data["e_zeta"], data["e_rho"]).T / data["|e_zeta x e_rho|"]
+    ).T
     return data
 
 
@@ -3478,13 +3502,21 @@
     profiles=[],
     coordinates="rtz",
     data=["e_rho", "e_theta", "|e_rho x e_theta|"],
+    axis_limit_data=["e_theta_r", "|e_rho x e_theta|_r"],
     parameterization=[
         "desc.equilibrium.equilibrium.Equilibrium",
         "desc.geometry.core.Surface",
     ],
 )
 def _n_zeta(params, transforms, profiles, data, **kwargs):
-    data["n_zeta"] = (
-        cross(data["e_rho"], data["e_theta"]) / data["|e_rho x e_theta|"][:, None]
+    # Equal to 𝐞^ζ / ‖𝐞^ζ‖ but works correctly for surfaces as well that don't
+    # have contravariant basis defined.
+    data["n_zeta"] = transforms["grid"].replace_at_axis(
+        (cross(data["e_rho"], data["e_theta"]).T / data["|e_rho x e_theta|"]).T,
+        # At the magnetic axis, this function returns the multivalued map whose
+        # image is the set { 𝐞^ζ / ‖𝐞^ζ‖ | ρ=0 }.
+        lambda: (
+            cross(data["e_rho"], data["e_theta_r"]).T / data["|e_rho x e_theta|_r"]
+        ).T,
     )
     return data