hermit.csdl_helpers
===================

.. py:module:: hermit.csdl_helpers

.. autoapi-nested-parse::

   Native-CSDL preprocessing / postprocessing helpers.

   Everything here is ordinary CSDL (auto-differentiated) -- gathers, reshapes, the
   isotropic ABD assembly, the force->pressure L2 solve, stress aggregation, nodal
   extraction. No FEniCSx, no custom operations.

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Functions
---------

.. autoapisummary::

   hermit.csdl_helpers.aggregate
   hermit.csdl_helpers.assemble_abd_isotropic
   hermit.csdl_helpers.broadcast0
   hermit.csdl_helpers.build_moment
   hermit.csdl_helpers.build_pressure
   hermit.csdl_helpers.extract_nodal
   hermit.csdl_helpers.orientation_angle
   hermit.csdl_helpers.reorder
   hermit.csdl_helpers.resolve_mesh_nodes
   hermit.csdl_helpers.rotate_abd


Module Contents
---------------

.. py:function:: aggregate(pnorm_stress, m, rho)

   
   Aggregated stress ``(1/m) * (pnorm + guard)**(1/rho)``.

   ``m`` is a problem-specific *scaling*, not a smoothing knob: the aggregate is
   mathematically invariant under ``m`` (it cancels), and only the finite exponent
   range of float64 breaks that invariance -- which it does violently once
   ``m*max(vm)`` strays far from 1. ``_warn_if_degenerate`` says so out loud.















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.. py:function:: assemble_abd_isotropic(E, nu, thickness)

   
   Isotropic single-layer A, B, D (n,3,3) and As (n,2,2) from E, nu, thickness (n,).

   Port of ``MaterialInputFactory.from_isotropic`` (femo dev_coupling).















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.. py:function:: broadcast0(var: csdl_alpha.Variable, n: int) -> csdl_alpha.Variable

   
   Broadcast ``var`` along axis 0 to length ``n``.

   A scalar (``()`` / ``(1,)``) or a leading axis of length 1 is expanded to ``n``
   (differentiably); an axis already of length ``n`` is returned unchanged. Used to
   let material inputs be given as a single value instead of a per-node / per-cell
   array.















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.. py:function:: build_moment(loads, maps, vf_size: int)

.. py:function:: build_pressure(loads, maps, vf_size: int)

   
   Combine nodal pressure + (force -> pressure) into the VF-dof RHS vector.
















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.. py:function:: extract_nodal(disp_vec, sparse_map, geom_shape, reverse_node_idx)

   
   (state dof vec) -> (n_nodes, 3) nodal field, reordered back to user node ordering.
















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.. py:function:: orientation_angle(direction, frames) -> numpy.ndarray

   
   Per-cell angle (rad) from each cell's local e0 to the tangent-plane projection of
   ``direction`` (a global ``(3,)`` vector or a per-cell ``(n, 3)`` field). ``frames``:
   ``(n, 3, 3)`` local frames, rows e0, e1, e2. Pure numpy -- fibre layout is fixed.
















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.. py:function:: reorder(var: csdl_alpha.Variable, idx) -> csdl_alpha.Variable

   
   Gather ``var`` along axis 0 by integer index array ``idx`` (user -> FE ordering).
















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.. py:function:: resolve_mesh_nodes(reference_nodes, node_disp=None, mesh_nodes=None)

   
   Return (mesh_nodes_variable, geometry_is_differentiable).
















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.. py:function:: rotate_abd(A, B, D, As, theta)

   
   Rotate the ABD stiffness ``(n,3,3)`` and transverse shear ``As`` ``(n,2,2)`` by a
   per-cell in-plane angle ``theta`` ``(n,)``. ``theta`` may be numpy (fixed fibre
   layout) or a ``csdl.Variable`` (differentiable, e.g. a fibre-angle design field).
   ``X_rot = Tsig_inv(theta) @ X @ Teps(theta)`` -- LamAD's CLT transform.

   ``As`` is in the shell's standard (xz, yz) transverse-shear ordering (the CLT seam
   in ``hm.laminate`` permutes it there), so its rotation uses
   ``r2t @ As @ r2 == R(theta)^T As R(theta)`` -- the ``Teps``-consistent convention
   (``r2 == R(theta)``, ``r2t == R(theta)^T``), matching
   ``hermit.fenics.kinematics.shear_rotation`` / ``congruent_transform``. (``r2 @ As
   @ r2t`` would instead be correct for a swapped ``(yz, xz)`` ordering.)















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