probe_derivatives_model
=======================

.. py:function:: t3toolbox.fitting.probe_derivatives_model(geometry, x, ww, pp, order, residual, weight = None, regularizer = None)

   .. code-block:: python

      def probe_derivatives_model(
              geometry,                            # MANIFOLD / COREWISE (or the UNIFORM_* twin for a uniform x)
              x:          typ.Union[t3.TuckerTensorTrain, ut3.UniformTuckerTensorTrain],   # the current point
              ww:         typ.Sequence[NDArray],   # probe vectors X,        len=d, elm_shape=W+(Ni,)
              pp:         typ.Sequence[NDArray],   # perturbation vectors P, len=d, elm_shape=W+(Ni,)
              order:      int,
              residual:   typ.Sequence[NDArray],   # RAW r = probe_derivatives(x) − y, len=d, elm_shape=(order+1)+W+C+(Ni,)
              weight:     typ.Optional[typ.Any] = None,  # residual weight ω[mode,order], (d,order+1) broadcast; None = 1
              regularizer: typ.Any = None,         # optional regularizer, e.g. optimizers.IdentityRegularizer(λ)
      ) -> typ.Union[GaussNewtonModel, UniformGaussNewtonModel]:


   The ``probe``-derivatives Gauss-Newton model -- vector-valued (one free mode per probe), so
   ``residual`` is a sequence of ``d`` jets. Probe has both a mode and an order axis, so ``weight`` is the
   full ``ω[mode, order]`` matrix ``(d, order+1)``: a bare row ``(order+1,)`` = per-order (broadcast over
   modes), a column ``(d, 1)`` = per-mode (broadcast over orders), a matrix = both. The objective is
   ``½ Σ_i ‖ω_i ⊙ r_i‖²`` over the ``d`` per-mode residual jets.