gradient_descent
================

.. py:function:: t3toolbox.optimizers.gradient_descent(geometry, kind, sample, data, x0, order = None, weight = None, regularizer = None, chunk_size = 'auto', **kwargs)

   .. code-block:: python

      def gradient_descent(
              geometry,                       # ragged or uniform geometry singleton (must match x0's representation)
              kind:     str,                  # 'apply' / 'entries' / 'probe' (+ '_derivatives')
              sample:   typ.Any,              # ww / index, or (ww, pp) / (index, pp) for derivatives
              data:     typ.Any,             # observed values to fit
              x0:       Point,                # initial point (any cores; the geometry orthogonalizes internally)
              order:    typ.Optional[int] = None,  # derivative kinds: highest order (required)
              weight:   typ.Optional[typ.Any] = None,  # residual weight ω: per-mode (probe) / ω[mode,order] (derivatives)
              regularizer: typ.Any = None,    # optional regularizer, e.g. optimizers.IdentityRegularizer(λ) (ragged only)
              chunk_size: typ.Any = 'auto',   # probe_derivatives 𝒥ᵀ memory chunk; 'auto' -> estimate_chunk_size (docs/chunking.md)
              **kwargs,                       # forwarded to backend.optimizers.gradient_descent (n_iter, gtol_rel, ...)
      ) -> typ.Tuple[Point, dict]:            # (x_opt, stats)


   Fit ``x`` to ``data`` by steepest descent (Cauchy step + Armijo line search) on ``geometry``.

   Accepts a ragged ``TuckerTensorTrain`` (with ``manifold.MANIFOLD`` / ``COREWISE``) or a uniform
   ``UniformTuckerTensorTrain`` (with ``uniform_manifold.UNIFORM_MANIFOLD`` / ``UNIFORM_COREWISE``); the
   representation is inferred from ``x0`` and returned in kind. Pass ``regularizer`` (e.g.
   ``optimizers.IdentityRegularizer(λ)``) to add ``ρ(x)`` to the objective (ragged only for now). See
   :py:func:`t3toolbox.backend.optimizers.gradient_descent`.