T3Tangent.absorb_weights
========================

.. py:method:: t3toolbox.manifold.T3Tangent.absorb_weights(weights)

   .. code-block:: python

      def absorb_weights(self, weights: 'bvf.T3FrameWeights') -> 'T3Tangent':


   Absorb the metric ``weights`` into this tangent's **variation** cores (``down``->V,
   ``up``/``left``/``right``->H), returning the weighted tangent **at the same frame**. Its
   :py:meth:`corewise_norm` equals :py:meth:`weighted_norm`.

   **Warning -- the result is not gauged.** Scaling the variation coordinates breaks the gauge
   conditions (the frame's orthogonality is untouched), so the returned tangent is a *coordinate*
   reweighting: :py:meth:`corewise_norm` / :py:meth:`corewise_inner` are correct on it, but the
   Hilbert-Schmidt :py:meth:`ManifoldGeometry.norm` / :py:meth:`~ManifoldGeometry.inner` need a gauged
   tangent. Re-gauge with :py:meth:`ManifoldGeometry.project_oblique` (which preserves the represented
   vector) or :py:meth:`ManifoldGeometry.project` if you need HS semantics.

   .. rubric:: Examples

   >>> import numpy as np
   >>> import t3toolbox.tucker_tensor_train as t3
   >>> import t3toolbox.frame_variations_format as bvf
   >>> import t3toolbox.manifold as t3m
   >>> np.random.seed(0)
   >>> x = t3.TuckerTensorTrain.randn((6, 7, 8), (2, 2, 2), (1, 2, 2, 1))
   >>> frame, _ = bvf.t3_orthogonal_representations(x)
   >>> v = t3m.MANIFOLD.project_oblique(t3m.COREWISE.randn(frame))   # a gauged tangent at the frame
   >>> print(v.is_gauged())
   True
   >>> W = bvf.T3FrameWeights.from_t3weights(t3.T3Weights.from_t3svd(x))   # a metric (the point's sigmas)
   >>> vw = v.absorb_weights(W)                                      # weighted tangent, same frame
   >>> print(vw.is_gauged())                                        # weighting broke the gauge...
   False
   >>> print(t3m.MANIFOLD.project_oblique(vw).is_gauged())          # ...project_oblique re-gauges it
   True