ManifoldGeometry.randn
======================

.. py:method:: t3toolbox.manifold.ManifoldGeometry.randn(frame, stack_shape = ())

   .. code-block:: python

      def randn(
              self,
              frame:          bvf.T3Frame,
              stack_shape:    typ.Tuple[int, ...] = (),  # extra tangent stack K (a batch of tangents)
      ) -> T3Tangent:  # gauged random tangent at frame


   Random tangent at ``frame``: a standard Gaussian on the tangent space ``T_xM``.

   Raw i.i.d. N(0, 1) variation cores, then the gauge projection :py:meth:`project` (``Pi``). For
   an **orthogonal** ``frame`` this is exactly the standard Gaussian on ``T_xM`` -- equivalently the
   orthogonal projection onto ``T_xM`` of the ambient standard normal. Minimal rank is **not**
   required: the gauge projection absorbs any rank redundancy, so the draw lands in the true tangent
   space regardless (verified against the ambient-normal projection on a non-minimal frame).
   ``stack_shape`` is the extra outer tangent stack ``K`` (default ``()``).

   Inherits :py:meth:`project`'s **safe-mode ORTH precondition**: a non-orthogonal ``frame`` raises
   (skipped under ``safety.unsafe()`` / a jax trace, where it yields a merely-gauged -- not true
   Gaussian -- tangent).