t3toolbox.manifold.tangent_randn
================================

.. py:function:: t3toolbox.manifold.tangent_randn(base: Union[t3toolbox.basis_coordinates_format.T3Base, t3toolbox.OLD_uniform.UniformT3Base], masks: Union[t3toolbox.OLD_uniform.UniformEdgeWeights, t3toolbox.OLD_uniform.UniformBVEdgeWeights] = (None, None, None), apply_gauge_projection: bool = True, randn: Callable[Ellipsis, NDArray] = np.random.randn, use_jax: bool = False) -> Union[t3toolbox.basis_coordinates_format.T3Variation, t3toolbox.OLD_uniform.UniformT3Variation]

   Draw a random T3Variation.

   :param orthogonal_base: Representations of base point on manifold where tangent space is attached.
   :type orthogonal_base: T3Base
   :param randn: Function for creating random arrays. Arguments are a sequence of ints defining the shape of the array.
                 Default: np.random.randn (numpy)
   :type randn: typ.Callable[[..., NDArray]

   :returns: * *T3Tangent* -- Random tangent vector. If base is orthogonal, ranks are minimal, and gauge projection is applied,
               then the random tangent vector is distributed according to
               a standard multivariate distribution on the tangent space.
             * **use_jax** (*bool*) -- If True, return jax arrays, if False return numpy. Should update this to use pure jax, rather than converting numpy->jax.
             * **apply_gauge_projection** (*bool*) -- Default: True. If False, gauge projection is not applied and vector is not i.i.d. N(0,1) on the tangent space

   .. seealso:: :py:obj:`t3tangent_zeros`

   .. rubric:: Examples

   Apply Gauge projection (default):

   >>> import numpy as np
   >>> import t3toolbox.tucker_tensor_train as t3
   >>> import t3toolbox.manifold as t3m
   >>> import t3toolbox.orthogonalization as orth
   >>> p = t3.t3_corewise_randn(((14,15,16), (4,5,6), (1,3,2,1)))
   >>> base, vars0 = orth.orthogonal_representations(p)
   >>> v = t3m.tangent_randn(base) # Random tangent vector, gauged.

   Don't apply Gauge projection:

   >>> import numpy as np
   >>> import t3toolbox.tucker_tensor_train as t3
   >>> import t3toolbox.manifold as t3m
   >>> import t3toolbox.orthogonalization as orth
   >>> p = t3.t3_corewise_randn(((14,15,16), (4,5,6), (1,3,2,1)))
   >>> base, vars0 = orth.orthogonal_representations(p)
   >>> v = t3m.tangent_randn(base, apply_gauge_projection=False) # Random tangent vector, ungauged