T3Variations
============

.. toctree::
   :hidden:

   /autoapi/t3toolbox/frame_variations_format/T3Variations.d
   /autoapi/t3toolbox/frame_variations_format/T3Variations.shape
   /autoapi/t3toolbox/frame_variations_format/T3Variations.stack_shape
   /autoapi/t3toolbox/frame_variations_format/T3Variations.variation_shapes
   /autoapi/t3toolbox/frame_variations_format/T3Variations.data
   /autoapi/t3toolbox/frame_variations_format/T3Variations.to_jax
   /autoapi/t3toolbox/frame_variations_format/T3Variations.to_numpy
   /autoapi/t3toolbox/frame_variations_format/T3Variations.copy
   /autoapi/t3toolbox/frame_variations_format/T3Variations.contains_jax
   /autoapi/t3toolbox/frame_variations_format/T3Variations.size
   /autoapi/t3toolbox/frame_variations_format/T3Variations.data_size
   /autoapi/t3toolbox/frame_variations_format/T3Variations.__repr__
   /autoapi/t3toolbox/frame_variations_format/T3Variations.validate
   /autoapi/t3toolbox/frame_variations_format/T3Variations.__post_init__
   /autoapi/t3toolbox/frame_variations_format/T3Variations.unstack
   /autoapi/t3toolbox/frame_variations_format/T3Variations.stack
   /autoapi/t3toolbox/frame_variations_format/T3Variations.zeros
   /autoapi/t3toolbox/frame_variations_format/T3Variations.randn
   /autoapi/t3toolbox/frame_variations_format/T3Variations.unit
   /autoapi/t3toolbox/frame_variations_format/T3Variations.zeros_like
   /autoapi/t3toolbox/frame_variations_format/T3Variations.randn_like
   /autoapi/t3toolbox/frame_variations_format/T3Variations.to_vector
   /autoapi/t3toolbox/frame_variations_format/T3Variations.from_vector
   /autoapi/t3toolbox/frame_variations_format/T3Variations.save
   /autoapi/t3toolbox/frame_variations_format/T3Variations.load
   /autoapi/t3toolbox/frame_variations_format/T3Variations.reverse
   /autoapi/t3toolbox/frame_variations_format/T3Variations.sum_stack
   /autoapi/t3toolbox/frame_variations_format/T3Variations.__add__
   /autoapi/t3toolbox/frame_variations_format/T3Variations.__sub__
   /autoapi/t3toolbox/frame_variations_format/T3Variations.__mul__
   /autoapi/t3toolbox/frame_variations_format/T3Variations.__neg__
   /autoapi/t3toolbox/frame_variations_format/T3Variations.allclose

.. py:class:: t3toolbox.frame_variations_format.T3Variations

   Tuple containing variation cores for frame-variation representations of TuckerTensorTrains.

   *Components*
       - tucker_variations    = (V0, ..., V(d-1)), elm_shape=stack_shape+(nDi, Ni)
       - tt_variations        = (H0, ..., H(d-1)), elm_shape=stack_shape+(rLi, nUi, rRi)

   The variations should fit in the "holes" of a T3Frame.

   .. seealso:: :py:obj:`T3Frame`

   .. rubric:: Examples

   Build variations that fill the holes of a base point (so ``check_fv_pair`` accepts them):

   >>> import numpy as np
   >>> import t3toolbox.frame_variations_format as bvf
   >>> ss = (2, 3)                                       # stack shape, shared by frame and variations
   >>> up_tucker_cores = (np.ones(ss+(10, 14)), np.ones(ss+(11, 15)), np.ones(ss+(12, 16)))
   >>> left_tt_cores = (np.ones(ss+(1, 10, 2)), np.ones(ss+(2, 11, 3)), np.ones(ss+(3, 12, 5)))
   >>> right_tt_cores = (np.ones(ss+(2, 10, 4)), np.ones(ss+(4, 11, 5)), np.ones(ss+(5, 12, 1)))
   >>> down_tt_cores = (np.ones(ss+(1, 9, 4)), np.ones(ss+(2, 8, 5)), np.ones(ss+(3, 7, 1)))
   >>> frame = bvf.T3Frame(up_tucker_cores, down_tt_cores, left_tt_cores, right_tt_cores)
   >>> tucker_shapes, tt_shapes = frame.variation_shapes  # the holes to fill
   >>> tucker_variations = tuple(np.ones(ss + s) for s in tucker_shapes)
   >>> tt_variations = tuple(np.ones(ss + s) for s in tt_shapes)
   >>> variations = bvf.T3Variations(tucker_variations, tt_variations)
   >>> print(variations.variation_shapes == frame.variation_shapes)   # fits the frame's holes exactly
   True


   .. py:attribute:: tucker_variations
      :type:  t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.NDArray, Ellipsis]


   .. py:attribute:: tt_variations
      :type:  t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.NDArray, Ellipsis]


   .. py:attribute:: __rmul__

Methods
-------

.. autoapisummary::

   t3toolbox.frame_variations_format.T3Variations.d
   t3toolbox.frame_variations_format.T3Variations.shape
   t3toolbox.frame_variations_format.T3Variations.stack_shape
   t3toolbox.frame_variations_format.T3Variations.variation_shapes
   t3toolbox.frame_variations_format.T3Variations.data
   t3toolbox.frame_variations_format.T3Variations.to_jax
   t3toolbox.frame_variations_format.T3Variations.to_numpy
   t3toolbox.frame_variations_format.T3Variations.copy
   t3toolbox.frame_variations_format.T3Variations.contains_jax
   t3toolbox.frame_variations_format.T3Variations.size
   t3toolbox.frame_variations_format.T3Variations.data_size
   t3toolbox.frame_variations_format.T3Variations.__repr__
   t3toolbox.frame_variations_format.T3Variations.validate
   t3toolbox.frame_variations_format.T3Variations.__post_init__
   t3toolbox.frame_variations_format.T3Variations.unstack
   t3toolbox.frame_variations_format.T3Variations.stack
   t3toolbox.frame_variations_format.T3Variations.zeros
   t3toolbox.frame_variations_format.T3Variations.randn
   t3toolbox.frame_variations_format.T3Variations.unit
   t3toolbox.frame_variations_format.T3Variations.zeros_like
   t3toolbox.frame_variations_format.T3Variations.randn_like
   t3toolbox.frame_variations_format.T3Variations.to_vector
   t3toolbox.frame_variations_format.T3Variations.from_vector
   t3toolbox.frame_variations_format.T3Variations.save
   t3toolbox.frame_variations_format.T3Variations.load
   t3toolbox.frame_variations_format.T3Variations.reverse
   t3toolbox.frame_variations_format.T3Variations.sum_stack
   t3toolbox.frame_variations_format.T3Variations.__add__
   t3toolbox.frame_variations_format.T3Variations.__sub__
   t3toolbox.frame_variations_format.T3Variations.__mul__
   t3toolbox.frame_variations_format.T3Variations.__neg__
   t3toolbox.frame_variations_format.T3Variations.allclose