T3Frame.variation_shapes

t3toolbox.frame_variations_format.T3Frame.variation_shapes()

def variation_shapes(
        self,
) -> typ.Tuple[
    typ.Tuple[typ.Tuple[int, ...], ...],  # tucker_variation_shapes. len=d. elm_len=2
    typ.Tuple[typ.Tuple[int, ...], ...],  # tt_variation_shapes. len=d. elm_len=3
]:

T3Variations shapes that fit with this T3Frame.

Shapes of the “holes” in the following tensor diagrams:

1 -- L0 -- ( ) -- R2 -- R3 -- 1
     |      |      |      |
     U0     U1     U2     U3
     |      |      |      |

1 -- L0 -- L1 -- O2 -- R3 -- 1
     |     |     |     |
     U0    U1    ( )   U3
     |     |     |     |

Examples

>>> import numpy as np
>>> import t3toolbox.frame_variations_format as bvf
>>> ss = (2, 3)                                   # stack C -- NOT part of variation_shapes
>>> up_tucker_cores = (np.ones(ss+(10, 14)), np.ones(ss+(11, 15)), np.ones(ss+(12, 16)))
>>> down_tt_cores = (np.ones(ss+(1, 9, 4)), np.ones(ss+(2, 8, 5)), np.ones(ss+(3, 7, 1)))
>>> 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)))
>>> frame = bvf.T3Frame(up_tucker_cores, down_tt_cores, left_tt_cores, right_tt_cores)
>>> tucker_holes, tt_holes = frame.variation_shapes   # (tucker hole shapes, tt hole shapes)
>>> print(tucker_holes)   # one (nDi, Ni) per mode
((9, 14), (8, 15), (7, 16))
>>> print(tt_holes)       # one (rLi, nUi, rRi) per mode
((1, 10, 4), (2, 11, 5), (3, 12, 1))

Return type:

t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Tuple[int, Ellipsis], Ellipsis], t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Tuple[int, Ellipsis], Ellipsis]]