t3_inner_product#

t3toolbox.backend.t3_linalg.t3_inner_product(x, y, use_orthogonalization=True)#
def t3_inner_product(
        x: typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]],  # (tucker_cores_x, tt_cores_x)
        y: typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]],  # (tucker_cores_y, tt_cores_y)
        use_orthogonalization: bool = True,  # for numerical stability
) -> NDArray:  # HS inner product, shape=stack_shape (scalar if unstacked)

Compute Hilbert-Schmidt inner product of two Tucker tensor trains.

Parameters:

  • x (t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Sequence[NDArray], t3toolbox.backend.common.typ.Sequence[NDArray]])

  • y (t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Sequence[NDArray], t3toolbox.backend.common.typ.Sequence[NDArray]])

  • use_orthogonalization (bool)

Return type:

NDArray