t3toolbox.uniform_tucker_tensor_train.ut3_inner_product

t3toolbox.uniform_tucker_tensor_train.ut3_inner_product(x: UniformTuckerTensorTrain, y: UniformTuckerTensorTrain, use_orthogonalization: bool = True, use_jax: bool = False)

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

Examples

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> import t3toolbox.uniform_tucker_tensor_train as ut3
>>> x = t3.t3_corewise_randn((14,15,16), (4,6,5), (2,3,2,2), stack_shape=(2,3))
>>> ux = ut3.t3_to_ut3(x)
>>> y = t3.t3_corewise_randn((14,15,16), (6,7,8), (3,5,6,1), stack_shape=(2,3))
>>> uy = ut3.t3_to_ut3(y)
>>> ux_dot_uy = ut3.ut3_inner_product(ux, uy)
>>> ux_dot_uy2 = np.einsum('...xyz,...xyz->...', x.to_dense(), y.to_dense())
>>> print(np.linalg.norm(ux_dot_uy - ux_dot_uy2) / np.linalg.norm(ux_dot_uy))
7.667494312151743e-15