t3toolbox.weighted_tucker_tensor_train.wt3_inner_product

t3toolbox.weighted_tucker_tensor_train.wt3_inner_product(A: WeightedTuckerTensorTrain, B: WeightedTuckerTensorTrain, use_orthogonalization: bool = True, use_jax: bool = False)

Computes the Hilbert-Schmidt inner product between two Tucker tensor trains.

Examples

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> import t3toolbox.weighted_tucker_tensor_train as wt3
>>> randn = np.random.randn
>>> x0 = t3.t3_corewise_randn((6,7,8), (5,6,7), (2,3,3,1), stack_shape=(4,))
>>> x_tucker_vectors = tuple([randn(4, 5), randn(4, 6), randn(4, 7)])
>>> x_tt_vectors = tuple([randn(4, 2), randn(4, 3), randn(4, 3), randn(4, 1)])
>>> x_weights = wt3.EdgeVectors(x_tucker_vectors, x_tt_vectors)
>>> x = wt3.WeightedTuckerTensorTrain(x0, x_weights)
>>> y0 = t3.t3_corewise_randn((6,7,8), (2,4,2), (1,3,1,2), stack_shape=(4,))
>>> y_tucker_vectors = tuple([randn(4, 2), randn(4, 4), randn(4, 2)])
>>> y_tt_vectors = tuple([randn(4, 1), randn(4, 3), randn(4, 1), randn(4, 2)])
>>> y_weights = wt3.EdgeVectors(y_tucker_vectors, y_tt_vectors)
>>> y = wt3.WeightedTuckerTensorTrain(y0, y_weights)
>>> x_dot_y = wt3.wt3_inner_product(x,y)
>>> print(x_dot_y)
[   8.20032492   -8.97264769 -344.13076394   -3.72479156]
>>> x_dense = x.contract_edge_weights_into_cores().to_dense()
>>> y_dense = y.contract_edge_weights_into_cores().to_dense()
>>> print(np.array([np.sum(x_dense[ii] * y_dense[ii]) for ii in range(4)]))
[   8.20032492   -8.97264769 -344.13076394   -3.72479156]