TuckerTensorTrain.to_dense

t3toolbox.tucker_tensor_train.TuckerTensorTrain.to_dense(squash_tails=True)

def to_dense(
        self,
        squash_tails: bool = True,
) -> NDArray:

Form dense tensor from this TuckerTensorTrain.

Parameters:

squash_tails (bool, optional) – Whether to contract the leading and trailing 1s with the first and last TT indices. (Default: True)

Returns:

Dense tensor represented by this TuckerTensorTrain, which has shape=stack_shape+(N0, ..., N(d-1)) if squash_tails=True, or shape=stack_shape+(r0,N0,...,N(d-1),rd) if squash_tails=False.

Return type:

NDArray

Examples

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> np.random.seed(0)
>>> randn = np.random.randn
>>> tucker_cores = (randn(4,14),randn(5,15),randn(6,16))
>>> tt_cores = (randn(2,4,3), randn(3,5,2), randn(2,6,5))
>>> x = t3.TuckerTensorTrain(tucker_cores, tt_cores)
>>> x_dense = x.to_dense() # Convert TuckerTensorTrain to dense tensor
>>> ((B0,B1,B2), (G0,G1,G2)) = tucker_cores, tt_cores
>>> x_dense2 = np.einsum('xi,yj,zk,axb,byc,czd->ijk', B0, B1, B2, G0, G1, G2)
>>> print(np.allclose(x_dense, x_dense2))
True

Example where leading and trailing ones are not contracted

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> np.random.seed(0)
>>> randn = np.random.randn
>>> tucker_cores = (randn(4,14),randn(5,15),randn(6,16))
>>> tt_cores = (randn(2,4,3), randn(3,5,2), randn(2,6,2))
>>> x = t3.TuckerTensorTrain(tucker_cores, tt_cores)
>>> x_dense = x.to_dense(squash_tails=False) # Convert TuckerTensorTrain to dense tensor
>>> print(x_dense.shape)                    # keeps the outer TT bonds r0=rd=2
(2, 14, 15, 16, 2)
>>> ((B0,B1,B2), (G0,G1,G2)) = tucker_cores, tt_cores
>>> x_dense2 = np.einsum('xi,yj,zk,axb,byc,czd->aijkd', B0, B1, B2, G0, G1, G2)
>>> print(np.allclose(x_dense, x_dense2))
True

Example with stacking

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> np.random.seed(0)
>>> randn = np.random.randn
>>> tucker_cores = (randn(2,3, 4,10), randn(2,3, 5,11), randn(2,3, 6,12))
>>> tt_cores = (randn(2,3, 2,4,3), randn(2,3, 3,5,2), randn(2,3, 2,6,5))
>>> x = t3.TuckerTensorTrain(tucker_cores, tt_cores)
>>> x_dense = x.to_dense() # Convert TuckerTensorTrain to dense tensor
>>> print(x_dense.shape)                    # leading (2,3) is the stack_shape
(2, 3, 10, 11, 12)
>>> ((B0,B1,B2), (G0,G1,G2)) = tucker_cores, tt_cores
>>> x_dense2 = np.einsum('uvxi,uvyj,uvzk,uvaxb,uvbyc,uvczd->uvijk', B0, B1, B2, G0, G1, G2)
>>> print(np.allclose(x_dense, x_dense2))
True