tensorlearn 1.1.0

A Python Package for Advanced Tensor Learning Methods

TensorLearn

TensorLearn is a Python library distributed on Pypi for implementing tensor learning methods.

This is a package under development. Yet, the available methods are final and functional. The backend is Numpy.

Installation

Use the package manager pip to install tensorlearn in Python.

pip install tensorlearn

methods

Decomposition Methods

• auto_rank_tt(tensor, error_bound)

Tensor Operations for Tensor-Train

• tt_to_tensor(factors)

• tt_compression_ratio(factors)

Tensor Operations

• tensor_resize(tensor,new_shape)

• unfold(tensor)

• tensor_frobenius_norm(tensor)

Matrix Operations

• error_truncated_svd(x,error)

---

auto_rank_tt

tensorlearn.auto_rank_tt(tensor, epsilon)

This implementation of tensor-train decomposition determines the ranks automatically based on a given error bound according to Oseledets (2011). Therefore the user does not need to specify the ranks. Instead the user specifies an upper error bound (epsilon) which bounds the error of the decomposition. For more information and details please see the page tensor-train decomposition.

Arguments

@tensor < numpy array > - The given tensor to be decomposed.

@epsilon < float > - The error bound of decomposition in the range [0,1].

Return

TT factors < list of numpy arrays > - The list includes numpy arrays of factors (or TT cores) according to TT decomposition. Length of the list equals the dimension of the given tensor to be decomposed.

Example

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tt_to_tensor

tensorlearn.tt_to_tensor(factors)

Return the full tensor given the TT factors

Arguments

@factors < list of numpy arrays > - TT factors

Return

full tensor < numpy array >

Example

---

tt_compression_ratio

tensorlearn.tt_compression_ratio(factors)

Calculate data compression ratio for tensor-train decompostion

Arguments

@factors < list of numpy arrays > - TT factors

Return

Compression ratio < float >

Example

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tensor_resize

tensorlearn.tensor_resize(tensor, new_shape)

Reshape the given tensor to a new shape. The new size must be bigger than or equal to the original shape. If the new shape results in a tensor of greater size (number of elements) the tensor fills with zeros. This works similar to numpy.ndarray.resize()

Arguments

@tensor < numpy array > - the given tensor

@new_shape < tuple > - new shape

Return

tensor < numpy array > - tensor with new given shape

---

unfold

tensorlearn.unfold(tensor, n)

Unfold the tensor with respect to dimension n.

Arguments

@tensor < numpy array > - tensor to be unfolded

@n < int > - dimension based on which the tensor is unfolded

Return

matrix < numpy array > - unfolded tensor with respect to dimension n

---

tensor_frobenius_norm

tensorlearn.tensor_frobenius_norm(tensor)

Calculate the frobenius norm of the given tensor.

Arguments

@tensor < numpy array > - the given tensor

Return

frobenius norm < float >

Example

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error_truncated_svd

tensorlearn.error_truncated_svd(x, error)

Conduct a compact svd and return sigma (error)-truncated SVD of a given matrix. This is an implementation using numpy.linalg.svd with full_matrices=False. This method is used in TT-SVD algorithm in auto_rank_tt.

Arguments

@x < 2D numpy array > - the given matrix to be decomposed

@error < float > - the given error in the range [0,1]

Return

r, u, s, vh < int, numpy array, numpy array, numpy array >