tt_sketch.drm

class tt_sketch.drm.dense_gaussian_drm.DenseGaussianDRM(rank: Union[Tuple[int, ...], int], shape: Tuple[int, ...], transpose: bool, seed: Optional[int] = None, **kwargs)

Dense Gaussian DRM.

The DRM is stored as a list of matrices, one for each mode.

sketch_dense(tensor)

Return list of dense DRMs. Of shape (np.prod(tensor.shape[ :mu+1]), rank[mu])

sketch_sparse(tensor)

Computes list of sketching matrices sampled into a vector using the indices of tensor for each unfolding. Shape of each vector is v[mu] = (rank[mu], tensor.nnz). This way the contraction between tensor and the sketching matrix is of form np.dot(tensor.entries, v[mu])

sketch_tt(tensor)

List of contractions of form \(Y_\mu^\top\mathcal{T}^{\leq\mu}\) where \(Y_\mu\) is the DRM, and \(\mathcal T^{\leq\mu}\) the contraction of the first \(\mu\) cores of tensor.

Returns array of shape (tensor.rank[mu], drm.rank[mu])

sketching_mats: List[ndarray[Any, dtype[float64]]]

class tt_sketch.drm.sparse_gaussian_drm.SparseGaussianDRM(rank: Union[Tuple[int, ...], int], shape: Tuple[int, ...], transpose: bool, seed: Optional[int] = None, **kwargs)

‘Sparse’ Gaussian DRM

Mathematically equivalent DenseGaussianDRM, but entries of the DRM are computed lazily/on-demand using a hashing algorithm. This makes it computationally feasible for very sparse tensors.

rank: Tuple[int, ...]

sketch_sparse(tensor)

Computes list of sketching matrices sampled into a vector using the indices of tensor for each unfolding. Shape of each vector is v[mu] = (rank[mu], tensor.nnz). This way the contraction between tensor and the sketching matrix is of form np.dot(tensor.entries, v[mu])

class tt_sketch.drm.sparse_sign_drm.SparseSignDRM(rank: Union[Tuple[int, ...], int], shape: Tuple[int, ...], transpose: bool, seed: Optional[int] = None, num_non_zero_per_row: Optional[Tuple[int, ...]] = None, **kwargs)

Sparse DRM where each row is a vector with fixed number of +/-1 entries.

The number of nonzero entries are determined by num_non_zero_per_row. Like SparseGaussianDRM, entries are computed lazily/on-demand using a hashing algorithm.

rank: Tuple[int, ...]

sketch_sparse(tensor)

Computes list of sketching matrices sampled into a vector using the indices of tensor for each unfolding. Shape of each vector is v[mu] = (rank[mu], tensor.nnz). This way the contraction between tensor and the sketching matrix is of form np.dot(tensor.entries, v[mu])

class tt_sketch.drm.tensor_train_drm.TensorTrainDRM(rank: Union[Tuple[int, ...], int], shape: Tuple[int, ...], transpose: bool, seed: Optional[int] = None, **kwargs)

Tensor train DRM. Sketches with partial contractions of a fixed TT.

cores: List[ndarray[Any, dtype[float64]]]

sketch_cp(tensor)

List of contractions of form \(Y_\mu^\top\mathcal{T}^{\leq\mu}\) where \(Y_\mu\) is the DRM, and \(\mathcal T^{\leq\mu}\) the contraction of the first \(\mu\) cores of tensor.

Returns array of shape (tensor.rank[mu], drm.rank[mu])

sketch_dense(tensor)

Return list of dense DRMs. Of shape (np.prod(tensor.shape[ :mu+1]), rank[mu])

sketch_sparse(tensor)

Computes list of sketching matrices sampled into a vector using the indices of tensor for each unfolding. Shape of each vector is v[mu] = (rank[mu], tensor.nnz). This way the contraction between tensor and the sketching matrix is of form np.dot(tensor.entries, v[mu])

sketch_tt(tensor)

List of contractions of form \(Y_\mu^\top\mathcal{T}^{\leq\mu}\) where \(Y_\mu\) is the DRM, and \(\mathcal T^{\leq\mu}\) the contraction of the first \(\mu\) cores of tensor.

Returns array of shape (tensor.rank[mu], drm.rank[mu])

sketch_tucker(tensor)

List of contractions of form \(Y_\mu^\top(U_1\otimes\cdots\otimes U_\mu)\) where Y_\mu is the DRM, and \(U_\mu\) denotes the factors of the Tucker decomposition.

Returns array of shape (np.prod(tensor.rank[:mu]), drm.rank[mu])

tt_sketch.drm.fast_lazy_gaussian.hash_int_c()

Use simple hashing for generating random numbers from indices deterministically. See https://stackoverflow.com/questions/664014/what-integer-hash-function-are-good-that-accepts-an-integer-hash-key

tt_sketch.drm.fast_lazy_gaussian.inds_to_normal()

Converts a list of indices into the associated entries of gaussian matrix

tt_sketch.drm.fast_lazy_gaussian.inds_to_sparse_sign()

Converts a list of indices into the non-zero entries of a sparse sign matrix