To reference or cite the objects present in the Software Heritage archive, permalinks based on SoftWare Heritage persistent IDentifiers (SWHIDs) must be used instead of copying and pasting the url from the address bar of the browser (as there is no guarantee the current URI scheme will remain the same over time).
Select below a type of object currently browsed in order to display its associated SWHID and permalink.
""" Core operations on Kruskal tensors. """ import numpy as np from .base import fold, tensor_to_vec from .tenalg import khatri_rao # Author: Jean Kossaifi # License: BSD 3 clause def kruskal_to_tensor(factors): """Turns the Khatri-product of matrices into a full tensor ``factor_matrices = [|U_1, ... U_n|]`` becomes a tensor shape ``(U.shape, U.shape, ... U[-1].shape)`` Parameters ---------- factors : ndarray list list of factor matrices, all with the same number of columns i.e. for all matrix U in factor_matrices: U has shape ``(s_i, R)``, where R is fixed and s_i varies with i Returns ------- ndarray full tensor of shape ``(U.shape, ... U[-1].shape)`` Notes ----- This version works by first computing the mode-0 unfolding of the tensor and then refolding it. There are other possible and equivalent alternate implementation. Version slower but closer to the mathematical definition of a tensor decomposition: >>> from functools import reduce >>> def kt_to_tensor(factors): ... for r in range(factors.shape): ... vecs = np.ix_(*[u[:, r] for u in factors]) ... if r: ... res += reduce(np.multiply, vecs) ... else: ... res = reduce(np.multiply, vecs) ... return res """ shape = [factor.shape for factor in factors] full_tensor = np.dot(factors, khatri_rao(factors[1:]).T) return fold(full_tensor, 0, shape) def kruskal_to_unfolded(factors, mode): """Turns the khatri-product of matrices into an unfolded tensor turns ``factors = [|U_1, ... U_n|]`` into a mode-`mode` unfolding of the tensor Parameters ---------- factors : ndarray list list of matrices, all with the same number of columns ie for all u in factor_matrices: u[i] has shape (s_u_i, R), where R is fixed mode: int mode of the desired unfolding Returns ------- ndarray unfolded tensor of shape (tensor_shape[mode], -1) Notes ----- Writing factors = [U_1, ..., U_n], we exploit the fact that ``U_k = U[k].dot(khatri_rao(U_1, ..., U_k-1, U_k+1, ..., U_n))`` """ return factors[mode].dot(khatri_rao(factors, skip_matrix=mode).T) def kruskal_to_vec(factors): """Turns the khatri-product of matrices into a vector (the tensor ``factors = [|U_1, ... U_n|]`` is converted into a raveled mode-0 unfolding) Parameters ---------- factors : ndarray list list of matrices, all with the same number of columns i.e.:: for u in U: u[i].shape == (s_i, R) where `R` is fixed while `s_i` can vary with `i` Returns ------- ndarray vectorised tensor """ return tensor_to_vec(kruskal_to_tensor(factors))
Computing file changes ...