Source code for tensorly.tenalg.core_tenalg.generalised_inner_product

from ... import backend as T
import numpy as np

# Author: Jean Kossaifi
# License: BSD 3 clause

[docs]def inner(tensor1, tensor2, n_modes=None): """Generalised inner products between tensors Takes the inner product between the last (respectively first) `n_modes` of `tensor1` (respectively `tensor2`) Parameters ---------- tensor1, tensor2 : tensor n_modes : int, default is None * if None, the traditional inner product is returned (i.e. a float) * otherwise, the product between the `n_modes` last modes of `tensor1` and the `n_modes` first modes of `tensor2` is returned. The resulting tensor's order is `ndim(tensor1) - n_modes`. Returns ------- inner_product : float if n_modes is None, tensor otherwise """ # Traditional inner product if n_modes is None: if tensor1.shape != tensor2.shape: raise ValueError( "Taking a generalised product between two tensors without specifying common modes" " is equivalent to taking inner product." "This requires tensor1.shape == tensor2.shape." f"However, got shapes {tensor1.shape} and {tensor2.shape}" ) return T.sum(tensor1 * tensor2) # Inner product along `n_modes` common modes shape_t1 = list(T.shape(tensor1)) shape_t2 = list(T.shape(tensor2)) common_modes = shape_t1[len(shape_t1) - n_modes :] common_size = int( output_shape = shape_t1[:-n_modes] + shape_t2[n_modes:] if common_modes != shape_t2[:n_modes]: raise ValueError( f"Incorrect shapes for inner product along {n_modes} common modes." f"Shapes {tensor1.shape} and {tensor2.shape}" ) inner_product = T.reshape(tensor1, (-1, common_size)), T.reshape(tensor2, (common_size, -1)) ) return T.reshape(inner_product, output_shape)