Wood SN, Scheipl F, Faraway J (2013) Straightforward intermediate rank tensor product smoothing in mixed models. Stat Comput 23(3):341-360Wood, S. N., F. Scheipl, and J. J. Faraway (2013). "Straightforward intermediate rank tensor product smoothing in mixed models". In: Statistics and...
Although there has been some work on low-rank models for tensorial data, such as[5,6,12,13,18,19], the “rank” of tensors they have used are far from satisfactory. Although CP decomposition[9]based tensor rank is a natural generalization of matrix rank, unfortunately it is not in gen...
classSum(object):rank=Nonedefget_shape(self,sy):returnsy[:-1]definterp(self,sy,vy,vz):p=product(sy[:-1])foriinxrange(p):vz[i]=0foriinxrange(sy[-1]):vyi=vy.subview(i,sy[-1])forjinxrange(p):vz[j]+=vyi[j] 先算出dimension的积,这样多个循环就合并成了一个循环 defproduct(...
Fast multidimensional convolution in low-rank tensor formats via cross approximation. SIAM J. Sci. Comput., 37(2):A565-A582, 2015.Rakhuba MV, Oseledets IV. Fast multidimensional convolution in low-rank formats via cross approximation. SIAM J. Sci. Comput. 2015; :in press....
To present these relations, we first note that one of the defining properties of the Deligne series is the appearance of precisely three real irreducible representations in the decomposition of the symmetric tensor product of two adjoint representations.Footnote 8 Following the notations of [30], we...
the scalar product A.B is a scalar quantity, the vector product AxB is a vector and the tensor product AB is a tensor of rank 2 (often a cross with a circle around is used for the operator). Tensors of rank 3 typically arise by taking the gradient of tensors of rank 2 (eg stres...
However, a suitable sparsity measure for tensor needs to be defined, unlike vectors or matrices, which is always not an easy task. On the basis of tensor-tensor product (t-product), Kilmer et al. [15] extend matrix-based singular value decomposition (SVD) to tensor SVD (t-SVD), and ...
Source: Tensor.cs Gets a value indicating the rank, or number of dimensions, of this Tensor<T>. C# Copy public int Rank { get; } Property Value Int32 IntPtr with the number of dimensions. Implements Rank Applies to ProductVersions .NET 8 (package-provided), 9 (package-provided),...
TensorProductOfRepresentations Library Tensor Tools Overview Overview of General Relativity Computations Working with Abstract Forms &algmult &minus &mult &plus &tensor &wedge AlgebraicOperations Annihilator ApplyTransformation ChangeFrame ComplementaryBasis ComposeTransformations Convert DeRhamHomotopy DGbasis DGconju...
The t-SVD, derived from tensor–tensor product (t-product), can be regarded as a high-dimensional generalization of matrix SVD, which exploits the intrinsic structure in tensor form. Further, we can easily calculate the tubal rank, defined by t-SVD, and its corresponding convex relaxation [2...