Dense Tensor

Some operations with respect to basic dense tensor, I need to add some latex equations to my document

Functions

# SAIGtensor.initTensor — Function.

InitTensor(N, I, D)

create a tensor object, here is some inline math: $\sqrt[n]{1+x+x^2+\ldots}$

Arguments

  • N: Int64, dimensions
  • I: Array{Int64}, size of each dimension
  • D: Array{Float64}, multi-dimension array

Returns

  • X: tensor object

Example

julia> N = 5; I = [23, 42, 13, 14, 17]; D = rand(I...)
julia> X = InitTensor(N, I, D)

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# SAIGtensor.matricization — Function.

Xn = matricization(X::tensor, n::Int64)

unfolding tensor along n dimension

Arguments

  • X: tensor, tensor object
  • n: Int64, unfolding along n dimension, 1<= n <= N

Returns

  • Xn: Array{Float64,2}, matrix

Example

julia> N = 3; I = [3, 4, 2]; D = reshape(collect(1:prod(I)), I...)
julia> X = initTensor(N, I, D)
julia> n = 3
julia> Xn = matricization(X, n)

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# SAIGtensor.unmatricization — Function.

X = unmatricization(Xn, n, I)

folding an Array back to tensor

Arguments

  • Xn: Array{Float64}, the array to be folded
  • n: Int64, folding along n dimension, 1<= n <= N
  • I: Array{Int64}, size of tensor

Returns

  • X: tensor

Example

julia> N = 3; I = [3, 4, 2]; D = reshape(collect(1:prod(I)), I[1], prod(I[2:N]))
julia> n = 1; X = unmatricization(D, n, I)

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# SAIGtensor.KRP — Function.

r = KRP(a1, a2)

Khatri-Rao product a2 ⊙ a1

Arguments

  • a1: Array{Float64}, it can be a 1D or 2D array
  • a2: Array{Float64}, it can be a 1D or 2D array

Returns

  • r: Array{Float64}, it can be a 1D or 2D array

Example

julia> R = 20; m1 = 77; m2 = 33;
julia> a1 = rand(m1,R); a2 = rand(m2,R);
julia> r = KRP(a1, a2)

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# SAIGtensor.recursiveKRP — Function.

r = recursiveKRP(A)

recursive Khatri-Rao product A[N]⊙...⊙A[1]

Arguments

  • A: Array{Array{Float64}}, each element can be 1D or 2D array

Returns

  • r: Array{Float64}, it may be a 1D or 2D array

Example

julia> I = [21, 32, 43, 24]; R = 3;
julia> N = length(I);
julia> A = Array{Array{Float64}}(N)
julia> for m = 1 : N
julia>     A[m] = rand(I[m], R)
julia> end
julia> r1 = recursiveKRP(A);

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# SAIGtensor.tnorm — Function.

l = tnorm(X)

compute the frobenius norm of tensor

Arguments

  • X: tensor

Returns

  • l: the frobenius norm of X

Example

julia> I = [21, 32, 43]; N = 3; D = rand(I...)
julia> l = tnorm(tensor(N, I, D))

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# SAIGtensor.ttv — Function.

y = ttv(X, v, dims)

compute tensor times a set of vectors

Arguments

  • X: tensor
  • v: Array{Array{Float64,1}}
  • dims: specification the multiplication on which dimension

Returns

  • y: Array{Float64,1}, length is prod(remdims)

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