Tensor Inversion

Inversion of 2nd and 4th order tensors are supported.

Base.inv
Tensorial.adj

Base.inv — Function

inv(::AbstractSecondOrderTensor)
inv(::AbstractSymmetricSecondOrderTensor)
inv(::AbstractFourthOrderTensor)
inv(::AbstractSymmetricFourthOrderTensor)

Compute the inverse of a tensor.

Examples

julia> x = rand(SecondOrderTensor{3})
3×3 Tensor{Tuple{3, 3}, Float64, 2, 9}:
 0.325977  0.894245  0.953125
 0.549051  0.353112  0.795547
 0.218587  0.394255  0.49425

julia> inv(x)
3×3 Tensor{Tuple{3, 3}, Float64, 2, 9}:
 -587.685  -279.668   1583.46
 -411.743  -199.494   1115.12
  588.35    282.819  -1587.79

julia> x ⋅ inv(x) ≈ one(I)
true

source

Tensorial.adj — Function

adj(::AbstractSecondOrderTensor)
adj(::AbstractSymmetricSecondOrderTensor)

Compute the adjugate matrix.

Examples

julia> x = rand(Mat{3,3});

julia> Tensorial.adj(x) / det(x) ≈ inv(x)
true

source