Inexact error when constructing SymmetricTensor

[henrij22]

Dear all,

I now came across the following behavior multiple times.
When costructing a SymmetricTensor, either from an expression or a Matrix i sometimes get an InexactError.

    SymmetricTensor{2, 𝔇}(N * diagm(S) * N')

produces

ERROR: InexactError: convert(SymmetricTensor{2, 3, Float64}, 
[1808.135883822873 549.1225426055513 0.0; 549.1225426055512 1016.2664852460059 0.0; 0.0 0.0 678.3238495344586])
Stacktrace:
 [1] convert
   @ C:\Users\xxx\.julia\packages\Tensors\DZnYM\src\promotion_conversion.jl:86 [inlined]

as you can see the off diagonal entry only differs at the last digit. Is there somehow a way to set a tolerance for the symmetry check?
As far as i can tell the check happens here:

Tensors.jl/src/symmetric.jl

Line 86 in b7dae0e

@inline LinearAlgebra.issymmetric(t::Tensor{2, 1}) = true

Of course you can circumvent the check by doing the construction via a function

    S_ = N * diagm(S) * N'
    SymmetricTensor{2, 𝔇}((i,j) -> S_[i,j])

But this adds another line and sometimes a symmetry check (with a tolerance) might be beneficial.

Thank you so much

[fredrikekre]

Is there a reason why N and S in your case arent' Tensors? If they were I would do this:

symmetric(N ⋅ D ⋅ N')

If you need to keep them as matrices, perhaps casting to Tensor first:

symmetric(Tensor{2, 𝔇}(N * diagm(S) * N'))

[henrij22]

Hi Thank you for your quick answer.

This actually helped me. I didn't know about the symmetric function.
From my side we can close this issue.

[fredrikekre]

Note that symmetric will compute the symmetric part, i.e. (A + A') / 2, but of course if you know A is already symmetric it is the same.

[fredrikekre]

Could be usefule to export

Tensors.jl/src/symmetric.jl

Lines 68 to 75 in b7dae0e

	# Unsafe versions that just truncates
	@inline unsafe_symmetric(S::SymmetricTensors) = S
	@inline function unsafe_symmetric(S::Tensor{2, dim}) where {dim}
	SymmetricTensor{2, dim}(@inline function(i, j) @inbounds S[i,j] end)
	end
	@inline function unsafe_symmetric(S::Tensor{4, dim}) where {dim}
	SymmetricTensor{4, dim}(@inline function(i, j, k, l) @inbounds return S[i,j,k,l] end)
	end

to do "truncated symmetric" to avoid the extra computation.

[henrij22]

Thank you fir your help, this is indeed very useful.