Add an integer power function for second order tensors

[KeitaNakamura]

This would be useful in some cases.

julia> t = rand(Tensor{2,3});

julia> t^0 ≈ one(t)
true

julia> t^1 ≈ t
true

julia> t^2 ≈ t ⋅ t
true

julia> t^3 ≈ t ⋅ t ⋅ t
true

julia> t^-1 ≈ inv(t)
true

[KristofferC]

If we allowed for * we would get this atuomatically... The implementation here is a bit inefficient because they do not use the power by squaring method.

[KeitaNakamura]

If we allowed for * we would get this atuomatically...

Yes, I know but I thought you don't want to allow to use * operator. So, should I follow the original julia's code?

[KristofferC]

I think this is fine. I don't expect large powers to be used much and we can fix it then if someone complains.

[KristofferC]

Why throw domain error here? Can't you do inv(S)^(-p)?

[KeitaNakamura]

Oh, I would fix it. But might be inv(S)^p?

[KeitaNakamura]

No, sorry.

[KeitaNakamura]

BTW, how could I avoid errors in julia v0.6?

[KristofferC]

What's the problem on 0.6?

[KeitaNakamura]

Oh, actually Travis would fail in "constructors" section, not in "simple math".

[KeitaNakamura]

The errors are following:

constructors: Test Failed
Expression: eltype(tens_arr1) == (Tensors.Tensor){1, 1, Float64, N}
Evaluated: Tensors.Tensor{1,1,T,M} where M where T<:Real == Tensors.Tensor{1,1,Float64,1}

[KeitaNakamura]

I would add more error message just in case.

Stacktrace:
[1] macro expansion at /home/travis/.julia/v0.6/Tensors/test/test_misc.jl:42 [inlined]
[2] macro expansion at ./test.jl:853 [inlined]
[3] macro expansion at /home/travis/.julia/v0.6/Tensors/test/runtests.jl:9 [inlined]
[4] macro expansion at /home/travis/.julia/v0.6/TimerOutputs/src/TimerOutput.jl:128 [inlined]
[5] macro expansion at /home/travis/.julia/v0.6/Tensors/test/runtests.jl:8 [inlined]
[6] anonymous at ./:?

[KristofferC]

Could you add a test for t^-2 as well

[fredrikekre]

I think we should do this with Base.literal_pow on julia06

[KristofferC]

Some change in Base made tests fail..

[fredrikekre]

Its this:

julia> zeros(Tensor{2, 3}, 3)
3-element Array{Tensors.Tensor{2,3,T,M} where M where T<:Real,1}:
 [0.0 0.0 0.0; 0.0 0.0 0.0; 0.0 0.0 0.0]
 [0.0 0.0 0.0; 0.0 0.0 0.0; 0.0 0.0 0.0]
 [0.0 0.0 0.0; 0.0 0.0 0.0; 0.0 0.0 0.0]

before T and M where correct here

[KristofferC]

julia> @code_warntype zeros(Tensor{2, 3}, 3)

julia> 

wut?

julia> @which zeros(Tensor{2, 3}, 3)
ERROR: no method found for the specified argument types
Stacktrace:
 [1] which(::Any, ::Any) at ./reflection.jl:824


julia> zeros(Tensor{2, 3}, 3)
3-element Array{Tensors.Tensor{2,3,T,M} where M where T<:Real,1}:
 [0.0 0.0 0.0; 0.0 0.0 0.0; 0.0 0.0 0.0]
 [0.0 0.0 0.0; 0.0 0.0 0.0; 0.0 0.0 0.0]
 [0.0 0.0 0.0; 0.0 0.0 0.0; 0.0 0.0 0.0]

wutwut?

[KeitaNakamura]

Also

julia> methods(zeros, (Type{Tensor{2,3}}, Int))
# 0 methods for generic function "zeros":

[KristofferC]

Bisected to JuliaLang/julia#21183