Remove zero(::UnitQuaternion)

[hyrodium]

This PR fixes #157.

[codecov-commenter]

Codecov Report

Merging #159 (8aa6e26) into master (38b208b) will increase coverage by 0.17%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #159      +/-   ##
==========================================
+ Coverage   85.40%   85.57%   +0.17%     
==========================================
  Files          12       12              
  Lines        1261     1269       +8     
==========================================
+ Hits         1077     1086       +9     
+ Misses        184      183       -1     

Impacted Files	Coverage Δ
src/unitquaternion.jl	96.17% <ø> (+0.52%)	⬆️
src/core_types.jl	89.83% <100.00%> (+0.83%)	⬆️

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[hyrodium]

I've also added ArgumentError to avoid zero(<:Rotation).

Before this PR

julia> zero(RotMatrix3{Float64})
3×3 RotMatrix3{Float64} with indices SOneTo(3)×SOneTo(3):
 0.0  0.0  0.0
 0.0  0.0  0.0
 0.0  0.0  0.0

After this PR

julia> zero(RotMatrix3{Float64})
ERROR: ArgumentError: There is no additive identity for Rotation. Consider using the one(RotMatrix3{Float64}) method instead.
Stacktrace:
 [1] zero(T::Type{RotMatrix3{Float64}})
   @ Rotations ~/.julia/dev/Rotations/src/core_types.jl:14
 [2] top-level scope
   @ REPL[2]:1

[goretkin]

See comment at #157 (comment)

[hyrodium]

Here's an updated error message:

"$T is a subtype of AbstractMatrix, but there is no additive identity for Rotation. To get a non-rotation instance, consider using the one($T) method instead."

Is there any problem with this? I'm not native English speaker, so there may be some mistakes. :)

[andyferris]

Thanks @hyrodium.

I'm a bit concerned about the argument error, though. Every rotation is meant to be a fully-functioning AbstractMatrix. Generic code might call zero(x), in which case we can just return an SMatrix. Just like rotation + rotation gives an SMatrix (you can think of zero() providing the identity for the + operation, which is defined but not closed) so should zero.

Currently we have:

julia> r = one(RotMatrix3{Float64})
3×3 RotMatrix3{Float64} with indices SOneTo(3)×SOneTo(3):
 1.0  0.0  0.0
 0.0  1.0  0.0
 0.0  0.0  1.0

julia> r + r
3×3 StaticArrays.SMatrix{3, 3, Float64, 9} with indices SOneTo(3)×SOneTo(3):
 2.0  0.0  0.0
 0.0  2.0  0.0
 0.0  0.0  2.0

julia> zero(r)
3×3 RotMatrix3{Float64} with indices SOneTo(3)×SOneTo(3):
 0.0  0.0  0.0
 0.0  0.0  0.0
 0.0  0.0  0.0

EDIT - we should fix up this last one

We are extending the AbstractArray interface here - as a general rule, we can add functionality but not subtract functionality.

[hyrodium]

At first, I thought zero(T) should be a instance of T, but now, I agree with that zero(::Rotation) returns SMatrix{3,3}(0,0,0,0,0,0,0,0,0).

I'll fix it!

[hyrodium]

I've updated the zero funciton.

julia> zero(MRP)
3×3 StaticArrays.SMatrix{3, 3, Float64, 9} with indices SOneTo(3)×SOneTo(3):
 0.0  0.0  0.0
 0.0  0.0  0.0
 0.0  0.0  0.0

julia> zero(RotMatrix{3})
3×3 StaticArrays.SMatrix{3, 3, Float64, 9} with indices SOneTo(3)×SOneTo(3):
 0.0  0.0  0.0
 0.0  0.0  0.0
 0.0  0.0  0.0

julia> zero(RotMatrix{2})
2×2 StaticArrays.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
 0.0  0.0
 0.0  0.0

julia> zero(Angle2d)
2×2 StaticArrays.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
 0.0  0.0
 0.0  0.0

But, there sitll be some issues around zeros funciton.

julia> zeros(MRP,2)
2-element Vector{MRP}:
 [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0]
 [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0]

julia> zeros(RotMatrix{3},2)
2-element Vector{RotMatrix{3, T, L} where {T, L}}:
 [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]

julia> zeros(RotMatrix{2},2)
2-element Vector{RotMatrix{2, T, L} where {T, L}}:
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]

julia> zeros(Angle2d,2)
2-element Vector{Angle2d}:
Error showing value of type Vector{Angle2d}:
ERROR: MethodError: no method matching cos(::NTuple{4, Float64})

I'll fix them after tomorrow.

[andyferris]

Awesome.

At first, I thought zero(T) should be a instance of T

There was an old discussion at julialang/julia about this once... here's a recent one quoting the docs: JuliaLang/julia#40796 (comment)

Basically we want things like isequal(x, x + zero(x)) and isequal(x, x * one(x)), but not always that zero(x) isa typeof(x) or one(x) isa typeof(x).

[hyrodium]

I've updated zeros method:

julia> zeros(MRP,2)
2-element Vector{StaticArrays.SMatrix{3, 3, Float64, 9}}:
 [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]

julia> zeros(RotMatrix{3},2)
2-element Vector{StaticArrays.SMatrix{3, 3, Float64, 9}}:
 [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]

julia> zeros(RotMatrix{2},2)
2-element Vector{StaticArrays.SMatrix{2, 2, Float64, 4}}:
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]

julia> zeros(Angle2d,2)
2-element Vector{StaticArrays.SMatrix{2, 2, Float64, 4}}:
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]

Usually, zeros(T,n) returns a instance of Vector{T}. (e.g. zeros(Real, 3))
But, zeros(MRP,2) can't be Vector{MRP} because zero(MRP) <: MRP is false.

[hyrodium]

There was an old discussion at julialang/julia about this once... here's a recent one quoting the docs: JuliaLang/julia#40796 (comment)

Basically we want things like isequal(x, x + zero(x)) and isequal(x, x * one(x)), but not always that zero(x) isa typeof(x) or one(x) isa typeof(x).

Thanks for the information!

[hyrodium]

bump :)