revised with AbstractReal, AbstractComplex, etc..

Project.toml

@@ -1,7 +1,7 @@
 name = "TensorFields"
 uuid = "86e2b4fd-d9c8-44dc-a03f-e0a387f3b4e6"
 authors = ["Michael Reed"]
-version = "0.1.1"
+version = "0.1.2"
 
 [deps]
 Requires = "ae029012-a4dd-5104-9daa-d747884805df"

README.md

@@ -6,33 +6,32 @@
 
 *TensorField with product topology using [Grassmann.jl](https://github.com/chakravala/Grassmann.jl) element parameters*
 
-[![DOI](https://zenodo.org/badge/223493781.svg)](https://zenodo.org/badge/latestdoi/223493781)
+[![DOI](https://zenodo.org/badge/673606851.svg)](https://zenodo.org/badge/latestdoi/673606851)
 [![Docs Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://grassmann.crucialflow.com/stable)
 [![Docs Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://grassmann.crucialflow.com/dev)
 [![Gitter](https://badges.gitter.im/Grassmann-jl/community.svg)](https://gitter.im/Grassmann-jl/community?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge)
-[![Build status](https://ci.appveyor.com/api/projects/status/oxi2qutlsaytloap?svg=true)](https://ci.appveyor.com/project/chakravala/tensorfields-jl)
+[![Build status](https://ci.appveyor.com/api/projects/status/cuh681med9ijieua?svg=true)](https://ci.appveyor.com/project/chakravala/tensorfields-jl)
 
-Provides `TensorField{R,B,T,N} <: FiberBundle{Section{R,T},N}` implementation for both a local `ProductSpace` topology and the simplicial mesh topologies imported with [Grassmann.jl](https://github.com/chakravala/Grassmann.jl).
+Provides `TensorField{B,T,F,N} <: FiberBundle{Section{B,F},N}` implementation for both a local `ProductSpace` topology and the simplicial mesh topologies imported with [Grassmann.jl](https://github.com/chakravala/Grassmann.jl).
 Many of these modular methods can work on input meshes or product topologies of any dimension, although there are some methods which are specialized.
 Utility package for differential geometry and tensor calculus intended for packages such as [Adapode.jl](https://github.com/chakravala/Adapode.jl).
 
 ```Julia
-MeshFunction (alias for TensorField{B, T, F, 1} where {B, T<:ChainBundle, F<:Real})
-ElementFunction (alias for TensorField{B, T, F, 1} where {B, T<:AbstractVector{B}, F<:Real})
-IntervalMap{B} where B<:Real (alias for TensorField{B, T, F, 1} where {B<:Real, T<:AbstractArray{B, 1}, F})
-RealFunction (alias for TensorField{B, T, F, 1} where {B<:Real, T<:AbstractVector{B}, F<:Union{Real, Single, Chain{V, G, <:Real, 1} where {V, G}}})
-PlaneCurve (alias for TensorField{B, T, F, 1} where {B<:Real, T<:AbstractVector{B}, F<:(Chain{V, G, Q, 2} where {V, G, Q})})
-SpaceCurve (alias for TensorField{B, T, F, 1} where {B<:Real, T<:AbstractVector{B}, F<:(Chain{V, G, Q, 3} where {V, G, Q})})
-GridSurface (alias for TensorField{B, T, F, 2} where {B, T<:AbstractMatrix{B}, F<:Real})
-GridParametric{B} where B (alias for TensorField{B, T, F} where {B, T<:(AbstractArray{B}), F<:Real})
-ComplexMapping (alias for TensorField{B, T, F} where {B, T, F<:Complex})
-ComplexMap (alias for TensorField{B, T, F} where {B, T, F<:Couple})
+MeshFunction (alias for TensorField{B, T, F, 1} where {B, T<:ChainBundle, F<:AbstractReal})
+ElementFunction (alias for TensorField{B, T, F, 1} where {B, T<:AbstractVector{B}, F<:AbstractReal})
+IntervalMap{B} where B<:AbstractReal (alias for TensorField{B, T, F, 1} where {B<:Union{Real, Single{V, G, B, <:Real} where {V, G, B}, Chain{V, G, <:Real, 1} where {V, G}}, T<:AbstractArray{B, 1}, F})
+RealFunction (alias for TensorField{B, T, F, 1} where {B<:AbstractReal, T<:AbstractVector{B}, F<:AbstractReal})
+PlaneCurve (alias for TensorField{B, T, F, 1} where {B<:AbstractReal, T<:AbstractVector{B}, F<:(Chain{V, G, Q, 2} where {V, G, Q})})
+SpaceCurve (alias for TensorField{B, T, F, 1} where {B<:AbstractReal, T<:AbstractVector{B}, F<:(Chain{V, G, Q, 3} where {V, G, Q})})
+SurfaceGrid (alias for TensorField{B, T, F, 2} where {B, T<:AbstractMatrix{B}, F<:AbstractReal})
+ScalarGrid (alias for TensorField{B, T, F} where {B, T<:(AbstractArray{B}), F<:AbstractReal})
+CliffordField (alias for TensorField{B, T, F} where {B, T, F<:Multivector})
+QuaternionField (alias for TensorField{B, T, F} where {B, T, F<:(Quaternion)})
+ComplexMap (alias for TensorField{B, T, F} where {B, T, F<:(Union{Complex{T}, Single{V, G, B, Complex{T}} where {V, G, B}, Chain{V, G, Complex{T}, 1} where {V, G}, Couple{V, B, T} where {V, B}} where T<:Real)})
+SpinorField (alias for TensorField{B, T, F} where {B, T, F<:AbstractSpinor})
 GradedField{G} where G (alias for TensorField{B, T, F} where {G, B, T, F<:(Chain{V, G} where V)})
-ScalarField (alias for TensorField{B, T, F} where {B, T, F<:Single})
+ScalarField (alias for TensorField{B, T, F} where {B, T, F<:Union{Real, Single{V, G, B, <:Real} where {V, G, B}, Chain{V, G, <:Real, 1} where {V, G}}})
 VectorField (alias for TensorField{B, T, F} where {B, T, F<:(Chain{V, 1} where V)})
-SpinorField (alias for TensorField{B, T, F} where {B, T, F<:Spinor})
-QuaternionField (alias for TensorField{B, T, F} where {B, T, F<:(Quaternion)})
-CliffordField (alias for TensorField{B, T, F} where {B, T, F<:Multivector})
 BivectorField (alias for TensorField{B, T, F} where {B, T, F<:(Chain{V, 2} where V)})
 TrivectorField (alias for TensorField{B, T, F} where {B, T, F<:(Chain{V, 3} where V)})
 ```
@@ -50,34 +49,34 @@ julia> using Grassmann, TensorFields, UnicodePlots
 
 julia> dom = (2π:0.01:4π)⊕(0:0.01:2π);
 
-julia> fun(v) = (v[1]-v[2])*cos(v[1]*v[2]/2);
+julia> fun(v) = (0.1v[1]-0.3v[2])*cos(v[1]*v[2]/5);
 
 julia> cat = dom → fun; # dom → fun.(dom)
 
 julia> typeof(cat)
-TensorField{Chain{⟨++⟩, 1, Float64, 2}, ProductSpace{⟨++⟩, Float64, 2, 2, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Float64, 2}
+TensorField{Chain{⟨××⟩, 1, Float64, 2}, ProductSpace{⟨××⟩, Float64, 2, 2, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Float64, 2}
 
 julia> supertype(ans)
-FiberBundle{Section{Chain{⟨++⟩, 1, Float64, 2}, Float64}, 2}
+FiberBundle{Section{Chain{⟨××⟩, 1, Float64, 2}, Float64}, 2}
 
 julia> contourplot(cat)
-     ┌────────────────────────────────────────┐  500
+     ┌────────────────────────────────────────┐  50 
    7 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ ┌──┐
-     │⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀⠠⢤⣀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
-     │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣍⡓⠦⢄⣀⠀⠀⠀⠀⠉⠓⠲⢬⣙⡲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
-     │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⡙⠲⢤⣀⡀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣖⠆⠀⠀│ │▄▄│
-     │⠀⠀⠀⠀⠘⢿⣒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢭⣓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀│ │▄▄│
-     │⠀⠀⠀⠀⠀⠀⠈⠓⠦⢬⣉⠓⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣍⣉⠓⠒⠂⠀⠀│ │▄▄│
-     │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠮⠽⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠈⠉⠙⠂⠀⠀│ │▄▄│
-     │⠀⢐⡒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠤⣄⣉⡉⠉⠓⠒⠲⠄⠀⠀│ │▄▄│
-     │⠀⠀⠈⠙⠒⠦⠭⢽⣲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠉⠙⠒⣒⡆⠀⠀│ │▄▄│
-     │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠤⢤⣀⣈⡉⠉⠉⠓⠒⠒⠲⠤⠭⠇⠀⠀│ │▄▄│
-     │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢓⣒⣒⣲⣤⣬⡇⠀⠀│ │▄▄│
-     │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣍⣉⣉⠉⠉⠉⠉⠙⠒⠒⠒⠒⠒⠦⠬⠭⠷⠶⢶⣦⡄⠀⠀│ │▄▄│
-     │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠒⠒⠒⢦⣤⣤⣤⣼⣿⣿⣯⣭⡅⠀⠀│ │▄▄│
-     │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡠⠤⠤⠤⠤⣄⣀⣀⣀⣀⣀⣀⣛⣛⣒⣦⣤⣤⣤⣬⣭⣍⡁⠀⠀│ │▄▄│
-   0 │⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⢥⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣶⣯⣭⣭⣭⢍⣉⣉⣉⡁⠀⠀│ └──┘
-     └────────────────────────────────────────┘ -400
+     │⠀⠀⠀⠀⠀⠀⠠⣄⡀⢤⣀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀│ │▄▄│
+     │⠀⠠⣄⡀⠀⠀⠀⠀⠙⠦⣌⠙⠲⣍⡙⠲⠤⣄⣀⡀⠀⠀⠀⠙⢦⠀⠀⠈⠉⠉⠙⠒⠒⠋⠉⠁⠀⠀⠀⠀│ │▄▄│
+     │⠀⠠⣄⡉⠓⠲⠤⣄⣀⡀⠈⢳⠀⠀⠉⠓⠲⢤⣀⠉⠉⠉⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
+     │⠀⢀⡀⠉⠓⠦⣄⣀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠄⠀⠀│ │▄▄│
+     │⠀⠀⠙⢦⡀⠀⠀⠈⠙⠒⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡷⠀⠀⠀⠀⠸⢭⣀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
+     │⠀⢀⣀⣀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⠤⡄⠀⠀│ │▄▄│
+     │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀│ │▄▄│
+     │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀│ │▄▄│
+     │⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠒⠒⠒⠒⠒⠲⠤⠤⠤⠤⢤⡀⠀⠀│ │▄▄│
+     │⠀⢀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
+     │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠒⠒⠒⠆⠀⠀│ │▄▄│
+     │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
+     │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠄⠀⠀│ │▄▄│
+   0 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣒⣒⡋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ └──┘
+     └────────────────────────────────────────┘ -40 
      ⠀6⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀13⠀     
 ```
 Visualizing `TensorField` reperesentations can be standardized in combination with [Makie.jl](https://github.com/MakieOrg/Makie.jl) or [UnicodePlots.jl](https://github.com/JuliaPlots/UnicodePlots.jl).