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annotate TensorMappings.jl @ 159:b790082032da boundary_conditions

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Add discussion about what a TensorMapping apply()s to
author Jonatan Werpers <jonatan@werpers.com>
date Fri, 10 May 2019 15:05:26 +0200
parents a3fac8298e3c
children d33b13d2d92b
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1 module TensorMappings
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2 # Needs a better name ImplicitTensorMappings? Get rid of "Tensor" in the name_
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3
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4 abstract type TensorMapping{T,R,D} end
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5 abstract type TensorOperator{T,D} <: TensorMapping{T,D,D} end # Does this help?
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7 range_dim(::TensorMapping{T,R,D}) where {T,R,D} = R
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8 domain_dim(::TensorMapping{T,R,D}) where {T,R,D} = D
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10 range_size(::TensorOperator{T,D}, domain_size::NTuple{D,Integer}) where {T,D} = domain_size
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11 domain_size(::TensorOperator{T,D}, range_size::NTuple{D,Integer}) where {T,D} = range_size
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12 # More precise domain_size/range_size type?
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14 # Should be implemented by a TensorMapping
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15 # ========================================
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16 # apply(t::TensorMapping{T,R,D}, v::AbstractArray{T,D}, I::Vararg) where {R,D,T} =
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17 # apply_transpose(t::TensorMapping{T,R,D}, v::AbstractArray{T,D}, I::Vararg) where {R,D,T} =
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18 # Does it make sense that apply should work for any size of v? And the application adapts?
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19 # Think about boundschecking!
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21 # range_size(::TensorMapping{T,R,D}, domain_size::NTuple{D,Integer}) where {T,R,D} =
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22 # More prciese domain_size type?
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23 # domain_size(::TensorMapping{T,R,D}, range_size::NTuple{R,Integer}) where {T,R,D} =
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24
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25 # Implementing apply_transpose and domain_size is only needed if you want to take transposes of the TensorMapping.
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27 # What does a TensorMapping apply() to?
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28 # =====================================
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29 # Is it too strict that TensorMappings apply to AbstractArrays? Maybe we don't need
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30 # to know the operands size. That could simplify the handeling of the range_size...
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31 # It would just fail if apply does something out of bounds..
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32 # No i think knowing the size is a requirement. The TensorMapping must be able to do
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33 # different things for different indecies based for example on how close to the boundary we are.
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36 # Allow using the ' operator:
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37 struct TensorMappingTranspose{T,R,D} <: TensorMapping{T,D,R}
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38 tm::TensorMapping{T,R,D}
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39 end
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40
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41 Base.adjoint(t::TensorMapping) = TensorMappingTranspose(t) # Maybe this should be implemented on a type by type basis or through a trait to provide earlier errors.
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42 Base.adjoint(t::TensorMappingTranspose) = t.tm
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43
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44 apply(tm::TensorMappingTranspose{T,R,D}, v::AbstractArray{T,R}, I::Vararg) where {T,R,D} = apply_transpose(tm.tm, v, I...)
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45 apply_transpose(tm::TensorMappingTranspose{T,R,D}, v::AbstractArray{T,D}, I::Vararg) where {T,R,D} = apply(tm.tm, v, I...)
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46
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47 # range_size(::TensorMappingTranspose{T,R,D}, domain_size::NTuple{}) = range_size_of_transpose???
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51 struct TensorApplication{T,R,D} <: AbstractArray{T,R}
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52 t::TensorMapping{R,D}
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53 o::AbstractArray{T,D}
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54 end
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55
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56 Base.size(ta::TensorApplication) = range_size(ta.t,size(ta.o))
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57 ## What else is needed so that we have a proper AbstractArray?
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58
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59 Base.getindex(tm::TensorApplication, I::Vararg) = apply(tm.t, tm.o, I...)
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60
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61 →(t::TensorMapping{T,R,D}, o::AbstractArray{T,D}) where {T,R,D} = TensorApplication(t,o)
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62 # Should we overload some other infix binary operator?
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63 # * has the wrong parsing properties... a*b*c is parsed to (a*b)*c (through a*b*c = *(a,b,c))
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64 # while a→b→c is parsed as a→(b→c)
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65 # The associativity of the operators might be fixed somehow... (rfold/lfold?)
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66 # ∘ also is an option but that has the same problem as * (but is not n-ary) (or is this best used for composition of Mappings?)
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67
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68 # If we want to use * it would be something like this:
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69 import Base.*
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70 *(args::Union{TensorMapping{T}, AbstractArray{T}}...) where T = foldr(*,args)
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71 *(t::TensorMapping{T,R,D}, o::AbstractArray{T,D}) where {T,R,D} = TensorApplication(t,o)
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72 # We need to be really careful about good error messages.
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73 # For example what happens if you try to multiply TensorApplication with a TensorMapping(wrong order)?
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76
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77 struct TensorMappingComposition{T,R,K,D} <: TensorMapping{T,R,D}
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78 t1::TensorMapping{T,R,K}
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79 t2::TensorMapping{T,K,D}
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80 end
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81
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82 import Base.∘
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83 ∘(s::TensorMapping{T,R,K}, t::TensorMapping{T,K,D}) where {T,R,K,D} = TensorMappingComposition(s,t)
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84
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85 function apply(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{T,D}, I::Vararg) where {T,R,K,D}
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86 apply(c.t1, TensorApplication(c.t2,v), I...)
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87 end
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88
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89 function apply_transpose(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{T,D}, I::Vararg) where {T,R,K,D}
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90 apply_transpose(c.t2, TensorApplication(c.t1',v), I...)
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91 end
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92
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93 # Have i gone too crazy with the type parameters? Maybe they aren't all needed?
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95
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96 export apply
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97 export apply_transpose
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98 export range_dim
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99 export domain_dim
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100 export range_size
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101 export →
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102
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103
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104 end #module