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annotate TensorMappings.jl @ 155:9fdbae11dd77 boundary_conditions

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Add sketch of how Implicitly definied tensor mappings might work
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 23 Apr 2019 09:54:42 +0200
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children ef3e6c70b6f9
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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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6
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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 # More prciese domain_size type?
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12
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13 # Should be implemented by a TensorMapping
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14 # ========================================
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15 # apply(t::TensorMapping{T,R,D}, v::AbstractArray{T,D}, I::Vararg) where {R,D,T} =
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16 # apply_transpose(t::TensorMapping{T,R,D}, v::AbstractArray{T,D}, I::Vararg) where {R,D,T} =
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17 # Does it make sense that apply should work for any size of v? And the application adapts?
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18 # Think about boundschecking!
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19
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20 # range_size(::TensorMapping{T,R,D}, domain_size::NTuple{D,Integer}) where {T,R,D} =
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21 # More prciese domain_size type?
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22 # range_size_of_transpose()???
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23
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24
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25
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26 # Allow using the ' operator:
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27 struct TensorMappingTranspose{T,R,D} <: TensorMapping{T,D,R}
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28 tm::TensorMapping{T,R,D}
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29 end
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30
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31 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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32 Base.adjoint(t::TensorMappingTranspose) = t.tm
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33
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34 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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35 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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36
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37 # range_size(::TensorMappingTranspose{T,R,D}, domain_size::NTuple{}) = range_size_of_transpose???
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38
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39 struct TensorApplication{T,R,D} <: AbstractArray{T,R}
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40 t::TensorMapping{R,D}
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41 o::AbstractArray{T,D}
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42 end
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43
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44 Base.size(ta::TensorApplication) = range_size(ta.t,size(ta.o))
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45 ## What else is needed so that we have a proper AbstractArray?
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46
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47 Base.getindex(tm::TensorApplication, I::Vararg) = apply(tm.t, tm.o, I...)
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48
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49 →(t::TensorMapping{R,D}, o::AbstractArray{T,D}) where {T,R,D} = TensorApplication(t,o)
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50 # Should we overload some other infix binary operator?
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51 # * 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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52 # while a→b→c is parsed as a→(b→c)
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53 # The associativity of the operators might be fixed somehow... (rfold/lfold?)
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54 # ∘ 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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55
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56
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57 struct TensorMappingComposition{T,R,K,D} <: TensorMapping{T,R,D}
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58 t1::TensorMapping{T,R,K}
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59 t2::TensorMapping{T,K,D}
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60 end
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61
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62 import Base.∘
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63 ∘(s::TensorMapping{T,R,K}, t::TensorMapping{T,K,D}) where {T,R,K,D} = TensorMappingComposition(s,t)
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64
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65 function apply(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{T,D}, I::Vararg) where {T,R,K,D}
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66 apply(c.t1, TensorApplication(c.t2,v), I...)
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67 end
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68
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69 function apply_transpose(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{T,D}, I::Vararg) where {T,R,K,D}
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70 apply_transpose(c.t2, TensorApplication(c.t1',v), I...)
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71 end
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72
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73 # Have i gone too crazy with the type parameters? Maybe they aren't all needed?
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74
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75
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76 export apply
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77 export apply_transpose
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78 export range_dim
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79 export domain_dim
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80 export range_size
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81 export →
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82
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83
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84 end #module