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annotate src/LazyTensors/lazy_tensor_operations.jl @ 958:8b0ff2fddc32 feature/variable_derivatives

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Merge default
author Jonatan Werpers <jonatan@werpers.com>
date Mon, 14 Mar 2022 09:08:23 +0100
parents b41180efb6c2 6a2e30fa3bd8
children e9752c1e92f8
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1 """
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2 LazyTensorMappingApplication{T,R,D} <: LazyArray{T,R}
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3
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4 Struct for lazy application of a TensorMapping. Created using `*`.
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5
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6 Allows the result of a `TensorMapping` applied to a vector to be treated as an `AbstractArray`.
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7 With a mapping `m` and a vector `v` the LazyTensorMappingApplication object can be created by `m*v`.
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8 The actual result will be calcualted when indexing into `m*v`.
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9 """
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10 struct LazyTensorMappingApplication{T,R,D, TM<:TensorMapping{T,R,D}, AA<:AbstractArray{T,D}} <: LazyArray{T,R}
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11 t::TM
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12 o::AA
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13 end
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14 # TODO: Do boundschecking on creation!
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15 export LazyTensorMappingApplication
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16
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17 Base.getindex(ta::LazyTensorMappingApplication{T,R}, I::Vararg{Any,R}) where {T,R} = apply(ta.t, ta.o, I...)
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18 Base.getindex(ta::LazyTensorMappingApplication{T,1}, I::CartesianIndex{1}) where {T} = apply(ta.t, ta.o, I.I...) # Would otherwise be caught in the previous method.
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19 Base.size(ta::LazyTensorMappingApplication) = range_size(ta.t)
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20 # TODO: What else is needed to implement the AbstractArray interface?
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21
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22 Base.:*(a::TensorMapping, v::AbstractArray) = LazyTensorMappingApplication(a,v)
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23 Base.:*(a::TensorMapping, b::TensorMapping) = throw(MethodError(Base.:*,(a,b)))
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24 Base.:*(a::TensorMapping, args::Union{TensorMapping, AbstractArray}...) = foldr(*,(a,args...))
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26 # # We need the associativity to be a→b→c = a→(b→c), which is the case for '→'
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27 # # Should we overload some other infix binary opesrator?
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28 # →(tm::TensorMapping{T,R,D}, o::AbstractArray{T,D}) where {T,R,D} = LazyTensorMappingApplication(tm,o)
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29 # TODO: We need to be really careful about good error messages.
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30 # For example what happens if you try to multiply LazyTensorMappingApplication with a TensorMapping(wrong order)?
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31
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32 """
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33 LazyTensorMappingTranspose{T,R,D} <: TensorMapping{T,D,R}
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34
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35 Struct for lazy transpose of a TensorMapping.
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36
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37 If a mapping implements the the `apply_transpose` method this allows working with
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38 the transpose of mapping `m` by using `m'`. `m'` will work as a regular TensorMapping lazily calling
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39 the appropriate methods of `m`.
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40 """
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41 struct LazyTensorMappingTranspose{T,R,D, TM<:TensorMapping{T,R,D}} <: TensorMapping{T,D,R}
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42 tm::TM
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43 end
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44 export LazyTensorMappingTranspose
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45
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46 # # TBD: Should this be implemented on a type by type basis or through a trait to provide earlier errors?
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47 # Jonatan 2020-09-25: Is the problem that you can take the transpose of any TensorMapping even if it doesn't implement `apply_transpose`?
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48 Base.adjoint(tm::TensorMapping) = LazyTensorMappingTranspose(tm)
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49 Base.adjoint(tmt::LazyTensorMappingTranspose) = tmt.tm
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50
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51 apply(tmt::LazyTensorMappingTranspose{T,R,D}, v::AbstractArray{T,R}, I::Vararg{Any,D}) where {T,R,D} = apply_transpose(tmt.tm, v, I...)
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52 apply_transpose(tmt::LazyTensorMappingTranspose{T,R,D}, v::AbstractArray{T,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmt.tm, v, I...)
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53
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54 range_size(tmt::LazyTensorMappingTranspose) = domain_size(tmt.tm)
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55 domain_size(tmt::LazyTensorMappingTranspose) = range_size(tmt.tm)
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57
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58 struct LazyTensorMappingBinaryOperation{Op,T,R,D,T1<:TensorMapping{T,R,D},T2<:TensorMapping{T,R,D}} <: TensorMapping{T,D,R}
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59 tm1::T1
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60 tm2::T2
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61
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62 @inline function LazyTensorMappingBinaryOperation{Op,T,R,D}(tm1::T1,tm2::T2) where {Op,T,R,D, T1<:TensorMapping{T,R,D},T2<:TensorMapping{T,R,D}}
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63 return new{Op,T,R,D,T1,T2}(tm1,tm2)
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64 end
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65 end
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66 # TODO: Boundschecking in constructor.
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67
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68 apply(tmBinOp::LazyTensorMappingBinaryOperation{:+,T,R,D}, v::AbstractArray{T,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmBinOp.tm1, v, I...) + apply(tmBinOp.tm2, v, I...)
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69 apply(tmBinOp::LazyTensorMappingBinaryOperation{:-,T,R,D}, v::AbstractArray{T,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmBinOp.tm1, v, I...) - apply(tmBinOp.tm2, v, I...)
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70
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71 range_size(tmBinOp::LazyTensorMappingBinaryOperation) = range_size(tmBinOp.tm1)
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72 domain_size(tmBinOp::LazyTensorMappingBinaryOperation) = domain_size(tmBinOp.tm1)
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73
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74 Base.:+(tm1::TensorMapping{T,R,D}, tm2::TensorMapping{T,R,D}) where {T,R,D} = LazyTensorMappingBinaryOperation{:+,T,R,D}(tm1,tm2)
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75 Base.:-(tm1::TensorMapping{T,R,D}, tm2::TensorMapping{T,R,D}) where {T,R,D} = LazyTensorMappingBinaryOperation{:-,T,R,D}(tm1,tm2)
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76
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77 """
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78 TensorMappingComposition{T,R,K,D}
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79
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80 Lazily compose two `TensorMapping`s, so that they can be handled as a single `TensorMapping`.
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81 """
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82 struct TensorMappingComposition{T,R,K,D, TM1<:TensorMapping{T,R,K}, TM2<:TensorMapping{T,K,D}} <: TensorMapping{T,R,D}
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83 t1::TM1
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84 t2::TM2
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85
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86 @inline function TensorMappingComposition(t1::TensorMapping{T,R,K}, t2::TensorMapping{T,K,D}) where {T,R,K,D}
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87 @boundscheck check_domain_size(t1, range_size(t2))
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88 return new{T,R,K,D, typeof(t1), typeof(t2)}(t1,t2)
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89 end
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90 end
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91 export TensorMappingComposition
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92
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93 range_size(tm::TensorMappingComposition) = range_size(tm.t1)
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94 domain_size(tm::TensorMappingComposition) = domain_size(tm.t2)
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96 function apply(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{T,D}, I::Vararg{Any,R}) where {T,R,K,D}
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97 apply(c.t1, c.t2*v, I...)
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98 end
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99
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100 function apply_transpose(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{T,R}, I::Vararg{Any,D}) where {T,R,K,D}
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101 apply_transpose(c.t2, c.t1'*v, I...)
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102 end
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103
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104 Base.@propagate_inbounds Base.:∘(s::TensorMapping, t::TensorMapping) = TensorMappingComposition(s,t)
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105
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106 """
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107 LazyLinearMap{T,R,D,...}(A, range_indicies, domain_indicies)
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108
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109 TensorMapping defined by the AbstractArray A. `range_indicies` and `domain_indicies` define which indicies of A should
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110 be considerd the range and domain of the TensorMapping. Each set of indices must be ordered in ascending order.
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111
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112 For instance, if A is a m x n matrix, and range_size = (1,), domain_size = (2,), then the LazyLinearMap performs the
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113 standard matrix-vector product on vectors of size n.
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114 """
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115 struct LazyLinearMap{T,R,D, RD, AA<:AbstractArray{T,RD}} <: TensorMapping{T,R,D}
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116 A::AA
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117 range_indicies::NTuple{R,Int}
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118 domain_indicies::NTuple{D,Int}
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119
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120 function LazyLinearMap(A::AA, range_indicies::NTuple{R,Int}, domain_indicies::NTuple{D,Int}) where {T,R,D, RD, AA<:AbstractArray{T,RD}}
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121 if !issorted(range_indicies) || !issorted(domain_indicies)
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122 throw(DomainError("range_indicies and domain_indicies must be sorted in ascending order"))
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123 end
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124
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125 return new{T,R,D,RD,AA}(A,range_indicies,domain_indicies)
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126 end
377
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127 end
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128 export LazyLinearMap
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129
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130 range_size(llm::LazyLinearMap) = size(llm.A)[[llm.range_indicies...]]
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131 domain_size(llm::LazyLinearMap) = size(llm.A)[[llm.domain_indicies...]]
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132
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133 function apply(llm::LazyLinearMap{T,R,D}, v::AbstractArray{T,D}, I::Vararg{Any,R}) where {T,R,D}
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134 view_index = ntuple(i->:,ndims(llm.A))
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135 for i ∈ 1:R
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136 view_index = Base.setindex(view_index, Int(I[i]), llm.range_indicies[i])
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137 end
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138 A_view = @view llm.A[view_index...]
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139 return sum(A_view.*v)
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140 end
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141
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142 function apply_transpose(llm::LazyLinearMap{T,R,D}, v::AbstractArray{T,R}, I::Vararg{Any,D}) where {T,R,D}
411
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143 apply(LazyLinearMap(llm.A, llm.domain_indicies, llm.range_indicies), v, I...)
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144 end
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145
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146
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147 """
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148 IdentityMapping{T,D} <: TensorMapping{T,D,D}
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149
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150 The lazy identity TensorMapping for a given size. Usefull for building up higher dimensional tensor mappings from lower
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151 dimensional ones through outer products. Also used in the Implementation for InflatedTensorMapping.
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152 """
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153 struct IdentityMapping{T,D} <: TensorMapping{T,D,D}
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154 size::NTuple{D,Int}
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155 end
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156 export IdentityMapping
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157
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158 IdentityMapping{T}(size::NTuple{D,Int}) where {T,D} = IdentityMapping{T,D}(size)
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159 IdentityMapping{T}(size::Vararg{Int,D}) where {T,D} = IdentityMapping{T,D}(size)
442
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160 IdentityMapping(size::Vararg{Int,D}) where D = IdentityMapping{Float64,D}(size)
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161
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162 range_size(tmi::IdentityMapping) = tmi.size
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163 domain_size(tmi::IdentityMapping) = tmi.size
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164
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165 apply(tmi::IdentityMapping{T,D}, v::AbstractArray{T,D}, I::Vararg{Any,D}) where {T,D} = v[I...]
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166 apply_transpose(tmi::IdentityMapping{T,D}, v::AbstractArray{T,D}, I::Vararg{Any,D}) where {T,D} = v[I...]
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167
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168 """
838
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169 Base.:∘(tm, tmi)
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170 Base.:∘(tmi, tm)
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171
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172 Composes a `Tensormapping` `tm` with an `IdentityMapping` `tmi`, by returning `tm`
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173 """
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174 @inline function Base.:∘(tm::TensorMapping{T,R,D}, tmi::IdentityMapping{T,D}) where {T,R,D}
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175 @boundscheck check_domain_size(tm, range_size(tmi))
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176 return tm
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177 end
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178
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179 @inline function Base.:∘(tmi::IdentityMapping{T,R}, tm::TensorMapping{T,R,D}) where {T,R,D}
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180 @boundscheck check_domain_size(tmi, range_size(tm))
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181 return tm
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182 end
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183 # Specialization for the case where tm is an IdentityMapping. Required to resolve ambiguity.
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184 @inline function Base.:∘(tm::IdentityMapping{T,D}, tmi::IdentityMapping{T,D}) where {T,D}
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185 @boundscheck check_domain_size(tm, range_size(tmi))
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186 return tmi
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187 end
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188
460
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189
459
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190 """
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191 InflatedTensorMapping{T,R,D} <: TensorMapping{T,R,D}
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192
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193 An inflated `TensorMapping` with dimensions added before and afer its actual dimensions.
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194 """
449
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195 struct InflatedTensorMapping{T,R,D,D_before,R_middle,D_middle,D_after, TM<:TensorMapping{T,R_middle,D_middle}} <: TensorMapping{T,R,D}
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196 before::IdentityMapping{T,D_before}
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197 tm::TM
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198 after::IdentityMapping{T,D_after}
446
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199
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200 function InflatedTensorMapping(before, tm::TensorMapping{T}, after) where T
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201 R_before = range_dim(before)
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202 R_middle = range_dim(tm)
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203 R_after = range_dim(after)
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204 R = R_before+R_middle+R_after
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205
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206 D_before = domain_dim(before)
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207 D_middle = domain_dim(tm)
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208 D_after = domain_dim(after)
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209 D = D_before+D_middle+D_after
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210 return new{T,R,D,D_before,R_middle,D_middle,D_after, typeof(tm)}(before, tm, after)
448
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211 end
446
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212 end
451
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213 export InflatedTensorMapping
461
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214 """
464
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215 InflatedTensorMapping(before, tm, after)
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216 InflatedTensorMapping(before,tm)
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217 InflatedTensorMapping(tm,after)
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218
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219 The outer product of `before`, `tm` and `after`, where `before` and `after` are `IdentityMapping`s.
465
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220
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221 If one of `before` or `after` is left out, a 0-dimensional `IdentityMapping` is used as the default value.
493
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222
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223 If `tm` already is an `InflatedTensorMapping`, `before` and `after` will be extended instead of
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224 creating a nested `InflatedTensorMapping`.
461
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225 """
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226 InflatedTensorMapping(::IdentityMapping, ::TensorMapping, ::IdentityMapping)
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227
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228 function InflatedTensorMapping(before, itm::InflatedTensorMapping, after)
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229 return InflatedTensorMapping(
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230 IdentityMapping(before.size..., itm.before.size...),
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231 itm.tm,
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232 IdentityMapping(itm.after.size..., after.size...),
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233 )
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234 end
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235
462
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diff changeset
236 InflatedTensorMapping(before::IdentityMapping, tm::TensorMapping{T}) where T = InflatedTensorMapping(before,tm,IdentityMapping{T}())
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237 InflatedTensorMapping(tm::TensorMapping{T}, after::IdentityMapping) where T = InflatedTensorMapping(IdentityMapping{T}(),tm,after)
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238 # Resolve ambiguity between the two previous methods
462
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239 InflatedTensorMapping(I1::IdentityMapping{T}, I2::IdentityMapping{T}) where T = InflatedTensorMapping(I1,I2,IdentityMapping{T}())
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240
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241 # TODO: Implement some pretty printing in terms of ⊗. E.g InflatedTensorMapping(I(3),B,I(2)) -> I(3)⊗B⊗I(2)
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242
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243 function range_size(itm::InflatedTensorMapping)
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244 return flatten_tuple(
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245 range_size(itm.before),
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246 range_size(itm.tm),
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247 range_size(itm.after),
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248 )
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249 end
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250
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251 function domain_size(itm::InflatedTensorMapping)
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252 return flatten_tuple(
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253 domain_size(itm.before),
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254 domain_size(itm.tm),
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255 domain_size(itm.after),
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256 )
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257 end
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258
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259 function apply(itm::InflatedTensorMapping{T,R,D}, v::AbstractArray{T,D}, I::Vararg{Any,R}) where {T,R,D}
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260 dim_before = range_dim(itm.before)
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261 dim_domain = domain_dim(itm.tm)
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262 dim_range = range_dim(itm.tm)
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263 dim_after = range_dim(itm.after)
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264
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265 view_index, inner_index = split_index(Val(dim_before), Val(dim_domain), Val(dim_range), Val(dim_after), I...)
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266
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267 v_inner = view(v, view_index...)
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268 return apply(itm.tm, v_inner, inner_index...)
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269 end
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270
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271 function apply_transpose(itm::InflatedTensorMapping{T,R,D}, v::AbstractArray{T,R}, I::Vararg{Any,D}) where {T,R,D}
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272 dim_before = range_dim(itm.before)
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273 dim_domain = domain_dim(itm.tm)
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274 dim_range = range_dim(itm.tm)
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275 dim_after = range_dim(itm.after)
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276
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277 view_index, inner_index = split_index(Val(dim_before), Val(dim_range), Val(dim_domain), Val(dim_after), I...)
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278
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279 v_inner = view(v, view_index...)
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280 return apply_transpose(itm.tm, v_inner, inner_index...)
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281 end
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282
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283
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284 """
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285 split_index(::Val{dim_before}, ::Val{dim_view}, ::Val{dim_index}, ::Val{dim_after}, I...)
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286
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287 Splits the multi-index `I` into two parts. One part which is expected to be
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288 used as a view, and one which is expected to be used as an index.
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289 Eg.
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290 ```
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291 split_index(Val(1),Val(3),Val(2),Val(1),(1,2,3,4)) -> (1,:,:,:,4), (2,3)
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292 ```
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293
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294 `dim_view` controls how many colons are in the view, and `dim_index` controls
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295 how many elements are extracted from the middle.
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296 `dim_before` and `dim_after` decides the length of the index parts before and after the colons in the view index.
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297
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298 Arguments should satisfy `length(I) == dim_before+B_domain+dim_after`.
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299
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300 The returned values satisfy
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301 * `length(view_index) == dim_before + dim_view + dim_after`
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302 * `length(I_middle) == dim_index`
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303 """
533
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304 function split_index(::Val{dim_before}, ::Val{dim_view}, ::Val{dim_index}, ::Val{dim_after}, I...) where {dim_before,dim_view, dim_index,dim_after}
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305 I_before, I_middle, I_after = split_tuple(I, Val(dim_before), Val(dim_index))
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306
533
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307 view_index = (I_before..., ntuple((i)->:, dim_view)..., I_after...)
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308
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309 return view_index, I_middle
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310 end
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311
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312 # TODO: Can this be replaced by something more elegant while still being type stable? 2020-10-21
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313 # See:
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314 # https://github.com/JuliaLang/julia/issues/34884
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315 # https://github.com/JuliaLang/julia/issues/30386
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316 """
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317 slice_tuple(t, Val(l), Val(u))
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318
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319 Get a slice of a tuple in a type stable way.
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320 Equivalent to `t[l:u]` but type stable.
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321 """
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322 function slice_tuple(t,::Val{L},::Val{U}) where {L,U}
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323 return ntuple(i->t[i+L-1], U-L+1)
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324 end
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325
457
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326 """
532
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327 split_tuple(t::Tuple{...}, ::Val{M}) where {N,M}
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328
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329 Split the tuple `t` into two parts. the first part is `M` long.
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330 E.g
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331 ```julia
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332 split_tuple((1,2,3,4),Val(3)) -> (1,2,3), (4,)
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333 ```
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334 """
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335 function split_tuple(t::NTuple{N,Any},::Val{M}) where {N,M}
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336 return slice_tuple(t,Val(1), Val(M)), slice_tuple(t,Val(M+1), Val(N))
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337 end
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338
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339 """
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340 split_tuple(t::Tuple{...},::Val{M},::Val{K}) where {N,M,K}
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341
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342 Same as `split_tuple(t::NTuple{N},::Val{M})` but splits the tuple in three parts. With the first
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343 two parts having lenght `M` and `K`.
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344 """
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345 function split_tuple(t::NTuple{N,Any},::Val{M},::Val{K}) where {N,M,K}
532
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346 p1, tail = split_tuple(t, Val(M))
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347 p2, p3 = split_tuple(tail, Val(K))
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348 return p1,p2,p3
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349 end
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350
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351
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352 """
457
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353 flatten_tuple(t)
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354
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355 Takes a nested tuple and flattens the whole structure
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356 """
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357 flatten_tuple(t::NTuple{N, Number} where N) = t
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358 flatten_tuple(t::Tuple) = ((flatten_tuple.(t)...)...,) # simplify?
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359 flatten_tuple(ts::Vararg) = flatten_tuple(ts)
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360
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361 @doc raw"""
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362 LazyOuterProduct(tms...)
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363
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364 Creates a `TensorMappingComposition` for the outerproduct of `tms...`.
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365 This is done by separating the outer product into regular products of outer products involving only identity mappings and one non-identity mapping.
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366
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367 First let
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368 ```math
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369 \begin{aligned}
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370 A &= A_{I,J} \\
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371 B &= B_{M,N} \\
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372 C &= C_{P,Q} \\
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373 \end{aligned}
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374 ```
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375
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376 where ``I``, ``M``, ``P`` are multi-indexes for the ranges of ``A``, ``B``, ``C``, and ``J``, ``N``, ``Q`` are multi-indexes of the domains.
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377
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378 We use ``⊗`` to denote the outer product
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379 ```math
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380 (A⊗B)_{IM,JN} = A_{I,J}B_{M,N}
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381 ```
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382
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383 We note that
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384 ```math
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385 A⊗B⊗C = (A⊗B⊗C)_{IMP,JNQ} = A_{I,J}B_{M,N}C_{P,Q}
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386 ```
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387 And that
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388 ```math
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389 A⊗B⊗C = (A⊗I_{|M|}⊗I_{|P|})(I_{|J|}⊗B⊗I_{|P|})(I_{|J|}⊗I_{|N|}⊗C)
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390 ```
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391 where ``|⋅|`` of a multi-index is a vector of sizes for each dimension. ``I_v`` denotes the identity tensor of size ``v[i]`` in each direction
468
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392 To apply ``A⊗B⊗C`` we evaluate
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393
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394 ```math
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395 (A⊗B⊗C)v = [(A⊗I_{|M|}⊗I_{|P|}) [(I_{|J|}⊗B⊗I_{|P|}) [(I_{|J|}⊗I_{|N|}⊗C)v]]]
838
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396 ```
468
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397 """
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398 function LazyOuterProduct end
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399 export LazyOuterProduct
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400
470
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401 function LazyOuterProduct(tm1::TensorMapping{T}, tm2::TensorMapping{T}) where T
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402 itm1 = InflatedTensorMapping(tm1, IdentityMapping{T}(range_size(tm2)))
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403 itm2 = InflatedTensorMapping(IdentityMapping{T}(domain_size(tm1)),tm2)
468
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404
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405 return itm1∘itm2
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406 end
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407
491
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408 LazyOuterProduct(t1::IdentityMapping{T}, t2::IdentityMapping{T}) where T = IdentityMapping{T}(t1.size...,t2.size...)
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409 LazyOuterProduct(t1::TensorMapping, t2::IdentityMapping) = InflatedTensorMapping(t1, t2)
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410 LazyOuterProduct(t1::IdentityMapping, t2::TensorMapping) = InflatedTensorMapping(t1, t2)
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411
470
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412 LazyOuterProduct(tms::Vararg{TensorMapping}) = foldl(LazyOuterProduct, tms)
468
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413
474
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414 ⊗(a::TensorMapping, b::TensorMapping) = LazyOuterProduct(a,b)
470
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415 export ⊗
468
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416
498
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417
487
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418 function check_domain_size(tm::TensorMapping, sz)
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419 if domain_size(tm) != sz
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420 throw(SizeMismatch(tm,sz))
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421 end
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422 end
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423
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424 struct SizeMismatch <: Exception
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425 tm::TensorMapping
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426 sz
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427 end
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428 export SizeMismatch
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429
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430 function Base.showerror(io::IO, err::SizeMismatch)
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431 print(io, "SizeMismatch: ")
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432 print(io, "domain size $(domain_size(err.tm)) of TensorMapping not matching size $(err.sz)")
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433 end
919
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434
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435 function apply_with_region(op, v, boundary_width::Integer, dim_size::Integer, i)
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436 if 0 < i <= boundary_width
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437 return LazyTensors.apply(op,v,Index(i,Lower))
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438 elseif boundary_width < i <= dim_size-boundary_width
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439 return LazyTensors.apply(op,v,Index(i,Interior))
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440 elseif dim_size-boundary_width < i <= dim_size
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441 return LazyTensors.apply(op,v,Index(i,Upper))
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442 else
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443 error("Bounds error") # TODO: Make this more standard
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444 end
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445 end
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446 # TBD: Can these methods be merge by having a function as an arguement instead?
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447 # TODO: Add inference test that show where things break and how this rewrite fixes it.
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448 function apply_transpose_with_region(op, v, boundary_width::Integer, dim_size::Integer, i)
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449 if 0 < i <= boundary_width
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450 return LazyTensors.apply_transpose(op,v,Index(i,Lower))
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451 elseif boundary_width < i <= dim_size-boundary_width
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452 return LazyTensors.apply_transpose(op,v,Index(i,Interior))
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453 elseif dim_size-boundary_width < i <= dim_size
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454 return LazyTensors.apply_transpose(op,v,Index(i,Upper))
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455 else
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456 error("Bounds error") # TODO: Make this more standard
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457 end
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diff changeset
458 end