annotate src/LazyTensors/lazy_tensor_operations.jl @ 971:bc12be1b1ae5 feature/variable_derivatives

Fix typo
author Jonatan Werpers <jonatan@werpers.com>
date Mon, 14 Mar 2022 10:20:39 +0100
parents e79debd10f7d
children df562695b1b5
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1 using Sbplib.RegionIndices
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2
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3 export LazyTensorMappingApplication
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4 export LazyTensorMappingTranspose
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5 export TensorMappingComposition
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6 export LazyLinearMap
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7 export IdentityMapping
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8 export InflatedTensorMapping
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9 export LazyOuterProduct
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10 export ⊗
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11 export SizeMismatch
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12
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13 """
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14 LazyTensorMappingApplication{T,R,D} <: LazyArray{T,R}
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15
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16 Struct for lazy application of a TensorMapping. Created using `*`.
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17
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18 Allows the result of a `TensorMapping` applied to a vector to be treated as an `AbstractArray`.
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19 With a mapping `m` and a vector `v` the LazyTensorMappingApplication object can be created by `m*v`.
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20 The actual result will be calcualted when indexing into `m*v`.
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21 """
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22 struct LazyTensorMappingApplication{T,R,D, TM<:TensorMapping{<:Any,R,D}, AA<:AbstractArray{<:Any,D}} <: LazyArray{T,R}
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23 t::TM
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24 o::AA
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26 function LazyTensorMappingApplication(t::TensorMapping{<:Any,R,D}, o::AbstractArray{<:Any,D}) where {R,D}
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27 T = promote_type(eltype(t), eltype(o))
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28 return new{T,R,D,typeof(t), typeof(o)}(t,o)
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29 end
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30 end
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31 # TODO: Do boundschecking on creation!
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32
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33 Base.getindex(ta::LazyTensorMappingApplication{T,R}, I::Vararg{Any,R}) where {T,R} = apply(ta.t, ta.o, I...)
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34 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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35 Base.size(ta::LazyTensorMappingApplication) = range_size(ta.t)
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36 # TODO: What else is needed to implement the AbstractArray interface?
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37
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38 Base.:*(a::TensorMapping, v::AbstractArray) = LazyTensorMappingApplication(a,v)
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39 Base.:*(a::TensorMapping, b::TensorMapping) = throw(MethodError(Base.:*,(a,b)))
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40 Base.:*(a::TensorMapping, args::Union{TensorMapping, AbstractArray}...) = foldr(*,(a,args...))
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41
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42 # # We need the associativity to be a→b→c = a→(b→c), which is the case for '→'
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43 # # Should we overload some other infix binary opesrator?
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44 # →(tm::TensorMapping{T,R,D}, o::AbstractArray{T,D}) where {T,R,D} = LazyTensorMappingApplication(tm,o)
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45 # TODO: We need to be really careful about good error messages.
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46 # For example what happens if you try to multiply LazyTensorMappingApplication with a TensorMapping(wrong order)?
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47
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48 """
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49 LazyTensorMappingTranspose{T,R,D} <: TensorMapping{T,D,R}
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50
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51 Struct for lazy transpose of a TensorMapping.
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52
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53 If a mapping implements the the `apply_transpose` method this allows working with
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54 the transpose of mapping `m` by using `m'`. `m'` will work as a regular TensorMapping lazily calling
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55 the appropriate methods of `m`.
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56 """
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57 struct LazyTensorMappingTranspose{T,R,D, TM<:TensorMapping{T,R,D}} <: TensorMapping{T,D,R}
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58 tm::TM
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59 end
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60
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61 # # TBD: Should this be implemented on a type by type basis or through a trait to provide earlier errors?
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62 # 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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63 Base.adjoint(tm::TensorMapping) = LazyTensorMappingTranspose(tm)
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64 Base.adjoint(tmt::LazyTensorMappingTranspose) = tmt.tm
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65
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66 apply(tmt::LazyTensorMappingTranspose{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,D} = apply_transpose(tmt.tm, v, I...)
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67 apply_transpose(tmt::LazyTensorMappingTranspose{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmt.tm, v, I...)
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68
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69 range_size(tmt::LazyTensorMappingTranspose) = domain_size(tmt.tm)
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70 domain_size(tmt::LazyTensorMappingTranspose) = range_size(tmt.tm)
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71
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72
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73 struct LazyTensorMappingBinaryOperation{Op,T,R,D,T1<:TensorMapping{T,R,D},T2<:TensorMapping{T,R,D}} <: TensorMapping{T,D,R}
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74 tm1::T1
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75 tm2::T2
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76
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77 @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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78 return new{Op,T,R,D,T1,T2}(tm1,tm2)
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79 end
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80 end
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81 # TODO: Boundschecking in constructor.
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82
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83 apply(tmBinOp::LazyTensorMappingBinaryOperation{:+,T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmBinOp.tm1, v, I...) + apply(tmBinOp.tm2, v, I...)
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84 apply(tmBinOp::LazyTensorMappingBinaryOperation{:-,T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmBinOp.tm1, v, I...) - apply(tmBinOp.tm2, v, I...)
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85
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86 range_size(tmBinOp::LazyTensorMappingBinaryOperation) = range_size(tmBinOp.tm1)
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87 domain_size(tmBinOp::LazyTensorMappingBinaryOperation) = domain_size(tmBinOp.tm1)
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88
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89 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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90 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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91
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92 """
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93 TensorMappingComposition{T,R,K,D}
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94
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95 Lazily compose two `TensorMapping`s, so that they can be handled as a single `TensorMapping`.
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96 """
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97 struct TensorMappingComposition{T,R,K,D, TM1<:TensorMapping{T,R,K}, TM2<:TensorMapping{T,K,D}} <: TensorMapping{T,R,D}
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98 t1::TM1
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99 t2::TM2
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100
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101 @inline function TensorMappingComposition(t1::TensorMapping{T,R,K}, t2::TensorMapping{T,K,D}) where {T,R,K,D}
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102 @boundscheck check_domain_size(t1, range_size(t2))
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103 return new{T,R,K,D, typeof(t1), typeof(t2)}(t1,t2)
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104 end
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105 end
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106
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107 range_size(tm::TensorMappingComposition) = range_size(tm.t1)
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108 domain_size(tm::TensorMappingComposition) = domain_size(tm.t2)
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109
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110 function apply(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,K,D}
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111 apply(c.t1, c.t2*v, I...)
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112 end
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113
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114 function apply_transpose(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,K,D}
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115 apply_transpose(c.t2, c.t1'*v, I...)
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116 end
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117
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118 Base.@propagate_inbounds Base.:∘(s::TensorMapping, t::TensorMapping) = TensorMappingComposition(s,t)
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119
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120 """
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121 LazyLinearMap{T,R,D,...}(A, range_indicies, domain_indicies)
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123 TensorMapping defined by the AbstractArray A. `range_indicies` and `domain_indicies` define which indicies of A should
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124 be considerd the range and domain of the TensorMapping. Each set of indices must be ordered in ascending order.
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125
400
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126 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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127 standard matrix-vector product on vectors of size n.
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128 """
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129 struct LazyLinearMap{T,R,D, RD, AA<:AbstractArray{T,RD}} <: TensorMapping{T,R,D}
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130 A::AA
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131 range_indicies::NTuple{R,Int}
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132 domain_indicies::NTuple{D,Int}
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133
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134 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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135 if !issorted(range_indicies) || !issorted(domain_indicies)
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136 throw(DomainError("range_indicies and domain_indicies must be sorted in ascending order"))
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137 end
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138
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139 return new{T,R,D,RD,AA}(A,range_indicies,domain_indicies)
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140 end
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141 end
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142
392
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143 range_size(llm::LazyLinearMap) = size(llm.A)[[llm.range_indicies...]]
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144 domain_size(llm::LazyLinearMap) = size(llm.A)[[llm.domain_indicies...]]
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145
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146 function apply(llm::LazyLinearMap{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D}
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147 view_index = ntuple(i->:,ndims(llm.A))
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148 for i ∈ 1:R
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149 view_index = Base.setindex(view_index, Int(I[i]), llm.range_indicies[i])
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150 end
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151 A_view = @view llm.A[view_index...]
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152 return sum(A_view.*v)
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153 end
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154
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155 function apply_transpose(llm::LazyLinearMap{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,D}
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156 apply(LazyLinearMap(llm.A, llm.domain_indicies, llm.range_indicies), v, I...)
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157 end
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158
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159
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160 """
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161 IdentityMapping{T,D} <: TensorMapping{T,D,D}
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162
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163 The lazy identity TensorMapping for a given size. Usefull for building up higher dimensional tensor mappings from lower
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164 dimensional ones through outer products. Also used in the Implementation for InflatedTensorMapping.
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165 """
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166 struct IdentityMapping{T,D} <: TensorMapping{T,D,D}
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167 size::NTuple{D,Int}
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168 end
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169
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170 IdentityMapping{T}(size::NTuple{D,Int}) where {T,D} = IdentityMapping{T,D}(size)
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171 IdentityMapping{T}(size::Vararg{Int,D}) where {T,D} = IdentityMapping{T,D}(size)
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172 IdentityMapping(size::Vararg{Int,D}) where D = IdentityMapping{Float64,D}(size)
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173
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174 range_size(tmi::IdentityMapping) = tmi.size
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175 domain_size(tmi::IdentityMapping) = tmi.size
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176
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177 apply(tmi::IdentityMapping{T,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,D}) where {T,D} = v[I...]
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178 apply_transpose(tmi::IdentityMapping{T,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,D}) where {T,D} = v[I...]
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179
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180 """
838
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181 Base.:∘(tm, tmi)
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182 Base.:∘(tmi, tm)
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183
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184 Composes a `Tensormapping` `tm` with an `IdentityMapping` `tmi`, by returning `tm`
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185 """
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186 @inline function Base.:∘(tm::TensorMapping{T,R,D}, tmi::IdentityMapping{T,D}) where {T,R,D}
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187 @boundscheck check_domain_size(tm, range_size(tmi))
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188 return tm
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189 end
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190
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191 @inline function Base.:∘(tmi::IdentityMapping{T,R}, tm::TensorMapping{T,R,D}) where {T,R,D}
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192 @boundscheck check_domain_size(tmi, range_size(tm))
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193 return tm
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194 end
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195 # Specialization for the case where tm is an IdentityMapping. Required to resolve ambiguity.
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196 @inline function Base.:∘(tm::IdentityMapping{T,D}, tmi::IdentityMapping{T,D}) where {T,D}
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197 @boundscheck check_domain_size(tm, range_size(tmi))
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198 return tmi
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199 end
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200
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201
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202 """
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203 InflatedTensorMapping{T,R,D} <: TensorMapping{T,R,D}
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204
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205 An inflated `TensorMapping` with dimensions added before and afer its actual dimensions.
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206 """
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207 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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208 before::IdentityMapping{T,D_before}
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209 tm::TM
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210 after::IdentityMapping{T,D_after}
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211
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212 function InflatedTensorMapping(before, tm::TensorMapping{T}, after) where T
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213 R_before = range_dim(before)
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214 R_middle = range_dim(tm)
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215 R_after = range_dim(after)
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216 R = R_before+R_middle+R_after
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217
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218 D_before = domain_dim(before)
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219 D_middle = domain_dim(tm)
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220 D_after = domain_dim(after)
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221 D = D_before+D_middle+D_after
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222 return new{T,R,D,D_before,R_middle,D_middle,D_after, typeof(tm)}(before, tm, after)
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223 end
446
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224 end
461
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225 """
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226 InflatedTensorMapping(before, tm, after)
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227 InflatedTensorMapping(before,tm)
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228 InflatedTensorMapping(tm,after)
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229
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230 The outer product of `before`, `tm` and `after`, where `before` and `after` are `IdentityMapping`s.
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231
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232 If one of `before` or `after` is left out, a 0-dimensional `IdentityMapping` is used as the default value.
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233
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234 If `tm` already is an `InflatedTensorMapping`, `before` and `after` will be extended instead of
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235 creating a nested `InflatedTensorMapping`.
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236 """
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237 InflatedTensorMapping(::IdentityMapping, ::TensorMapping, ::IdentityMapping)
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238
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239 function InflatedTensorMapping(before, itm::InflatedTensorMapping, after)
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240 return InflatedTensorMapping(
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241 IdentityMapping(before.size..., itm.before.size...),
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242 itm.tm,
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243 IdentityMapping(itm.after.size..., after.size...),
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244 )
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245 end
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246
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247 InflatedTensorMapping(before::IdentityMapping, tm::TensorMapping{T}) where T = InflatedTensorMapping(before,tm,IdentityMapping{T}())
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248 InflatedTensorMapping(tm::TensorMapping{T}, after::IdentityMapping) where T = InflatedTensorMapping(IdentityMapping{T}(),tm,after)
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249 # Resolve ambiguity between the two previous methods
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250 InflatedTensorMapping(I1::IdentityMapping{T}, I2::IdentityMapping{T}) where T = InflatedTensorMapping(I1,I2,IdentityMapping{T}())
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251
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252 # 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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253
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254 function range_size(itm::InflatedTensorMapping)
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255 return flatten_tuple(
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256 range_size(itm.before),
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257 range_size(itm.tm),
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258 range_size(itm.after),
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259 )
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260 end
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261
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262 function domain_size(itm::InflatedTensorMapping)
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263 return flatten_tuple(
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264 domain_size(itm.before),
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265 domain_size(itm.tm),
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266 domain_size(itm.after),
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267 )
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268 end
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269
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270 function apply(itm::InflatedTensorMapping{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D}
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271 dim_before = range_dim(itm.before)
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272 dim_domain = domain_dim(itm.tm)
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273 dim_range = range_dim(itm.tm)
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274 dim_after = range_dim(itm.after)
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275
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276 view_index, inner_index = split_index(Val(dim_before), Val(dim_domain), Val(dim_range), Val(dim_after), I...)
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277
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278 v_inner = view(v, view_index...)
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279 return apply(itm.tm, v_inner, inner_index...)
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280 end
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281
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282 function apply_transpose(itm::InflatedTensorMapping{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,D}
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283 dim_before = range_dim(itm.before)
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284 dim_domain = domain_dim(itm.tm)
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285 dim_range = range_dim(itm.tm)
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286 dim_after = range_dim(itm.after)
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287
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288 view_index, inner_index = split_index(Val(dim_before), Val(dim_range), Val(dim_domain), Val(dim_after), I...)
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289
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290 v_inner = view(v, view_index...)
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291 return apply_transpose(itm.tm, v_inner, inner_index...)
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292 end
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293
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294
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295 """
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296 split_index(::Val{dim_before}, ::Val{dim_view}, ::Val{dim_index}, ::Val{dim_after}, I...)
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297
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298 Splits the multi-index `I` into two parts. One part which is expected to be
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299 used as a view, and one which is expected to be used as an index.
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300 Eg.
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301 ```
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302 split_index(Val(1),Val(3),Val(2),Val(1),(1,2,3,4)) -> (1,:,:,:,4), (2,3)
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303 ```
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304
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305 `dim_view` controls how many colons are in the view, and `dim_index` controls
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306 how many elements are extracted from the middle.
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307 `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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308
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309 Arguments should satisfy `length(I) == dim_before+B_domain+dim_after`.
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310
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311 The returned values satisfy
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312 * `length(view_index) == dim_before + dim_view + dim_after`
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313 * `length(I_middle) == dim_index`
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314 """
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315 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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316 I_before, I_middle, I_after = split_tuple(I, Val(dim_before), Val(dim_index))
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317
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318 view_index = (I_before..., ntuple((i)->:, dim_view)..., I_after...)
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319
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320 return view_index, I_middle
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321 end
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322
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323 # TODO: Can this be replaced by something more elegant while still being type stable? 2020-10-21
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324 # See:
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325 # https://github.com/JuliaLang/julia/issues/34884
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326 # https://github.com/JuliaLang/julia/issues/30386
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327 """
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328 slice_tuple(t, Val(l), Val(u))
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329
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330 Get a slice of a tuple in a type stable way.
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331 Equivalent to `t[l:u]` but type stable.
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332 """
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333 function slice_tuple(t,::Val{L},::Val{U}) where {L,U}
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334 return ntuple(i->t[i+L-1], U-L+1)
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335 end
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336
457
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337 """
532
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338 split_tuple(t::Tuple{...}, ::Val{M}) where {N,M}
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339
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340 Split the tuple `t` into two parts. the first part is `M` long.
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341 E.g
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342 ```julia
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343 split_tuple((1,2,3,4),Val(3)) -> (1,2,3), (4,)
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344 ```
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345 """
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346 function split_tuple(t::NTuple{N,Any},::Val{M}) where {N,M}
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347 return slice_tuple(t,Val(1), Val(M)), slice_tuple(t,Val(M+1), Val(N))
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348 end
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349
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350 """
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351 split_tuple(t::Tuple{...},::Val{M},::Val{K}) where {N,M,K}
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352
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353 Same as `split_tuple(t::NTuple{N},::Val{M})` but splits the tuple in three parts. With the first
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354 two parts having lenght `M` and `K`.
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355 """
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356 function split_tuple(t::NTuple{N,Any},::Val{M},::Val{K}) where {N,M,K}
532
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357 p1, tail = split_tuple(t, Val(M))
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358 p2, p3 = split_tuple(tail, Val(K))
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359 return p1,p2,p3
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360 end
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361
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362
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363 """
457
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364 flatten_tuple(t)
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365
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366 Takes a nested tuple and flattens the whole structure
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367 """
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368 flatten_tuple(t::NTuple{N, Number} where N) = t
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369 flatten_tuple(t::Tuple) = ((flatten_tuple.(t)...)...,) # simplify?
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370 flatten_tuple(ts::Vararg) = flatten_tuple(ts)
487
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371
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372 @doc raw"""
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373 LazyOuterProduct(tms...)
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374
501
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375 Creates a `TensorMappingComposition` for the outerproduct of `tms...`.
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376 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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377
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378 First let
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379 ```math
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380 \begin{aligned}
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381 A &= A_{I,J} \\
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382 B &= B_{M,N} \\
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383 C &= C_{P,Q} \\
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384 \end{aligned}
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385 ```
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386
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387 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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388
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389 We use ``⊗`` to denote the outer product
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390 ```math
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391 (A⊗B)_{IM,JN} = A_{I,J}B_{M,N}
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392 ```
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393
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394 We note that
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395 ```math
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396 A⊗B⊗C = (A⊗B⊗C)_{IMP,JNQ} = A_{I,J}B_{M,N}C_{P,Q}
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397 ```
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398 And that
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399 ```math
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400 A⊗B⊗C = (A⊗I_{|M|}⊗I_{|P|})(I_{|J|}⊗B⊗I_{|P|})(I_{|J|}⊗I_{|N|}⊗C)
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401 ```
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402 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
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403 To apply ``A⊗B⊗C`` we evaluate
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404
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405 ```math
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406 (A⊗B⊗C)v = [(A⊗I_{|M|}⊗I_{|P|}) [(I_{|J|}⊗B⊗I_{|P|}) [(I_{|J|}⊗I_{|N|}⊗C)v]]]
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407 ```
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408 """
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409 function LazyOuterProduct end
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410
470
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411 function LazyOuterProduct(tm1::TensorMapping{T}, tm2::TensorMapping{T}) where T
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412 itm1 = InflatedTensorMapping(tm1, IdentityMapping{T}(range_size(tm2)))
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413 itm2 = InflatedTensorMapping(IdentityMapping{T}(domain_size(tm1)),tm2)
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414
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415 return itm1∘itm2
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416 end
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417
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418 LazyOuterProduct(t1::IdentityMapping{T}, t2::IdentityMapping{T}) where T = IdentityMapping{T}(t1.size...,t2.size...)
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419 LazyOuterProduct(t1::TensorMapping, t2::IdentityMapping) = InflatedTensorMapping(t1, t2)
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420 LazyOuterProduct(t1::IdentityMapping, t2::TensorMapping) = InflatedTensorMapping(t1, t2)
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421
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422 LazyOuterProduct(tms::Vararg{TensorMapping}) = foldl(LazyOuterProduct, tms)
468
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423
474
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424 ⊗(a::TensorMapping, b::TensorMapping) = LazyOuterProduct(a,b)
468
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425
498
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426
487
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427 function check_domain_size(tm::TensorMapping, sz)
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428 if domain_size(tm) != sz
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429 throw(SizeMismatch(tm,sz))
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430 end
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431 end
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432
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433 struct SizeMismatch <: Exception
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434 tm::TensorMapping
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435 sz
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436 end
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437
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438 function Base.showerror(io::IO, err::SizeMismatch)
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439 print(io, "SizeMismatch: ")
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440 print(io, "domain size $(domain_size(err.tm)) of TensorMapping not matching size $(err.sz)")
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441 end
919
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442
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443 function apply_with_region(op, v, boundary_width::Integer, dim_size::Integer, i)
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444 if 0 < i <= boundary_width
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445 return LazyTensors.apply(op,v,Index(i,Lower))
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446 elseif boundary_width < i <= dim_size-boundary_width
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447 return LazyTensors.apply(op,v,Index(i,Interior))
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448 elseif dim_size-boundary_width < i <= dim_size
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449 return LazyTensors.apply(op,v,Index(i,Upper))
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450 else
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451 error("Bounds error") # TODO: Make this more standard
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452 end
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453 end
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454 # TBD: Can these methods be merge by having a function as an arguement instead?
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455 # TODO: Add inference test that show where things break and how this rewrite fixes it.
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456 function apply_transpose_with_region(op, v, boundary_width::Integer, dim_size::Integer, i)
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457 if 0 < i <= boundary_width
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458 return LazyTensors.apply_transpose(op,v,Index(i,Lower))
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459 elseif boundary_width < i <= dim_size-boundary_width
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460 return LazyTensors.apply_transpose(op,v,Index(i,Interior))
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461 elseif dim_size-boundary_width < i <= dim_size
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462 return LazyTensors.apply_transpose(op,v,Index(i,Upper))
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463 else
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464 error("Bounds error") # TODO: Make this more standard
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465 end
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466 end