annotate src/LazyTensors/lazy_tensor_operations.jl @ 541:62d96e2cd165 refactor/tensor_index_coupling

Make the coupling between all the LazyTensors code and the Index type much weaker to make the module more flexible
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 26 Nov 2020 21:35:34 +0100
parents 848dec405332
children 53828d3ed132
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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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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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17 # TODO: Go through and remove unneccerary type parameters on functions
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19 Base.getindex(ta::LazyTensorMappingApplication{T,R,D}, I::Vararg{Any,R}) where {T,R,D} = apply(ta.t, ta.o, I...)
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20 Base.size(ta::LazyTensorMappingApplication) = range_size(ta.t)
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21 # TODO: What else is needed to implement the AbstractArray interface?
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23 Base.:*(a::TensorMapping, v::AbstractArray) = LazyTensorMappingApplication(a,v)
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24 Base.:*(a::TensorMapping, b::TensorMapping) = throw(MethodError(Base.:*,(a,b)))
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25 Base.:*(a::TensorMapping, args::Union{TensorMapping, AbstractArray}...) = foldr(*,(a,args...))
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27 # # We need the associativity to be a→b→c = a→(b→c), which is the case for '→'
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28 # # Should we overload some other infix binary opesrator?
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29 # →(tm::TensorMapping{T,R,D}, o::AbstractArray{T,D}) where {T,R,D} = LazyTensorMappingApplication(tm,o)
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30 # TODO: We need to be really careful about good error messages.
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31 # For example what happens if you try to multiply LazyTensorMappingApplication with a TensorMapping(wrong order)?
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33 """
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34 LazyTensorMappingTranspose{T,R,D} <: TensorMapping{T,D,R}
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35
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36 Struct for lazy transpose of a TensorMapping.
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38 If a mapping implements the the `apply_transpose` method this allows working with
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39 the transpose of mapping `m` by using `m'`. `m'` will work as a regular TensorMapping lazily calling
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40 the appropriate methods of `m`.
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41 """
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42 struct LazyTensorMappingTranspose{T,R,D, TM<:TensorMapping{T,R,D}} <: TensorMapping{T,D,R}
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43 tm::TM
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44 end
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45 export LazyTensorMappingTranspose
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46
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47 # # TBD: Should this be implemented on a type by type basis or through a trait to provide earlier errors?
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48 # 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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49 Base.adjoint(tm::TensorMapping) = LazyTensorMappingTranspose(tm)
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50 Base.adjoint(tmt::LazyTensorMappingTranspose) = tmt.tm
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51
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52 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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53 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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54
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55 range_size(tmt::LazyTensorMappingTranspose) = domain_size(tmt.tm)
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56 domain_size(tmt::LazyTensorMappingTranspose) = range_size(tmt.tm)
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58
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59 struct LazyTensorMappingBinaryOperation{Op,T,R,D,T1<:TensorMapping{T,R,D},T2<:TensorMapping{T,R,D}} <: TensorMapping{T,D,R}
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60 tm1::T1
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61 tm2::T2
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63 @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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64 return new{Op,T,R,D,T1,T2}(tm1,tm2)
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65 end
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66 end
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67 # TODO: Boundschecking in constructor.
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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 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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71
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72 range_size(tmBinOp::LazyTensorMappingBinaryOperation{Op,T,R,D}) where {Op,T,R,D} = range_size(tmBinOp.tm1)
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73 domain_size(tmBinOp::LazyTensorMappingBinaryOperation{Op,T,R,D}) where {Op,T,R,D} = domain_size(tmBinOp.tm1)
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74
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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 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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78 """
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79 TensorMappingComposition{T,R,K,D}
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81 Lazily compose two TensorMappings, so that they can be handled as a single TensorMapping.
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82 """
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83 struct TensorMappingComposition{T,R,K,D, TM1<:TensorMapping{T,R,K}, TM2<:TensorMapping{T,K,D}} <: TensorMapping{T,R,D}
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84 t1::TM1
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85 t2::TM2
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86
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87 @inline function TensorMappingComposition(t1::TensorMapping{T,R,K}, t2::TensorMapping{T,K,D}) where {T,R,K,D}
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88 @boundscheck check_domain_size(t1, range_size(t2))
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89 return new{T,R,K,D, typeof(t1), typeof(t2)}(t1,t2)
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90 end
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91 end
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92 export TensorMappingComposition
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94 range_size(tm::TensorMappingComposition) = range_size(tm.t1)
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95 domain_size(tm::TensorMappingComposition) = domain_size(tm.t2)
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97 function apply(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{T,D}, I::Vararg{S,R} where S) where {T,R,K,D}
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98 apply(c.t1, c.t2*v, I...)
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99 end
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100
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101 function apply_transpose(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{T,R}, I::Vararg{S,D} where S) where {T,R,K,D}
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102 apply_transpose(c.t2, c.t1'*v, I...)
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103 end
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104
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105 Base.@propagate_inbounds Base.:∘(s::TensorMapping, t::TensorMapping) = TensorMappingComposition(s,t)
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106
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107 """
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108 LazyLinearMap{T,R,D,...}(A, range_indicies, domain_indicies)
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109
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110 TensorMapping defined by the AbstractArray A. `range_indicies` and `domain_indicies` define which indicies of A should
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111 be considerd the range and domain of the TensorMapping. Each set of indices must be ordered in ascending order.
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112
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113 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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114 standard matrix-vector product on vectors of size n.
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115 """
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116 struct LazyLinearMap{T,R,D, RD, AA<:AbstractArray{T,RD}} <: TensorMapping{T,R,D}
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117 A::AA
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118 range_indicies::NTuple{R,Int}
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119 domain_indicies::NTuple{D,Int}
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120
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121 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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122 if !issorted(range_indicies) || !issorted(domain_indicies)
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123 throw(DomainError("range_indicies and domain_indicies must be sorted in ascending order"))
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124 end
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125
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126 return new{T,R,D,RD,AA}(A,range_indicies,domain_indicies)
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127 end
377
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128 end
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129 export LazyLinearMap
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130
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131 range_size(llm::LazyLinearMap) = size(llm.A)[[llm.range_indicies...]]
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132 domain_size(llm::LazyLinearMap) = size(llm.A)[[llm.domain_indicies...]]
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133
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134 function apply(llm::LazyLinearMap{T,R,D}, v::AbstractArray{T,D}, I::Vararg{Any,R}) where {T,R,D}
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135 view_index = ntuple(i->:,ndims(llm.A))
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136 for i ∈ 1:R
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137 view_index = Base.setindex(view_index, Int(I[i]), llm.range_indicies[i])
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138 end
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139 A_view = @view llm.A[view_index...]
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140 return sum(A_view.*v)
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141 end
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142
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143 function apply_transpose(llm::LazyLinearMap{T,R,D}, v::AbstractArray{T,R}, I::Vararg{Any,D}) where {T,R,D}
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144 apply(LazyLinearMap(llm.A, llm.domain_indicies, llm.range_indicies), v, I...)
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145 end
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146
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147
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148 """
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149 IdentityMapping{T,D} <: TensorMapping{T,D,D}
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150
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151 The lazy identity TensorMapping for a given size. Usefull for building up higher dimensional tensor mappings from lower
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152 dimensional ones through outer products. Also used in the Implementation for InflatedTensorMapping.
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153 """
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154 struct IdentityMapping{T,D} <: TensorMapping{T,D,D}
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155 size::NTuple{D,Int}
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156 end
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157 export IdentityMapping
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158
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159 IdentityMapping{T}(size::NTuple{D,Int}) where {T,D} = IdentityMapping{T,D}(size)
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160 IdentityMapping{T}(size::Vararg{Int,D}) where {T,D} = IdentityMapping{T,D}(size)
442
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161 IdentityMapping(size::Vararg{Int,D}) where D = IdentityMapping{Float64,D}(size)
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162
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163 range_size(tmi::IdentityMapping) = tmi.size
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164 domain_size(tmi::IdentityMapping) = tmi.size
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165
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166 apply(tmi::IdentityMapping{T,D}, v::AbstractArray{T,D}, I::Vararg{Any,D}) where {T,D} = v[I...]
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167 apply_transpose(tmi::IdentityMapping{T,D}, v::AbstractArray{T,D}, I::Vararg{Any,D}) where {T,D} = v[I...]
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168
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169 """
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170 Base.:∘(tm, tmi)
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171 Base.:∘(tmi, tm)
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172
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173 Composes a `Tensormapping` `tm` with an `IdentityMapping` `tmi`, by returning `tm`
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174 """
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175 @inline function Base.:∘(tm::TensorMapping{T,R,D}, tmi::IdentityMapping{T,D}) where {T,R,D}
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176 @boundscheck check_domain_size(tm, range_size(tmi))
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177 return tm
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178 end
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179
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180 @inline function Base.:∘(tmi::IdentityMapping{T,R}, tm::TensorMapping{T,R,D}) where {T,R,D}
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181 @boundscheck check_domain_size(tmi, range_size(tm))
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182 return tm
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183 end
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184 # Specialization for the case where tm is an IdentityMapping. Required to resolve ambiguity.
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185 @inline function Base.:∘(tm::IdentityMapping{T,D}, tmi::IdentityMapping{T,D}) where {T,D}
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186 @boundscheck check_domain_size(tm, range_size(tmi))
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187 return tmi
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188 end
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189
460
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190
459
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191 """
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192 InflatedTensorMapping{T,R,D} <: TensorMapping{T,R,D}
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193
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194 An inflated `TensorMapping` with dimensions added before and afer its actual dimensions.
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195 """
449
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196 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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197 before::IdentityMapping{T,D_before}
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198 tm::TM
448
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199 after::IdentityMapping{T,D_after}
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200
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201 function InflatedTensorMapping(before, tm::TensorMapping{T}, after) where T
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202 R_before = range_dim(before)
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203 R_middle = range_dim(tm)
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204 R_after = range_dim(after)
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205 R = R_before+R_middle+R_after
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206
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207 D_before = domain_dim(before)
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208 D_middle = domain_dim(tm)
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209 D_after = domain_dim(after)
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210 D = D_before+D_middle+D_after
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211 return new{T,R,D,D_before,R_middle,D_middle,D_after, typeof(tm)}(before, tm, after)
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212 end
446
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213 end
451
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214 export InflatedTensorMapping
461
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215 """
464
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216 InflatedTensorMapping(before, tm, after)
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217 InflatedTensorMapping(before,tm)
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218 InflatedTensorMapping(tm,after)
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219
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220 The outer product of `before`, `tm` and `after`, where `before` and `after` are `IdentityMapping`s.
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221
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222 If one of `before` or `after` is left out, a 0-dimensional `IdentityMapping` is used as the default value.
493
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223
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224 If `tm` already is an `InflatedTensorMapping`, `before` and `after` will be extended instead of
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225 creating a nested `InflatedTensorMapping`.
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226 """
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227 InflatedTensorMapping(::IdentityMapping, ::TensorMapping, ::IdentityMapping)
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228
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229 function InflatedTensorMapping(before, itm::InflatedTensorMapping, after)
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230 return InflatedTensorMapping(
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231 IdentityMapping(before.size..., itm.before.size...),
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232 itm.tm,
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233 IdentityMapping(itm.after.size..., after.size...),
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234 )
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235 end
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236
462
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diff changeset
237 InflatedTensorMapping(before::IdentityMapping, tm::TensorMapping{T}) where T = InflatedTensorMapping(before,tm,IdentityMapping{T}())
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238 InflatedTensorMapping(tm::TensorMapping{T}, after::IdentityMapping) where T = InflatedTensorMapping(IdentityMapping{T}(),tm,after)
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239 # Resolve ambiguity between the two previous methods
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240 InflatedTensorMapping(I1::IdentityMapping{T}, I2::IdentityMapping{T}) where T = InflatedTensorMapping(I1,I2,IdentityMapping{T}())
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241
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242 # 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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243
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244 function range_size(itm::InflatedTensorMapping)
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245 return flatten_tuple(
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246 range_size(itm.before),
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247 range_size(itm.tm),
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248 range_size(itm.after),
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249 )
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250 end
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251
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252 function domain_size(itm::InflatedTensorMapping)
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253 return flatten_tuple(
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254 domain_size(itm.before),
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255 domain_size(itm.tm),
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256 domain_size(itm.after),
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257 )
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258 end
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259
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260 function apply(itm::InflatedTensorMapping{T,R,D}, v::AbstractArray{T,D}, I::Vararg{Any,R}) where {T,R,D}
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261 dim_before = range_dim(itm.before)
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262 dim_domain = domain_dim(itm.tm)
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263 dim_range = range_dim(itm.tm)
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264 dim_after = range_dim(itm.after)
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265
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266 view_index, inner_index = split_index(Val(dim_before), Val(dim_domain), Val(dim_range), Val(dim_after), I...)
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267
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268 v_inner = view(v, view_index...)
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269 return apply(itm.tm, v_inner, inner_index...)
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270 end
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271
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272 function apply_transpose(itm::InflatedTensorMapping{T,R,D}, v::AbstractArray{T,R}, I::Vararg{Any,D}) where {T,R,D}
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273 dim_before = range_dim(itm.before)
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274 dim_domain = domain_dim(itm.tm)
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275 dim_range = range_dim(itm.tm)
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276 dim_after = range_dim(itm.after)
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277
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278 view_index, inner_index = split_index(Val(dim_before), Val(dim_range), Val(dim_domain), Val(dim_after), I...)
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279
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280 v_inner = view(v, view_index...)
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281 return apply_transpose(itm.tm, v_inner, inner_index...)
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282 end
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283
446
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284
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285 """
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286 split_index(::Val{dim_before}, ::Val{dim_view}, ::Val{dim_index}, ::Val{dim_after}, I...)
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287
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288 Splits the multi-index `I` into two parts. One part which is expected to be
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289 used as a view, and one which is expected to be used as an index.
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290 Eg.
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291 ```
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292 split_index(Val(1),Val(3),Val(2),Val(1),(1,2,3,4)) -> (1,:,:,:,4), (2,3)
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293 ```
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294
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295 `dim_view` controls how many colons are in the view, and `dim_index` controls
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296 how many elements are extracted from the middle.
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297 `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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298
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299 Arguments should satisfy `length(I) == dim_before+B_domain+dim_after`.
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300
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301 The returned values satisfy
533
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302 * `length(view_index) == dim_before + dim_view + dim_after`
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303 * `length(I_middle) == dim_index`
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304 """
533
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305 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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306 I_before, I_middle, I_after = split_tuple(I, Val(dim_before), Val(dim_index))
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307
533
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308 view_index = (I_before..., ntuple((i)->:, dim_view)..., I_after...)
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309
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310 return view_index, I_middle
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311 end
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312
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313 # TODO: Can this be replaced by something more elegant while still being type stable? 2020-10-21
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314 # See:
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315 # https://github.com/JuliaLang/julia/issues/34884
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316 # https://github.com/JuliaLang/julia/issues/30386
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317 """
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318 slice_tuple(t, Val(l), Val(u))
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319
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320 Get a slice of a tuple in a type stable way.
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321 Equivalent to t[l:u] but type stable.
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322 """
455
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323 function slice_tuple(t,::Val{L},::Val{U}) where {L,U}
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324 return ntuple(i->t[i+L-1], U-L+1)
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325 end
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326
457
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327 """
532
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328 split_tuple(t::Tuple{...}, ::Val{M}) where {N,M}
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329
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330 Split the tuple `t` into two parts. the first part is `M` long.
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331 E.g
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332 ```
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333 split_tuple((1,2,3,4),Val(3)) -> (1,2,3), (4,)
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334 ```
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335 """
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336 function split_tuple(t::NTuple{N},::Val{M}) where {N,M}
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337 return slice_tuple(t,Val(1), Val(M)), slice_tuple(t,Val(M+1), Val(N))
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338 end
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339
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340 """
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341 split_tuple(t::Tuple{...},::Val{M},::Val{K}) where {N,M,K}
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342
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343 Same as `split_tuple(t::NTuple{N},::Val{M})` but splits the tuple in three parts. With the first
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344 two parts having lenght `M` and `K`.
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345 """
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346 function split_tuple(t::NTuple{N},::Val{M},::Val{K}) where {N,M,K}
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347 p1, tail = split_tuple(t, Val(M))
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348 p2, p3 = split_tuple(tail, Val(K))
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349 return p1,p2,p3
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350 end
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351
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352
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353 """
457
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354 flatten_tuple(t)
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355
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356 Takes a nested tuple and flattens the whole structure
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357 """
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358 flatten_tuple(t::NTuple{N, Number} where N) = t
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359 flatten_tuple(t::Tuple) = ((flatten_tuple.(t)...)...,) # simplify?
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360 flatten_tuple(ts::Vararg) = flatten_tuple(ts)
487
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361
468
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362 """
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363 LazyOuterProduct(tms...)
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364
501
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365 Creates a `TensorMappingComposition` for the outerproduct of `tms...`.
468
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366 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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367
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368 First let
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369 ```math
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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 ```
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374
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375 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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376
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377 We use ``⊗`` to denote the outer product
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378 ```math
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379 (A⊗B)_{IM,JN} = A_{I,J}B_{M,N}
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380 ```
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381
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382 We note that
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383 ```math
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384 A⊗B⊗C = (A⊗B⊗C)_{IMP,JNQ} = A_{I,J}B_{M,N}C_{P,Q}
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385 ```
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386 And that
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387 ```math
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388 A⊗B⊗C = (A⊗I_{|M|}⊗I_{|P|})(I_{|J|}⊗B⊗I_{|P|})(I_{|J|}⊗I_{|N|}⊗C)
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389 ```
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390 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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391 To apply ``A⊗B⊗C`` we evaluate
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392
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393 (A⊗B⊗C)v = [(A⊗I_{|M|}⊗I_{|P|}) [(I_{|J|}⊗B⊗I_{|P|}) [(I_{|J|}⊗I_{|N|}⊗C)v]]]
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394 """
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395 function LazyOuterProduct end
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396 export LazyOuterProduct
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397
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398 function LazyOuterProduct(tm1::TensorMapping{T}, tm2::TensorMapping{T}) where T
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399 itm1 = InflatedTensorMapping(tm1, IdentityMapping{T}(range_size(tm2)))
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400 itm2 = InflatedTensorMapping(IdentityMapping{T}(domain_size(tm1)),tm2)
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401
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402 return itm1∘itm2
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403 end
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404
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405 LazyOuterProduct(t1::IdentityMapping{T}, t2::IdentityMapping{T}) where T = IdentityMapping{T}(t1.size...,t2.size...)
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406 LazyOuterProduct(t1::TensorMapping, t2::IdentityMapping) = InflatedTensorMapping(t1, t2)
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407 LazyOuterProduct(t1::IdentityMapping, t2::TensorMapping) = InflatedTensorMapping(t1, t2)
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408
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409 LazyOuterProduct(tms::Vararg{TensorMapping}) = foldl(LazyOuterProduct, tms)
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410
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411 ⊗(a::TensorMapping, b::TensorMapping) = LazyOuterProduct(a,b)
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412 export ⊗
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413
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414
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415 function check_domain_size(tm::TensorMapping, sz)
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416 if domain_size(tm) != sz
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417 throw(SizeMismatch(tm,sz))
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418 end
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419 end
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420
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421 struct SizeMismatch <: Exception
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422 tm::TensorMapping
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423 sz
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424 end
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425 export SizeMismatch
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426
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427 function Base.showerror(io::IO, err::SizeMismatch)
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428 print(io, "SizeMismatch: ")
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429 print(io, "domain size $(domain_size(err.tm)) of TensorMapping not matching size $(err.sz)")
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430 end