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annotate src/LazyTensors/lazy_tensor_operations.jl @ 1880:378002c78e86 refactor/lazy_tensors/elementwise_ops

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Add implementation of apply_transpose to TensorSum
author Jonatan Werpers <jonatan@werpers.com>
date Mon, 27 Jan 2025 17:11:31 +0100
parents 765f42559c47
children ed50eec18365
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1 """
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2 TensorApplication{T,R,D} <: LazyArray{T,R}
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3
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4 Struct for lazy application of a LazyTensor. Created using `*`.
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5
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6 Allows the result of a `LazyTensor` applied to a vector to be treated as an `AbstractArray`.
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7 With a mapping `m` and a vector `v` the TensorApplication object can be created by `m*v`.
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8 The actual result will be calculated when indexing into `m*v`.
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9 """
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10 struct TensorApplication{T,R,D, TM<:LazyTensor{<:Any,R,D}, AA<:AbstractArray{<:Any,D}} <: LazyArray{T,R}
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11 t::TM
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12 o::AA
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13
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14 function TensorApplication(t::LazyTensor{<:Any,R,D}, o::AbstractArray{<:Any,D}) where {R,D}
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15 @boundscheck check_domain_size(t, size(o))
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16 I = ntuple(i->1, range_dim(t))
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17 T = typeof(apply(t,o,I...))
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18 return new{T,R,D,typeof(t), typeof(o)}(t,o)
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19 end
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20 end
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21
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22 function Base.getindex(ta::TensorApplication{T,R}, I::Vararg{Any,R}) where {T,R}
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23 @boundscheck checkbounds(ta, Int.(I)...)
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24 return @inbounds apply(ta.t, ta.o, I...)
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25 end
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26 Base.@propagate_inbounds Base.getindex(ta::TensorApplication{T,1} where T, I::CartesianIndex{1}) = ta[Tuple(I)...] # Would otherwise be caught in the previous method.
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27 Base.size(ta::TensorApplication) = range_size(ta.t)
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30 """
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31 TensorTranspose{T,R,D} <: LazyTensor{T,D,R}
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32
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33 Struct for lazy transpose of a LazyTensor.
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35 If a mapping implements the the `apply_transpose` method this allows working with
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36 the transpose of mapping `m` by using `m'`. `m'` will work as a regular LazyTensor lazily calling
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37 the appropriate methods of `m`.
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38 """
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39 struct TensorTranspose{T,R,D, TM<:LazyTensor{T,R,D}} <: LazyTensor{T,D,R}
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40 tm::TM
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41 end
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43 # # TBD: Should this be implemented on a type by type basis or through a trait to provide earlier errors?
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44 # Jonatan 2020-09-25: Is the problem that you can take the transpose of any LazyTensor even if it doesn't implement `apply_transpose`?
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45 Base.adjoint(tm::LazyTensor) = TensorTranspose(tm)
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46 Base.adjoint(tmt::TensorTranspose) = tmt.tm
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48 apply(tmt::TensorTranspose{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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49 apply_transpose(tmt::TensorTranspose{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmt.tm, v, I...)
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50
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51 range_size(tmt::TensorTranspose) = domain_size(tmt.tm)
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52 domain_size(tmt::TensorTranspose) = range_size(tmt.tm)
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55 """
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56 TensorNegation{T,R,D,...} <: LazyTensor{T,R,D}
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57
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58 The negation of a LazyTensor.
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59 """
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60 struct TensorNegation{T,R,D,TM<:LazyTensor{T,R,D}} <: LazyTensor{T,R,D}
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61 tm::TM
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62 end
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63
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64 apply(tm::TensorNegation, v, I...) = -apply(tm.tm, v, I...)
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65 apply_transpose(tm::TensorNegation, v, I...) = -apply_transpose(tm.tm, v, I...)
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66
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67 range_size(tm::TensorNegation) = range_size(tm.tm)
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68 domain_size(tm::TensorNegation) = domain_size(tm.tm)
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71 """
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72 TensorSum{T,R,D,...} <: LazyTensor{T,R,D}
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73
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74 The lazy sum of 2 or more lazy tensors.
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75 """
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76 struct TensorSum{T,R,D,TT<:NTuple{N, LazyTensor{T,R,D}} where N} <: LazyTensor{T,R,D}
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77 tms::TT
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78
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79 function TensorSum{T,R,D}(tms::TT) where {T,R,D, TT<:NTuple{N, LazyTensor{T,R,D}} where N}
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80 @boundscheck map(tms) do tm
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81 check_domain_size(tm, domain_size(tms[1]))
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82 check_range_size(tm, range_size(tms[1]))
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83 end
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84
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85 return new{T,R,D,TT}(tms)
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86 end
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87 end
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88
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89 """
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90 TensorSum(ts::Vararg{LazyTensor})
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91
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92 The lazy sum of the tensors `ts`.
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93 """
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94 function TensorSum(ts::Vararg{LazyTensor})
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95 T = eltype(ts[1])
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96 R = range_dim(ts[1])
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97 D = domain_dim(ts[1])
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98 return TensorSum{T,R,D}(ts)
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99 end
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100
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101 function apply(tmBinOp::TensorSum{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D}
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102 vs = map(tmBinOp.tms) do tm
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103 apply(tm,v,I...)
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104 end
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105
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106 return +(vs...)
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107 end
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108
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109 function apply_transpose(tmBinOp::TensorSum{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D}
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110 vs = map(tmBinOp.tms) do tm
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111 apply_transpose(tm,v,I...)
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112 end
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113
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114 return +(vs...)
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115 end
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116
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117 range_size(tmBinOp::TensorSum) = range_size(tmBinOp.tms[1])
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118 domain_size(tmBinOp::TensorSum) = domain_size(tmBinOp.tms[1])
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119
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120
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121 """
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122 TensorComposition{T,R,K,D}
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123
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124 Lazily compose two `LazyTensor`s, so that they can be handled as a single `LazyTensor`.
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125 """
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126 struct TensorComposition{T,R,K,D, TM1<:LazyTensor{T,R,K}, TM2<:LazyTensor{T,K,D}} <: LazyTensor{T,R,D}
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127 t1::TM1
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128 t2::TM2
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129
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130 function TensorComposition(t1::LazyTensor{T,R,K}, t2::LazyTensor{T,K,D}) where {T,R,K,D}
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131 @boundscheck check_domain_size(t1, range_size(t2))
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132 return new{T,R,K,D, typeof(t1), typeof(t2)}(t1,t2)
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133 end
412
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134 end
190
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135
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136 range_size(tm::TensorComposition) = range_size(tm.t1)
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137 domain_size(tm::TensorComposition) = domain_size(tm.t2)
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138
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139 function apply(c::TensorComposition{T,R,K,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,K,D}
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140 apply(c.t1, c.t2*v, I...)
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141 end
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142
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143 function apply_transpose(c::TensorComposition{T,R,K,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,K,D}
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144 apply_transpose(c.t2, c.t1'*v, I...)
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145 end
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146
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147 """
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148 TensorComposition(tm, tmi::IdentityTensor)
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149 TensorComposition(tmi::IdentityTensor, tm)
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150
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151 Composes a `LazyTensor` `tm` with an `IdentityTensor` `tmi`, by returning `tm`
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152 """
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153 function TensorComposition(tm::LazyTensor{T,R,D}, tmi::IdentityTensor{T,D}) where {T,R,D}
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154 @boundscheck check_domain_size(tm, range_size(tmi))
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155 return tm
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156 end
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157
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158 function TensorComposition(tmi::IdentityTensor{T,R}, tm::LazyTensor{T,R,D}) where {T,R,D}
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159 @boundscheck check_domain_size(tmi, range_size(tm))
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160 return tm
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161 end
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162 # Specialization for the case where tm is an IdentityTensor. Required to resolve ambiguity.
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163 function TensorComposition(tm::IdentityTensor{T,D}, tmi::IdentityTensor{T,D}) where {T,D}
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164 @boundscheck check_domain_size(tm, range_size(tmi))
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165 return tmi
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166 end
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167
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168 Base.:*(a::T, tm::LazyTensor{T}) where T = TensorComposition(ScalingTensor{T,range_dim(tm)}(a,range_size(tm)), tm)
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169 Base.:*(tm::LazyTensor{T}, a::T) where T = a*tm
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170
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171 """
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172 InflatedTensor{T,R,D} <: LazyTensor{T,R,D}
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173
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174 An inflated `LazyTensor` with dimensions added before and after its actual dimensions.
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175 """
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176 struct InflatedTensor{T,R,D,D_before,R_middle,D_middle,D_after, TM<:LazyTensor{T,R_middle,D_middle}} <: LazyTensor{T,R,D}
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177 before::IdentityTensor{T,D_before}
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178 tm::TM
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179 after::IdentityTensor{T,D_after}
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180
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181 function InflatedTensor(before, tm::LazyTensor{T}, after) where T
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182 R_before = range_dim(before)
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183 R_middle = range_dim(tm)
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184 R_after = range_dim(after)
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185 R = R_before+R_middle+R_after
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186
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187 D_before = domain_dim(before)
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188 D_middle = domain_dim(tm)
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189 D_after = domain_dim(after)
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190 D = D_before+D_middle+D_after
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191 return new{T,R,D,D_before,R_middle,D_middle,D_after, typeof(tm)}(before, tm, after)
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192 end
446
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193 end
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194
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195 """
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196 InflatedTensor(before, tm, after)
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197 InflatedTensor(before,tm)
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198 InflatedTensor(tm,after)
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199
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200 The outer product of `before`, `tm` and `after`, where `before` and `after` are `IdentityTensor`s.
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201
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202 If one of `before` or `after` is left out, a 0-dimensional `IdentityTensor` is used as the default value.
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203
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204 If `tm` already is an `InflatedTensor`, `before` and `after` will be extended instead of
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205 creating a nested `InflatedTensor`.
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206 """
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207 InflatedTensor(::IdentityTensor, ::LazyTensor, ::IdentityTensor)
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208
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209 function InflatedTensor(before, itm::InflatedTensor, after)
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210 return InflatedTensor(
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211 IdentityTensor(before.size..., itm.before.size...),
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212 itm.tm,
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213 IdentityTensor(itm.after.size..., after.size...),
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214 )
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215 end
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216
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217 InflatedTensor(before::IdentityTensor, tm::LazyTensor) = InflatedTensor(before,tm,IdentityTensor{eltype(tm)}())
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218 InflatedTensor(tm::LazyTensor, after::IdentityTensor) = InflatedTensor(IdentityTensor{eltype(tm)}(),tm,after)
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219 # Resolve ambiguity between the two previous methods
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220 InflatedTensor(I1::IdentityTensor, I2::IdentityTensor) = InflatedTensor(I1,I2,IdentityTensor{promote_type(eltype(I1), eltype(I2))}())
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221
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222 # TODO: Implement some pretty printing in terms of ⊗. E.g InflatedTensor(I(3),B,I(2)) -> I(3)⊗B⊗I(2)
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223
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224 function range_size(itm::InflatedTensor)
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225 return concatenate_tuples(
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226 range_size(itm.before),
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227 range_size(itm.tm),
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228 range_size(itm.after),
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229 )
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230 end
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231
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232 function domain_size(itm::InflatedTensor)
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233 return concatenate_tuples(
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234 domain_size(itm.before),
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235 domain_size(itm.tm),
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236 domain_size(itm.after),
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237 )
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238 end
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239
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240 function apply(itm::InflatedTensor{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D}
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241 dim_before = range_dim(itm.before)
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242 dim_domain = domain_dim(itm.tm)
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243 dim_range = range_dim(itm.tm)
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244 dim_after = range_dim(itm.after)
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245
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246 view_index, inner_index = split_index(dim_before, dim_domain, dim_range, dim_after, I...)
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247
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248 v_inner = view(v, view_index...)
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249 return apply(itm.tm, v_inner, inner_index...)
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250 end
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251
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252 function apply_transpose(itm::InflatedTensor{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,D}
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253 dim_before = range_dim(itm.before)
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254 dim_domain = domain_dim(itm.tm)
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255 dim_range = range_dim(itm.tm)
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256 dim_after = range_dim(itm.after)
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257
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258 view_index, inner_index = split_index(dim_before, dim_range, dim_domain, dim_after, I...)
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259
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260 v_inner = view(v, view_index...)
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261 return apply_transpose(itm.tm, v_inner, inner_index...)
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262 end
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263
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264
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265 @doc raw"""
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266 LazyOuterProduct(tms...)
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267
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268 Creates a `TensorComposition` for the outer product of `tms...`.
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269 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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270
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271 First let
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272 ```math
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273 \begin{aligned}
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274 A &= A_{I,J} \\
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275 B &= B_{M,N} \\
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276 C &= C_{P,Q} \\
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277 \end{aligned}
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278 ```
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279
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280 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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281
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282 We use ``⊗`` to denote the outer product
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283 ```math
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284 (A⊗B)_{IM,JN} = A_{I,J}B_{M,N}
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285 ```
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286
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287 We note that
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288 ```math
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289 A⊗B⊗C = (A⊗B⊗C)_{IMP,JNQ} = A_{I,J}B_{M,N}C_{P,Q}
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290 ```
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291 And that
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292 ```math
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293 A⊗B⊗C = (A⊗I_{|M|}⊗I_{|P|})(I_{|J|}⊗B⊗I_{|P|})(I_{|J|}⊗I_{|N|}⊗C)
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294 ```
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295 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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296 To apply ``A⊗B⊗C`` we evaluate
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297
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298 ```math
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299 (A⊗B⊗C)v = [(A⊗I_{|M|}⊗I_{|P|}) [(I_{|J|}⊗B⊗I_{|P|}) [(I_{|J|}⊗I_{|N|}⊗C)v]]]
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300 ```
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301 """
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302 function LazyOuterProduct end
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303
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304 function LazyOuterProduct(tm1::LazyTensor{T}, tm2::LazyTensor{T}) where T
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305 itm1 = InflatedTensor(tm1, IdentityTensor{T}(range_size(tm2)))
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306 itm2 = InflatedTensor(IdentityTensor{T}(domain_size(tm1)),tm2)
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307
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308 return itm1∘itm2
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309 end
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310
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311 LazyOuterProduct(t1::IdentityTensor, t2::IdentityTensor) = IdentityTensor{promote_type(eltype(t1),eltype(t2))}(t1.size...,t2.size...)
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312 LazyOuterProduct(t1::LazyTensor, t2::IdentityTensor) = InflatedTensor(t1, t2)
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313 LazyOuterProduct(t1::IdentityTensor, t2::LazyTensor) = InflatedTensor(t1, t2)
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314
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315 LazyOuterProduct(tms::Vararg{LazyTensor}) = foldl(LazyOuterProduct, tms)
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316
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317
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318
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319 """
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320 inflate(tm::LazyTensor, sz, dir)
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321
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322 Inflate `tm` such that it gets the size `sz` in all directions except `dir`.
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323 Here `sz[dir]` is ignored and replaced with the range and domains size of
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324 `tm`.
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325
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326 An example of when this operation is useful is when extending a one
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327 dimensional difference operator `D` to a 2D grid of a certain size. In that
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328 case we could have
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329
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330 ```julia
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331 Dx = inflate(D, (10,10), 1)
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332 Dy = inflate(D, (10,10), 2)
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333 ```
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334 """
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335 function inflate(tm::LazyTensor, sz, dir)
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336 Is = IdentityTensor{eltype(tm)}.(sz)
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337 parts = Base.setindex(Is, tm, dir)
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338 return foldl(⊗, parts)
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339 end
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340
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341 function check_domain_size(tm::LazyTensor, sz)
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342 if domain_size(tm) != sz
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343 throw(DomainSizeMismatch(tm,sz))
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344 end
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345 end
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346
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347 function check_range_size(tm::LazyTensor, sz)
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348 if range_size(tm) != sz
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349 throw(RangeSizeMismatch(tm,sz))
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350 end
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351 end
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352
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353 struct DomainSizeMismatch <: Exception
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354 tm::LazyTensor
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355 sz
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356 end
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357
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358 function Base.showerror(io::IO, err::DomainSizeMismatch)
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359 print(io, "DomainSizeMismatch: ")
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360 print(io, "domain size $(domain_size(err.tm)) of LazyTensor not matching size $(err.sz)")
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361 end
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362
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363
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364 struct RangeSizeMismatch <: Exception
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365 tm::LazyTensor
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366 sz
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367 end
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368
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369 function Base.showerror(io::IO, err::RangeSizeMismatch)
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370 print(io, "RangeSizeMismatch: ")
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371 print(io, "range size $(range_size(err.tm)) of LazyTensor not matching size $(err.sz)")
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372 end