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annotate src/LazyTensors/lazy_tensor_operations.jl @ 1879:765f42559c47 refactor/lazy_tensors/elementwise_ops

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Add some more docs
author Jonatan Werpers <jonatan@werpers.com>
date Mon, 27 Jan 2025 17:11:14 +0100
parents b12e28a03b2e
children 378002c78e86
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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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42
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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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54
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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 range_size(tmBinOp::TensorSum) = range_size(tmBinOp.tms[1])
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110 domain_size(tmBinOp::TensorSum) = domain_size(tmBinOp.tms[1])
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111
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112
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113 """
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114 TensorComposition{T,R,K,D}
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115
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116 Lazily compose two `LazyTensor`s, so that they can be handled as a single `LazyTensor`.
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117 """
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118 struct TensorComposition{T,R,K,D, TM1<:LazyTensor{T,R,K}, TM2<:LazyTensor{T,K,D}} <: LazyTensor{T,R,D}
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119 t1::TM1
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120 t2::TM2
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121
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122 function TensorComposition(t1::LazyTensor{T,R,K}, t2::LazyTensor{T,K,D}) where {T,R,K,D}
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123 @boundscheck check_domain_size(t1, range_size(t2))
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124 return new{T,R,K,D, typeof(t1), typeof(t2)}(t1,t2)
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125 end
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126 end
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127
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128 range_size(tm::TensorComposition) = range_size(tm.t1)
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129 domain_size(tm::TensorComposition) = domain_size(tm.t2)
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131 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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132 apply(c.t1, c.t2*v, I...)
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133 end
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134
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135 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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136 apply_transpose(c.t2, c.t1'*v, I...)
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137 end
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138
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139 """
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140 TensorComposition(tm, tmi::IdentityTensor)
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141 TensorComposition(tmi::IdentityTensor, tm)
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142
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143 Composes a `LazyTensor` `tm` with an `IdentityTensor` `tmi`, by returning `tm`
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144 """
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145 function TensorComposition(tm::LazyTensor{T,R,D}, tmi::IdentityTensor{T,D}) where {T,R,D}
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146 @boundscheck check_domain_size(tm, range_size(tmi))
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147 return tm
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148 end
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149
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150 function TensorComposition(tmi::IdentityTensor{T,R}, tm::LazyTensor{T,R,D}) where {T,R,D}
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151 @boundscheck check_domain_size(tmi, range_size(tm))
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152 return tm
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153 end
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154 # Specialization for the case where tm is an IdentityTensor. Required to resolve ambiguity.
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155 function TensorComposition(tm::IdentityTensor{T,D}, tmi::IdentityTensor{T,D}) where {T,D}
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156 @boundscheck check_domain_size(tm, range_size(tmi))
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157 return tmi
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158 end
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159
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160 Base.:*(a::T, tm::LazyTensor{T}) where T = TensorComposition(ScalingTensor{T,range_dim(tm)}(a,range_size(tm)), tm)
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161 Base.:*(tm::LazyTensor{T}, a::T) where T = a*tm
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162
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163 """
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164 InflatedTensor{T,R,D} <: LazyTensor{T,R,D}
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165
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166 An inflated `LazyTensor` with dimensions added before and after its actual dimensions.
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167 """
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168 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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169 before::IdentityTensor{T,D_before}
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170 tm::TM
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171 after::IdentityTensor{T,D_after}
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172
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173 function InflatedTensor(before, tm::LazyTensor{T}, after) where T
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174 R_before = range_dim(before)
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175 R_middle = range_dim(tm)
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176 R_after = range_dim(after)
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177 R = R_before+R_middle+R_after
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178
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179 D_before = domain_dim(before)
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180 D_middle = domain_dim(tm)
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181 D_after = domain_dim(after)
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182 D = D_before+D_middle+D_after
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183 return new{T,R,D,D_before,R_middle,D_middle,D_after, typeof(tm)}(before, tm, after)
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184 end
446
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185 end
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186
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187 """
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188 InflatedTensor(before, tm, after)
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189 InflatedTensor(before,tm)
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190 InflatedTensor(tm,after)
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191
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192 The outer product of `before`, `tm` and `after`, where `before` and `after` are `IdentityTensor`s.
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193
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194 If one of `before` or `after` is left out, a 0-dimensional `IdentityTensor` is used as the default value.
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195
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196 If `tm` already is an `InflatedTensor`, `before` and `after` will be extended instead of
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197 creating a nested `InflatedTensor`.
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198 """
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199 InflatedTensor(::IdentityTensor, ::LazyTensor, ::IdentityTensor)
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200
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201 function InflatedTensor(before, itm::InflatedTensor, after)
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202 return InflatedTensor(
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203 IdentityTensor(before.size..., itm.before.size...),
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204 itm.tm,
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205 IdentityTensor(itm.after.size..., after.size...),
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206 )
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207 end
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208
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209 InflatedTensor(before::IdentityTensor, tm::LazyTensor) = InflatedTensor(before,tm,IdentityTensor{eltype(tm)}())
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210 InflatedTensor(tm::LazyTensor, after::IdentityTensor) = InflatedTensor(IdentityTensor{eltype(tm)}(),tm,after)
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211 # Resolve ambiguity between the two previous methods
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212 InflatedTensor(I1::IdentityTensor, I2::IdentityTensor) = InflatedTensor(I1,I2,IdentityTensor{promote_type(eltype(I1), eltype(I2))}())
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213
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214 # 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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215
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216 function range_size(itm::InflatedTensor)
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217 return concatenate_tuples(
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218 range_size(itm.before),
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219 range_size(itm.tm),
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220 range_size(itm.after),
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221 )
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222 end
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223
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224 function domain_size(itm::InflatedTensor)
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225 return concatenate_tuples(
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226 domain_size(itm.before),
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227 domain_size(itm.tm),
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228 domain_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 apply(itm::InflatedTensor{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D}
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233 dim_before = range_dim(itm.before)
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234 dim_domain = domain_dim(itm.tm)
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235 dim_range = range_dim(itm.tm)
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236 dim_after = range_dim(itm.after)
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237
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238 view_index, inner_index = split_index(dim_before, dim_domain, dim_range, dim_after, I...)
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239
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240 v_inner = view(v, view_index...)
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241 return apply(itm.tm, v_inner, inner_index...)
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242 end
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243
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244 function apply_transpose(itm::InflatedTensor{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,D}
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245 dim_before = range_dim(itm.before)
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246 dim_domain = domain_dim(itm.tm)
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247 dim_range = range_dim(itm.tm)
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248 dim_after = range_dim(itm.after)
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249
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250 view_index, inner_index = split_index(dim_before, dim_range, dim_domain, dim_after, I...)
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251
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252 v_inner = view(v, view_index...)
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253 return apply_transpose(itm.tm, v_inner, inner_index...)
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254 end
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255
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256
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257 @doc raw"""
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258 LazyOuterProduct(tms...)
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259
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260 Creates a `TensorComposition` for the outer product of `tms...`.
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261 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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262
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263 First let
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264 ```math
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265 \begin{aligned}
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266 A &= A_{I,J} \\
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267 B &= B_{M,N} \\
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268 C &= C_{P,Q} \\
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269 \end{aligned}
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270 ```
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271
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272 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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273
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274 We use ``⊗`` to denote the outer product
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275 ```math
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276 (A⊗B)_{IM,JN} = A_{I,J}B_{M,N}
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277 ```
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278
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279 We note that
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280 ```math
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281 A⊗B⊗C = (A⊗B⊗C)_{IMP,JNQ} = A_{I,J}B_{M,N}C_{P,Q}
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282 ```
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283 And that
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284 ```math
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285 A⊗B⊗C = (A⊗I_{|M|}⊗I_{|P|})(I_{|J|}⊗B⊗I_{|P|})(I_{|J|}⊗I_{|N|}⊗C)
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286 ```
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287 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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288 To apply ``A⊗B⊗C`` we evaluate
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289
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290 ```math
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291 (A⊗B⊗C)v = [(A⊗I_{|M|}⊗I_{|P|}) [(I_{|J|}⊗B⊗I_{|P|}) [(I_{|J|}⊗I_{|N|}⊗C)v]]]
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292 ```
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293 """
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294 function LazyOuterProduct end
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295
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296 function LazyOuterProduct(tm1::LazyTensor{T}, tm2::LazyTensor{T}) where T
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297 itm1 = InflatedTensor(tm1, IdentityTensor{T}(range_size(tm2)))
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298 itm2 = InflatedTensor(IdentityTensor{T}(domain_size(tm1)),tm2)
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299
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300 return itm1∘itm2
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301 end
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302
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303 LazyOuterProduct(t1::IdentityTensor, t2::IdentityTensor) = IdentityTensor{promote_type(eltype(t1),eltype(t2))}(t1.size...,t2.size...)
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304 LazyOuterProduct(t1::LazyTensor, t2::IdentityTensor) = InflatedTensor(t1, t2)
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305 LazyOuterProduct(t1::IdentityTensor, t2::LazyTensor) = InflatedTensor(t1, t2)
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306
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307 LazyOuterProduct(tms::Vararg{LazyTensor}) = foldl(LazyOuterProduct, tms)
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308
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309
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310
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311 """
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312 inflate(tm::LazyTensor, sz, dir)
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313
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314 Inflate `tm` such that it gets the size `sz` in all directions except `dir`.
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315 Here `sz[dir]` is ignored and replaced with the range and domains size of
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316 `tm`.
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317
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318 An example of when this operation is useful is when extending a one
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319 dimensional difference operator `D` to a 2D grid of a certain size. In that
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320 case we could have
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321
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322 ```julia
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323 Dx = inflate(D, (10,10), 1)
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324 Dy = inflate(D, (10,10), 2)
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325 ```
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326 """
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327 function inflate(tm::LazyTensor, sz, dir)
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328 Is = IdentityTensor{eltype(tm)}.(sz)
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329 parts = Base.setindex(Is, tm, dir)
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330 return foldl(⊗, parts)
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331 end
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332
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333 function check_domain_size(tm::LazyTensor, sz)
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334 if domain_size(tm) != sz
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335 throw(DomainSizeMismatch(tm,sz))
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336 end
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337 end
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338
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339 function check_range_size(tm::LazyTensor, sz)
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340 if range_size(tm) != sz
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341 throw(RangeSizeMismatch(tm,sz))
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342 end
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343 end
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344
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345 struct DomainSizeMismatch <: Exception
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346 tm::LazyTensor
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347 sz
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348 end
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349
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350 function Base.showerror(io::IO, err::DomainSizeMismatch)
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351 print(io, "DomainSizeMismatch: ")
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352 print(io, "domain size $(domain_size(err.tm)) of LazyTensor not matching size $(err.sz)")
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353 end
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354
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355
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356 struct RangeSizeMismatch <: Exception
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357 tm::LazyTensor
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358 sz
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359 end
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360
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361 function Base.showerror(io::IO, err::RangeSizeMismatch)
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362 print(io, "RangeSizeMismatch: ")
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363 print(io, "range size $(range_size(err.tm)) of LazyTensor not matching size $(err.sz)")
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364 end