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annotate src/LazyTensors/lazy_tensor_operations.jl @ 1049:3bb94ce74697 feature/variable_derivatives

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Merge default
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 23 Mar 2022 12:54:45 +0100
parents df562695b1b5 9e76bf19904c
children 5a3281429a48
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1 using Sbplib.RegionIndices
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2
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3 """
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4 TensorApplication{T,R,D} <: LazyArray{T,R}
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6 Struct for lazy application of a LazyTensor. Created using `*`.
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7
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8 Allows the result of a `LazyTensor` applied to a vector to be treated as an `AbstractArray`.
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9 With a mapping `m` and a vector `v` the TensorApplication object can be created by `m*v`.
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10 The actual result will be calcualted when indexing into `m*v`.
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11 """
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12 struct TensorApplication{T,R,D, TM<:LazyTensor{<:Any,R,D}, AA<:AbstractArray{<:Any,D}} <: LazyArray{T,R}
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13 t::TM
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14 o::AA
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15
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16 function TensorApplication(t::LazyTensor{<:Any,R,D}, o::AbstractArray{<:Any,D}) where {R,D}
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17 @boundscheck check_domain_size(t, size(o))
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18 I = ntuple(i->1, range_dim(t))
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19 T = typeof(apply(t,o,I...))
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20 return new{T,R,D,typeof(t), typeof(o)}(t,o)
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21 end
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22 end
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23
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24 function Base.getindex(ta::TensorApplication{T,R}, I::Vararg{Any,R}) where {T,R}
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25 @boundscheck checkbounds(ta, Int.(I)...)
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26 return @inbounds apply(ta.t, ta.o, I...)
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27 end
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28 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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29 Base.size(ta::TensorApplication) = range_size(ta.t)
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30
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31
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32 """
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33 TensorTranspose{T,R,D} <: LazyTensor{T,D,R}
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34
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35 Struct for lazy transpose of a LazyTensor.
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36
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37 If a mapping implements the the `apply_transpose` method this allows working with
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38 the transpose of mapping `m` by using `m'`. `m'` will work as a regular LazyTensor lazily calling
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39 the appropriate methods of `m`.
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40 """
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41 struct TensorTranspose{T,R,D, TM<:LazyTensor{T,R,D}} <: LazyTensor{T,D,R}
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42 tm::TM
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43 end
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44
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45 # # TBD: Should this be implemented on a type by type basis or through a trait to provide earlier errors?
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46 # 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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47 Base.adjoint(tm::LazyTensor) = TensorTranspose(tm)
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48 Base.adjoint(tmt::TensorTranspose) = tmt.tm
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49
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50 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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51 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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52
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53 range_size(tmt::TensorTranspose) = domain_size(tmt.tm)
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54 domain_size(tmt::TensorTranspose) = range_size(tmt.tm)
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55
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56
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57 struct ElementwiseTensorOperation{Op,T,R,D,T1<:LazyTensor{T,R,D},T2<:LazyTensor{T,R,D}} <: LazyTensor{T,D,R}
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58 tm1::T1
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59 tm2::T2
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60
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61 function ElementwiseTensorOperation{Op,T,R,D}(tm1::T1,tm2::T2) where {Op,T,R,D, T1<:LazyTensor{T,R,D},T2<:LazyTensor{T,R,D}}
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62 @boundscheck check_domain_size(tm2, domain_size(tm1))
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63 @boundscheck check_range_size(tm2, range_size(tm1))
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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
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68 ElementwiseTensorOperation{Op}(s,t) where Op = ElementwiseTensorOperation{Op,eltype(s), range_dim(s), domain_dim(s)}(s,t)
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69
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70 apply(tmBinOp::ElementwiseTensorOperation{:+,T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmBinOp.tm1, v, I...) + apply(tmBinOp.tm2, v, I...)
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71 apply(tmBinOp::ElementwiseTensorOperation{:-,T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmBinOp.tm1, v, I...) - apply(tmBinOp.tm2, v, I...)
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72
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73 range_size(tmBinOp::ElementwiseTensorOperation) = range_size(tmBinOp.tm1)
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74 domain_size(tmBinOp::ElementwiseTensorOperation) = domain_size(tmBinOp.tm1)
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75
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76
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77 """
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78 TensorComposition{T,R,K,D}
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79
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80 Lazily compose two `LazyTensor`s, so that they can be handled as a single `LazyTensor`.
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81 """
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82 struct TensorComposition{T,R,K,D, TM1<:LazyTensor{T,R,K}, TM2<:LazyTensor{T,K,D}} <: LazyTensor{T,R,D}
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83 t1::TM1
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84 t2::TM2
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85
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86 function TensorComposition(t1::LazyTensor{T,R,K}, t2::LazyTensor{T,K,D}) where {T,R,K,D}
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87 @boundscheck check_domain_size(t1, range_size(t2))
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88 return new{T,R,K,D, typeof(t1), typeof(t2)}(t1,t2)
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89 end
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90 end
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91
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92 range_size(tm::TensorComposition) = range_size(tm.t1)
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93 domain_size(tm::TensorComposition) = domain_size(tm.t2)
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94
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95 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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96 apply(c.t1, c.t2*v, I...)
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97 end
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98
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99 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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100 apply_transpose(c.t2, c.t1'*v, I...)
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101 end
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103
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104 """
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105 TensorComposition(tm, tmi::IdentityTensor)
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106 TensorComposition(tmi::IdentityTensor, tm)
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107
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108 Composes a `Tensormapping` `tm` with an `IdentityTensor` `tmi`, by returning `tm`
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109 """
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110 function TensorComposition(tm::LazyTensor{T,R,D}, tmi::IdentityTensor{T,D}) where {T,R,D}
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111 @boundscheck check_domain_size(tm, range_size(tmi))
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112 return tm
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113 end
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114
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115 function TensorComposition(tmi::IdentityTensor{T,R}, tm::LazyTensor{T,R,D}) where {T,R,D}
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116 @boundscheck check_domain_size(tmi, range_size(tm))
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117 return tm
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118 end
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119 # Specialization for the case where tm is an IdentityTensor. Required to resolve ambiguity.
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120 function TensorComposition(tm::IdentityTensor{T,D}, tmi::IdentityTensor{T,D}) where {T,D}
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121 @boundscheck check_domain_size(tm, range_size(tmi))
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122 return tmi
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123 end
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124
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125
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126 """
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127 InflatedTensor{T,R,D} <: LazyTensor{T,R,D}
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128
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129 An inflated `LazyTensor` with dimensions added before and afer its actual dimensions.
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130 """
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131 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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132 before::IdentityTensor{T,D_before}
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133 tm::TM
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134 after::IdentityTensor{T,D_after}
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135
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136 function InflatedTensor(before, tm::LazyTensor{T}, after) where T
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137 R_before = range_dim(before)
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138 R_middle = range_dim(tm)
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139 R_after = range_dim(after)
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140 R = R_before+R_middle+R_after
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141
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142 D_before = domain_dim(before)
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143 D_middle = domain_dim(tm)
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144 D_after = domain_dim(after)
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145 D = D_before+D_middle+D_after
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146 return new{T,R,D,D_before,R_middle,D_middle,D_after, typeof(tm)}(before, tm, after)
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147 end
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148 end
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149
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150 """
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151 InflatedTensor(before, tm, after)
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152 InflatedTensor(before,tm)
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153 InflatedTensor(tm,after)
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154
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155 The outer product of `before`, `tm` and `after`, where `before` and `after` are `IdentityTensor`s.
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156
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157 If one of `before` or `after` is left out, a 0-dimensional `IdentityTensor` is used as the default value.
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158
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159 If `tm` already is an `InflatedTensor`, `before` and `after` will be extended instead of
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160 creating a nested `InflatedTensor`.
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161 """
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162 InflatedTensor(::IdentityTensor, ::LazyTensor, ::IdentityTensor)
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163
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164 function InflatedTensor(before, itm::InflatedTensor, after)
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165 return InflatedTensor(
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166 IdentityTensor(before.size..., itm.before.size...),
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167 itm.tm,
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168 IdentityTensor(itm.after.size..., after.size...),
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169 )
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170 end
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171
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172 InflatedTensor(before::IdentityTensor, tm::LazyTensor{T}) where T = InflatedTensor(before,tm,IdentityTensor{T}())
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173 InflatedTensor(tm::LazyTensor{T}, after::IdentityTensor) where T = InflatedTensor(IdentityTensor{T}(),tm,after)
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174 # Resolve ambiguity between the two previous methods
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175 InflatedTensor(I1::IdentityTensor{T}, I2::IdentityTensor{T}) where T = InflatedTensor(I1,I2,IdentityTensor{T}())
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176
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177 # 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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178
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179 function range_size(itm::InflatedTensor)
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180 return flatten_tuple(
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181 range_size(itm.before),
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182 range_size(itm.tm),
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183 range_size(itm.after),
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184 )
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185 end
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186
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187 function domain_size(itm::InflatedTensor)
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188 return flatten_tuple(
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189 domain_size(itm.before),
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190 domain_size(itm.tm),
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191 domain_size(itm.after),
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192 )
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193 end
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194
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195 function apply(itm::InflatedTensor{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D}
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196 dim_before = range_dim(itm.before)
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197 dim_domain = domain_dim(itm.tm)
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198 dim_range = range_dim(itm.tm)
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199 dim_after = range_dim(itm.after)
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200
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201 view_index, inner_index = split_index(Val(dim_before), Val(dim_domain), Val(dim_range), Val(dim_after), I...)
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202
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203 v_inner = view(v, view_index...)
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204 return apply(itm.tm, v_inner, inner_index...)
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205 end
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206
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207 function apply_transpose(itm::InflatedTensor{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,D}
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208 dim_before = range_dim(itm.before)
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209 dim_domain = domain_dim(itm.tm)
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210 dim_range = range_dim(itm.tm)
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211 dim_after = range_dim(itm.after)
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212
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213 view_index, inner_index = split_index(Val(dim_before), Val(dim_range), Val(dim_domain), Val(dim_after), I...)
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214
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215 v_inner = view(v, view_index...)
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216 return apply_transpose(itm.tm, v_inner, inner_index...)
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217 end
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218
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219
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220 @doc raw"""
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221 LazyOuterProduct(tms...)
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222
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223 Creates a `TensorComposition` for the outerproduct of `tms...`.
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224 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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225
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226 First let
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227 ```math
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228 \begin{aligned}
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229 A &= A_{I,J} \\
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230 B &= B_{M,N} \\
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231 C &= C_{P,Q} \\
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232 \end{aligned}
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233 ```
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234
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235 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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236
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237 We use ``⊗`` to denote the outer product
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238 ```math
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239 (A⊗B)_{IM,JN} = A_{I,J}B_{M,N}
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240 ```
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241
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242 We note that
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243 ```math
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244 A⊗B⊗C = (A⊗B⊗C)_{IMP,JNQ} = A_{I,J}B_{M,N}C_{P,Q}
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245 ```
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246 And that
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247 ```math
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248 A⊗B⊗C = (A⊗I_{|M|}⊗I_{|P|})(I_{|J|}⊗B⊗I_{|P|})(I_{|J|}⊗I_{|N|}⊗C)
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249 ```
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250 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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251 To apply ``A⊗B⊗C`` we evaluate
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252
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253 ```math
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254 (A⊗B⊗C)v = [(A⊗I_{|M|}⊗I_{|P|}) [(I_{|J|}⊗B⊗I_{|P|}) [(I_{|J|}⊗I_{|N|}⊗C)v]]]
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255 ```
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256 """
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257 function LazyOuterProduct end
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258
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259 function LazyOuterProduct(tm1::LazyTensor{T}, tm2::LazyTensor{T}) where T
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260 itm1 = InflatedTensor(tm1, IdentityTensor{T}(range_size(tm2)))
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261 itm2 = InflatedTensor(IdentityTensor{T}(domain_size(tm1)),tm2)
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262
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263 return itm1∘itm2
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264 end
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265
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266 LazyOuterProduct(t1::IdentityTensor{T}, t2::IdentityTensor{T}) where T = IdentityTensor{T}(t1.size...,t2.size...)
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267 LazyOuterProduct(t1::LazyTensor, t2::IdentityTensor) = InflatedTensor(t1, t2)
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268 LazyOuterProduct(t1::IdentityTensor, t2::LazyTensor) = InflatedTensor(t1, t2)
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269
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270 LazyOuterProduct(tms::Vararg{LazyTensor}) = foldl(LazyOuterProduct, tms)
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271
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272
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273 function check_domain_size(tm::LazyTensor, sz)
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274 if domain_size(tm) != sz
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275 throw(DomainSizeMismatch(tm,sz))
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276 end
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277 end
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278
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279 function check_range_size(tm::LazyTensor, sz)
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280 if range_size(tm) != sz
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281 throw(RangeSizeMismatch(tm,sz))
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282 end
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283 end
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284
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285 struct DomainSizeMismatch <: Exception
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286 tm::LazyTensor
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287 sz
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288 end
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289
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290 function Base.showerror(io::IO, err::DomainSizeMismatch)
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291 print(io, "DomainSizeMismatch: ")
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292 print(io, "domain size $(domain_size(err.tm)) of LazyTensor not matching size $(err.sz)")
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293 end
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294
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295 struct RangeSizeMismatch <: Exception
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296 tm::LazyTensor
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297 sz
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298 end
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299
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300 function Base.showerror(io::IO, err::RangeSizeMismatch)
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301 print(io, "RangeSizeMismatch: ")
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302 print(io, "range size $(range_size(err.tm)) of LazyTensor not matching size $(err.sz)")
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303 end
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304
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305
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306 function apply_with_region(op, v, boundary_width::Integer, dim_size::Integer, i)
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307 if 0 < i <= boundary_width
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308 return LazyTensors.apply(op,v,Index(i,Lower))
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309 elseif boundary_width < i <= dim_size-boundary_width
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310 return LazyTensors.apply(op,v,Index(i,Interior))
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311 elseif dim_size-boundary_width < i <= dim_size
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312 return LazyTensors.apply(op,v,Index(i,Upper))
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313 else
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314 error("Bounds error") # TODO: Make this more standard
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315 end
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316 end
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317 # TBD: Can these methods be merge by having a function as an arguement instead?
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318 # TODO: Add inference test that show where things break and how this rewrite fixes it.
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319 function apply_transpose_with_region(op, v, boundary_width::Integer, dim_size::Integer, i)
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320 if 0 < i <= boundary_width
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321 return LazyTensors.apply_transpose(op,v,Index(i,Lower))
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322 elseif boundary_width < i <= dim_size-boundary_width
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323 return LazyTensors.apply_transpose(op,v,Index(i,Interior))
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324 elseif dim_size-boundary_width < i <= dim_size
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325 return LazyTensors.apply_transpose(op,v,Index(i,Upper))
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326 else
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327 error("Bounds error") # TODO: Make this more standard
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328 end
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329 end