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annotate src/LazyTensors/lazy_tensor_operations.jl @ 1033:0cb4c6b15d8e feature/dissipation_operators

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Make closures have the same number of weights in all stencils
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 22 Mar 2022 11:27:45 +0100
parents 52f07c77299d
children f857057e61e6
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b3c252280a19 Move LazyArray and make LazyTensorMappingApplication and LazyElementwiseOperation subtypes of it
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1 """
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2 LazyTensorApplication{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 LazyTensorApplication object can be created by `m*v`.
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8 The actual result will be calcualted when indexing into `m*v`.
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9 """
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10 struct LazyTensorApplication{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 LazyTensorApplication(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::LazyTensorApplication{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 apply(ta.t, ta.o, I...)
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25 end
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26 Base.getindex(ta::LazyTensorApplication{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::LazyTensorApplication) = range_size(ta.t)
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30 """
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31 LazyTensorTranspose{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 LazyTensorTranspose{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) = LazyTensorTranspose(tm)
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46 Base.adjoint(tmt::LazyTensorTranspose) = tmt.tm
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47
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48 apply(tmt::LazyTensorTranspose{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::LazyTensorTranspose{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmt.tm, v, I...)
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51 range_size(tmt::LazyTensorTranspose) = domain_size(tmt.tm)
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52 domain_size(tmt::LazyTensorTranspose) = range_size(tmt.tm)
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55 struct LazyTensorBinaryOperation{Op,T,R,D,T1<:LazyTensor{T,R,D},T2<:LazyTensor{T,R,D}} <: LazyTensor{T,D,R}
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56 tm1::T1
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57 tm2::T2
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58
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59 function LazyTensorBinaryOperation{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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60 @boundscheck check_domain_size(tm2, domain_size(tm1))
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61 @boundscheck check_range_size(tm2, range_size(tm1))
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62 return new{Op,T,R,D,T1,T2}(tm1,tm2)
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63 end
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64 end
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66 LazyTensorBinaryOperation{Op}(s,t) where Op = LazyTensorBinaryOperation{Op,eltype(s), range_dim(s), domain_dim(s)}(s,t)
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68 apply(tmBinOp::LazyTensorBinaryOperation{:+,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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69 apply(tmBinOp::LazyTensorBinaryOperation{:-,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 range_size(tmBinOp::LazyTensorBinaryOperation) = range_size(tmBinOp.tm1)
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72 domain_size(tmBinOp::LazyTensorBinaryOperation) = domain_size(tmBinOp.tm1)
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75 """
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76 LazyTensorComposition{T,R,K,D}
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77
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78 Lazily compose two `LazyTensor`s, so that they can be handled as a single `LazyTensor`.
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79 """
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80 struct LazyTensorComposition{T,R,K,D, TM1<:LazyTensor{T,R,K}, TM2<:LazyTensor{T,K,D}} <: LazyTensor{T,R,D}
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81 t1::TM1
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82 t2::TM2
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83
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84 function LazyTensorComposition(t1::LazyTensor{T,R,K}, t2::LazyTensor{T,K,D}) where {T,R,K,D}
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85 @boundscheck check_domain_size(t1, range_size(t2))
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86 return new{T,R,K,D, typeof(t1), typeof(t2)}(t1,t2)
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87 end
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88 end
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89
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90 range_size(tm::LazyTensorComposition) = range_size(tm.t1)
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91 domain_size(tm::LazyTensorComposition) = domain_size(tm.t2)
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92
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93 function apply(c::LazyTensorComposition{T,R,K,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,K,D}
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94 apply(c.t1, c.t2*v, I...)
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95 end
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96
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97 function apply_transpose(c::LazyTensorComposition{T,R,K,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,K,D}
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98 apply_transpose(c.t2, c.t1'*v, I...)
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99 end
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101
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102 """
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103 LazyTensorComposition(tm, tmi::IdentityTensor)
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104 LazyTensorComposition(tmi::IdentityTensor, tm)
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105
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106 Composes a `Tensormapping` `tm` with an `IdentityTensor` `tmi`, by returning `tm`
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107 """
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108 function LazyTensorComposition(tm::LazyTensor{T,R,D}, tmi::IdentityTensor{T,D}) where {T,R,D}
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109 @boundscheck check_domain_size(tm, range_size(tmi))
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110 return tm
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111 end
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112
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113 function LazyTensorComposition(tmi::IdentityTensor{T,R}, tm::LazyTensor{T,R,D}) where {T,R,D}
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114 @boundscheck check_domain_size(tmi, range_size(tm))
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115 return tm
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116 end
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117 # Specialization for the case where tm is an IdentityTensor. Required to resolve ambiguity.
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118 function LazyTensorComposition(tm::IdentityTensor{T,D}, tmi::IdentityTensor{T,D}) where {T,D}
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119 @boundscheck check_domain_size(tm, range_size(tmi))
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120 return tmi
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121 end
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122
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124 """
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125 InflatedLazyTensor{T,R,D} <: LazyTensor{T,R,D}
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126
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127 An inflated `LazyTensor` with dimensions added before and afer its actual dimensions.
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128 """
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129 struct InflatedLazyTensor{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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130 before::IdentityTensor{T,D_before}
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131 tm::TM
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132 after::IdentityTensor{T,D_after}
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133
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134 function InflatedLazyTensor(before, tm::LazyTensor{T}, after) where T
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135 R_before = range_dim(before)
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136 R_middle = range_dim(tm)
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137 R_after = range_dim(after)
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138 R = R_before+R_middle+R_after
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139
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140 D_before = domain_dim(before)
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141 D_middle = domain_dim(tm)
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142 D_after = domain_dim(after)
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143 D = D_before+D_middle+D_after
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144 return new{T,R,D,D_before,R_middle,D_middle,D_after, typeof(tm)}(before, tm, after)
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145 end
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146 end
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147
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148 """
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149 InflatedLazyTensor(before, tm, after)
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150 InflatedLazyTensor(before,tm)
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151 InflatedLazyTensor(tm,after)
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152
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153 The outer product of `before`, `tm` and `after`, where `before` and `after` are `IdentityTensor`s.
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154
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155 If one of `before` or `after` is left out, a 0-dimensional `IdentityTensor` is used as the default value.
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156
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157 If `tm` already is an `InflatedLazyTensor`, `before` and `after` will be extended instead of
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158 creating a nested `InflatedLazyTensor`.
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159 """
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160 InflatedLazyTensor(::IdentityTensor, ::LazyTensor, ::IdentityTensor)
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161
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162 function InflatedLazyTensor(before, itm::InflatedLazyTensor, after)
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163 return InflatedLazyTensor(
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164 IdentityTensor(before.size..., itm.before.size...),
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165 itm.tm,
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166 IdentityTensor(itm.after.size..., after.size...),
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167 )
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168 end
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169
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170 InflatedLazyTensor(before::IdentityTensor, tm::LazyTensor{T}) where T = InflatedLazyTensor(before,tm,IdentityTensor{T}())
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171 InflatedLazyTensor(tm::LazyTensor{T}, after::IdentityTensor) where T = InflatedLazyTensor(IdentityTensor{T}(),tm,after)
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172 # Resolve ambiguity between the two previous methods
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173 InflatedLazyTensor(I1::IdentityTensor{T}, I2::IdentityTensor{T}) where T = InflatedLazyTensor(I1,I2,IdentityTensor{T}())
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174
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175 # TODO: Implement some pretty printing in terms of ⊗. E.g InflatedLazyTensor(I(3),B,I(2)) -> I(3)⊗B⊗I(2)
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176
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177 function range_size(itm::InflatedLazyTensor)
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178 return flatten_tuple(
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179 range_size(itm.before),
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180 range_size(itm.tm),
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181 range_size(itm.after),
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182 )
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183 end
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184
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185 function domain_size(itm::InflatedLazyTensor)
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186 return flatten_tuple(
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187 domain_size(itm.before),
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188 domain_size(itm.tm),
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189 domain_size(itm.after),
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190 )
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191 end
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192
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193 function apply(itm::InflatedLazyTensor{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D}
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194 dim_before = range_dim(itm.before)
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195 dim_domain = domain_dim(itm.tm)
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196 dim_range = range_dim(itm.tm)
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197 dim_after = range_dim(itm.after)
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198
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199 view_index, inner_index = split_index(Val(dim_before), Val(dim_domain), Val(dim_range), Val(dim_after), I...)
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200
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201 v_inner = view(v, view_index...)
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202 return apply(itm.tm, v_inner, inner_index...)
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203 end
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204
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205 function apply_transpose(itm::InflatedLazyTensor{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,D}
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206 dim_before = range_dim(itm.before)
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207 dim_domain = domain_dim(itm.tm)
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208 dim_range = range_dim(itm.tm)
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209 dim_after = range_dim(itm.after)
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210
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211 view_index, inner_index = split_index(Val(dim_before), Val(dim_range), Val(dim_domain), Val(dim_after), I...)
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212
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213 v_inner = view(v, view_index...)
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214 return apply_transpose(itm.tm, v_inner, inner_index...)
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215 end
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216
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217
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218 @doc raw"""
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219 LazyOuterProduct(tms...)
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220
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221 Creates a `LazyTensorComposition` for the outerproduct of `tms...`.
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222 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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223
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224 First let
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225 ```math
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226 \begin{aligned}
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227 A &= A_{I,J} \\
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228 B &= B_{M,N} \\
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229 C &= C_{P,Q} \\
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230 \end{aligned}
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231 ```
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232
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233 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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234
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235 We use ``⊗`` to denote the outer product
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236 ```math
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237 (A⊗B)_{IM,JN} = A_{I,J}B_{M,N}
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238 ```
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239
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240 We note that
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241 ```math
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242 A⊗B⊗C = (A⊗B⊗C)_{IMP,JNQ} = A_{I,J}B_{M,N}C_{P,Q}
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243 ```
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244 And that
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245 ```math
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246 A⊗B⊗C = (A⊗I_{|M|}⊗I_{|P|})(I_{|J|}⊗B⊗I_{|P|})(I_{|J|}⊗I_{|N|}⊗C)
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247 ```
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248 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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249 To apply ``A⊗B⊗C`` we evaluate
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250
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251 ```math
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252 (A⊗B⊗C)v = [(A⊗I_{|M|}⊗I_{|P|}) [(I_{|J|}⊗B⊗I_{|P|}) [(I_{|J|}⊗I_{|N|}⊗C)v]]]
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253 ```
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254 """
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255 function LazyOuterProduct end
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256
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257 function LazyOuterProduct(tm1::LazyTensor{T}, tm2::LazyTensor{T}) where T
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258 itm1 = InflatedLazyTensor(tm1, IdentityTensor{T}(range_size(tm2)))
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259 itm2 = InflatedLazyTensor(IdentityTensor{T}(domain_size(tm1)),tm2)
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260
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261 return itm1∘itm2
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262 end
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263
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264 LazyOuterProduct(t1::IdentityTensor{T}, t2::IdentityTensor{T}) where T = IdentityTensor{T}(t1.size...,t2.size...)
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265 LazyOuterProduct(t1::LazyTensor, t2::IdentityTensor) = InflatedLazyTensor(t1, t2)
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266 LazyOuterProduct(t1::IdentityTensor, t2::LazyTensor) = InflatedLazyTensor(t1, t2)
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267
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268 LazyOuterProduct(tms::Vararg{LazyTensor}) = foldl(LazyOuterProduct, tms)
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269
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270
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271
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272 """
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273 inflate(tm, sz, dir)
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274
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275 Inflate `tm` with identity tensors in all directions `d` for `d != dir`.
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276
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277 # TODO: Describe when it is useful
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278 """
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279 function inflate(tm::LazyTensor, sz, dir)
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280 Is = IdentityTensor{eltype(tm)}.(sz)
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281 parts = Base.setindex(Is, tm, dir)
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282 return foldl(⊗, parts)
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283 end
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284
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285 function check_domain_size(tm::LazyTensor, sz)
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286 if domain_size(tm) != sz
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287 throw(DomainSizeMismatch(tm,sz))
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288 end
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289 end
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290
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291 function check_range_size(tm::LazyTensor, sz)
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292 if range_size(tm) != sz
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293 throw(RangeSizeMismatch(tm,sz))
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294 end
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295 end
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296
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297 struct DomainSizeMismatch <: Exception
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298 tm::LazyTensor
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299 sz
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300 end
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301
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302 function Base.showerror(io::IO, err::DomainSizeMismatch)
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303 print(io, "DomainSizeMismatch: ")
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304 print(io, "domain size $(domain_size(err.tm)) of LazyTensor not matching size $(err.sz)")
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305 end
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306
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307
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308 struct RangeSizeMismatch <: Exception
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309 tm::LazyTensor
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310 sz
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311 end
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312
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313 function Base.showerror(io::IO, err::RangeSizeMismatch)
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314 print(io, "RangeSizeMismatch: ")
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315 print(io, "range size $(range_size(err.tm)) of LazyTensor not matching size $(err.sz)")
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316 end