Mercurial > repos > public > sbplib_julia
annotate src/LazyTensors/lazy_tensor_operations.jl @ 1139:9625360faf06 feature/grids
Closing branch before merge to default
| author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
|---|---|
| date | Wed, 12 Oct 2022 10:42:45 +0200 |
| parents | 2e606d4c0ab1 |
| children | 2278730f9cee 95464a1af340 1e8270c18edb b4ee47f2aafb 87576b0ca0e3 |
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1 """ |
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2 TensorApplication{T,R,D} <: LazyArray{T,R} |
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| 995 | 4 Struct for lazy application of a LazyTensor. Created using `*`. |
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| 995 | 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 calcualted 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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28 |
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29 |
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30 """ |
| 1037 | 31 TensorTranspose{T,R,D} <: LazyTensor{T,D,R} |
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| 995 | 33 Struct for lazy transpose of a LazyTensor. |
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34 |
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35 If a mapping implements the the `apply_transpose` method this allows working with |
| 995 | 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 """ |
| 1037 | 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? |
| 995 | 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`? |
| 1037 | 45 Base.adjoint(tm::LazyTensor) = TensorTranspose(tm) |
| 46 Base.adjoint(tmt::TensorTranspose) = tmt.tm | |
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47 |
| 1037 | 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...) |
| 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 |
| 1037 | 51 range_size(tmt::TensorTranspose) = domain_size(tmt.tm) |
| 52 domain_size(tmt::TensorTranspose) = range_size(tmt.tm) | |
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53 |
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| 1037 | 55 struct ElementwiseTensorOperation{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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| 1037 | 59 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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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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65 |
| 1037 | 66 ElementwiseTensorOperation{Op}(s,t) where Op = ElementwiseTensorOperation{Op,eltype(s), range_dim(s), domain_dim(s)}(s,t) |
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67 |
| 1037 | 68 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...) |
| 69 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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| 1037 | 71 range_size(tmBinOp::ElementwiseTensorOperation) = range_size(tmBinOp.tm1) |
| 72 domain_size(tmBinOp::ElementwiseTensorOperation) = domain_size(tmBinOp.tm1) | |
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73 |
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74 |
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75 """ |
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76 TensorComposition{T,R,K,D} |
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77 |
| 995 | 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 TensorComposition{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 TensorComposition(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::TensorComposition) = range_size(tm.t1) |
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91 domain_size(tm::TensorComposition) = domain_size(tm.t2) |
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92 |
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93 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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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::TensorComposition{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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100 |
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101 """ |
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102 TensorComposition(tm, tmi::IdentityTensor) |
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103 TensorComposition(tmi::IdentityTensor, tm) |
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104 |
| 995 | 105 Composes a `Tensormapping` `tm` with an `IdentityTensor` `tmi`, by returning `tm` |
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106 """ |
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107 function TensorComposition(tm::LazyTensor{T,R,D}, tmi::IdentityTensor{T,D}) where {T,R,D} |
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108 @boundscheck check_domain_size(tm, range_size(tmi)) |
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109 return tm |
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110 end |
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111 |
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112 function TensorComposition(tmi::IdentityTensor{T,R}, tm::LazyTensor{T,R,D}) where {T,R,D} |
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113 @boundscheck check_domain_size(tmi, range_size(tm)) |
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114 return tm |
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115 end |
| 995 | 116 # Specialization for the case where tm is an IdentityTensor. Required to resolve ambiguity. |
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117 function TensorComposition(tm::IdentityTensor{T,D}, tmi::IdentityTensor{T,D}) where {T,D} |
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118 @boundscheck check_domain_size(tm, range_size(tmi)) |
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119 return tmi |
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120 end |
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121 |
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122 Base.:*(a::T, tm::LazyTensor{T}) where T = TensorComposition(ScalingTensor{T,range_dim(tm)}(a,range_size(tm)), tm) |
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123 Base.:*(tm::LazyTensor{T}, a::T) where T = a*tm |
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124 |
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125 """ |
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126 InflatedTensor{T,R,D} <: LazyTensor{T,R,D} |
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127 |
| 995 | 128 An inflated `LazyTensor` with dimensions added before and afer its actual dimensions. |
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129 """ |
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130 struct InflatedTensor{T,R,D,D_before,R_middle,D_middle,D_after, TM<:LazyTensor{T,R_middle,D_middle}} <: LazyTensor{T,R,D} |
| 995 | 131 before::IdentityTensor{T,D_before} |
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132 tm::TM |
| 995 | 133 after::IdentityTensor{T,D_after} |
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134 |
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135 function InflatedTensor(before, tm::LazyTensor{T}, after) where T |
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136 R_before = range_dim(before) |
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137 R_middle = range_dim(tm) |
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138 R_after = range_dim(after) |
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139 R = R_before+R_middle+R_after |
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140 |
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141 D_before = domain_dim(before) |
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142 D_middle = domain_dim(tm) |
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143 D_after = domain_dim(after) |
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144 D = D_before+D_middle+D_after |
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145 return new{T,R,D,D_before,R_middle,D_middle,D_after, typeof(tm)}(before, tm, after) |
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146 end |
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147 end |
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148 |
| 461 | 149 """ |
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150 InflatedTensor(before, tm, after) |
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151 InflatedTensor(before,tm) |
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152 InflatedTensor(tm,after) |
| 461 | 153 |
| 995 | 154 The outer product of `before`, `tm` and `after`, where `before` and `after` are `IdentityTensor`s. |
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155 |
| 995 | 156 If one of `before` or `after` is left out, a 0-dimensional `IdentityTensor` is used as the default value. |
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157 |
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158 If `tm` already is an `InflatedTensor`, `before` and `after` will be extended instead of |
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159 creating a nested `InflatedTensor`. |
| 461 | 160 """ |
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161 InflatedTensor(::IdentityTensor, ::LazyTensor, ::IdentityTensor) |
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162 |
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163 function InflatedTensor(before, itm::InflatedTensor, after) |
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164 return InflatedTensor( |
| 995 | 165 IdentityTensor(before.size..., itm.before.size...), |
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166 itm.tm, |
| 995 | 167 IdentityTensor(itm.after.size..., after.size...), |
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168 ) |
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169 end |
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170 |
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171 InflatedTensor(before::IdentityTensor, tm::LazyTensor{T}) where T = InflatedTensor(before,tm,IdentityTensor{T}()) |
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172 InflatedTensor(tm::LazyTensor{T}, after::IdentityTensor) where T = InflatedTensor(IdentityTensor{T}(),tm,after) |
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173 # Resolve ambiguity between the two previous methods |
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174 InflatedTensor(I1::IdentityTensor{T}, I2::IdentityTensor{T}) where T = InflatedTensor(I1,I2,IdentityTensor{T}()) |
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175 |
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176 # 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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177 |
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178 function range_size(itm::InflatedTensor) |
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179 return flatten_tuple( |
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180 range_size(itm.before), |
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181 range_size(itm.tm), |
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182 range_size(itm.after), |
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183 ) |
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184 end |
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185 |
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186 function domain_size(itm::InflatedTensor) |
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187 return flatten_tuple( |
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188 domain_size(itm.before), |
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189 domain_size(itm.tm), |
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190 domain_size(itm.after), |
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191 ) |
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192 end |
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193 |
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194 function apply(itm::InflatedTensor{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D} |
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195 dim_before = range_dim(itm.before) |
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196 dim_domain = domain_dim(itm.tm) |
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197 dim_range = range_dim(itm.tm) |
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198 dim_after = range_dim(itm.after) |
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199 |
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200 view_index, inner_index = split_index(Val(dim_before), Val(dim_domain), Val(dim_range), Val(dim_after), I...) |
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201 |
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202 v_inner = view(v, view_index...) |
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203 return apply(itm.tm, v_inner, inner_index...) |
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204 end |
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205 |
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206 function apply_transpose(itm::InflatedTensor{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,D} |
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207 dim_before = range_dim(itm.before) |
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208 dim_domain = domain_dim(itm.tm) |
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209 dim_range = range_dim(itm.tm) |
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210 dim_after = range_dim(itm.after) |
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211 |
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212 view_index, inner_index = split_index(Val(dim_before), Val(dim_range), Val(dim_domain), Val(dim_after), I...) |
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213 |
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214 v_inner = view(v, view_index...) |
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215 return apply_transpose(itm.tm, v_inner, inner_index...) |
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216 end |
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217 |
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218 |
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219 @doc raw""" |
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220 LazyOuterProduct(tms...) |
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221 |
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222 Creates a `TensorComposition` for the outerproduct of `tms...`. |
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223 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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224 |
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225 First let |
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226 ```math |
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227 \begin{aligned} |
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228 A &= A_{I,J} \\ |
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229 B &= B_{M,N} \\ |
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230 C &= C_{P,Q} \\ |
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231 \end{aligned} |
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232 ``` |
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233 |
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234 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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235 |
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236 We use ``⊗`` to denote the outer product |
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237 ```math |
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238 (A⊗B)_{IM,JN} = A_{I,J}B_{M,N} |
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239 ``` |
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240 |
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241 We note that |
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242 ```math |
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243 A⊗B⊗C = (A⊗B⊗C)_{IMP,JNQ} = A_{I,J}B_{M,N}C_{P,Q} |
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244 ``` |
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245 And that |
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246 ```math |
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247 A⊗B⊗C = (A⊗I_{|M|}⊗I_{|P|})(I_{|J|}⊗B⊗I_{|P|})(I_{|J|}⊗I_{|N|}⊗C) |
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248 ``` |
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249 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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250 To apply ``A⊗B⊗C`` we evaluate |
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251 |
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252 ```math |
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253 (A⊗B⊗C)v = [(A⊗I_{|M|}⊗I_{|P|}) [(I_{|J|}⊗B⊗I_{|P|}) [(I_{|J|}⊗I_{|N|}⊗C)v]]] |
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254 ``` |
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255 """ |
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256 function LazyOuterProduct end |
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257 |
| 995 | 258 function LazyOuterProduct(tm1::LazyTensor{T}, tm2::LazyTensor{T}) where T |
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259 itm1 = InflatedTensor(tm1, IdentityTensor{T}(range_size(tm2))) |
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260 itm2 = InflatedTensor(IdentityTensor{T}(domain_size(tm1)),tm2) |
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261 |
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262 return itm1∘itm2 |
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263 end |
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264 |
| 995 | 265 LazyOuterProduct(t1::IdentityTensor{T}, t2::IdentityTensor{T}) where T = IdentityTensor{T}(t1.size...,t2.size...) |
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266 LazyOuterProduct(t1::LazyTensor, t2::IdentityTensor) = InflatedTensor(t1, t2) |
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267 LazyOuterProduct(t1::IdentityTensor, t2::LazyTensor) = InflatedTensor(t1, t2) |
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268 |
| 995 | 269 LazyOuterProduct(tms::Vararg{LazyTensor}) = foldl(LazyOuterProduct, tms) |
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270 |
| 498 | 271 |
| 995 | 272 function check_domain_size(tm::LazyTensor, sz) |
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273 if domain_size(tm) != sz |
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274 throw(DomainSizeMismatch(tm,sz)) |
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275 end |
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276 end |
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277 |
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278 function check_range_size(tm::LazyTensor, sz) |
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279 if range_size(tm) != sz |
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280 throw(RangeSizeMismatch(tm,sz)) |
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281 end |
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282 end |
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283 |
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284 struct DomainSizeMismatch <: Exception |
| 995 | 285 tm::LazyTensor |
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286 sz |
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287 end |
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288 |
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289 function Base.showerror(io::IO, err::DomainSizeMismatch) |
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290 print(io, "DomainSizeMismatch: ") |
| 995 | 291 print(io, "domain size $(domain_size(err.tm)) of LazyTensor not matching size $(err.sz)") |
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292 end |
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293 |
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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 |
