Mercurial > repos > public > sbplib_julia
annotate src/LazyTensors/lazy_tensor_operations.jl @ 541:62d96e2cd165 refactor/tensor_index_coupling
Make the coupling between all the LazyTensors code and the Index type much weaker to make the module more flexible
author | Jonatan Werpers <jonatan@werpers.com> |
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date | Thu, 26 Nov 2020 21:35:34 +0100 |
parents | 848dec405332 |
children | 53828d3ed132 |
rev | line source |
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1 """ |
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2 LazyTensorMappingApplication{T,R,D} <: LazyArray{T,R} |
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3 |
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4 Struct for lazy application of a TensorMapping. Created using `*`. |
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5 |
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6 Allows the result of a `TensorMapping` applied to a vector to be treated as an `AbstractArray`. |
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7 With a mapping `m` and a vector `v` the LazyTensorMappingApplication 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 LazyTensorMappingApplication{T,R,D, TM<:TensorMapping{T,R,D}, AA<:AbstractArray{T,D}} <: LazyArray{T,R} |
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11 t::TM |
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12 o::AA |
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13 end |
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14 # TODO: Do boundschecking on creation! |
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15 export LazyTensorMappingApplication |
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17 # TODO: Go through and remove unneccerary type parameters on functions |
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19 Base.getindex(ta::LazyTensorMappingApplication{T,R,D}, I::Vararg{Any,R}) where {T,R,D} = apply(ta.t, ta.o, I...) |
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20 Base.size(ta::LazyTensorMappingApplication) = range_size(ta.t) |
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21 # TODO: What else is needed to implement the AbstractArray interface? |
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22 |
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23 Base.:*(a::TensorMapping, v::AbstractArray) = LazyTensorMappingApplication(a,v) |
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24 Base.:*(a::TensorMapping, b::TensorMapping) = throw(MethodError(Base.:*,(a,b))) |
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25 Base.:*(a::TensorMapping, args::Union{TensorMapping, AbstractArray}...) = foldr(*,(a,args...)) |
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26 |
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27 # # We need the associativity to be a→b→c = a→(b→c), which is the case for '→' |
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28 # # Should we overload some other infix binary opesrator? |
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29 # →(tm::TensorMapping{T,R,D}, o::AbstractArray{T,D}) where {T,R,D} = LazyTensorMappingApplication(tm,o) |
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30 # TODO: We need to be really careful about good error messages. |
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31 # For example what happens if you try to multiply LazyTensorMappingApplication with a TensorMapping(wrong order)? |
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32 |
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33 """ |
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34 LazyTensorMappingTranspose{T,R,D} <: TensorMapping{T,D,R} |
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35 |
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36 Struct for lazy transpose of a TensorMapping. |
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37 |
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38 If a mapping implements the the `apply_transpose` method this allows working with |
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39 the transpose of mapping `m` by using `m'`. `m'` will work as a regular TensorMapping lazily calling |
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40 the appropriate methods of `m`. |
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41 """ |
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42 struct LazyTensorMappingTranspose{T,R,D, TM<:TensorMapping{T,R,D}} <: TensorMapping{T,D,R} |
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43 tm::TM |
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44 end |
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45 export LazyTensorMappingTranspose |
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46 |
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47 # # TBD: Should this be implemented on a type by type basis or through a trait to provide earlier errors? |
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48 # Jonatan 2020-09-25: Is the problem that you can take the transpose of any TensorMapping even if it doesn't implement `apply_transpose`? |
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49 Base.adjoint(tm::TensorMapping) = LazyTensorMappingTranspose(tm) |
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50 Base.adjoint(tmt::LazyTensorMappingTranspose) = tmt.tm |
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51 |
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52 apply(tmt::LazyTensorMappingTranspose{T,R,D}, v::AbstractArray{T,R}, I::Vararg{Any,D}) where {T,R,D} = apply_transpose(tmt.tm, v, I...) |
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53 apply_transpose(tmt::LazyTensorMappingTranspose{T,R,D}, v::AbstractArray{T,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmt.tm, v, I...) |
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54 |
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55 range_size(tmt::LazyTensorMappingTranspose) = domain_size(tmt.tm) |
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56 domain_size(tmt::LazyTensorMappingTranspose) = range_size(tmt.tm) |
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57 |
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58 |
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59 struct LazyTensorMappingBinaryOperation{Op,T,R,D,T1<:TensorMapping{T,R,D},T2<:TensorMapping{T,R,D}} <: TensorMapping{T,D,R} |
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60 tm1::T1 |
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61 tm2::T2 |
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62 |
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63 @inline function LazyTensorMappingBinaryOperation{Op,T,R,D}(tm1::T1,tm2::T2) where {Op,T,R,D, T1<:TensorMapping{T,R,D},T2<:TensorMapping{T,R,D}} |
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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 # TODO: Boundschecking in constructor. |
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68 |
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69 apply(tmBinOp::LazyTensorMappingBinaryOperation{:+,T,R,D}, v::AbstractArray{T,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmBinOp.tm1, v, I...) + apply(tmBinOp.tm2, v, I...) |
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70 apply(tmBinOp::LazyTensorMappingBinaryOperation{:-,T,R,D}, v::AbstractArray{T,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmBinOp.tm1, v, I...) - apply(tmBinOp.tm2, v, I...) |
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71 |
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72 range_size(tmBinOp::LazyTensorMappingBinaryOperation{Op,T,R,D}) where {Op,T,R,D} = range_size(tmBinOp.tm1) |
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73 domain_size(tmBinOp::LazyTensorMappingBinaryOperation{Op,T,R,D}) where {Op,T,R,D} = domain_size(tmBinOp.tm1) |
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74 |
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75 Base.:+(tm1::TensorMapping{T,R,D}, tm2::TensorMapping{T,R,D}) where {T,R,D} = LazyTensorMappingBinaryOperation{:+,T,R,D}(tm1,tm2) |
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76 Base.:-(tm1::TensorMapping{T,R,D}, tm2::TensorMapping{T,R,D}) where {T,R,D} = LazyTensorMappingBinaryOperation{:-,T,R,D}(tm1,tm2) |
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77 |
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78 """ |
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79 TensorMappingComposition{T,R,K,D} |
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80 |
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81 Lazily compose two TensorMappings, so that they can be handled as a single TensorMapping. |
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82 """ |
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83 struct TensorMappingComposition{T,R,K,D, TM1<:TensorMapping{T,R,K}, TM2<:TensorMapping{T,K,D}} <: TensorMapping{T,R,D} |
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84 t1::TM1 |
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85 t2::TM2 |
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86 |
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87 @inline function TensorMappingComposition(t1::TensorMapping{T,R,K}, t2::TensorMapping{T,K,D}) where {T,R,K,D} |
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88 @boundscheck check_domain_size(t1, range_size(t2)) |
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89 return new{T,R,K,D, typeof(t1), typeof(t2)}(t1,t2) |
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90 end |
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91 end |
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92 export TensorMappingComposition |
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93 |
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94 range_size(tm::TensorMappingComposition) = range_size(tm.t1) |
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95 domain_size(tm::TensorMappingComposition) = domain_size(tm.t2) |
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96 |
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97 function apply(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{T,D}, I::Vararg{S,R} where S) where {T,R,K,D} |
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98 apply(c.t1, c.t2*v, I...) |
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99 end |
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101 function apply_transpose(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{T,R}, I::Vararg{S,D} where S) where {T,R,K,D} |
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102 apply_transpose(c.t2, c.t1'*v, I...) |
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103 end |
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105 Base.@propagate_inbounds Base.:∘(s::TensorMapping, t::TensorMapping) = TensorMappingComposition(s,t) |
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106 |
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107 """ |
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108 LazyLinearMap{T,R,D,...}(A, range_indicies, domain_indicies) |
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109 |
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110 TensorMapping defined by the AbstractArray A. `range_indicies` and `domain_indicies` define which indicies of A should |
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111 be considerd the range and domain of the TensorMapping. Each set of indices must be ordered in ascending order. |
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112 |
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113 For instance, if A is a m x n matrix, and range_size = (1,), domain_size = (2,), then the LazyLinearMap performs the |
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114 standard matrix-vector product on vectors of size n. |
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115 """ |
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116 struct LazyLinearMap{T,R,D, RD, AA<:AbstractArray{T,RD}} <: TensorMapping{T,R,D} |
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117 A::AA |
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118 range_indicies::NTuple{R,Int} |
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119 domain_indicies::NTuple{D,Int} |
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120 |
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121 function LazyLinearMap(A::AA, range_indicies::NTuple{R,Int}, domain_indicies::NTuple{D,Int}) where {T,R,D, RD, AA<:AbstractArray{T,RD}} |
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122 if !issorted(range_indicies) || !issorted(domain_indicies) |
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123 throw(DomainError("range_indicies and domain_indicies must be sorted in ascending order")) |
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124 end |
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125 |
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126 return new{T,R,D,RD,AA}(A,range_indicies,domain_indicies) |
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127 end |
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128 end |
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129 export LazyLinearMap |
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130 |
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131 range_size(llm::LazyLinearMap) = size(llm.A)[[llm.range_indicies...]] |
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132 domain_size(llm::LazyLinearMap) = size(llm.A)[[llm.domain_indicies...]] |
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133 |
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134 function apply(llm::LazyLinearMap{T,R,D}, v::AbstractArray{T,D}, I::Vararg{Any,R}) where {T,R,D} |
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135 view_index = ntuple(i->:,ndims(llm.A)) |
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136 for i ∈ 1:R |
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137 view_index = Base.setindex(view_index, Int(I[i]), llm.range_indicies[i]) |
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138 end |
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139 A_view = @view llm.A[view_index...] |
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140 return sum(A_view.*v) |
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141 end |
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142 |
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143 function apply_transpose(llm::LazyLinearMap{T,R,D}, v::AbstractArray{T,R}, I::Vararg{Any,D}) where {T,R,D} |
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144 apply(LazyLinearMap(llm.A, llm.domain_indicies, llm.range_indicies), v, I...) |
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145 end |
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146 |
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147 |
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148 """ |
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149 IdentityMapping{T,D} <: TensorMapping{T,D,D} |
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150 |
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151 The lazy identity TensorMapping for a given size. Usefull for building up higher dimensional tensor mappings from lower |
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152 dimensional ones through outer products. Also used in the Implementation for InflatedTensorMapping. |
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153 """ |
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154 struct IdentityMapping{T,D} <: TensorMapping{T,D,D} |
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155 size::NTuple{D,Int} |
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156 end |
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157 export IdentityMapping |
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158 |
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159 IdentityMapping{T}(size::NTuple{D,Int}) where {T,D} = IdentityMapping{T,D}(size) |
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160 IdentityMapping{T}(size::Vararg{Int,D}) where {T,D} = IdentityMapping{T,D}(size) |
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161 IdentityMapping(size::Vararg{Int,D}) where D = IdentityMapping{Float64,D}(size) |
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162 |
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163 range_size(tmi::IdentityMapping) = tmi.size |
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164 domain_size(tmi::IdentityMapping) = tmi.size |
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165 |
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166 apply(tmi::IdentityMapping{T,D}, v::AbstractArray{T,D}, I::Vararg{Any,D}) where {T,D} = v[I...] |
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167 apply_transpose(tmi::IdentityMapping{T,D}, v::AbstractArray{T,D}, I::Vararg{Any,D}) where {T,D} = v[I...] |
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168 |
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169 """ |
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170 Base.:∘(tm, tmi) |
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171 Base.:∘(tmi, tm) |
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172 |
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173 Composes a `Tensormapping` `tm` with an `IdentityMapping` `tmi`, by returning `tm` |
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174 """ |
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175 @inline function Base.:∘(tm::TensorMapping{T,R,D}, tmi::IdentityMapping{T,D}) where {T,R,D} |
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176 @boundscheck check_domain_size(tm, range_size(tmi)) |
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177 return tm |
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178 end |
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179 |
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180 @inline function Base.:∘(tmi::IdentityMapping{T,R}, tm::TensorMapping{T,R,D}) where {T,R,D} |
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181 @boundscheck check_domain_size(tmi, range_size(tm)) |
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182 return tm |
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183 end |
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184 # Specialization for the case where tm is an IdentityMapping. Required to resolve ambiguity. |
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185 @inline function Base.:∘(tm::IdentityMapping{T,D}, tmi::IdentityMapping{T,D}) where {T,D} |
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186 @boundscheck check_domain_size(tm, range_size(tmi)) |
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187 return tmi |
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188 end |
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189 |
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190 |
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191 """ |
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192 InflatedTensorMapping{T,R,D} <: TensorMapping{T,R,D} |
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193 |
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194 An inflated `TensorMapping` with dimensions added before and afer its actual dimensions. |
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195 """ |
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196 struct InflatedTensorMapping{T,R,D,D_before,R_middle,D_middle,D_after, TM<:TensorMapping{T,R_middle,D_middle}} <: TensorMapping{T,R,D} |
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197 before::IdentityMapping{T,D_before} |
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198 tm::TM |
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199 after::IdentityMapping{T,D_after} |
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200 |
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201 function InflatedTensorMapping(before, tm::TensorMapping{T}, after) where T |
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202 R_before = range_dim(before) |
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203 R_middle = range_dim(tm) |
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204 R_after = range_dim(after) |
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205 R = R_before+R_middle+R_after |
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206 |
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207 D_before = domain_dim(before) |
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208 D_middle = domain_dim(tm) |
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209 D_after = domain_dim(after) |
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210 D = D_before+D_middle+D_after |
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211 return new{T,R,D,D_before,R_middle,D_middle,D_after, typeof(tm)}(before, tm, after) |
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212 end |
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213 end |
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214 export InflatedTensorMapping |
461 | 215 """ |
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216 InflatedTensorMapping(before, tm, after) |
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217 InflatedTensorMapping(before,tm) |
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218 InflatedTensorMapping(tm,after) |
461 | 219 |
220 The outer product of `before`, `tm` and `after`, where `before` and `after` are `IdentityMapping`s. | |
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221 |
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222 If one of `before` or `after` is left out, a 0-dimensional `IdentityMapping` is used as the default value. |
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223 |
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224 If `tm` already is an `InflatedTensorMapping`, `before` and `after` will be extended instead of |
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225 creating a nested `InflatedTensorMapping`. |
461 | 226 """ |
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227 InflatedTensorMapping(::IdentityMapping, ::TensorMapping, ::IdentityMapping) |
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228 |
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229 function InflatedTensorMapping(before, itm::InflatedTensorMapping, after) |
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230 return InflatedTensorMapping( |
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231 IdentityMapping(before.size..., itm.before.size...), |
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232 itm.tm, |
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233 IdentityMapping(itm.after.size..., after.size...), |
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234 ) |
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235 end |
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236 |
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237 InflatedTensorMapping(before::IdentityMapping, tm::TensorMapping{T}) where T = InflatedTensorMapping(before,tm,IdentityMapping{T}()) |
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238 InflatedTensorMapping(tm::TensorMapping{T}, after::IdentityMapping) where T = InflatedTensorMapping(IdentityMapping{T}(),tm,after) |
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239 # Resolve ambiguity between the two previous methods |
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240 InflatedTensorMapping(I1::IdentityMapping{T}, I2::IdentityMapping{T}) where T = InflatedTensorMapping(I1,I2,IdentityMapping{T}()) |
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241 |
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242 # TODO: Implement some pretty printing in terms of ⊗. E.g InflatedTensorMapping(I(3),B,I(2)) -> I(3)⊗B⊗I(2) |
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243 |
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244 function range_size(itm::InflatedTensorMapping) |
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245 return flatten_tuple( |
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246 range_size(itm.before), |
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247 range_size(itm.tm), |
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248 range_size(itm.after), |
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249 ) |
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250 end |
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251 |
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252 function domain_size(itm::InflatedTensorMapping) |
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253 return flatten_tuple( |
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254 domain_size(itm.before), |
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255 domain_size(itm.tm), |
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256 domain_size(itm.after), |
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257 ) |
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258 end |
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259 |
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260 function apply(itm::InflatedTensorMapping{T,R,D}, v::AbstractArray{T,D}, I::Vararg{Any,R}) where {T,R,D} |
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261 dim_before = range_dim(itm.before) |
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262 dim_domain = domain_dim(itm.tm) |
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263 dim_range = range_dim(itm.tm) |
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264 dim_after = range_dim(itm.after) |
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265 |
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266 view_index, inner_index = split_index(Val(dim_before), Val(dim_domain), Val(dim_range), Val(dim_after), I...) |
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267 |
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268 v_inner = view(v, view_index...) |
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269 return apply(itm.tm, v_inner, inner_index...) |
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270 end |
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271 |
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272 function apply_transpose(itm::InflatedTensorMapping{T,R,D}, v::AbstractArray{T,R}, I::Vararg{Any,D}) where {T,R,D} |
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273 dim_before = range_dim(itm.before) |
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274 dim_domain = domain_dim(itm.tm) |
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275 dim_range = range_dim(itm.tm) |
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276 dim_after = range_dim(itm.after) |
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277 |
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278 view_index, inner_index = split_index(Val(dim_before), Val(dim_range), Val(dim_domain), Val(dim_after), I...) |
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279 |
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280 v_inner = view(v, view_index...) |
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281 return apply_transpose(itm.tm, v_inner, inner_index...) |
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282 end |
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283 |
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284 |
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285 """ |
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286 split_index(::Val{dim_before}, ::Val{dim_view}, ::Val{dim_index}, ::Val{dim_after}, I...) |
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287 |
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288 Splits the multi-index `I` into two parts. One part which is expected to be |
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289 used as a view, and one which is expected to be used as an index. |
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290 Eg. |
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291 ``` |
537 | 292 split_index(Val(1),Val(3),Val(2),Val(1),(1,2,3,4)) -> (1,:,:,:,4), (2,3) |
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293 ``` |
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294 |
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295 `dim_view` controls how many colons are in the view, and `dim_index` controls |
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296 how many elements are extracted from the middle. |
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297 `dim_before` and `dim_after` decides the length of the index parts before and after the colons in the view index. |
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298 |
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299 Arguments should satisfy `length(I) == dim_before+B_domain+dim_after`. |
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300 |
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301 The returned values satisfy |
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302 * `length(view_index) == dim_before + dim_view + dim_after` |
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303 * `length(I_middle) == dim_index` |
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304 """ |
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305 function split_index(::Val{dim_before}, ::Val{dim_view}, ::Val{dim_index}, ::Val{dim_after}, I...) where {dim_before,dim_view, dim_index,dim_after} |
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306 I_before, I_middle, I_after = split_tuple(I, Val(dim_before), Val(dim_index)) |
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307 |
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308 view_index = (I_before..., ntuple((i)->:, dim_view)..., I_after...) |
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309 |
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310 return view_index, I_middle |
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311 end |
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312 |
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313 # TODO: Can this be replaced by something more elegant while still being type stable? 2020-10-21 |
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314 # See: |
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315 # https://github.com/JuliaLang/julia/issues/34884 |
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316 # https://github.com/JuliaLang/julia/issues/30386 |
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317 """ |
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318 slice_tuple(t, Val(l), Val(u)) |
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319 |
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320 Get a slice of a tuple in a type stable way. |
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321 Equivalent to t[l:u] but type stable. |
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322 """ |
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323 function slice_tuple(t,::Val{L},::Val{U}) where {L,U} |
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324 return ntuple(i->t[i+L-1], U-L+1) |
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325 end |
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326 |
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327 """ |
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328 split_tuple(t::Tuple{...}, ::Val{M}) where {N,M} |
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329 |
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330 Split the tuple `t` into two parts. the first part is `M` long. |
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331 E.g |
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332 ``` |
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333 split_tuple((1,2,3,4),Val(3)) -> (1,2,3), (4,) |
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334 ``` |
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335 """ |
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336 function split_tuple(t::NTuple{N},::Val{M}) where {N,M} |
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337 return slice_tuple(t,Val(1), Val(M)), slice_tuple(t,Val(M+1), Val(N)) |
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338 end |
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339 |
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340 """ |
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341 split_tuple(t::Tuple{...},::Val{M},::Val{K}) where {N,M,K} |
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342 |
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343 Same as `split_tuple(t::NTuple{N},::Val{M})` but splits the tuple in three parts. With the first |
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344 two parts having lenght `M` and `K`. |
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345 """ |
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346 function split_tuple(t::NTuple{N},::Val{M},::Val{K}) where {N,M,K} |
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347 p1, tail = split_tuple(t, Val(M)) |
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348 p2, p3 = split_tuple(tail, Val(K)) |
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349 return p1,p2,p3 |
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350 end |
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351 |
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352 |
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353 """ |
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354 flatten_tuple(t) |
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355 |
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356 Takes a nested tuple and flattens the whole structure |
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357 """ |
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358 flatten_tuple(t::NTuple{N, Number} where N) = t |
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359 flatten_tuple(t::Tuple) = ((flatten_tuple.(t)...)...,) # simplify? |
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360 flatten_tuple(ts::Vararg) = flatten_tuple(ts) |
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361 |
468
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362 """ |
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363 LazyOuterProduct(tms...) |
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364 |
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365 Creates a `TensorMappingComposition` for the outerproduct of `tms...`. |
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366 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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367 |
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368 First let |
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369 ```math |
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370 A = A_{I,J} |
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371 B = B_{M,N} |
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372 C = C_{P,Q} |
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373 ``` |
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374 |
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375 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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376 |
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377 We use ``⊗`` to denote the outer product |
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378 ```math |
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379 (A⊗B)_{IM,JN} = A_{I,J}B_{M,N} |
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380 ``` |
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381 |
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382 We note that |
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383 ```math |
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384 A⊗B⊗C = (A⊗B⊗C)_{IMP,JNQ} = A_{I,J}B_{M,N}C_{P,Q} |
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385 ``` |
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386 And that |
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387 ```math |
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388 A⊗B⊗C = (A⊗I_{|M|}⊗I_{|P|})(I_{|J|}⊗B⊗I_{|P|})(I_{|J|}⊗I_{|N|}⊗C) |
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389 ``` |
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390 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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391 To apply ``A⊗B⊗C`` we evaluate |
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392 |
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393 (A⊗B⊗C)v = [(A⊗I_{|M|}⊗I_{|P|}) [(I_{|J|}⊗B⊗I_{|P|}) [(I_{|J|}⊗I_{|N|}⊗C)v]]] |
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394 """ |
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395 function LazyOuterProduct end |
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396 export LazyOuterProduct |
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397 |
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398 function LazyOuterProduct(tm1::TensorMapping{T}, tm2::TensorMapping{T}) where T |
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399 itm1 = InflatedTensorMapping(tm1, IdentityMapping{T}(range_size(tm2))) |
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400 itm2 = InflatedTensorMapping(IdentityMapping{T}(domain_size(tm1)),tm2) |
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401 |
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402 return itm1∘itm2 |
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403 end |
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404 |
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405 LazyOuterProduct(t1::IdentityMapping{T}, t2::IdentityMapping{T}) where T = IdentityMapping{T}(t1.size...,t2.size...) |
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406 LazyOuterProduct(t1::TensorMapping, t2::IdentityMapping) = InflatedTensorMapping(t1, t2) |
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407 LazyOuterProduct(t1::IdentityMapping, t2::TensorMapping) = InflatedTensorMapping(t1, t2) |
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408 |
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409 LazyOuterProduct(tms::Vararg{TensorMapping}) = foldl(LazyOuterProduct, tms) |
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410 |
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411 ⊗(a::TensorMapping, b::TensorMapping) = LazyOuterProduct(a,b) |
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412 export ⊗ |
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413 |
498 | 414 |
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415 function check_domain_size(tm::TensorMapping, sz) |
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416 if domain_size(tm) != sz |
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417 throw(SizeMismatch(tm,sz)) |
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418 end |
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419 end |
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420 |
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421 struct SizeMismatch <: Exception |
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422 tm::TensorMapping |
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423 sz |
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424 end |
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425 export SizeMismatch |
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426 |
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427 function Base.showerror(io::IO, err::SizeMismatch) |
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428 print(io, "SizeMismatch: ") |
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429 print(io, "domain size $(domain_size(err.tm)) of TensorMapping not matching size $(err.sz)") |
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430 end |