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annotate src/LazyTensors/lazy_tensor_operations.jl @ 994:55ab7801c45f refactor/lazy_tensors

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Fix typo in doc
author Jonatan Werpers <jonatan@werpers.com>
date Fri, 18 Mar 2022 20:44:17 +0100
parents bc384aaade30
children 1ba8a398af9c
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1 # TBD: Is there a good way to split this file?
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2
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3 """
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4 LazyTensorMappingApplication{T,R,D} <: LazyArray{T,R}
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6 Struct for lazy application of a TensorMapping. Created using `*`.
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7
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8 Allows the result of a `TensorMapping` applied to a vector to be treated as an `AbstractArray`.
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9 With a mapping `m` and a vector `v` the LazyTensorMappingApplication object can be created by `m*v`.
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10 The actual result will be calcualted when indexing into `m*v`.
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11 """
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12 struct LazyTensorMappingApplication{T,R,D, TM<:TensorMapping{<:Any,R,D}, AA<:AbstractArray{<:Any,D}} <: LazyArray{T,R}
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13 t::TM
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14 o::AA
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16 function LazyTensorMappingApplication(t::TensorMapping{<:Any,R,D}, o::AbstractArray{<:Any,D}) where {R,D}
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17 I = ntuple(i->1, range_dim(t))
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18 T = typeof(apply(t,o,I...))
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19 return new{T,R,D,typeof(t), typeof(o)}(t,o)
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20 end
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21 end
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22 # TODO: Do boundschecking on creation!
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24 Base.getindex(ta::LazyTensorMappingApplication{T,R}, I::Vararg{Any,R}) where {T,R} = apply(ta.t, ta.o, I...)
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25 Base.getindex(ta::LazyTensorMappingApplication{T,1}, I::CartesianIndex{1}) where {T} = apply(ta.t, ta.o, I.I...) # Would otherwise be caught in the previous method.
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26 Base.size(ta::LazyTensorMappingApplication) = range_size(ta.t)
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27 # TODO: What else is needed to implement the AbstractArray interface?
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28
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29 Base.:*(a::TensorMapping, v::AbstractArray) = LazyTensorMappingApplication(a,v)
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30 Base.:*(a::TensorMapping, b::TensorMapping) = throw(MethodError(Base.:*,(a,b)))
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31 Base.:*(a::TensorMapping, args::Union{TensorMapping, AbstractArray}...) = foldr(*,(a,args...))
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33 # # We need the associativity to be a→b→c = a→(b→c), which is the case for '→'
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34 # # Should we overload some other infix binary opesrator?
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35 # →(tm::TensorMapping{T,R,D}, o::AbstractArray{T,D}) where {T,R,D} = LazyTensorMappingApplication(tm,o)
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36 # TODO: We need to be really careful about good error messages.
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37 # For example what happens if you try to multiply LazyTensorMappingApplication with a TensorMapping(wrong order)?
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38
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39 """
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40 LazyTensorMappingTranspose{T,R,D} <: TensorMapping{T,D,R}
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41
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42 Struct for lazy transpose of a TensorMapping.
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43
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44 If a mapping implements the the `apply_transpose` method this allows working with
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45 the transpose of mapping `m` by using `m'`. `m'` will work as a regular TensorMapping lazily calling
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46 the appropriate methods of `m`.
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47 """
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48 struct LazyTensorMappingTranspose{T,R,D, TM<:TensorMapping{T,R,D}} <: TensorMapping{T,D,R}
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49 tm::TM
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50 end
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51
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52 # # TBD: Should this be implemented on a type by type basis or through a trait to provide earlier errors?
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53 # 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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54 Base.adjoint(tm::TensorMapping) = LazyTensorMappingTranspose(tm)
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55 Base.adjoint(tmt::LazyTensorMappingTranspose) = tmt.tm
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56
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57 apply(tmt::LazyTensorMappingTranspose{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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58 apply_transpose(tmt::LazyTensorMappingTranspose{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmt.tm, v, I...)
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59
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60 range_size(tmt::LazyTensorMappingTranspose) = domain_size(tmt.tm)
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61 domain_size(tmt::LazyTensorMappingTranspose) = range_size(tmt.tm)
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63
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64 struct LazyTensorMappingBinaryOperation{Op,T,R,D,T1<:TensorMapping{T,R,D},T2<:TensorMapping{T,R,D}} <: TensorMapping{T,D,R}
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65 tm1::T1
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66 tm2::T2
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67
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68 @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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69 return new{Op,T,R,D,T1,T2}(tm1,tm2)
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70 end
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71 end
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72 # TODO: Boundschecking in constructor.
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73
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74 apply(tmBinOp::LazyTensorMappingBinaryOperation{:+,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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75 apply(tmBinOp::LazyTensorMappingBinaryOperation{:-,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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76
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77 range_size(tmBinOp::LazyTensorMappingBinaryOperation) = range_size(tmBinOp.tm1)
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78 domain_size(tmBinOp::LazyTensorMappingBinaryOperation) = domain_size(tmBinOp.tm1)
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79
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80 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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81 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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82
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83 """
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84 TensorMappingComposition{T,R,K,D}
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85
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86 Lazily compose two `TensorMapping`s, so that they can be handled as a single `TensorMapping`.
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87 """
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88 struct TensorMappingComposition{T,R,K,D, TM1<:TensorMapping{T,R,K}, TM2<:TensorMapping{T,K,D}} <: TensorMapping{T,R,D}
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89 t1::TM1
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90 t2::TM2
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91
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92 @inline function TensorMappingComposition(t1::TensorMapping{T,R,K}, t2::TensorMapping{T,K,D}) where {T,R,K,D}
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93 @boundscheck check_domain_size(t1, range_size(t2))
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94 return new{T,R,K,D, typeof(t1), typeof(t2)}(t1,t2)
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95 end
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96 end
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97
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98 range_size(tm::TensorMappingComposition) = range_size(tm.t1)
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99 domain_size(tm::TensorMappingComposition) = domain_size(tm.t2)
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100
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101 function apply(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,K,D}
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102 apply(c.t1, c.t2*v, I...)
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103 end
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104
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105 function apply_transpose(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,K,D}
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106 apply_transpose(c.t2, c.t1'*v, I...)
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107 end
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108
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109 Base.@propagate_inbounds Base.:∘(s::TensorMapping, t::TensorMapping) = TensorMappingComposition(s,t)
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110
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111 """
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112 LazyLinearMap{T,R,D,...}(A, range_indicies, domain_indicies)
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113
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114 TensorMapping defined by the AbstractArray A. `range_indicies` and `domain_indicies` define which indicies of A should
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115 be considerd the range and domain of the TensorMapping. Each set of indices must be ordered in ascending order.
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116
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117 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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118 standard matrix-vector product on vectors of size n.
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119 """
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120 struct LazyLinearMap{T,R,D, RD, AA<:AbstractArray{T,RD}} <: TensorMapping{T,R,D}
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121 A::AA
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122 range_indicies::NTuple{R,Int}
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123 domain_indicies::NTuple{D,Int}
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124
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125 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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126 if !issorted(range_indicies) || !issorted(domain_indicies)
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127 throw(DomainError("range_indicies and domain_indicies must be sorted in ascending order"))
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128 end
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129
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130 return new{T,R,D,RD,AA}(A,range_indicies,domain_indicies)
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131 end
377
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132 end
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133
392
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134 range_size(llm::LazyLinearMap) = size(llm.A)[[llm.range_indicies...]]
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135 domain_size(llm::LazyLinearMap) = size(llm.A)[[llm.domain_indicies...]]
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136
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137 function apply(llm::LazyLinearMap{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D}
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138 view_index = ntuple(i->:,ndims(llm.A))
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139 for i ∈ 1:R
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140 view_index = Base.setindex(view_index, Int(I[i]), llm.range_indicies[i])
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141 end
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142 A_view = @view llm.A[view_index...]
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143 return sum(A_view.*v)
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144 end
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145
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146 function apply_transpose(llm::LazyLinearMap{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,D}
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147 apply(LazyLinearMap(llm.A, llm.domain_indicies, llm.range_indicies), v, I...)
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148 end
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149
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150
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151 """
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152 IdentityMapping{T,D} <: TensorMapping{T,D,D}
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153
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154 The lazy identity TensorMapping for a given size. Usefull for building up higher dimensional tensor mappings from lower
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155 dimensional ones through outer products. Also used in the Implementation for InflatedTensorMapping.
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156 """
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157 struct IdentityMapping{T,D} <: TensorMapping{T,D,D}
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158 size::NTuple{D,Int}
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159 end
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160
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161 IdentityMapping{T}(size::NTuple{D,Int}) where {T,D} = IdentityMapping{T,D}(size)
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162 IdentityMapping{T}(size::Vararg{Int,D}) where {T,D} = IdentityMapping{T,D}(size)
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163 IdentityMapping(size::Vararg{Int,D}) where D = IdentityMapping{Float64,D}(size)
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164
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165 range_size(tmi::IdentityMapping) = tmi.size
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166 domain_size(tmi::IdentityMapping) = tmi.size
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167
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168 apply(tmi::IdentityMapping{T,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,D}) where {T,D} = v[I...]
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169 apply_transpose(tmi::IdentityMapping{T,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,D}) where {T,D} = v[I...]
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170
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171 """
838
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172 Base.:∘(tm, tmi)
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173 Base.:∘(tmi, tm)
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174
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175 Composes a `Tensormapping` `tm` with an `IdentityMapping` `tmi`, by returning `tm`
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176 """
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177 @inline function Base.:∘(tm::TensorMapping{T,R,D}, tmi::IdentityMapping{T,D}) where {T,R,D}
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178 @boundscheck check_domain_size(tm, range_size(tmi))
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179 return tm
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180 end
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181
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182 @inline function Base.:∘(tmi::IdentityMapping{T,R}, tm::TensorMapping{T,R,D}) where {T,R,D}
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183 @boundscheck check_domain_size(tmi, range_size(tm))
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184 return tm
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185 end
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186 # Specialization for the case where tm is an IdentityMapping. Required to resolve ambiguity.
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187 @inline function Base.:∘(tm::IdentityMapping{T,D}, tmi::IdentityMapping{T,D}) where {T,D}
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188 @boundscheck check_domain_size(tm, range_size(tmi))
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189 return tmi
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190 end
992
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191 # TODO: Implement the above as TensorMappingComposition instead
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192 # TODO: Move the operator definitions to one place
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193
992
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194 """
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195 ScalingTensor{T,D} <: TensorMapping{T,D,D}
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196
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197 A lazy tensor that scales its input with `λ`.
992
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198 """
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199 struct ScalingTensor{T,D} <: TensorMapping{T,D,D}
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200 λ::T
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201 size::NTuple{D,Int}
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202 end
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203
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204 LazyTensors.apply(tm::ScalingTensor{T,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,D}) where {T,D} = tm.λ*v[I...]
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205 LazyTensors.apply_transpose(tm::ScalingTensor{T,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,D}) where {T,D} = tm.λ*v[I...]
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206
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207 LazyTensors.range_size(m::ScalingTensor) = m.size
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208 LazyTensors.domain_size(m::ScalingTensor) = m.size
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209
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210 # TODO: Rename everything with mapping
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211 # TODO: Remove ScalingOperator from tests
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212
459
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213 """
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214 InflatedTensorMapping{T,R,D} <: TensorMapping{T,R,D}
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215
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216 An inflated `TensorMapping` with dimensions added before and afer its actual dimensions.
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217 """
449
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diff changeset
218 struct InflatedTensorMapping{T,R,D,D_before,R_middle,D_middle,D_after, TM<:TensorMapping{T,R_middle,D_middle}} <: TensorMapping{T,R,D}
448
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219 before::IdentityMapping{T,D_before}
449
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220 tm::TM
448
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diff changeset
221 after::IdentityMapping{T,D_after}
446
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222
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223 function InflatedTensorMapping(before, tm::TensorMapping{T}, after) where T
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224 R_before = range_dim(before)
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225 R_middle = range_dim(tm)
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226 R_after = range_dim(after)
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227 R = R_before+R_middle+R_after
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228
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229 D_before = domain_dim(before)
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230 D_middle = domain_dim(tm)
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231 D_after = domain_dim(after)
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232 D = D_before+D_middle+D_after
449
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233 return new{T,R,D,D_before,R_middle,D_middle,D_after, typeof(tm)}(before, tm, after)
448
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234 end
446
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235 end
461
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diff changeset
236 """
464
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237 InflatedTensorMapping(before, tm, after)
465
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diff changeset
238 InflatedTensorMapping(before,tm)
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239 InflatedTensorMapping(tm,after)
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240
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241 The outer product of `before`, `tm` and `after`, where `before` and `after` are `IdentityMapping`s.
465
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242
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243 If one of `before` or `after` is left out, a 0-dimensional `IdentityMapping` is used as the default value.
493
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244
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diff changeset
245 If `tm` already is an `InflatedTensorMapping`, `before` and `after` will be extended instead of
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246 creating a nested `InflatedTensorMapping`.
461
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247 """
464
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248 InflatedTensorMapping(::IdentityMapping, ::TensorMapping, ::IdentityMapping)
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249
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diff changeset
250 function InflatedTensorMapping(before, itm::InflatedTensorMapping, after)
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251 return InflatedTensorMapping(
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252 IdentityMapping(before.size..., itm.before.size...),
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253 itm.tm,
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254 IdentityMapping(itm.after.size..., after.size...),
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255 )
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256 end
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257
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258 InflatedTensorMapping(before::IdentityMapping, tm::TensorMapping{T}) where T = InflatedTensorMapping(before,tm,IdentityMapping{T}())
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259 InflatedTensorMapping(tm::TensorMapping{T}, after::IdentityMapping) where T = InflatedTensorMapping(IdentityMapping{T}(),tm,after)
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260 # Resolve ambiguity between the two previous methods
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261 InflatedTensorMapping(I1::IdentityMapping{T}, I2::IdentityMapping{T}) where T = InflatedTensorMapping(I1,I2,IdentityMapping{T}())
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262
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263 # 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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264
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265 function range_size(itm::InflatedTensorMapping)
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266 return flatten_tuple(
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267 range_size(itm.before),
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268 range_size(itm.tm),
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269 range_size(itm.after),
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270 )
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271 end
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272
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273 function domain_size(itm::InflatedTensorMapping)
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274 return flatten_tuple(
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275 domain_size(itm.before),
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276 domain_size(itm.tm),
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277 domain_size(itm.after),
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278 )
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279 end
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280
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281 function apply(itm::InflatedTensorMapping{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D}
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282 dim_before = range_dim(itm.before)
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283 dim_domain = domain_dim(itm.tm)
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284 dim_range = range_dim(itm.tm)
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285 dim_after = range_dim(itm.after)
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286
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287 view_index, inner_index = split_index(Val(dim_before), Val(dim_domain), Val(dim_range), Val(dim_after), I...)
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288
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289 v_inner = view(v, view_index...)
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290 return apply(itm.tm, v_inner, inner_index...)
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291 end
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292
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293 function apply_transpose(itm::InflatedTensorMapping{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,D}
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294 dim_before = range_dim(itm.before)
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295 dim_domain = domain_dim(itm.tm)
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296 dim_range = range_dim(itm.tm)
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297 dim_after = range_dim(itm.after)
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298
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299 view_index, inner_index = split_index(Val(dim_before), Val(dim_range), Val(dim_domain), Val(dim_after), I...)
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300
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301 v_inner = view(v, view_index...)
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302 return apply_transpose(itm.tm, v_inner, inner_index...)
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303 end
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304
446
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305
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306 """
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307 split_index(::Val{dim_before}, ::Val{dim_view}, ::Val{dim_index}, ::Val{dim_after}, I...)
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308
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309 Splits the multi-index `I` into two parts. One part which is expected to be
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310 used as a view, and one which is expected to be used as an index.
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311 Eg.
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312 ```
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313 split_index(Val(1),Val(3),Val(2),Val(1),(1,2,3,4)) -> (1,:,:,:,4), (2,3)
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314 ```
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315
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316 `dim_view` controls how many colons are in the view, and `dim_index` controls
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317 how many elements are extracted from the middle.
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318 `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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319
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320 Arguments should satisfy `length(I) == dim_before+B_domain+dim_after`.
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321
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322 The returned values satisfy
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323 * `length(view_index) == dim_before + dim_view + dim_after`
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324 * `length(I_middle) == dim_index`
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325 """
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326 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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327 I_before, I_middle, I_after = split_tuple(I, Val(dim_before), Val(dim_index))
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328
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329 view_index = (I_before..., ntuple((i)->:, dim_view)..., I_after...)
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330
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331 return view_index, I_middle
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332 end
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333
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334 # TODO: Can this be replaced by something more elegant while still being type stable? 2020-10-21
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335 # See:
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336 # https://github.com/JuliaLang/julia/issues/34884
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337 # https://github.com/JuliaLang/julia/issues/30386
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338 """
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339 slice_tuple(t, Val(l), Val(u))
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340
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341 Get a slice of a tuple in a type stable way.
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342 Equivalent to `t[l:u]` but type stable.
456
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343 """
455
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344 function slice_tuple(t,::Val{L},::Val{U}) where {L,U}
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345 return ntuple(i->t[i+L-1], U-L+1)
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346 end
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347
457
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348 """
532
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349 split_tuple(t::Tuple{...}, ::Val{M}) where {N,M}
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350
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351 Split the tuple `t` into two parts. the first part is `M` long.
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352 E.g
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353 ```julia
532
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354 split_tuple((1,2,3,4),Val(3)) -> (1,2,3), (4,)
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355 ```
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356 """
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357 function split_tuple(t::NTuple{N,Any},::Val{M}) where {N,M}
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358 return slice_tuple(t,Val(1), Val(M)), slice_tuple(t,Val(M+1), Val(N))
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359 end
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360
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361 """
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362 split_tuple(t::Tuple{...},::Val{M},::Val{K}) where {N,M,K}
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363
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364 Same as `split_tuple(t::NTuple{N},::Val{M})` but splits the tuple in three parts. With the first
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365 two parts having lenght `M` and `K`.
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366 """
625
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367 function split_tuple(t::NTuple{N,Any},::Val{M},::Val{K}) where {N,M,K}
532
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368 p1, tail = split_tuple(t, Val(M))
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369 p2, p3 = split_tuple(tail, Val(K))
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370 return p1,p2,p3
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371 end
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372
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373
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374 """
457
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375 flatten_tuple(t)
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376
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377 Takes a nested tuple and flattens the whole structure
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378 """
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379 flatten_tuple(t::NTuple{N, Number} where N) = t
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380 flatten_tuple(t::Tuple) = ((flatten_tuple.(t)...)...,) # simplify?
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381 flatten_tuple(ts::Vararg) = flatten_tuple(ts)
487
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382
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383 @doc raw"""
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384 LazyOuterProduct(tms...)
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385
501
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diff changeset
386 Creates a `TensorMappingComposition` for the outerproduct of `tms...`.
468
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diff changeset
387 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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388
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389 First let
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390 ```math
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391 \begin{aligned}
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392 A &= A_{I,J} \\
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393 B &= B_{M,N} \\
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394 C &= C_{P,Q} \\
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395 \end{aligned}
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396 ```
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397
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398 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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399
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400 We use ``⊗`` to denote the outer product
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401 ```math
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402 (A⊗B)_{IM,JN} = A_{I,J}B_{M,N}
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403 ```
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404
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405 We note that
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406 ```math
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407 A⊗B⊗C = (A⊗B⊗C)_{IMP,JNQ} = A_{I,J}B_{M,N}C_{P,Q}
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408 ```
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409 And that
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410 ```math
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411 A⊗B⊗C = (A⊗I_{|M|}⊗I_{|P|})(I_{|J|}⊗B⊗I_{|P|})(I_{|J|}⊗I_{|N|}⊗C)
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412 ```
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413 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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414 To apply ``A⊗B⊗C`` we evaluate
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415
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416 ```math
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417 (A⊗B⊗C)v = [(A⊗I_{|M|}⊗I_{|P|}) [(I_{|J|}⊗B⊗I_{|P|}) [(I_{|J|}⊗I_{|N|}⊗C)v]]]
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418 ```
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419 """
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420 function LazyOuterProduct end
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421
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422 function LazyOuterProduct(tm1::TensorMapping{T}, tm2::TensorMapping{T}) where T
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423 itm1 = InflatedTensorMapping(tm1, IdentityMapping{T}(range_size(tm2)))
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424 itm2 = InflatedTensorMapping(IdentityMapping{T}(domain_size(tm1)),tm2)
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425
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426 return itm1∘itm2
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427 end
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428
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429 LazyOuterProduct(t1::IdentityMapping{T}, t2::IdentityMapping{T}) where T = IdentityMapping{T}(t1.size...,t2.size...)
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430 LazyOuterProduct(t1::TensorMapping, t2::IdentityMapping) = InflatedTensorMapping(t1, t2)
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431 LazyOuterProduct(t1::IdentityMapping, t2::TensorMapping) = InflatedTensorMapping(t1, t2)
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432
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433 LazyOuterProduct(tms::Vararg{TensorMapping}) = foldl(LazyOuterProduct, tms)
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434
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435 ⊗(a::TensorMapping, b::TensorMapping) = LazyOuterProduct(a,b)
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436
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437
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438 function check_domain_size(tm::TensorMapping, sz)
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439 if domain_size(tm) != sz
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440 throw(SizeMismatch(tm,sz))
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441 end
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442 end
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443
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444 struct SizeMismatch <: Exception
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445 tm::TensorMapping
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446 sz
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447 end
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448
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449 function Base.showerror(io::IO, err::SizeMismatch)
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450 print(io, "SizeMismatch: ")
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451 print(io, "domain size $(domain_size(err.tm)) of TensorMapping not matching size $(err.sz)")
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452 end