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Add a bunch of stuff to TODO.md and Notes.md
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 02 Dec 2020 09:35:14 +0100
parents 1c41f4fd3e61
children d26231227b89
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1 # Notes
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2
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3 ## Known size of range and domain?
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4 Is there any reason to use a trait to differentiate between fixed size and unknown size?
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5
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6 When do we need to know the size of the range and domain?
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7 * When indexing to provide boundschecking?
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8 * When doing specialised computations for different parts of the range/domain?
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9 * More?
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10
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11 Maybe if we should have dynamic sizing it could be only for the range. `domain_size` would not be implemented. And the `range_size` would be a function of a vector that the TensorMapping is applied to.
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13 ## Reasearch and thinking
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14 - [ ] Use a trait to indicate that a TensorMapping har the same range and domain?
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15 - [ ] Rename all the Tensor stuff to just LazyOperator, LazyApplication and so on?
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16 - [ ] Check how the native julia doc generator works
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17 - [ ] Check if Vidars design docs fit in there
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18 - [ ] Create a macro @lazy which replaces a binary op (+,-) by its lazy equivalent? Would be a neat way to indicate which evaluations are lazy without cluttering/confusing with special characters.
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19 - [ ] Specificera operatorer i TOML eller något liknande?
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20 H.. H_gamma etc.)
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21 - [ ] Dispatch on Lower() instead of the type Lower so `::Lower` instead of `::Type{Lower}` ???
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22 Seems better unless there is some specific reason to use the type instead of the value.
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23 - [ ] How do we handle mixes of periodic and non-periodic grids? Seems it should be supported on the grid level and on the 1d operator level. Between there it should be transparent.
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24 - [ ] Can we have a trait to tell if a TensorMapping is transposable?
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25 - [ ] Is it ok to have "Constructors" for abstract types which create subtypes? For example a Grids() functions that gives different kind of grids based on input?
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26
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27 ## Regions and tensormappings
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28 - [ ] Use a trait to indicate if a TensorMapping uses indices with regions.
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29 The default should be that they do NOT.
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30 - [ ] What to name this trait? Can we call it IndexStyle but not export it to avoid conflicts with Base.IndexStyle?
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31 - [ ] Figure out repeated application of regioned TensorMappings. Maybe an instance of a tensor mapping needs to know the exact size of the range and domain for this to work?
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32
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33 ## Boundschecking and dimension checking
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34 Does it make sense to have boundschecking only in getindex methods?
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35 This would mean no bounds checking in applys, however any indexing that they do would be boundschecked. The only loss would be readability of errors. But users aren't really supposed to call apply directly anyway.
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36
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37 Preferably dimensions and sizes should be checked when lazy objects are created, for example TensorApplication, TensorComposition and so on. If dimension checks decreases performance we can make them skippable later.
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38
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39 ## Vector valued grid functions
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40 Från slack konversation:
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41
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42 Jonatan Werpers:
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43 Med vektorvärda gridfunktioner vill vi ju fortfarande att grid funktionen ska vara till exempel AbstractArray{LitenVektor,2}
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44 Och att man ska kunna göra allt man vill med LitenVektor
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45 typ addera, jämföra osv
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46 Och då borde points returnera AbstractArray{LitenVektor{Float,2},2} för ett 2d nät
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47 Men det kanske bara ska vara Static arrays?
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48
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49 Vidar Stiernström:
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50 Ja, jag vet inte riktigt vad som är en rimlig representation
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51 Du menar en vektor av static arrays då?
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52
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53 Jonatan Werpers:
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54 Ja, att LitenVektor är en StaticArray
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55
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56 Vidar Stiernström:
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57 Tuplar känns typ rätt inuitivt för att representera värdet i en punkt
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58 men
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59 det suger att man inte har + och - för dem
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60
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61 Jonatan Werpers:
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62 Ja precis
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63
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64 Vidar Stiernström:
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65 så kanske är bra med static arrays i detta fall
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66
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67 Jonatan Werpers:
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68 Man vill ju kunna köra en Operator rakt på och vara klar eller?
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69
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70 Vidar Stiernström:
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71 Har inte alls tänkt på hur det vi gör funkar mot vektorvärda funktioner
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72 men känns som staticarrays är hur man vill göra det
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73 tuplar är ju immutable också
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74 blir jobbigt om man bara agerar på en komponent då
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75
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76 Jonatan Werpers:
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77 Hm…
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78 Tål att tänkas på
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79 Men det lär ju bli mer indirektion med mutables eller?
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80 Hur fungerar det?
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81 Det finns ju hur som helst både SVector och MVector i StaticArrays
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82
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83 Vidar Stiernström:
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84 När vi jobbat i c/c++ och kollat runt lite hur man brukar göra så lagrar man i princip alla sina obekanta i en lång vektor och så får man specificera i funktioerna vilken komponent man agerar på och till vilken man skriver
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85 så man lagrar grejer enl: w = [u1, v1, u2, v2, …] i 1D.
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86 Men alltså har ingen aning hur julia hanterar detta
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87
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88 Jonatan Werpers:
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89 Det vi är ute efter kanske är att en grid funcktion är en AbstractArray{T,2} where T<:NågotSomViKanRäknaMed
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90 Och så får den typen var lite vad som helst.
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91
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92 Vidar Stiernström:
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93 Tror det kan vara farligt att ha nåt som är AbstractArray{LitenArray{NDof},Dim}
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94 Jag gissar att det kompilatorn vill ha är en stor array med doubles
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95
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96 Jonatan Werpers:
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97 Och sen är det upp till den som använder grejerna att vara smart
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98 Vill man vara trixig kan man väl då imlementera SuperHaxxorGridFunction <: AbstractArray{Array{…},2} som lagrar allt linjärt eller något sånt
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99 Det kommer väl lösa sig när man börjar implementera vektorvärda saker
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100 Euler nästa!
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101 New
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102 Vidar Stiernström:
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103 Det vore skönt att inte behöva skriva såhär varje gång man testar mot en tupel :smile: @test [gp[i]...] ≈ [p[i]...] atol=5e-13
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104
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105 Jonatan Werpers:
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106 https://github.com/JuliaArrays/ArraysOfArrays.jl
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107 https://github.com/jw3126/Setfield.jl
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108
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109 ### Test-applikationer
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110 div och grad operationer
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111
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112 Enligt Wikipedia verkar det som att `∇⋅` agerar på första dimensionen av ett tensor fält och `div()` på sista.
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113 Om man generaliserar kanske `∇` i så fall bara lägger till en dimension i början.
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114
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115 Kan vi implementera `⋅`(\cdot) så att de fungerar som man vill för både tensor-fält och tensor-operatorer?
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116
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117 Är `∇` ett tensor-fält av tensor-operatorer? Vad är ett tensor-fält i vår kod? Är det en special-fall av en tensor-mapping?
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118
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119 ### Grid-funktionen
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120 Grid-funktionon har typen `AbstractArray{T,2} where T`.
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121 `T` kan vara lite vad som helst, tillexemel en SVector eller Array, eller tuple. TensorOperatorerna bryr sig inte om exakt vad det är, mer än att typen måste stödja de operationer som operatorn använder.
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122
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123 En nackdel kan vara hur man ska få ut gridfunktionen för tex andra komponenten.
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124
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125 Syntax:
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126 ```
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127 f(x̄) = x̄
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128 gf = evalOn(g, f)
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129 gf[2,3] # x̄ för en viss gridpunkt
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130 gf[2,3][2] # x̄[2] för en viss gridpunkt
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131 ```
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132
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133 Note: Behöver bestämma om eval on skickar in `x̄` eller `x̄...` till `f`. Eller om man kan stödja båda.
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134
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135 ### Tensor operatorer
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136 Vi kan ha tensor-operatorer som agerar på ett skalärt fält och ger ett vektorfält eller tensorfält.
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137 Vi kan också ha tensor-operatorer som agerar på ett vektorfält eller tensorfält och ger ett skalärt fält.
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138
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139 TBD: Just nu gör `apply_transpose` antagandet att domän-typen är samma som range-typen. Det behöver vi på något sätt bryta. Ett alternativ är låta en TensorMapping ha `T_domain` och `T_range` istället för bara `T`. Känns dock lite grötigt. Ett annat alternativ skulle vara någon typ av trait för transpose? Den skulle kunna innehålla typen som transponatet agerar på? Vet inte om det fungerar dock.
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140
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141 TBD: Vad är målet med `T`-parametern för en TensorMapping? Om vi vill kunna applicera en difference operator på vad som helst kan man inte anta att en `TensorMapping{T}` bara agerar på instanser av `T`.
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142
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143 Man kan implementera `∇` som en tensormapping som agerar på T och returnerar `StaticVector{N,T} where N`.
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144 (Man skulle eventuellt också kunna låta den agera på `StaticMatrix{N,T,D} where N` och returnera `StaticMatrix{M,T,D+1}`. Frågan är om man vinner något på det...)
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145
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146 Skulle kunna ha en funktion `range_type(::TensorMapping, ::Type{domain_type})`
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147
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148 Kanske kan man implementera `⋅(tm::TensorMapping{R,D}, v::AbstractArray{T,D})` där T är en AbstractArray, tm på något sätt har komponenter, lika många som T har element.
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149
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150 ### Ratade alternativ:
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151
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152
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153 #### 2.AbstractArray{T,2+1} where T (NOPE!)
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154 Blir inte den här. Bryter mot alla tankar om hur grid funktioner ska fungera. Om de tillåts ha en annan dimension än nätet blir allt hemskt.
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155
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156 Man låter helt enkelt arrayen ha en extra dimension. En fördel är att man har en väldigt "native" typ. En nackdel kan vara att det eventuellt blir rörigt vilken dimension olika operatorer ska agera på. I värsta fall behöver vi "kroneckra in" de tillagda dimensionerna. Vektorfältets index kommer också att bli det första eftersom vi vill att de ska lagras kontinuerligt i minnet pga chachen. (Går kanske att lösa med en custom typ men då krånglar man till det för sig). En fördel skulle vara att man enkelt får ut olika komponenter.
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157
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158 Syntax:
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159 ```
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160 gf = eval_on_grid(g,f)
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161 gf[:,2,3] # Hela vektorn för en gridpunkt
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162 gf[2,2,3] # Andra komponenten av vektor fältet i en punkt.
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163 gf[2,:,:] #
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164 ```
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165
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166 ### Evaluering av funktioner på nät
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167 Hur ska man skriva funktioner som evalueras på nätet? `f(x,y) = ...` eller `f(x̄) = ...`? Eller båda? Kan eval_on_grid se skillnad eller får användaren specificera?
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168
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169 ```
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170 f(x,y) = [x^2, y^2]
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171 f(x̄) = [x̄[1]^2, x̄[2]^2]
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172 ```
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173
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174 Påverkas detta av hur vi förväntar oss kunna skapa lata gridfunktioner?
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175
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176 ### Komponenter som gridfunktioner
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177 En viktig operation för vektor fält är att kunna få ut komponenter som grid-funktioner. Detta behöver antagligen kunna ske lazy.
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178 Det finns ett par olika lösningar:
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179 * Implementera en egen typ av view som tar hand om detta. Eller Accessors.jl?
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180 * Använda en TensorMapping
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181 * Någon typ av lazy-broadcast
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182 * En lazy array som applicerar en funktion för varje element.
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183
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184 Skulle vara en fördel om det är hyffsat generiskt så att en eventuell användare kan utöka det enkelt om de har någon egen exotisk typ. Eller ska man vila helt på
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185
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186 Syntax:
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187 ```
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188 gf = eval(...)
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189 component(gf,2) # Andra komponenten av en vektor
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190 component(gf,2,3) # (2,3) elementet av en matris
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191 component(gf,:,2) # Andra kolumnen av en matris
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192 @ourview gf[:,:][2]
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193 ```