annotate notebooks/display_examples_nb.jl @ 2076:832580b6d548 feature/sbp_operators/laplace_curvilinear tip

Add test for inverse_inner_product
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 18 Feb 2026 07:08:14 +0100
parents a8ea4f94f3c4
children
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1 ### A Pluto.jl notebook ###
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2 # v0.20.21
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3
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4 using Markdown
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5 using InteractiveUtils
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6
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7 # ╔═╡ 1f8a7cfa-94cc-41bf-a8c8-2dc5218741e0
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8 begin
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9 using Pkg
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10 Pkg.activate(".")
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11
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12 using Diffinitive
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13 using Diffinitive.Grids
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14 using Diffinitive.LazyTensors
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15 using Diffinitive.SbpOperators
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16 using PlutoUI
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17 using StaticArrays
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18 end
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19
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20 # ╔═╡ 885c60d7-d33c-4741-ae49-6a57510ec7b5
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21 md"""
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22 # Display tests
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23 """
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24
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25 # ╔═╡ 9ee3372a-e78d-4f74-84ce-e04208d1558d
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26 repl_show(v) = repr(MIME("text/plain"), v) |> println
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27
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28 # ╔═╡ 51c02ced-f684-417f-83f1-cade4edda43f
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29 md"""
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30 Common julia objects to compare with:
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31 """
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32
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33 # ╔═╡ 25c90528-22cd-41ca-8572-ccd946928318
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34 1 |> repl_show
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35
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36 # ╔═╡ e7f3e466-9833-428c-99ad-20bc9d88d951
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37 [1,1] |> repl_show
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38
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39 # ╔═╡ 2e74f9b5-5b4f-4887-8a30-4655d560a45c
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40 [1;; 2;;] |> repl_show
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41
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42 # ╔═╡ 365524b5-3182-4691-9817-1bbec1492c14
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43 [1; 2;;] |> repl_show
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44
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45 # ╔═╡ d5725e1b-bc4f-4a95-975d-179c193908c9
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46 [1; 2;; 3; 4;;] |> repl_show
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47
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48 # ╔═╡ b824ef8d-5026-4861-9a23-45a7939fd38c
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49 "hej" |> repl_show
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50
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51 # ╔═╡ fbe365a2-f95e-4297-8326-c18d22932869
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52 Dict("A" => 1, "B"=> 2) |> repl_show
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53
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54 # ╔═╡ 56670aff-0343-41cb-a653-35a61376dda4
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55 1//2 |> repl_show
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56
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57 # ╔═╡ b5a6491e-a93e-4058-8ceb-be1dc4d4c100
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58 BigInt(30) |> repl_show
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59
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60 # ╔═╡ 828d57a1-ee58-4204-8050-78127821a4c6
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61 1:10 |> repl_show
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62
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63 # ╔═╡ 127d34f6-69f7-4082-a74b-0be86942f153
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64 range(0,1,10) |> repl_show
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65
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66 # ╔═╡ c46a278e-a102-4544-82d8-7df816440410
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67 rand(2,2,2,2) |> repl_show
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68
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69 # ╔═╡ 5aa7079c-8005-47f1-bb82-c35f3aa54b42
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70 md"""
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71 ## Parameter spaces
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72 """
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73
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74 # ╔═╡ 08f493ed-189c-43f3-86f2-95fc475ec0e7
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75 Interval(1,2) |> repl_show
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76
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77 # ╔═╡ e2dc581f-0949-4be7-8e4b-74deeaffc68d
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78 md"""
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79 ## Stencil Set
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80 """
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81
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82 # ╔═╡ 272e564f-bd21-4ba2-8d6e-ae4714dc30bc
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83 read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=2) |> repl_show
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84
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85 # ╔═╡ f7244bf7-8266-469f-b07f-30c203d9af48
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86 md"""
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87 ## Grids
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88 """
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89
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90 # ╔═╡ 0e14bd28-5dd1-44c4-abf4-23b70546bd49
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91 equidistant_grid(0,1,11) |> repl_show
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92
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93 # ╔═╡ fcb74341-6b03-4ada-8f5d-bc245c23679b
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94 equidistant_grid((0,0),(1,1),10,20) |> repl_show
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95
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96 # ╔═╡ 8dec053b-eaae-463d-800b-b8d89d5d550b
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97 ZeroDimGrid(@SVector[1,2]) |> repl_show
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98
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99 # ╔═╡ c1172a36-c5d7-47dc-bc79-af0d43a8f6ee
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100 let
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101 x̄((ξ, η)) = @SVector[2ξ + η*(1-η), 3η+(1+η/2)*ξ^2]
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102 J((ξ, η)) = @SMatrix[
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103 2 1-2η;
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104 (2+η)*ξ 3+1/2*ξ^2;
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105 ]
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106
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107 mapped_grid(x̄, J, 10,10) |> repl_show
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108 end
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109
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110 # ╔═╡ 9c889176-865b-402d-81b5-71957d2878f7
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111 md"""
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112 ## LazyArrays
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113 """
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114
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115 # ╔═╡ 85e8e748-e575-4a29-80c7-22d110578343
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116 LazyTensors.LazyConstantArray(10, (5,)) |> repl_show
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117
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118 # ╔═╡ 804ad722-9081-4d1d-b0d2-c536a26fe20d
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119 LazyTensors.LazyFunctionArray((i,j)->10*i+j, (3,4)) |> repl_show
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120
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121 # ╔═╡ a70c689d-0851-497f-938a-e5c92ce59ddb
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122 md"""
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123 ## LazyTensors
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124 """
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125
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126 # ╔═╡ 68c7a1d8-729e-4f38-abf2-26deb7a90cb1
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127 md"""
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128 ### Basic tensors
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129 """
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130
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131 # ╔═╡ 2afde3fe-96ed-4d7e-a79b-fc880e0da268
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132 LazyTensors.IdentityTensor(5) |> repl_show
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133
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134 # ╔═╡ 5451a071-14ae-47ae-99c5-4d65508d280f
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135 LazyTensors.IdentityTensor(4,3) |> repl_show
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136
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137 # ╔═╡ b6b06fe9-de16-41ca-ad45-eef6dd038485
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138 LazyTensors.ScalingTensor(2., (4,3)) |> repl_show
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139
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140 # ╔═╡ d1c8c3a0-76ec-4c32-853e-0471d71e5cf0
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141 LazyTensors.DiagonalTensor([1,2,3,4]) |> repl_show
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142
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143 # ╔═╡ 6051c144-9982-4bd9-92f9-d0aaf3961872
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144 LazyTensors.DenseTensor(rand(2,2,2,2), (1,2), (3,4)) |> repl_show
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145
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146 # ╔═╡ 83ed7f7e-c88d-4ee4-a53a-1b91e775ff52
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147 md"""
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148 ### Simple SBP-operators
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149 """
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150
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151 # ╔═╡ 12a9f430-f96b-43f2-bf63-149b5a028fd7
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152 begin
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153 g1 = equidistant_grid(0,1,10)
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154 g2 = equidistant_grid((0,0),(1,1),10, 11)
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155 x̄((ξ, η)) = @SVector[2ξ + η*(1-η), 3η+(1+η/2)*ξ^2]
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156 J((ξ, η)) = @SMatrix[
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157 2 1-2η;
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158 (2+η)*ξ 3+1/2*ξ^2;
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159 ]
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160 mg = mapped_grid(x̄, J, 10,10)
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161 stencil_set2 = stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=2)
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162 stencil_set4 = stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=4)
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163 end;
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164
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165 # ╔═╡ e44f8d91-1cbf-44be-bef1-40e60c4a777f
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166 first_derivative(g1, stencil_set2) |> repl_show
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167
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168 # ╔═╡ c378b88a-1d74-44a2-bdc1-b371da478de8
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169 first_derivative(g1, stencil_set4) |> repl_show
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170
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171 # ╔═╡ 9614cda7-b48c-4925-89b5-113cf514f20f
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172 first_derivative(g2, stencil_set2, 1) |> repl_show
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173
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174 # ╔═╡ 725e9430-4821-4939-bfef-6c186d2dc500
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175 first_derivative(g2, stencil_set4, 2) |> repl_show
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176
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177 # ╔═╡ e8ca54a1-a6db-40a1-b44a-73e175894df4
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178 second_derivative(g1, stencil_set2) |> repl_show
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179
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180 # ╔═╡ 5d1f10fe-f620-469c-822c-55955a5541ad
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181 second_derivative(g1, stencil_set4) |> repl_show
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182
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183 # ╔═╡ fdc531d4-9d27-41dc-ba79-6febefde223a
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184 second_derivative(g2, stencil_set2, 1) |> repl_show
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185
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186 # ╔═╡ fff2e04a-357f-4254-996e-d5ccd9ff31f8
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187 second_derivative(g2, stencil_set4, 2) |> repl_show
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188
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189 # ╔═╡ 959b071e-1ef6-4f29-aa8b-d88bfef80c00
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190 second_derivative_variable(g1, map(x->2x, g1), stencil_set2) |> repl_show
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191
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192 # ╔═╡ 0a0f7e77-a789-4fb3-a4c2-7853b67788ec
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193 second_derivative_variable(g1, map(x->2x, g1), stencil_set4) |> repl_show
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194
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195 # ╔═╡ 177e0893-fbb1-4bb5-a108-e5990e943ab7
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196 second_derivative_variable(g2, map(x->x[1]+x[2], g2), stencil_set2, 1) |> repl_show
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197
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198 # ╔═╡ f1b6bd54-baf6-4360-aec0-bd8d52497894
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199 second_derivative_variable(g2, map(x->x[1]+x[2], g2), stencil_set4, 2) |> repl_show
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200
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201 # ╔═╡ a8f8343e-cd6f-451d-a2b3-e5f0f561f8af
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202 undivided_skewed04(g1,4)[1] |> repl_show
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203
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204 # ╔═╡ 50291998-7194-4a0d-9c19-eacc48b3f5da
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205 undivided_skewed04(g1,4)[2] |> repl_show
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206
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207 # ╔═╡ 1720af08-85e4-4502-b37e-9fa73008e221
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208 undivided_skewed04(g2,4,1)[1] |> repl_show
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209
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210 # ╔═╡ 4a72f217-2423-4bc1-8452-eb28dde36689
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211 undivided_skewed04(g2,4,2)[2] |> repl_show
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212
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213 # ╔═╡ d51b6bd7-0235-4a51-a989-4f7858363d02
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214 md"""
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215 ### Inner products
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216 """
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217
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218 # ╔═╡ 48a28ade-73bb-461d-ab96-82f92ed199c8
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219 inner_product(g1, stencil_set2) |> repl_show
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220
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221 # ╔═╡ 3c681a63-94a6-4677-aef7-df903c463896
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222 inner_product(g1, stencil_set4) |> repl_show
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223
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224 # ╔═╡ db735370-153a-40f9-b77f-9f60e30a35c4
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225 inner_product(g2, stencil_set2) |> repl_show
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226
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227 # ╔═╡ 613ebac7-50bc-424c-8fa2-064b64c93319
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228 inner_product(g2, stencil_set4) |> repl_show
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229
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230 # ╔═╡ 9e7d7667-960e-491f-8b83-e3b01a0db5b0
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231 inverse_inner_product(g2, stencil_set4) |> repl_show
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232
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233 # ╔═╡ 29488e48-1d42-4232-9d49-1ee77fb869d8
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234 md"""
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235 ### Boundary operators
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236 """
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237
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238 # ╔═╡ c3005e74-5b96-4b0c-9c57-b7d02968ed94
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239 boundary_restriction(g1, stencil_set, LowerBoundary()) |> repl_show
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240
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241 # ╔═╡ fd019973-0d54-4e31-b43b-f53a704cb01c
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242 boundary_restriction(g1, stencil_set, UpperBoundary()) |> repl_show
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243
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244 # ╔═╡ df2e8af0-9ca5-4972-8771-f8bea1591f85
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245 boundary_restriction(g2, stencil_set, CartesianBoundary{1,LowerBoundary}()) |> repl_show
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246
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247 # ╔═╡ 8e538109-16a1-4af7-a986-9dc1455b7de7
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248 boundary_restriction(g2, stencil_set, CartesianBoundary{2,UpperBoundary}()) |> repl_show
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249
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250 # ╔═╡ 5f3744a4-72d8-4448-820f-a928bfaaf825
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251 normal_derivative(g1, stencil_set, LowerBoundary()) |> repl_show
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252
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253 # ╔═╡ 4529b5c4-4905-4fd3-9aaa-5f88faa841c8
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254 normal_derivative(g1, stencil_set, UpperBoundary()) |> repl_show
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255
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256 # ╔═╡ c3bb0450-a7d5-44c1-9ca9-9e1ecf2db9f8
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257 normal_derivative(g2, stencil_set, CartesianBoundary{1,LowerBoundary}()) |> repl_show
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258
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259 # ╔═╡ da63e57a-0794-4cd8-9941-ada0e5c1c40e
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260 normal_derivative(g2, stencil_set, CartesianBoundary{2,UpperBoundary}()) |> repl_show
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261
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262 # ╔═╡ 0b951425-979c-4ac9-8581-f690b729bab4
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263 md"""
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264 ## Tensor operations
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265 """
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266
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267 # ╔═╡ a39bb6e2-f1fe-4206-8ee3-88ff0c075233
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268 begin
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269 Dx = first_derivative(g2, stencil_set2, 1)
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270 Dy = first_derivative(g2, stencil_set4, 2)
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271
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272 v = map(x->sin(x[1]^2+x[2]^2), g2)
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273 end;
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274
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275 # ╔═╡ 8cd052d9-f40e-4796-aeef-52c02b3bf156
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276 Dx+Dy |> repl_show
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277
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278 # ╔═╡ 1b1b7d12-50ef-4c4e-9376-a353a56540c3
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279 Dx∘Dy |> repl_show
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280
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281 # ╔═╡ 57e48b4c-eef6-433e-98a1-1006e844b368
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282 Dx*v |> repl_show
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283
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284 # ╔═╡ e2bf2649-4770-4f52-9752-b61ce03c6f82
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285 (Dx+Dy)*v |> repl_show
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286
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287 # ╔═╡ d163d363-853d-4d83-a2d3-f8dd6e8f552d
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288 (Dx∘Dy)*v |> repl_show
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289
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290 # ╔═╡ 1c38d3f9-1839-468c-a368-4ef101bd4f18
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291 laplace(g2, stencil_set2) |> repl_show
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292
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293 # ╔═╡ cf84cefb-2dbd-4b8d-880b-47cc350a7c43
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294 laplace(g2, stencil_set4) |> repl_show
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295
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296 # ╔═╡ 67c73667-1f41-47b5-b59a-459787767f29
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297 # laplace(mg, stencil_set2) |> repl_show
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298
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299 # ╔═╡ 4634c1a6-0520-4b0f-8d32-a1fdf2ebaea5
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300 md"""
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301 ## Appendix
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302 """
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303
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304 # ╔═╡ 24788161-b29a-450a-bd35-f9c29e7ded9a
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305 PlutoUI.TableOfContents()
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306
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307 # ╔═╡ Cell order:
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308 # ╟─885c60d7-d33c-4741-ae49-6a57510ec7b5
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309 # ╠═9ee3372a-e78d-4f74-84ce-e04208d1558d
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310 # ╟─51c02ced-f684-417f-83f1-cade4edda43f
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311 # ╠═25c90528-22cd-41ca-8572-ccd946928318
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312 # ╠═e7f3e466-9833-428c-99ad-20bc9d88d951
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313 # ╠═2e74f9b5-5b4f-4887-8a30-4655d560a45c
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314 # ╠═365524b5-3182-4691-9817-1bbec1492c14
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315 # ╠═d5725e1b-bc4f-4a95-975d-179c193908c9
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316 # ╠═b824ef8d-5026-4861-9a23-45a7939fd38c
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317 # ╠═fbe365a2-f95e-4297-8326-c18d22932869
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318 # ╠═56670aff-0343-41cb-a653-35a61376dda4
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319 # ╠═b5a6491e-a93e-4058-8ceb-be1dc4d4c100
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320 # ╠═828d57a1-ee58-4204-8050-78127821a4c6
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321 # ╠═127d34f6-69f7-4082-a74b-0be86942f153
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322 # ╠═c46a278e-a102-4544-82d8-7df816440410
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323 # ╟─5aa7079c-8005-47f1-bb82-c35f3aa54b42
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324 # ╠═08f493ed-189c-43f3-86f2-95fc475ec0e7
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325 # ╟─e2dc581f-0949-4be7-8e4b-74deeaffc68d
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326 # ╠═272e564f-bd21-4ba2-8d6e-ae4714dc30bc
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327 # ╟─f7244bf7-8266-469f-b07f-30c203d9af48
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328 # ╠═0e14bd28-5dd1-44c4-abf4-23b70546bd49
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329 # ╠═fcb74341-6b03-4ada-8f5d-bc245c23679b
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330 # ╠═8dec053b-eaae-463d-800b-b8d89d5d550b
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331 # ╠═c1172a36-c5d7-47dc-bc79-af0d43a8f6ee
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332 # ╟─9c889176-865b-402d-81b5-71957d2878f7
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333 # ╠═85e8e748-e575-4a29-80c7-22d110578343
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334 # ╠═804ad722-9081-4d1d-b0d2-c536a26fe20d
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335 # ╟─a70c689d-0851-497f-938a-e5c92ce59ddb
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336 # ╟─68c7a1d8-729e-4f38-abf2-26deb7a90cb1
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337 # ╠═2afde3fe-96ed-4d7e-a79b-fc880e0da268
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338 # ╠═5451a071-14ae-47ae-99c5-4d65508d280f
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339 # ╠═b6b06fe9-de16-41ca-ad45-eef6dd038485
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340 # ╠═d1c8c3a0-76ec-4c32-853e-0471d71e5cf0
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341 # ╠═6051c144-9982-4bd9-92f9-d0aaf3961872
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342 # ╟─83ed7f7e-c88d-4ee4-a53a-1b91e775ff52
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343 # ╠═12a9f430-f96b-43f2-bf63-149b5a028fd7
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344 # ╠═e44f8d91-1cbf-44be-bef1-40e60c4a777f
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345 # ╠═c378b88a-1d74-44a2-bdc1-b371da478de8
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346 # ╠═9614cda7-b48c-4925-89b5-113cf514f20f
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347 # ╠═725e9430-4821-4939-bfef-6c186d2dc500
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348 # ╠═e8ca54a1-a6db-40a1-b44a-73e175894df4
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349 # ╠═5d1f10fe-f620-469c-822c-55955a5541ad
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350 # ╠═fdc531d4-9d27-41dc-ba79-6febefde223a
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351 # ╠═fff2e04a-357f-4254-996e-d5ccd9ff31f8
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352 # ╠═959b071e-1ef6-4f29-aa8b-d88bfef80c00
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353 # ╠═0a0f7e77-a789-4fb3-a4c2-7853b67788ec
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354 # ╠═177e0893-fbb1-4bb5-a108-e5990e943ab7
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355 # ╠═f1b6bd54-baf6-4360-aec0-bd8d52497894
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356 # ╠═a8f8343e-cd6f-451d-a2b3-e5f0f561f8af
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357 # ╠═50291998-7194-4a0d-9c19-eacc48b3f5da
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358 # ╠═1720af08-85e4-4502-b37e-9fa73008e221
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359 # ╠═4a72f217-2423-4bc1-8452-eb28dde36689
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360 # ╟─d51b6bd7-0235-4a51-a989-4f7858363d02
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361 # ╠═48a28ade-73bb-461d-ab96-82f92ed199c8
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362 # ╠═3c681a63-94a6-4677-aef7-df903c463896
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363 # ╠═db735370-153a-40f9-b77f-9f60e30a35c4
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364 # ╠═613ebac7-50bc-424c-8fa2-064b64c93319
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365 # ╠═9e7d7667-960e-491f-8b83-e3b01a0db5b0
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