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annotate DiffOps/src/DiffOps.jl @ 217:4c62d0253bd4 package_refactor

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Add RegionIndices as dependency of Grids
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 26 Jun 2019 12:55:01 +0200
parents 3a93d8a799ce
children 235f0a771c8f
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3a93d8a799ce Add missing module in DiffOps
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1 module DiffOps
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2
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3 using RegionIndices
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4
2
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5 abstract type DiffOp end
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6
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7 # TBD: The "error("not implemented")" thing seems to be hiding good error information. How to fix that? Different way of saying that these should be implemented?
56
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8 function apply(D::DiffOp, v::AbstractVector, i::Int)
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9 error("not implemented")
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10 end
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11
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12 function innerProduct(D::DiffOp, u::AbstractVector, v::AbstractVector)::Real
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13 error("not implemented")
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14 end
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15
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16 function matrixRepresentation(D::DiffOp)
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17 error("not implemented")
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18 end
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19
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20 abstract type DiffOpCartesian{Dim} <: DiffOp end
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21
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22 # DiffOp must have a grid of dimension Dim!!!
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23 function apply!(D::DiffOpCartesian{Dim}, u::AbstractArray{T,Dim}, v::AbstractArray{T,Dim}) where {T,Dim}
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24 for I ∈ eachindex(D.grid)
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25 u[I] = apply(D, v, I)
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26 end
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27
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28 return nothing
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29 end
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30
112
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31 function apply_region!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}) where T
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32 apply_region!(D, u, v, Lower, Lower)
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33 apply_region!(D, u, v, Lower, Interior)
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34 apply_region!(D, u, v, Lower, Upper)
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35 apply_region!(D, u, v, Interior, Lower)
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36 apply_region!(D, u, v, Interior, Interior)
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37 apply_region!(D, u, v, Interior, Upper)
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38 apply_region!(D, u, v, Upper, Lower)
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39 apply_region!(D, u, v, Upper, Interior)
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40 apply_region!(D, u, v, Upper, Upper)
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41 return nothing
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42 end
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43
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44 # Maybe this should be split according to b3fbef345810 after all?! Seems like it makes performance more predictable
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45 function apply_region!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}, r1::Type{<:Region}, r2::Type{<:Region}) where T
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46 for I ∈ regionindices(D.grid.size, closureSize(D.op), (r1,r2))
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47 @inbounds indextuple = (Index{r1}(I[1]), Index{r2}(I[2]))
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48 @inbounds u[I] = apply(D, v, indextuple)
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49 end
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50 return nothing
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51 end
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52
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53 function apply_tiled!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}) where T
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54 apply_region_tiled!(D, u, v, Lower, Lower)
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55 apply_region_tiled!(D, u, v, Lower, Interior)
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56 apply_region_tiled!(D, u, v, Lower, Upper)
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57 apply_region_tiled!(D, u, v, Interior, Lower)
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58 apply_region_tiled!(D, u, v, Interior, Interior)
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59 apply_region_tiled!(D, u, v, Interior, Upper)
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60 apply_region_tiled!(D, u, v, Upper, Lower)
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61 apply_region_tiled!(D, u, v, Upper, Interior)
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62 apply_region_tiled!(D, u, v, Upper, Upper)
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63 return nothing
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64 end
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65
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66 using TiledIteration
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67 function apply_region_tiled!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}, r1::Type{<:Region}, r2::Type{<:Region}) where T
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68 ri = regionindices(D.grid.size, closureSize(D.op), (r1,r2))
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69 # TODO: Pass Tilesize to function
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70 for tileaxs ∈ TileIterator(axes(ri), padded_tilesize(T, (5,5), 2))
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71 for j ∈ tileaxs[2], i ∈ tileaxs[1]
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72 I = ri[i,j]
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73 u[I] = apply(D, v, (Index{r1}(I[1]), Index{r2}(I[2])))
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74 end
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75 end
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76 return nothing
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77 end
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78
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79 function apply(D::DiffOp, v::AbstractVector)::AbstractVector
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80 u = zeros(eltype(v), size(v))
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81 apply!(D,v,u)
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82 return u
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83 end
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84
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85 struct NormalDerivative{N,M,K}
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86 op::D2{Float64,N,M,K}
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87 grid::EquidistantGrid
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88 bId::CartesianBoundary
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89 end
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90
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91 function apply_transpose(d::NormalDerivative, v::AbstractArray, I::Integer)
172
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92 u = selectdim(v,3-dim(d.bId),I)
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93 return apply_d(d.op, d.grid.inverse_spacing[dim(d.bId)], u, region(d.bId))
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94 end
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95
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96 # Not correct abstraction level
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97 # TODO: Not type stable D:<
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98 function apply(d::NormalDerivative, v::AbstractArray, I::Tuple{Integer,Integer})
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99 i = I[dim(d.bId)]
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100 j = I[3-dim(d.bId)]
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101 N_i = d.grid.size[dim(d.bId)]
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102
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103 r = getregion(i, closureSize(d.op), N_i)
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104
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105 if r != region(d.bId)
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106 return 0
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107 end
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108
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109 if r == Lower
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110 # Note, closures are indexed by offset. Fix this D:<
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111 return d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[i-1]*v[j]
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112 elseif r == Upper
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113 return d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[N_i-j]*v[j]
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114 end
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115 end
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116
173
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117 struct BoundaryValue{N,M,K}
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118 op::D2{Float64,N,M,K}
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119 grid::EquidistantGrid
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120 bId::CartesianBoundary
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121 end
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122
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123 function apply(e::BoundaryValue, v::AbstractArray, I::Tuple{Integer,Integer})
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124 i = I[dim(e.bId)]
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125 j = I[3-dim(e.bId)]
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126 N_i = e.grid.size[dim(e.bId)]
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127
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128 r = getregion(i, closureSize(e.op), N_i)
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129
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130 if r != region(e.bId)
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131 return 0
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132 end
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133
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134 if r == Lower
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135 # Note, closures are indexed by offset. Fix this D:<
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136 return e.op.eClosure[i-1]*v[j]
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137 elseif r == Upper
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138 return e.op.eClosure[N_i-j]*v[j]
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139 end
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140 end
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141
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142 function apply_transpose(e::BoundaryValue, v::AbstractArray, I::Integer)
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143 u = selectdim(v,3-dim(e.bId),I)
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144 return apply_e(e.op, u, region(e.bId))
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145 end
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146
95
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147 struct Laplace{Dim,T<:Real,N,M,K} <: DiffOpCartesian{Dim}
168
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148 grid::EquidistantGrid{Dim,T}
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149 a::T
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150 op::D2{Float64,N,M,K}
173
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151 e::BoundaryValue
154
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152 d::NormalDerivative
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153 end
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154
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155 function apply(L::Laplace{Dim}, v::AbstractArray{T,Dim} where T, I::CartesianIndex{Dim}) where Dim
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156 error("not implemented")
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157 end
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158
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159 # u = L*v
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160 function apply(L::Laplace{1}, v::AbstractVector, i::Int)
124
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161 uᵢ = L.a * apply(L.op, L.grid.spacing[1], v, i)
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162 return uᵢ
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163 end
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164
129
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165 @inline function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, I::Tuple{Index{R1}, Index{R2}}) where {R1, R2}
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166 # 2nd x-derivative
118
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167 @inbounds vx = view(v, :, Int(I[2]))
129
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168 @inbounds uᵢ = L.a*apply(L.op, L.grid.inverse_spacing[1], vx , I[1])
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169 # 2nd y-derivative
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170 @inbounds vy = view(v, Int(I[1]), :)
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171 @inbounds uᵢ += L.a*apply(L.op, L.grid.inverse_spacing[2], vy, I[2])
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172 return uᵢ
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173 end
99
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174
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175 # Slow but maybe convenient?
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176 function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, i::CartesianIndex{2})
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177 I = Index{Unknown}.(Tuple(i))
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178 apply(L, v, I)
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179 end
135
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180
154
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181 struct BoundaryOperator
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182
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183 end
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184
168
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185
135
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186 """
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187 A BoundaryCondition should implement the method
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188 sat(::DiffOp, v::AbstractArray, data::AbstractArray, ...)
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189 """
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190 abstract type BoundaryCondition end
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191
174
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192 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
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193
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194 function sat(L::Laplace{2,T}, bc::Neumann{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, I::CartesianIndex{2}) where {T,Bid}
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195 e = BoundaryValue(L.op, L.grid, Bid())
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196 d = NormalDerivative(L.op, L.grid, Bid())
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197 Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid())
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198 # TODO: Implement BoundaryQuadrature method
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199
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200 return -L.Hi*e*Hᵧ*(d'*v - g)
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201 # Need to handle d'*v - g so that it is an AbstractArray that TensorMappings can act on
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202 end
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203
145
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204 struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
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205 tau::Float64
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206 end
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207
174
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208 function sat(L::Laplace{2,T}, bc::Dirichlet{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, i::CartesianIndex{2}) where {T,Bid}
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209 e = BoundaryValue(L.op, L.grid, Bid())
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210 d = NormalDerivative(L.op, L.grid, Bid())
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211 Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid())
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212 # TODO: Implement BoundaryQuadrature method
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213
174
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214 return -L.Hi*(tau/h*e + d)*Hᵧ*(e'*v - g)
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215 # Need to handle scalar multiplication and addition of TensorMapping
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216 end
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217
168
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218 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
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219 # return apply(s.L, v, i) +
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220 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
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221 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
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222 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
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223 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
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224 # end
215
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225
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226 end # module