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comparison DiffOps/src/DiffOps.jl @ 211:1ad91e11b1f4 package_refactor

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Move DiffOps and Grids into packages
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 26 Jun 2019 10:44:20 +0200
parents diffOp.jl@bcd2029c590d
children 3a93d8a799ce
comparison
equal deleted inserted replaced
210:2aa33d0eef90 211:1ad91e11b1f4
1 abstract type DiffOp end
2
3 # 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?
4 function apply(D::DiffOp, v::AbstractVector, i::Int)
5 error("not implemented")
6 end
7
8 function innerProduct(D::DiffOp, u::AbstractVector, v::AbstractVector)::Real
9 error("not implemented")
10 end
11
12 function matrixRepresentation(D::DiffOp)
13 error("not implemented")
14 end
15
16 abstract type DiffOpCartesian{Dim} <: DiffOp end
17
18 # DiffOp must have a grid of dimension Dim!!!
19 function apply!(D::DiffOpCartesian{Dim}, u::AbstractArray{T,Dim}, v::AbstractArray{T,Dim}) where {T,Dim}
20 for I ∈ eachindex(D.grid)
21 u[I] = apply(D, v, I)
22 end
23
24 return nothing
25 end
26
27 function apply_region!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}) where T
28 apply_region!(D, u, v, Lower, Lower)
29 apply_region!(D, u, v, Lower, Interior)
30 apply_region!(D, u, v, Lower, Upper)
31 apply_region!(D, u, v, Interior, Lower)
32 apply_region!(D, u, v, Interior, Interior)
33 apply_region!(D, u, v, Interior, Upper)
34 apply_region!(D, u, v, Upper, Lower)
35 apply_region!(D, u, v, Upper, Interior)
36 apply_region!(D, u, v, Upper, Upper)
37 return nothing
38 end
39
40 # Maybe this should be split according to b3fbef345810 after all?! Seems like it makes performance more predictable
41 function apply_region!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}, r1::Type{<:Region}, r2::Type{<:Region}) where T
42 for I ∈ regionindices(D.grid.size, closureSize(D.op), (r1,r2))
43 @inbounds indextuple = (Index{r1}(I[1]), Index{r2}(I[2]))
44 @inbounds u[I] = apply(D, v, indextuple)
45 end
46 return nothing
47 end
48
49 function apply_tiled!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}) where T
50 apply_region_tiled!(D, u, v, Lower, Lower)
51 apply_region_tiled!(D, u, v, Lower, Interior)
52 apply_region_tiled!(D, u, v, Lower, Upper)
53 apply_region_tiled!(D, u, v, Interior, Lower)
54 apply_region_tiled!(D, u, v, Interior, Interior)
55 apply_region_tiled!(D, u, v, Interior, Upper)
56 apply_region_tiled!(D, u, v, Upper, Lower)
57 apply_region_tiled!(D, u, v, Upper, Interior)
58 apply_region_tiled!(D, u, v, Upper, Upper)
59 return nothing
60 end
61
62 using TiledIteration
63 function apply_region_tiled!(D::DiffOpCartesian{2}, u::AbstractArray{T,2}, v::AbstractArray{T,2}, r1::Type{<:Region}, r2::Type{<:Region}) where T
64 ri = regionindices(D.grid.size, closureSize(D.op), (r1,r2))
65 # TODO: Pass Tilesize to function
66 for tileaxs ∈ TileIterator(axes(ri), padded_tilesize(T, (5,5), 2))
67 for j ∈ tileaxs[2], i ∈ tileaxs[1]
68 I = ri[i,j]
69 u[I] = apply(D, v, (Index{r1}(I[1]), Index{r2}(I[2])))
70 end
71 end
72 return nothing
73 end
74
75 function apply(D::DiffOp, v::AbstractVector)::AbstractVector
76 u = zeros(eltype(v), size(v))
77 apply!(D,v,u)
78 return u
79 end
80
81 struct NormalDerivative{N,M,K}
82 op::D2{Float64,N,M,K}
83 grid::EquidistantGrid
84 bId::CartesianBoundary
85 end
86
87 function apply_transpose(d::NormalDerivative, v::AbstractArray, I::Integer)
88 u = selectdim(v,3-dim(d.bId),I)
89 return apply_d(d.op, d.grid.inverse_spacing[dim(d.bId)], u, region(d.bId))
90 end
91
92 # Not correct abstraction level
93 # TODO: Not type stable D:<
94 function apply(d::NormalDerivative, v::AbstractArray, I::Tuple{Integer,Integer})
95 i = I[dim(d.bId)]
96 j = I[3-dim(d.bId)]
97 N_i = d.grid.size[dim(d.bId)]
98
99 r = getregion(i, closureSize(d.op), N_i)
100
101 if r != region(d.bId)
102 return 0
103 end
104
105 if r == Lower
106 # Note, closures are indexed by offset. Fix this D:<
107 return d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[i-1]*v[j]
108 elseif r == Upper
109 return d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[N_i-j]*v[j]
110 end
111 end
112
113 struct BoundaryValue{N,M,K}
114 op::D2{Float64,N,M,K}
115 grid::EquidistantGrid
116 bId::CartesianBoundary
117 end
118
119 function apply(e::BoundaryValue, v::AbstractArray, I::Tuple{Integer,Integer})
120 i = I[dim(e.bId)]
121 j = I[3-dim(e.bId)]
122 N_i = e.grid.size[dim(e.bId)]
123
124 r = getregion(i, closureSize(e.op), N_i)
125
126 if r != region(e.bId)
127 return 0
128 end
129
130 if r == Lower
131 # Note, closures are indexed by offset. Fix this D:<
132 return e.op.eClosure[i-1]*v[j]
133 elseif r == Upper
134 return e.op.eClosure[N_i-j]*v[j]
135 end
136 end
137
138 function apply_transpose(e::BoundaryValue, v::AbstractArray, I::Integer)
139 u = selectdim(v,3-dim(e.bId),I)
140 return apply_e(e.op, u, region(e.bId))
141 end
142
143 struct Laplace{Dim,T<:Real,N,M,K} <: DiffOpCartesian{Dim}
144 grid::EquidistantGrid{Dim,T}
145 a::T
146 op::D2{Float64,N,M,K}
147 e::BoundaryValue
148 d::NormalDerivative
149 end
150
151 function apply(L::Laplace{Dim}, v::AbstractArray{T,Dim} where T, I::CartesianIndex{Dim}) where Dim
152 error("not implemented")
153 end
154
155 # u = L*v
156 function apply(L::Laplace{1}, v::AbstractVector, i::Int)
157 uᵢ = L.a * apply(L.op, L.grid.spacing[1], v, i)
158 return uᵢ
159 end
160
161 @inline function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, I::Tuple{Index{R1}, Index{R2}}) where {R1, R2}
162 # 2nd x-derivative
163 @inbounds vx = view(v, :, Int(I[2]))
164 @inbounds uᵢ = L.a*apply(L.op, L.grid.inverse_spacing[1], vx , I[1])
165 # 2nd y-derivative
166 @inbounds vy = view(v, Int(I[1]), :)
167 @inbounds uᵢ += L.a*apply(L.op, L.grid.inverse_spacing[2], vy, I[2])
168 return uᵢ
169 end
170
171 # Slow but maybe convenient?
172 function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, i::CartesianIndex{2})
173 I = Index{Unknown}.(Tuple(i))
174 apply(L, v, I)
175 end
176
177 struct BoundaryOperator
178
179 end
180
181
182 """
183 A BoundaryCondition should implement the method
184 sat(::DiffOp, v::AbstractArray, data::AbstractArray, ...)
185 """
186 abstract type BoundaryCondition end
187
188 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
189
190 function sat(L::Laplace{2,T}, bc::Neumann{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, I::CartesianIndex{2}) where {T,Bid}
191 e = BoundaryValue(L.op, L.grid, Bid())
192 d = NormalDerivative(L.op, L.grid, Bid())
193 Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid())
194 # TODO: Implement BoundaryQuadrature method
195
196 return -L.Hi*e*Hᵧ*(d'*v - g)
197 # Need to handle d'*v - g so that it is an AbstractArray that TensorMappings can act on
198 end
199
200 struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
201 tau::Float64
202 end
203
204 function sat(L::Laplace{2,T}, bc::Dirichlet{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, i::CartesianIndex{2}) where {T,Bid}
205 e = BoundaryValue(L.op, L.grid, Bid())
206 d = NormalDerivative(L.op, L.grid, Bid())
207 Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid())
208 # TODO: Implement BoundaryQuadrature method
209
210 return -L.Hi*(tau/h*e + d)*Hᵧ*(e'*v - g)
211 # Need to handle scalar multiplication and addition of TensorMapping
212 end
213
214 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
215 # return apply(s.L, v, i) +
216 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
217 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
218 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
219 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
220 # end