Mercurial > repos > public > sbplib_julia
changeset 929:e9dd43cbd127 feature/variable_derivatives
Merge performance/get_region_type_inference
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Mon, 21 Feb 2022 10:34:48 +0100 |
| parents | 453fd1a2e858 (diff) b41180efb6c2 (current diff) |
| children | ba5f4a0ec879 |
| files | |
| diffstat | 12 files changed, 733 insertions(+), 53 deletions(-) [+] |
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--- a/Notes.md Mon Feb 21 10:33:58 2022 +0100 +++ b/Notes.md Mon Feb 21 10:34:48 2022 +0100 @@ -154,6 +154,43 @@ - [ ] What to name this trait? Can we call it IndexStyle but not export it to avoid conflicts with Base.IndexStyle? - [ ] 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? +### Ideas for information sharing functions +```julia +using StaticArrays + +function regions(op::SecondDerivativeVariable) + t = ntuple(i->(Interior(),),range_dim(op)) + return Base.setindex(t, (Lower(), Interior(), Upper()), derivative_direction(op)) +end + +function regionsizes(op::SecondDerivativeVariable) + sz = tuple.(range_size(op)) + + cl = closuresize(op) + return Base.setindex(sz, (cl, n-2cl, cl), derivative_direction(op)) +end + + +g = EquidistantGrid((11,9), (0.,0.), (10.,8.)) # h = 1 +c = evalOn(g, (x,y)->x+y) + +D₂ᶜ = SecondDerivativeVariable(g, c, interior_stencil, closure_stencils,1) +@test regions(D₂ᶜ) == ( + (Lower(), Interior(), Upper()), + (Interior(),), +) +@test regionsizes(D₂ᶜ) == ((1,9,1),(9,)) + + +D₂ᶜ = SecondDerivativeVariable(g, c, interior_stencil, closure_stencils,2) +@test regions(D₂ᶜ) == ( + (Interior(),), + (Lower(), Interior(), Upper()), +) +@test regionsizes(D₂ᶜ) == ((11,),(1,7,1)) +``` + + ## Boundschecking and dimension checking Does it make sense to have boundschecking only in getindex methods? 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.
--- a/TODO.md Mon Feb 21 10:33:58 2022 +0100 +++ b/TODO.md Mon Feb 21 10:34:48 2022 +0100 @@ -1,15 +1,12 @@ # TODO -## Skämskudde + - [ ] Ändra namn på variabler och funktioner så att det följer style-guide - - [ ] Skriv tester - -## Coding - [ ] Add new Laplace operator to DiffOps, probably named WaveEqOp(?!!?) - [ ] Create a struct that bundles the necessary Tensor operators for solving the wave equation. - - [ ] Add a quick and simple way of running all tests for all subpackages. - [ ] Replace getindex hack for flattening tuples with flatten_tuple. (eg. `getindex.(range_size.(L.D2),1)`) - [ ] Use `@inferred` in a lot of tests. + - [ ] Replace `@inferred` tests with a benchmark suite that automatically tests for regressions. - [ ] Make sure we are setting tolerances in tests in a consistent way - [ ] Add check for correct domain sizes to lazy tensor operations using SizeMismatch - [ ] Write down some coding guideline or checklist for code conventions. For example i,j,... for indices and I for multi-index @@ -23,11 +20,10 @@ - [ ] Add possibility to create tensor mapping application with `()`, e.g `D1(v) <=> D1*v`? - [ ] Add custom pretty printing to LazyTensors/SbpOperators to enhance readability of e.g error messages. See (https://docs.julialang.org/en/v1/manual/types/#man-custom-pretty-printing) + - [ ] Samla noggrannhets- och SBP-ness-tester för alla operatorer på ett ställe -## Repo - - [ ] Rename repo to Sbplib.jl -# Wrap up tasks + - [ ] Gå igenom alla typ parametrar och kolla om de är motiverade. Både i signaturer och typer, tex D i VariableSecondDerivative. Kan vi använda promote istället? - [ ] Kolla att vi har @inbounds och @propagate_inbounds på rätt ställen - [ ] Kolla att vi gör boundschecks överallt och att de är markerade med @boundscheck - [ ] Kolla att vi har @inline på rätt ställen
--- a/src/SbpOperators/SbpOperators.jl Mon Feb 21 10:33:58 2022 +0100 +++ b/src/SbpOperators/SbpOperators.jl Mon Feb 21 10:34:48 2022 +0100 @@ -9,11 +9,14 @@ even = 1 end +export closure_size + include("stencil.jl") include("readoperator.jl") include("volumeops/volume_operator.jl") include("volumeops/constant_interior_scaling_operator.jl") include("volumeops/derivatives/second_derivative.jl") +include("volumeops/derivatives/second_derivative_variable.jl") include("volumeops/laplace/laplace.jl") include("volumeops/inner_products/inner_product.jl") include("volumeops/inner_products/inverse_inner_product.jl")
--- a/src/SbpOperators/operators/standard_diagonal.toml Mon Feb 21 10:33:58 2022 +0100 +++ b/src/SbpOperators/operators/standard_diagonal.toml Mon Feb 21 10:34:48 2022 +0100 @@ -20,6 +20,10 @@ H.inner = "1" H.closure = ["1/2"] +e.closure = ["1"] +d1.closure = {s = ["3/2", "-2", "1/2"], c = 1} + + D1.inner_stencil = ["-1/2", "0", "1/2"] D1.closure_stencils = [ {s = ["-1", "1"], c = 1}, @@ -30,8 +34,10 @@ {s = ["1", "-2", "1"], c = 1}, ] -e.closure = ["1"] -d1.closure = {s = ["-3/2", "2", "-1/2"], c = 1} +D2variable.inner_stencil = [["1/2", "1/2", "0"],[ "-1/2", "-1", "-1/2"],["0", "1/2", "1/2"]] +D2variable.closure_stencils = [ + {s = [["2", "-1", "0"],["-3", "1", "0"],["1","0","0"]], c = 1}, +] [[stencil_set]] @@ -40,6 +46,9 @@ H.inner = "1" H.closure = ["17/48", "59/48", "43/48", "49/48"] +e.closure = ["1"] +d1.closure = {s = ["11/6", "-3", "3/2", "-1/3"], c = 1} + D1.inner_stencil = ["1/12","-2/3","0","2/3","-1/12"] D1.closure_stencils = [ {s = [ "-24/17", "59/34", "-4/17", "-3/34", "0", "0"], c = 1}, @@ -56,5 +65,79 @@ {s = [ "-1/49", "0", "59/49", "-118/49", "64/49", "-4/49"], c = 4}, ] +D2variable.inner_stencil = [ + ["-1/8", "1/6", "-1/8", "0", "0" ], + [ "1/6", "1/2", "1/2", "1/6", "0" ], + ["-1/24", "-5/6", "-3/4", "-5/6", "-1/24"], + [ "0", "1/6", "1/2", "1/2", "1/6" ], + [ "0", "0", "-1/8", "1/6", "-1/8" ], +] +D2variable.closure_stencils = [ + {c = 1, s = [ + [ "920/289", "-59/68", "-81031200387/366633756146", "-69462376031/733267512292", "0", "0", "0", "0" ], + ["-1740/289", "0", "6025413881/7482321554", "1612249989/7482321554", "0", "0", "0", "0" ], + [ "1128/289", "59/68", "-6251815797/8526366422", "-639954015/17052732844", "0", "0", "0", "0" ], + [ "-308/289", "0", "1244724001/7482321554", "-752806667/7482321554", "0", "0", "0", "0" ], + [ "0", "0", "-148737261/10783345769", "148737261/10783345769", "0", "0", "0", "0" ], + [ "0", "0", "-3/833", "3/833", "0", "0", "0", "0" ], + ]}, + {c = 2, s = [ + [ "12/17", "0", "102125659/440136562", "27326271/440136562", "0", "0", "0", "0" ], + [ "-59/68", "0", "-156920047993625/159775733917868", "-12001237118451/79887866958934", "0", "0", "0", "0" ], + [ "2/17", "0", "1489556735319/1857857371138", "149729180391/1857857371138", "0", "0", "0", "0" ], + [ "3/68", "0", "-13235456910147/159775733917868", "3093263736297/79887866958934", "0", "0", "0", "0" ], + [ "0", "0", "67535018271/2349643145851", "-67535018271/2349643145851", "0", "0", "0", "0" ], + [ "0", "0", "441/181507", "-441/181507", "0", "0", "0", "0" ], + ]}, + {c = 3, s = [ + [ "-96/731", "59/172", "-6251815797/21566691538", "-639954015/43133383076", "0", "0", "0", "0" ], + [ "118/731", "0", "87883847383821/79887866958934", "8834021643069/79887866958934", "0", "0", "0", "0" ], + [ "-16/731", "-59/172", "-1134866646907639536627/727679167377258785038", "-13777050223300597/23487032885926596", "-26254/557679", "0", "0", "0" ], + [ "-6/731", "0", "14509020271326561681/14850595252597118062", "17220493277981/79887866958934", "1500708/7993399", "0", "0", "0" ], + [ "0", "0", "-4841930283098652915/21402328452272317207", "31597236232005/115132514146699", "-26254/185893", "0", "0", "0" ], + [ "0", "0", "-2318724711/1653303156799", "960119/1147305747", "13564/23980197", "0", "0", "0" ], + ]}, + {c = 4, s = [ + [ "-36/833", "0", "1244724001/21566691538", "-752806667/21566691538", "0", "0", "0", "0" ], + [ "177/3332", "0", "-780891957698673/7829010961975532", "3724542049827/79887866958934", "0", "0", "0", "0" ], + [ "-6/833", "0", "14509020271326561681/16922771334354855466", "2460070468283/13005001597966", "1500708/9108757", "0", "0", "0" ], + [ "-9/3332", "0", "-217407431400324796377/207908333536359652868", "-1950062198436997/3914505480987766", "-7476412/9108757", "-2/49", "0", "0" ], + [ "0", "0", "4959271814984644613/21402328452272317207", "47996144728947/115132514146699", "4502124/9108757", "8/49", "0", "0" ], + [ "0", "0", "-2258420001/1653303156799", "-1063649/8893843", "1473580/9108757", "-6/49", "0", "0" ], + ]}, + {c = 5, s = [ + [ "0", "0", "-49579087/10149031312", "49579087/10149031312", "0", "0", "0", "0" ], + [ "0", "0", "1328188692663/37594290333616", "-1328188692663/37594290333616", "0", "0", "0", "0" ], + [ "0", "0", "-1613976761032884305/7963657098519931984", "10532412077335/42840005263888", "-564461/4461432", "0", "0", "0" ], + [ "0", "0", "4959271814984644613/20965546238960637264", "15998714909649/37594290333616", "375177/743572", "1/6", "0", "0" ], + [ "0", "0", "-8386761355510099813/128413970713633903242", "-2224717261773437/2763180339520776", "-280535/371786", "-5/6", "-1/24", "0" ], + [ "0", "0", "13091810925/13226425254392", "35039615/213452232", "1118749/2230716", "1/2", "1/6", "0" ], + [ "0", "0", "0", "0", "-1/8", "1/6", "-1/8", "0" ], + ]}, + {c = 6, s = [ + [ "0", "0", "-1/784", "1/784", "0", "0", "0", "0" ], + [ "0", "0", "8673/2904112", "-8673/2904112", "0", "0", "0", "0" ], + [ "0", "0", "-33235054191/26452850508784", "960119/1280713392", "3391/6692148", "0", "0", "0" ], + [ "0", "0", "-752806667/539854092016", "-1063649/8712336", "368395/2230716", "-1/8", "0", "0" ], + [ "0", "0", "13091810925/13226425254392", "35039615/213452232", "1118749/2230716", "1/2", "1/6", "0" ], + [ "0", "0", "-660204843/13226425254392", "-3290636/80044587", "-5580181/6692148", "-3/4", "-5/6", "-1/24"], + [ "0", "0", "0", "0", "1/6", "1/2", "1/2", "1/6" ], + [ "0", "0", "0", "0", "0", "-1/8", "1/6", "-1/8" ], + ]} +] + + + +[[stencil_set]] + +order = 6 + +H.inner = "1" +H.closure = ["13649/43200", "12013/8640", "2711/4320", "5359/4320", "7877/8640", "43801/43200"] + + + + + e.closure = ["1"] -d1.closure = {s = ["-11/6", "3", "-3/2", "1/3"], c = 1} +d1.closure = ["-25/12", "4", "-3", "4/3", "-1/4"]
--- a/src/SbpOperators/readoperator.jl Mon Feb 21 10:33:58 2022 +0100 +++ b/src/SbpOperators/readoperator.jl Mon Feb 21 10:34:48 2022 +0100 @@ -4,6 +4,7 @@ export get_stencil_set export parse_stencil +export parse_nested_stencil export parse_scalar export parse_tuple @@ -106,6 +107,33 @@ end end + +""" + parse_nested_stencil(parsed_toml) + +Accept parsed TOML and read it as a nested tuple. + +See also [`read_stencil_set`](@ref), [`parse_stencil`](@ref). +""" +function parse_nested_stencil(parsed_toml) + if parsed_toml isa Array + weights = parse_stencil.(parsed_toml) + return CenteredNestedStencil(weights...) + end + + center = parsed_toml["c"] + weights = parse_tuple.(parsed_toml["s"]) + return NestedStencil(weights...; center) +end + +""" + parse_nested_stencil(T, parsed_toml) + +Parse the input as a nested stencil with element type `T`. +""" +parse_nested_stencil(T, parsed_toml) = NestedStencil{T}(parse_nested_stencil(parsed_toml)) + + """ parse_scalar(parsed_toml)
--- a/src/SbpOperators/stencil.jl Mon Feb 21 10:33:58 2022 +0100 +++ b/src/SbpOperators/stencil.jl Mon Feb 21 10:34:48 2022 +0100 @@ -1,11 +1,12 @@ export CenteredStencil +export CenteredNestedStencil struct Stencil{T,N} - range::Tuple{Int,Int} + range::UnitRange{Int64} weights::NTuple{N,T} - function Stencil(range::Tuple{Int,Int},weights::NTuple{N,T}) where {T, N} - @assert range[2]-range[1]+1 == N + function Stencil(range::UnitRange,weights::NTuple{N,T}) where {T, N} + @assert length(range) == N new{T,N}(range,weights) end end @@ -15,27 +16,30 @@ Create a stencil with the given weights with element `center` as the center of the stencil. """ -function Stencil(weights::Vararg{T}; center::Int) where T # Type parameter T makes sure the weights are valid for the Stencil constuctors and throws an earlier, more readable, error +function Stencil(weights...; center::Int) + weights = promote(weights...) N = length(weights) - range = (1, N) .- center + range = (1:N) .- center return Stencil(range, weights) end -function Stencil{T}(s::Stencil) where T - return Stencil(s.range, T.(s.weights)) -end +Stencil{T,N}(s::Stencil{S,N}) where {T,S,N} = Stencil(s.range, T.(s.weights)) +Stencil{T}(s::Stencil) where T = Stencil{T,length(s)}(s) -Base.convert(::Type{Stencil{T}}, stencil) where T = Stencil{T}(stencil) +Base.convert(::Type{Stencil{T1,N}}, s::Stencil{T2,N}) where {T1,T2,N} = Stencil{T1,N}(s) +Base.convert(::Type{Stencil{T1}}, s::Stencil{T2,N}) where {T1,T2,N} = Stencil{T1,N}(s) -function CenteredStencil(weights::Vararg) +Base.promote_rule(::Type{Stencil{T1,N}}, ::Type{Stencil{T2,N}}) where {T1,T2,N} = Stencil{promote_type(T1,T2),N} + +function CenteredStencil(weights...) if iseven(length(weights)) throw(ArgumentError("a centered stencil must have an odd number of weights.")) end r = length(weights) ÷ 2 - return Stencil((-r, r), weights) + return Stencil(-r:r, weights) end @@ -48,7 +52,8 @@ return Stencil(s.range, a.*s.weights) end -Base.eltype(::Stencil{T}) where T = T +Base.eltype(::Stencil{T,N}) where {T,N} = T +Base.length(::Stencil{T,N}) where {T,N} = N function flip(s::Stencil) range = (-s.range[2], -s.range[1]) @@ -57,24 +62,103 @@ # Provides index into the Stencil based on offset for the root element @inline function Base.getindex(s::Stencil, i::Int) - @boundscheck if i < s.range[1] || s.range[2] < i + @boundscheck if i ∉ s.range return zero(eltype(s)) end return s.weights[1 + i - s.range[1]] end -Base.@propagate_inbounds @inline function apply_stencil(s::Stencil{T,N}, v::AbstractVector, i::Int) where {T,N} - w = s.weights[1]*v[i + s.range[1]] - @simd for k ∈ 2:N - w += s.weights[k]*v[i + s.range[1] + k-1] +Base.@propagate_inbounds @inline function apply_stencil(s::Stencil, v::AbstractVector, i::Int) + w = zero(promote_type(eltype(s),eltype(v))) + @simd for k ∈ 1:length(s) + w += s.weights[k]*v[i + s.range[k]] + end + + return w +end + +Base.@propagate_inbounds @inline function apply_stencil_backwards(s::Stencil, v::AbstractVector, i::Int) + w = zero(promote_type(eltype(s),eltype(v))) + @simd for k ∈ length(s):-1:1 + w += s.weights[k]*v[i - s.range[k]] end return w end -Base.@propagate_inbounds @inline function apply_stencil_backwards(s::Stencil{T,N}, v::AbstractVector, i::Int) where {T,N} - w = s.weights[N]*v[i - s.range[2]] - @simd for k ∈ N-1:-1:1 - w += s.weights[k]*v[i - s.range[1] - k + 1] - end - return w + +struct NestedStencil{T,N,M} + s::Stencil{Stencil{T,N},M} +end + +# Stencil input +NestedStencil(s::Vararg{Stencil}; center) = NestedStencil(Stencil(s... ; center)) +CenteredNestedStencil(s::Vararg{Stencil}) = NestedStencil(CenteredStencil(s...)) + +# Tuple input +function NestedStencil(weights::Vararg{NTuple{N,Any}}; center) where N + inner_stencils = map(w -> Stencil(w...; center), weights) + return NestedStencil(Stencil(inner_stencils... ; center)) +end +function CenteredNestedStencil(weights::Vararg{NTuple{N,Any}}) where N + inner_stencils = map(w->CenteredStencil(w...), weights) + return CenteredNestedStencil(inner_stencils...) +end + + +# Conversion +function NestedStencil{T,N,M}(ns::NestedStencil{S,N,M}) where {T,S,N,M} + return NestedStencil(Stencil{Stencil{T}}(ns.s)) +end + +function NestedStencil{T}(ns::NestedStencil{S,N,M}) where {T,S,N,M} + NestedStencil{T,N,M}(ns) +end + +function Base.convert(::Type{NestedStencil{T,N,M}}, s::NestedStencil{S,N,M}) where {T,S,N,M} + return NestedStencil{T,N,M}(s) +end +Base.convert(::Type{NestedStencil{T}}, stencil) where T = NestedStencil{T}(stencil) + +function Base.promote_rule(::Type{NestedStencil{T,N,M}}, ::Type{NestedStencil{S,N,M}}) where {T,S,N,M} + return NestedStencil{promote_type(T,S),N,M} end + +Base.eltype(::NestedStencil{T}) where T = T + +function scale(ns::NestedStencil, a) + range = ns.s.range + weights = ns.s.weights + + return NestedStencil(Stencil(range, scale.(weights,a))) +end + +function flip(ns::NestedStencil) + s_flip = flip(ns.s) + return NestedStencil(Stencil(s_flip.range, flip.(s_flip.weights))) +end + +Base.getindex(ns::NestedStencil, i::Int) = ns.s[i] + +"Apply inner stencils to `c` and get a concrete stencil" +Base.@propagate_inbounds function apply_inner_stencils(ns::NestedStencil, c::AbstractVector, i::Int) + weights = apply_stencil.(ns.s.weights, Ref(c), i) + return Stencil(ns.s.range, weights) +end + +"Apply the whole nested stencil" +Base.@propagate_inbounds function apply_stencil(ns::NestedStencil, c::AbstractVector, v::AbstractVector, i::Int) + s = apply_inner_stencils(ns,c,i) + return apply_stencil(s, v, i) +end + +"Apply inner stencils backwards to `c` and get a concrete stencil" +Base.@propagate_inbounds @inline function apply_inner_stencils_backwards(ns::NestedStencil, c::AbstractVector, i::Int) + weights = apply_stencil_backwards.(ns.s.weights, Ref(c), i) + return Stencil(ns.s.range, weights) +end + +"Apply the whole nested stencil backwards" +Base.@propagate_inbounds @inline function apply_stencil_backwards(ns::NestedStencil, c::AbstractVector, v::AbstractVector, i::Int) + s = apply_inner_stencils_backwards(ns,c,i) + return apply_stencil_backwards(s, v, i) +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/SbpOperators/volumeops/derivatives/second_derivative_variable.jl Mon Feb 21 10:34:48 2022 +0100 @@ -0,0 +1,120 @@ +export SecondDerivativeVariable + +# REVIEW: Fixa docs +""" + SecondDerivativeVariable{Dir,T,D,...} <: TensorMapping{T,D,D} + +A second derivative operator in direction `Dir` with a variable coefficient. +""" +struct SecondDerivativeVariable{Dir,T,D,M,IStencil<:NestedStencil{T},CStencil<:NestedStencil{T},TArray<:AbstractArray} <: TensorMapping{T,D,D} + inner_stencil::IStencil + closure_stencils::NTuple{M,CStencil} + size::NTuple{D,Int} + coefficient::TArray + + function SecondDerivativeVariable{Dir, D}(inner_stencil::NestedStencil{T}, closure_stencils::NTuple{M,NestedStencil{T}}, size::NTuple{D,Int}, coefficient::AbstractArray) where {Dir,T,D,M} + IStencil = typeof(inner_stencil) + CStencil = eltype(closure_stencils) + TArray = typeof(coefficient) + return new{Dir,T,D,M,IStencil,CStencil,TArray}(inner_stencil,closure_stencils,size, coefficient) + end +end + +function SecondDerivativeVariable(grid::EquidistantGrid, coeff::AbstractArray, inner_stencil, closure_stencils, dir) + Δxᵢ = spacing(grid)[dir] + scaled_inner_stencil = scale(inner_stencil, 1/Δxᵢ^2) + scaled_closure_stencils = scale.(Tuple(closure_stencils), 1/Δxᵢ^2) + return SecondDerivativeVariable{dir, dimension(grid)}(scaled_inner_stencil, scaled_closure_stencils, size(grid), coeff) +end + +function SecondDerivativeVariable(grid::EquidistantGrid{1}, coeff::AbstractVector, inner_stencil, closure_stencils) + return SecondDerivativeVariable(grid, coeff, inner_stencil, closure_stencils, 1) +end + +@doc raw""" + SecondDerivativeVariable(grid::EquidistantGrid, coeff::AbstractArray, stencil_set, dir) + +Create a `TensorMapping` for the second derivative with a variable coefficient +`coeff` on `grid` from the stencils in `stencil_set`. The direction is +determined by `dir`. + +`coeff` is a grid function on `grid`. + +# Example +With +``` +D = SecondDerivativeVariable(g, c, stencil_set, 2) +``` +then `D*u` approximates +```math +\frac{\partial}{\partial y} c(x,y) \frac{\partial u}{\partial y}, +``` +on ``(0,1)⨯(0,1)`` represented by `g`. +""" +function SecondDerivativeVariable(grid::EquidistantGrid, coeff::AbstractArray, stencil_set, dir) + inner_stencil = parse_nested_stencil(eltype(coeff), stencil_set["D2variable"]["inner_stencil"]) + closure_stencils = parse_nested_stencil.(eltype(coeff), stencil_set["D2variable"]["closure_stencils"]) + + return SecondDerivativeVariable(grid, coeff, inner_stencil, closure_stencils, dir) +end + +derivative_direction(::SecondDerivativeVariable{Dir}) where {Dir} = Dir + +closure_size(op::SecondDerivativeVariable) = length(op.closure_stencils) + +LazyTensors.range_size(op::SecondDerivativeVariable) = op.size +LazyTensors.domain_size(op::SecondDerivativeVariable) = op.size + + +function derivative_view(op, a, I) + d = derivative_direction(op) + + Iview = Base.setindex(I,:,d) + return @view a[Iview...] +end + +function apply_lower(op::SecondDerivativeVariable, v, I...) + ṽ = derivative_view(op, v, I) + c̃ = derivative_view(op, op.coefficient, I) + + i = I[derivative_direction(op)] + return @inbounds apply_stencil(op.closure_stencils[i], c̃, ṽ, i) +end + +function apply_interior(op::SecondDerivativeVariable, v, I...) + ṽ = derivative_view(op, v, I) + c̃ = derivative_view(op, op.coefficient, I) + + i = I[derivative_direction(op)] + return apply_stencil(op.inner_stencil, c̃, ṽ, i) +end + +function apply_upper(op::SecondDerivativeVariable, v, I...) + ṽ = derivative_view(op, v, I) + c̃ = derivative_view(op, op.coefficient, I) + + i = I[derivative_direction(op)] + stencil = op.closure_stencils[op.size[derivative_direction(op)]-i+1] + return @inbounds apply_stencil_backwards(stencil, c̃, ṽ, i) +end + +function LazyTensors.apply(op::SecondDerivativeVariable, v::AbstractArray, I::Vararg{Index}) + if I[derivative_direction(op)] isa Index{Lower} + return apply_lower(op, v, Int.(I)...) + elseif I[derivative_direction(op)] isa Index{Upper} + return apply_upper(op, v, Int.(I)...) + else + return apply_interior(op, v, Int.(I)...) + end +end + +function LazyTensors.apply(op::SecondDerivativeVariable, v::AbstractArray, I...) + dir = derivative_direction(op) + + i = I[dir] + r = getregion(i, closure_size(op), op.size[dir]) + + I = map(i->Index(i, Interior), I) + I = Base.setindex(I, Index(i, r), dir) + return LazyTensors.apply(op, v, I...) +end
--- a/test/SbpOperators/boundaryops/boundary_operator_test.jl Mon Feb 21 10:33:58 2022 +0100 +++ b/test/SbpOperators/boundaryops/boundary_operator_test.jl Mon Feb 21 10:34:48 2022 +0100 @@ -9,7 +9,7 @@ import Sbplib.SbpOperators.boundary_operator @testset "BoundaryOperator" begin - closure_stencil = Stencil((0,2), (2.,1.,3.)) + closure_stencil = Stencil(2.,1.,3.; center = 1) g_1D = EquidistantGrid(11, 0.0, 1.0) g_2D = EquidistantGrid((11,15), (0.0, 0.0), (1.0,1.0))
--- a/test/SbpOperators/boundaryops/normal_derivative_test.jl Mon Feb 21 10:33:58 2022 +0100 +++ b/test/SbpOperators/boundaryops/normal_derivative_test.jl Mon Feb 21 10:34:48 2022 +0100 @@ -45,24 +45,24 @@ d_s = normal_derivative(g_2D, d_closure, CartesianBoundary{2,Lower}()) d_n = normal_derivative(g_2D, d_closure, CartesianBoundary{2,Upper}()) - @test d_w*v ≈ v∂x[1,:] atol = 1e-13 - @test d_e*v ≈ -v∂x[end,:] atol = 1e-13 - @test d_s*v ≈ v∂y[:,1] atol = 1e-13 - @test d_n*v ≈ -v∂y[:,end] atol = 1e-13 + @test d_w*v ≈ -v∂x[1,:] atol = 1e-13 + @test d_e*v ≈ v∂x[end,:] atol = 1e-13 + @test d_s*v ≈ -v∂y[:,1] atol = 1e-13 + @test d_n*v ≈ v∂y[:,end] atol = 1e-13 end @testset "4th order" begin - stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=2) + stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=4) d_closure = parse_stencil(stencil_set["d1"]["closure"]) d_w = normal_derivative(g_2D, d_closure, CartesianBoundary{1,Lower}()) d_e = normal_derivative(g_2D, d_closure, CartesianBoundary{1,Upper}()) d_s = normal_derivative(g_2D, d_closure, CartesianBoundary{2,Lower}()) d_n = normal_derivative(g_2D, d_closure, CartesianBoundary{2,Upper}()) - @test d_w*v ≈ v∂x[1,:] atol = 1e-13 - @test d_e*v ≈ -v∂x[end,:] atol = 1e-13 - @test d_s*v ≈ v∂y[:,1] atol = 1e-13 - @test d_n*v ≈ -v∂y[:,end] atol = 1e-13 + @test d_w*v ≈ -v∂x[1,:] atol = 1e-13 + @test d_e*v ≈ v∂x[end,:] atol = 1e-13 + @test d_s*v ≈ -v∂y[:,1] atol = 1e-13 + @test d_n*v ≈ v∂y[:,end] atol = 1e-13 end end end
--- a/test/SbpOperators/readoperator_test.jl Mon Feb 21 10:33:58 2022 +0100 +++ b/test/SbpOperators/readoperator_test.jl Mon Feb 21 10:34:48 2022 +0100 @@ -4,6 +4,7 @@ using Sbplib.SbpOperators import Sbplib.SbpOperators.Stencil +import Sbplib.SbpOperators.NestedStencil @testset "readoperator" begin toml_str = """ @@ -170,3 +171,18 @@ @test SbpOperators.parse_rational(2) isa Rational @test SbpOperators.parse_rational(2) == 2//1 end + +@testset "parse_nested_stencil" begin + toml = TOML.parse(""" + s1 = [["1/2", "1/2", "0"],[ "-1/2", "-1", "-1/2"],["0", "1/2", "1/2"]] + s2 = {s = [[ "2", "-1", "0"],[ "-3", "1", "0"],["1", "0", "0"]], c = 1} + s3 = {s = [[ "2", "-1", "0"],[ "-3", "1", "0"],["1", "0", "0"]], c = 2} + """) + + @test parse_nested_stencil(toml["s1"]) == CenteredNestedStencil((1//2, 1//2, 0//1),( -1//2, -1//1, -1//2),(0//1, 1//2, 1//2)) + @test parse_nested_stencil(toml["s2"]) == NestedStencil((2//1, -1//1, 0//1),( -3//1, 1//1, 0//1),(1//1, 0//1, 0//1), center = 1) + @test parse_nested_stencil(toml["s3"]) == NestedStencil((2//1, -1//1, 0//1),( -3//1, 1//1, 0//1),(1//1, 0//1, 0//1), center = 2) + + @test parse_nested_stencil(Float64, toml["s1"]) == CenteredNestedStencil((1/2, 1/2, 0.),( -1/2, -1., -1/2),(0., 1/2, 1/2)) + @test parse_nested_stencil(Int, toml["s2"]) == NestedStencil((2, -1, 0),( -3, 1, 0),(1, 0, 0), center = 1) +end
--- a/test/SbpOperators/stencil_test.jl Mon Feb 21 10:33:58 2022 +0100 +++ b/test/SbpOperators/stencil_test.jl Mon Feb 21 10:34:48 2022 +0100 @@ -1,19 +1,25 @@ using Test using Sbplib.SbpOperators import Sbplib.SbpOperators.Stencil +import Sbplib.SbpOperators.NestedStencil +import Sbplib.SbpOperators.scale @testset "Stencil" begin - s = Stencil((-2,2), (1.,2.,2.,3.,4.)) + s = Stencil(-2:2, (1.,2.,2.,3.,4.)) @test s isa Stencil{Float64, 5} @test eltype(s) == Float64 - @test SbpOperators.scale(s, 2) == Stencil((-2,2), (2.,4.,4.,6.,8.)) + + @test length(s) == 5 + @test length(Stencil(-1:2, (1,2,3,4))) == 4 + + @test SbpOperators.scale(s, 2) == Stencil(-2:2, (2.,4.,4.,6.,8.)) - @test Stencil(1,2,3,4; center=1) == Stencil((0, 3),(1,2,3,4)) - @test Stencil(1,2,3,4; center=2) == Stencil((-1, 2),(1,2,3,4)) - @test Stencil(1,2,3,4; center=4) == Stencil((-3, 0),(1,2,3,4)) + @test Stencil(1,2,3,4; center=1) == Stencil(0:3,(1,2,3,4)) + @test Stencil(1,2,3,4; center=2) == Stencil(-1:2,(1,2,3,4)) + @test Stencil(1,2,3,4; center=4) == Stencil(-3:0,(1,2,3,4)) - @test CenteredStencil(1,2,3,4,5) == Stencil((-2, 2), (1,2,3,4,5)) + @test CenteredStencil(1,2,3,4,5) == Stencil(-2:2, (1,2,3,4,5)) @test_throws ArgumentError CenteredStencil(1,2,3,4) # Changing the type of the weights @@ -24,8 +30,145 @@ @testset "convert" begin @test convert(Stencil{Float64}, Stencil(1,2,3,4,5; center=2)) == Stencil(1.,2.,3.,4.,5.; center=2) - @test convert(Stencil{Float64}, CenteredStencil(1,2,3,4,5)) == CenteredStencil(1.,2.,3.,4.,5.) - @test convert(Stencil{Int}, Stencil(1.,2.,3.,4.,5.; center=2)) == Stencil(1,2,3,4,5; center=2) - @test convert(Stencil{Rational}, Stencil(1.,2.,3.,4.,5.; center=2)) == Stencil(1//1,2//1,3//1,4//1,5//1; center=2) + @test convert(Stencil{Float64,5}, CenteredStencil(1,2,3,4,5)) == CenteredStencil(1.,2.,3.,4.,5.) + @test convert(Stencil{Int,5}, Stencil(1.,2.,3.,4.,5.; center=2)) == Stencil(1,2,3,4,5; center=2) + @test convert(Stencil{Rational,5}, Stencil(1.,2.,3.,4.,5.; center=2)) == Stencil(1//1,2//1,3//1,4//1,5//1; center=2) + end + + @testset "promotion of weights" begin + @test Stencil(1.,2; center = 1) isa Stencil{Float64, 2} + @test Stencil(1,2//2; center = 1) isa Stencil{Rational{Int64}, 2} + end + + @testset "promotion" begin + @test promote(Stencil(1,1;center=1), Stencil(2.,2.;center=2)) == (Stencil(1.,1.;center=1), Stencil(2.,2.;center=2)) + end + + @testset "type stability" begin + s_int = CenteredStencil(1,2,3) + s_float = CenteredStencil(1.,2.,3.) + v_int = rand(1:10,10); + v_float = rand(10); + + @inferred SbpOperators.apply_stencil(s_int, v_int, 2) + @inferred SbpOperators.apply_stencil(s_float, v_float, 2) + @inferred SbpOperators.apply_stencil(s_int, v_float, 2) + @inferred SbpOperators.apply_stencil(s_float, v_int, 2) + + @inferred SbpOperators.apply_stencil_backwards(s_int, v_int, 5) + @inferred SbpOperators.apply_stencil_backwards(s_float, v_float, 5) + @inferred SbpOperators.apply_stencil_backwards(s_int, v_float, 5) + @inferred SbpOperators.apply_stencil_backwards(s_float, v_int, 5) end end + +@testset "NestedStencil" begin + + @testset "Constructors" begin + s1 = CenteredStencil(-1, 1, 0) + s2 = CenteredStencil(-1, 0, 1) + s3 = CenteredStencil( 0,-1, 1) + + ns = NestedStencil(CenteredStencil(s1,s2,s3)) + @test ns isa NestedStencil{Int,3} + + @test CenteredNestedStencil(s1,s2,s3) == ns + + @test NestedStencil(s1,s2,s3, center = 2) == ns + @test NestedStencil(s1,s2,s3, center = 1) == NestedStencil(Stencil(s1,s2,s3, center=1)) + + @test NestedStencil((-1,1,0),(-1,0,1),(0,-1,1), center=2) == ns + @test CenteredNestedStencil((-1,1,0),(-1,0,1),(0,-1,1)) == ns + @test NestedStencil((-1,1,0),(-1,0,1),(0,-1,1), center=1) == NestedStencil(Stencil( + Stencil(-1, 1, 0; center=1), + Stencil(-1, 0, 1; center=1), + Stencil( 0,-1, 1; center=1); + center=1 + )) + + @testset "Error handling" begin + end + end + + @testset "scale" begin + ns = NestedStencil((-1,1,0),(-1,0,1),(0,-1,1), center=2) + @test SbpOperators.scale(ns, 2) == NestedStencil((-2,2,0),(-2,0,2),(0,-2,2), center=2) + end + + @testset "conversion" begin + ns = NestedStencil((-1,1,0),(-1,0,1),(0,-1,1), center=2) + @test NestedStencil{Float64}(ns) == NestedStencil((-1.,1.,0.),(-1.,0.,1.),(0.,-1.,1.), center=2) + @test NestedStencil{Rational}(ns) == NestedStencil((-1//1,1//1,0//1),(-1//1,0//1,1//1),(0//1,-1//1,1//1), center=2) + + @test convert(NestedStencil{Float64}, ns) == NestedStencil((-1.,1.,0.),(-1.,0.,1.),(0.,-1.,1.), center=2) + @test convert(NestedStencil{Rational}, ns) == NestedStencil((-1//1,1//1,0//1),(-1//1,0//1,1//1),(0//1,-1//1,1//1), center=2) + end + + @testset "promotion of weights" begin + @test NestedStencil((-1,1,0),(-1.,0.,1.),(0,-1,1), center=2) isa NestedStencil{Float64,3,3} + @test NestedStencil((-1,1,0),(-1,0,1),(0//1,-1,1), center=2) isa NestedStencil{Rational{Int64},3,3} + end + + @testset "promotion" begin + promote( + CenteredNestedStencil((-1,1,0),(-1,0,1),(0,-1,1)), + CenteredNestedStencil((-1.,1.,0.),(-1.,0.,1.),(0.,-1.,1.)) + ) == ( + CenteredNestedStencil((-1.,1.,0.),(-1.,0.,1.),(0.,-1.,1.)), + CenteredNestedStencil((-1.,1.,0.),(-1.,0.,1.),(0.,-1.,1.)) + ) + end + + @testset "apply" begin + c = [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55] + v = [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29] + + # Centered + ns = NestedStencil((-1,1,0),(-1,0,1),(0,-2,2), center=2) + @test SbpOperators.apply_inner_stencils(ns, c, 4) == Stencil(4,9,10; center=2) + @test SbpOperators.apply_inner_stencils_backwards(ns, c, 4) == Stencil(-5,-9,-8; center=2) + + @test SbpOperators.apply_stencil(ns, c, v, 4) == 4*5 + 9*7 + 10*11 + @test SbpOperators.apply_stencil_backwards(ns, c, v, 4) == -8*5 - 9*7 - 5*11 + + # Non-centered + ns = NestedStencil((-1,1,0),(-1,0,1),(0,-1,1), center=1) + @test SbpOperators.apply_inner_stencils(ns, c, 4) == Stencil(5,11,6; center=1) + @test SbpOperators.apply_inner_stencils_backwards(ns, c, 4) == Stencil(-4,-7,-3; center=1) + + @test SbpOperators.apply_stencil(ns, c, v, 4) == 5*7 + 11*11 + 6*13 + @test SbpOperators.apply_stencil_backwards(ns, c, v, 4) == -3*3 - 7*5 - 4*7 + end + + @testset "type stability" begin + s_int = CenteredNestedStencil((1,2,3),(1,2,3),(1,2,3)) + s_float = CenteredNestedStencil((1.,2.,3.),(1.,2.,3.),(1.,2.,3.)) + + v_int = rand(1:10,10); + v_float = rand(10); + + c_int = rand(1:10,10); + c_float = rand(10); + + @inferred SbpOperators.apply_stencil(s_int, c_int, v_int, 2) + @inferred SbpOperators.apply_stencil(s_float, c_int, v_float, 2) + @inferred SbpOperators.apply_stencil(s_int, c_int, v_float, 2) + @inferred SbpOperators.apply_stencil(s_float, c_int, v_int, 2) + + @inferred SbpOperators.apply_stencil(s_int, c_float, v_int, 2) + @inferred SbpOperators.apply_stencil(s_float, c_float, v_float, 2) + @inferred SbpOperators.apply_stencil(s_int, c_float, v_float, 2) + @inferred SbpOperators.apply_stencil(s_float, c_float, v_int, 2) + + @inferred SbpOperators.apply_stencil_backwards(s_int, c_int, v_int, 2) + @inferred SbpOperators.apply_stencil_backwards(s_float, c_int, v_float, 2) + @inferred SbpOperators.apply_stencil_backwards(s_int, c_int, v_float, 2) + @inferred SbpOperators.apply_stencil_backwards(s_float, c_int, v_int, 2) + + @inferred SbpOperators.apply_stencil_backwards(s_int, c_float, v_int, 2) + @inferred SbpOperators.apply_stencil_backwards(s_float, c_float, v_float, 2) + @inferred SbpOperators.apply_stencil_backwards(s_int, c_float, v_float, 2) + @inferred SbpOperators.apply_stencil_backwards(s_float, c_float, v_int, 2) + end + +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/test/SbpOperators/volumeops/derivatives/second_derivative_variable_test.jl Mon Feb 21 10:34:48 2022 +0100 @@ -0,0 +1,170 @@ +using Test + +using Sbplib.Grids +using Sbplib.LazyTensors +using Sbplib.SbpOperators +using Sbplib.RegionIndices +using Sbplib.SbpOperators: NestedStencil, CenteredNestedStencil + +using LinearAlgebra + +@testset "SecondDerivativeVariable" begin + interior_stencil = CenteredNestedStencil((1/2, 1/2, 0.),(-1/2, -1., -1/2),( 0., 1/2, 1/2)) + closure_stencils = [ + NestedStencil(( 2., -1., 0.),(-3., 1., 0.), (1., 0., 0.), center = 1), + ] + + @testset "1D" begin + g = EquidistantGrid(11, 0., 1.) + c = [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66] + @testset "Constructors" begin + @test SecondDerivativeVariable(g, c, interior_stencil, closure_stencils) isa TensorMapping + + D₂ᶜ = SecondDerivativeVariable(g, c, interior_stencil, closure_stencils) + @test range_dim(D₂ᶜ) == 1 + @test domain_dim(D₂ᶜ) == 1 + end + + @testset "sizes" begin + D₂ᶜ = SecondDerivativeVariable(g, c, interior_stencil, closure_stencils) + @test closure_size(D₂ᶜ) == 1 + @test range_size(D₂ᶜ) == (11,) + @test domain_size(D₂ᶜ) == (11,) + end + + @testset "application" begin + + function apply_to_functions(; v, c) + g = EquidistantGrid(11, 0., 10.) # h = 1 + c̄ = evalOn(g,c) + v̄ = evalOn(g,v) + + D₂ᶜ = SecondDerivativeVariable(g, c̄, interior_stencil, closure_stencils) + return D₂ᶜ*v̄ + end + + @test apply_to_functions(v=x->1., c=x-> -1.) == zeros(11) + @test apply_to_functions(v=x->1., c=x-> -x ) == zeros(11) + @test apply_to_functions(v=x->x, c=x-> 1.) == zeros(11) + @test apply_to_functions(v=x->x, c=x-> -x ) == -ones(11) + @test apply_to_functions(v=x->x^2, c=x-> 1.) == 2ones(11) + end + + @testset "type stability" begin + g = EquidistantGrid(11, 0., 10.) # h = 1 + c̄ = evalOn(g,x-> -1) + v̄ = evalOn(g,x->1.) + + D₂ᶜ = SecondDerivativeVariable(g, c̄, interior_stencil, closure_stencils) + + @inferred SbpOperators.apply_lower(D₂ᶜ, v̄, 1) + @inferred SbpOperators.apply_interior(D₂ᶜ, v̄, 5) + @inferred SbpOperators.apply_upper(D₂ᶜ, v̄, 11) + @inferred (D₂ᶜ*v̄)[Index(1,Lower)] + end + end + + @testset "2D" begin + g = EquidistantGrid((11,9), (0.,0.), (10.,8.)) # h = 1 + c = evalOn(g, (x,y)->x+y) + @testset "Constructors" begin + @test SecondDerivativeVariable(g, c, interior_stencil, closure_stencils,1) isa TensorMapping + @test SecondDerivativeVariable(g, c, interior_stencil, closure_stencils,2) isa TensorMapping + + D₂ᶜ = SecondDerivativeVariable(g, c, interior_stencil, closure_stencils,1) + @test range_dim(D₂ᶜ) == 2 + @test domain_dim(D₂ᶜ) == 2 + end + + @testset "sizes" begin + D₂ᶜ = SecondDerivativeVariable(g, c, interior_stencil, closure_stencils,1) + @test range_size(D₂ᶜ) == (11,9) + @test domain_size(D₂ᶜ) == (11,9) + @test closure_size(D₂ᶜ) == 1 + + D₂ᶜ = SecondDerivativeVariable(g, c, interior_stencil, closure_stencils,2) + @test range_size(D₂ᶜ) == (11,9) + @test domain_size(D₂ᶜ) == (11,9) + @test closure_size(D₂ᶜ) == 1 + end + + @testset "application" begin + function apply_to_functions(dir; v, c) + g = EquidistantGrid((11,9), (0.,0.), (10.,8.)) # h = 1 + c̄ = evalOn(g,c) + v̄ = evalOn(g,v) + + D₂ᶜ = SecondDerivativeVariable(g, c̄, interior_stencil, closure_stencils,dir) + return D₂ᶜ*v̄ + end + + # x-direction + @test apply_to_functions(1,v=(x,y)->1., c=(x,y)-> -1.) == zeros(11,9) + @test apply_to_functions(1,v=(x,y)->1., c=(x,y)->- x ) == zeros(11,9) + @test apply_to_functions(1,v=(x,y)->x, c=(x,y)-> 1.) == zeros(11,9) + @test apply_to_functions(1,v=(x,y)->x, c=(x,y)-> -x ) == -ones(11,9) + @test apply_to_functions(1,v=(x,y)->x^2, c=(x,y)-> 1.) == 2ones(11,9) + + @test apply_to_functions(1,v=(x,y)->1., c=(x,y)->- y ) == zeros(11,9) + @test apply_to_functions(1,v=(x,y)->y, c=(x,y)-> 1.) == zeros(11,9) + @test apply_to_functions(1,v=(x,y)->y, c=(x,y)-> -y ) == zeros(11,9) + @test apply_to_functions(1,v=(x,y)->y^2, c=(x,y)-> 1.) == zeros(11,9) + + # y-direction + @test apply_to_functions(2,v=(x,y)->1., c=(x,y)-> -1.) == zeros(11,9) + @test apply_to_functions(2,v=(x,y)->1., c=(x,y)->- y ) == zeros(11,9) + @test apply_to_functions(2,v=(x,y)->y, c=(x,y)-> 1.) == zeros(11,9) + @test apply_to_functions(2,v=(x,y)->y, c=(x,y)-> -y ) == -ones(11,9) + @test apply_to_functions(2,v=(x,y)->y^2, c=(x,y)-> 1.) == 2ones(11,9) + + @test apply_to_functions(2,v=(x,y)->1., c=(x,y)->- x ) == zeros(11,9) + @test apply_to_functions(2,v=(x,y)->x, c=(x,y)-> 1.) == zeros(11,9) + @test apply_to_functions(2,v=(x,y)->x, c=(x,y)-> -x ) == zeros(11,9) + @test apply_to_functions(2,v=(x,y)->x^2, c=(x,y)-> 1.) == zeros(11,9) + + + @testset "standard diagonal operators" begin + c(x,y) = exp(x) + exp(1.5(1-y)) + v(x,y) = sin(x) + cos(1.5(1-y)) + + Dxv(x,y) = cos(x)*exp(x) - (exp(x) + exp(1.5 - 1.5y))*sin(x) + Dyv(x,y) = -1.5(1.5exp(x) + 1.5exp(1.5 - 1.5y))*cos(1.5 - 1.5y) - 2.25exp(1.5 - 1.5y)*sin(1.5 - 1.5y) + + g₁ = EquidistantGrid((60,67), (0.,0.), (1.,2.)) + g₂ = refine(g₁,2) + + c̄₁ = evalOn(g₁, c) + c̄₂ = evalOn(g₂, c) + + v̄₁ = evalOn(g₁, v) + v̄₂ = evalOn(g₂, v) + + + function convergence_rate_estimate(stencil_set, dir, Dv_true) + D₁ = SecondDerivativeVariable(g₁, c̄₁, stencil_set, dir) + D₂ = SecondDerivativeVariable(g₂, c̄₂, stencil_set, dir) + + Dv̄₁ = D₁*v̄₁ + Dv̄₂ = D₂*v̄₂ + + Dv₁ = evalOn(g₁,Dv_true) + Dv₂ = evalOn(g₂,Dv_true) + + e₁ = norm(Dv̄₁ - Dv₁)/norm(Dv₁) + e₂ = norm(Dv̄₂ - Dv₂)/norm(Dv₂) + + return log2(e₁/e₂) + end + + stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order = 2) + @test convergence_rate_estimate(stencil_set, 1, Dxv) ≈ 1.5 rtol = 1e-1 + @test convergence_rate_estimate(stencil_set, 2, Dyv) ≈ 1.5 rtol = 1e-1 + + stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order = 4) + @test convergence_rate_estimate(stencil_set, 1, Dxv) ≈ 2.5 rtol = 1e-1 + @test convergence_rate_estimate(stencil_set, 2, Dyv) ≈ 2.5 rtol = 2e-1 + end + end + end +end +