Interpolating if one or more of the dimensions has length 1.

.gitignore

@@ -16,3 +16,4 @@ dev/*
 # Build artifacts for creating documentation generated by the Documenter package
 docs/build/
 docs/site/
+.DS_Store

Project.toml

@@ -1,7 +1,7 @@
 name = "MethodOfLines"
 uuid = "94925ecb-adb7-4558-8ed8-f975c56a0bf4"
 authors = ["Alex Jones, <alex.jones@juliahub.com>"]
-version = "0.10.0"
+version = "0.10.2"
 
 [deps]
 Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
@@ -31,7 +31,7 @@ Interpolations = "0.14"
 Latexify = "0.15, 0.16"
 ModelingToolkit = "8"
 OrdinaryDiffEq = "6"
-PDEBase = "0.1.4"
+PDEBase = "0.1.6"
 PrecompileTools = "1"
 RuntimeGeneratedFunctions = "0.5.9"
 SafeTestsets = "0.0.1"

src/MethodOfLines.jl

@@ -50,6 +50,7 @@ import Base.ndims
 # Interface
 include("interface/grid_types.jl")
 include("interface/scheme_types.jl")
+include("interface/callbacks.jl")
 include("interface/disc_strategy_types.jl")
 include("interface/MOLFiniteDifference.jl")
 
@@ -72,6 +73,7 @@ include("discretization/schemes/upwind_difference/upwind_diff_weights.jl")
 include("discretization/schemes/half_offset_weights.jl")
 include("discretization/schemes/extrapolation_weights.jl")
 include("discretization/differential_discretizer.jl")
+include("discretization/schemes/callbacks/callback_rules.jl")
 
 # System Parsing
 include("system_parsing/pde_system_transformation.jl")
@@ -104,6 +106,6 @@ include("precompile.jl")
 
 # Export
 export MOLFiniteDifference, discretize, symbolic_discretize, ODEFunctionExpr, generate_code, grid_align, edge_align, center_align, get_discrete, chebyspace
-export UpwindScheme, WENOScheme, FunctionalScheme
+export UpwindScheme, WENOScheme, FunctionalScheme, MOLDiscCallback
 
 end

src/discretization/differential_discretizer.jl

@@ -8,13 +8,15 @@ struct DifferentialDiscretizer{T, D1, S} <: AbstractDifferentialDiscretizer
     interpmap::Dict{Num,DerivativeOperator}
     orders::Dict{Num,Vector{Int}}
     boundary::Dict{Num,DerivativeOperator}
+    callbacks
 end
 
 function PDEBase.construct_differential_discretizer(pdesys, s::DiscreteSpace, discretization::MOLFiniteDifference, orders)
     pdeeqs = pdesys.eqs isa Vector ? pdesys.eqs : [pdesys.eqs]
     bcs = pdesys.bcs isa Vector ? pdesys.bcs : [pdesys.bcs]
     approx_order = discretization.approx_order
     advection_scheme = discretization.advection_scheme
+    callbacks = discretization.callbacks
     upwind_order = advection_scheme isa UpwindScheme ? advection_scheme.order : 1
 
     differentialmap = Array{Pair{Num,DerivativeOperator},1}()
@@ -63,5 +65,5 @@ function PDEBase.construct_differential_discretizer(pdesys, s::DiscreteSpace, di
         push!(boundary, x => BoundaryInterpolatorExtrapolator(max(6, approx_order), dx))
     end
 
-    return DifferentialDiscretizer{eltype(orders),typeof(Dict(differentialmap)),typeof(advection_scheme)}(approx_order, advection_scheme, Dict(differentialmap), (Dict(nonlinlap_inner), Dict(nonlinlap_outer)), (Dict(windpos), Dict(windneg)), Dict(interp), Dict(orders), Dict(boundary))
+    return DifferentialDiscretizer{eltype(orders),typeof(Dict(differentialmap)),typeof(advection_scheme)}(approx_order, advection_scheme, Dict(differentialmap), (Dict(nonlinlap_inner), Dict(nonlinlap_outer)), (Dict(windpos), Dict(windneg)), Dict(interp), Dict(orders), Dict(boundary), callbacks)
 end

src/discretization/generate_finite_difference_rules.jl

@@ -80,6 +80,8 @@ function generate_finite_difference_rules(II::CartesianIndex, s::DiscreteSpace,
         integration_rules = []
     end
 
+    cb_rules = generate_cb_rules(II, s, depvars, derivweights, bmap, indexmap, terms)
+
     integration_rules = vcat(integration_rules, vec(generate_whole_domain_integration_rules(II, s, depvars, indexmap, terms)))
-    return vcat(vec(spherical_diffusion_rules), vec(nonlinlap_rules), vec(mixed_deriv_rules_cartesian), vec(central_deriv_rules_cartesian), vec(advection_rules), integration_rules)
+    return vcat(cb_rules, vec(spherical_diffusion_rules), vec(nonlinlap_rules), vec(mixed_deriv_rules_cartesian), vec(central_deriv_rules_cartesian), vec(advection_rules), integration_rules)
 end

src/discretization/schemes/callbacks/callback_rules.jl

@@ -0,0 +1,5 @@
+function generate_cb_rules(II, s, depvars, derivweights, bmap, indexmap, terms)
+    cbs = derivweights.callbacks
+    cb_rules = [cb.sym => cb(s) for cb in cbs]
+    return cb_rules
+end

src/discretization/schemes/nonlinear_laplacian/nonlinear_laplacian.jl

@@ -116,7 +116,7 @@ end
 
     rules = safe_vcat(rules, reduce(safe_vcat, [vec([@rule ($(Differential(x))($(Differential(x))(u) / ~a)) => cartesian_nonlinear_laplacian(1 / ~a, Idx(II, s, u, indexmap), derivweights, s, indexmap, bcmap, depvars, x, u) for x in ivs(u, s)]) for u in depvars], init = []))
 
-    rules = safe_vcat(rules, reduce(safe_vcat, [vec([@rule *(~~b, ($(Differential(x))($(Differential(x))(u) / ~a)), ~~c) => *(~b..., ~c..., cartesian_nonlinear_laplacian(1 / ~a, Idx(II, s, u, indexmap), derivweights, s, indexmapp, bcmap, depvars, x, u)) for x in ivs(u, s)]) for u in depvars], init = []))
+    rules = safe_vcat(rules, reduce(safe_vcat, [vec([@rule *(~~b, ($(Differential(x))($(Differential(x))(u) / ~a)), ~~c) => *(~b..., ~c..., cartesian_nonlinear_laplacian(1 / ~a, Idx(II, s, u, indexmap), derivweights, s, indexmap, bcmap, depvars, x, u)) for x in ivs(u, s)]) for u in depvars], init = []))
 
     rules = safe_vcat(rules, reduce(safe_vcat, [vec([@rule /(*(~~b, ($(Differential(x))(*(~~a, $(Differential(x))(u), ~~d))), ~~c), ~e) => /(*(~b..., ~c..., cartesian_nonlinear_laplacian(*(~a..., ~d...), Idx(II, s, u, indexmap), derivweights, s, indexmap, bcmap, depvars, x, u)), replacevals(~e, s, u, depvars, II, indexmap)) for x in ivs(u, s)]) for u in depvars], init = []))
 

src/interface/MOLFiniteDifference.jl

@@ -33,11 +33,12 @@ struct MOLFiniteDifference{G,D} <: AbstractEquationSystemDiscretization
     use_ODAE::Bool
     disc_strategy::D
     useIR::Bool
+    callbacks
     kwargs
 end
 
 # Constructors. If no order is specified, both upwind and centered differences will be 2nd order
-function MOLFiniteDifference(dxs, time=nothing; approx_order = 2, advection_scheme = UpwindScheme(), grid_align=CenterAlignedGrid(), discretization_strategy = ScalarizedDiscretization(), upwind_order = nothing, should_transform = true, use_ODAE = false, useIR = true, kwargs...)
+function MOLFiniteDifference(dxs, time=nothing; approx_order = 2, advection_scheme = UpwindScheme(), grid_align=CenterAlignedGrid(), discretization_strategy = ScalarizedDiscretization(), upwind_order = nothing, should_transform = true, use_ODAE = false, useIR = true, callbacks = [], kwargs...)
     if upwind_order !== nothing
         @warn "`upwind_order` no longer does anything, and will be removed in a future release. See the docs for the current interface."
     end
@@ -50,7 +51,7 @@ function MOLFiniteDifference(dxs, time=nothing; approx_order = 2, advection_sche
 
     dxs = dxs isa Dict ? dxs : Dict(dxs)
 
-    return MOLFiniteDifference{typeof(grid_align), typeof(discretization_strategy)}(dxs, time, approx_order, advection_scheme, grid_align, should_transform, use_ODAE, discretization_strategy, useIR, kwargs)
+    return MOLFiniteDifference{typeof(grid_align), typeof(discretization_strategy)}(dxs, time, approx_order, advection_scheme, grid_align, should_transform, use_ODAE, discretization_strategy, useIR, callbacks, kwargs)
 end
 
 PDEBase.get_time(disc::MOLFiniteDifference) = disc.time

src/interface/callbacks.jl

@@ -0,0 +1,13 @@
+struct MOLDiscCallback
+    f::Function
+    p
+    sym
+end
+
+function MOLDiscCallback(f, disc_ps)
+    symh = hash(f)
+    sym = unwrap(first(@parameters(Symbol("MOLDiscCallback_$symh"))))
+    return MOLDiscCallback(f, disc_ps, sym)
+end
+
+(M::MOLDiscCallback)(s) = M.f(s, M.p)

src/interface/solution/common.jl

@@ -19,13 +19,28 @@
                 @assert i !== nothing "Independent variable $(arg_iv) in dependent variable $(dv) not found in the solution."
                 i
             end
-
+            if any(length.(sol.ivdomain) .== 1)
+                is = drop_singleton_inds(is, sol.ivdomain)
+            end
             sol.interp[dv](args[is]...)
         end
     end
+    if any(length.(sol.ivdomain) .== 1)
+        good_inds = get_good_inds(sol.ivdomain)
+        return sol.interp[dv](args[good_inds]...)
+    end
     return sol.interp[dv](args...)
 end
 
+function drop_singleton_inds(is, ivdomain)
+    bad_is = findall(a->length(a) == 1, ivdomain)
+    filter(a->!(a in bad_is), is)
+end
+
+function get_good_inds(ivdomain)
+    findall(a->length(a) > 1, ivdomain)
+end
+
 Base.@propagate_inbounds function Base.getindex(A::SciMLBase.PDESolution{T,N,S,D},
     sym) where {T,N,S,D<:MOLMetadata}
     iv = nothing

src/interface/solution/solution_utils.jl

@@ -12,10 +12,14 @@
         kreplaced = get(replaced_vars, k, nothing)
         if all(length.(nodes) .> 1)
             interp = interpolate(nodes, umap[k], Gridded(Linear()))
-        else
-            i = findfirst(a -> a <= 1, length.(nodes))
-            @warn "Solution has length 1 in dimension $(ivs[i]). Interpolation will not be possible for variable $k. Solution return code is $(sol.retcode)."
+        elseif all(length.(nodes) .== 1)
+            @warn "Solution has length 1 in all dimensions. Interpolation will not be possible. Solution return code is $(sol.retcode)."
             interp = nothing
+        # If one or more ivs have only length 1 but not all
+        else
+            is_todrop = tuple(findall(a->a==1, length.(nodes))...)
+            is = findall(a->a > 1, length.(nodes))
+            interp = interpolate(nodes[is], dropdims(umap[k], dims=is_todrop), Gridded(Linear()))
         end
         if isnothing(kreplaced)
             [k => interp]
@@ -25,4 +29,5 @@
     end |> Dict
 end
 
+
 sym_to_index(sym, syms) = findfirst(isequal(sym), syms)

src/interface/solution/timeindep.jl

@@ -11,7 +11,7 @@ function SciMLBase.PDENoTimeSolution(sol::SciMLBase.NonlinearSolution{T}, metada
     umap = mapreduce(vcat, dvs) do u
         let discu = discretespace.discvars[u]
             solu = map(CartesianIndices(discu)) do I
-                i = sym_to_index(discu[I], odesys.states)
+                i = sym_to_index(discu[I], get_states(odesys))
                 # Handle Observed
                 if i !== nothing
                     sol.u[i]

src/system_parsing/pde_system_transformation.jl

@@ -35,6 +35,9 @@
 end
 
 function PDEBase.should_transform(pdesys::PDESystem, disc::MOLFiniteDifference, boundarymap)
+    if !disc.should_transform
+        return false
+    end
     if has_interfaces(boundarymap)
         @warn "The system contains interface boundaries, which are not compatible with system transformation. The system will not be transformed. Please post an issue if you need this feature."
         return false

test/components/callbacks.jl

@@ -0,0 +1,38 @@
+using ModelingToolkit, MethodOfLines, DomainSets, Test, Symbolics, SymbolicUtils, OrdinaryDiffEq
+
+@testset "Discrete callback" begin
+    @parameters x, t
+    @variables u(..)
+    Dt = Differential(t)
+    Dxx = Differential(x)^2
+    t_min = 0.0 
+    t_max = 2.0
+    x_min = 0.0
+    x_max = 2.0
+
+    a = 0.1*pi
+
+    eq = Dt(u(t, x)) ~ a*Dxx(u(t, x))
+
+    bcs = [u(t_min, x) ~ sinpi(x), u(t, x_min) ~ sinpi(t+x), u(t, x_max) ~ sinpi(t+x)]
+
+    domains = [t ∈ Interval(t_min, t_max), x ∈ Interval(x_min, x_max)]
+
+    @named pdesys = PDESystem(eq, bcs, domains, [t, x], [u(t, x)])
+
+    cb = MOLDiscCallback((s, p) -> prod(p), [0.1, pi])
+    a_cb = cb.sym
+    cbeq = Dt(u(t, x)) ~ a_cb*Dxx(u(t, x))
+
+    @named cbpdesys = PDESystem(cbeq, bcs, domains, [t, x], [u(t, x)])
+
+    disc = MOLFiniteDifference([x => 0.1], t; approx_order=2, callbacks = [cb])
+
+    prob = discretize(pdesys, disc)
+    cbprob = discretize(cbpdesys, disc)
+
+    sol1 = solve(prob, Tsit5(), saveat=0.1)
+    sol2 = solve(cbprob, Tsit5(), saveat=0.1) 
+
+    @test sol1[u(t, x)] ≈ sol2[u(t, x)]
+end

test/pde_systems/MOL_1D_Linear_Diffusion.jl

@@ -42,7 +42,7 @@ using ModelingToolkit: Differential
 
     for disc in [discretization, discretization_edge, discretization_centered, discretization_approx_order4]
         # Convert the PDE problem into an ODE problem
-        prob = discrebranch tize(pdesys, disc)
+        prob = discretize(pdesys, disc)
 
         # Solve ODE problem      # Solve ODE problem
         sol = solve(prob, Tsit5(), saveat=0.1)

test/runtests.jl

@@ -30,7 +30,6 @@ const is_TRAVIS = haskey(ENV, "TRAVIS")
         @time @safetestset "MOLFiniteDifference Interface: Advanced Nonlinear Diffusion" begin
             include("pde_systems/nonlinear_laplacian_advanced.jl")
         end
-        end
     end
 
     if GROUP == "All" || GROUP == "Sol_Interface"
@@ -72,6 +71,9 @@ const is_TRAVIS = haskey(ENV, "TRAVIS")
         @time @safetestset "ODEFunction" begin
             include("components/ODEFunction_test.jl")
         end
+        @time @safetestset "Discrete Callbacks" begin
+            include("components/callbacks.jl")
+        end
         #@time @safetestset "Finite Difference Schemes" begin include("components/finite_diff_schemes.jl") end
     end