I have attempted to update some code to the preferred updated syntax u(..)[1:n] since u[1:n](..) is slated for deprecation. When I modify this in the code, I get a new error.
I have attached an example problem from adapted from the tutorial with the fixes from a previous discussion (Vector equations LHS/RHS missing with MTK and MethodOfLines)
The error seems to have something to do with the variable map step, and specifically (I think) to something going wrong with getting the properties of the independent variable t in this case. Is there any workaround for this issue?
In the meantime, is the syntax deprecation of u(..)[1:n] likely to happen soon, and are there any resources I can use to learn how to figure out what is going wrong deep in packages like this?
using DifferentialEquations, ModelingToolkit, MethodOfLines, DomainSets
# Parameters, variables, and derivatives
n_comp = 2
@parameters t, x, p[1:n_comp], q[1:n_comp]
@variables u(..)[1:n_comp]
Dt = Differential(t)
Dx = Differential(x)
Dxx = Differential(x)^2
params = Symbolics.scalarize(reduce(vcat,[p .=> [1.5, 2.0], q .=> [1.2, 1.8]]))
# 1D PDE and boundary conditions
eqs = [Dt(u(t, x)[i]) ~ p[i] * Dxx(u(t, x)[i]) for i in 1:n_comp]
bcs = [[u(0, x)[i] ~ q[i] * cos(x),
u(t, 0)[i] ~ sin(t),
u(t, 1)[i] ~ exp(-t) * cos(1),
Dx(u(t,0)[i]) ~ 0.0] for i in 1:n_comp]
bcs_collected = reduce(vcat, bcs)
# Space and time domains
domains = [t ∈ Interval(0.0, 1.0),
x ∈ Interval(0.0, 1.0)]
# PDE system
@named pdesys = PDESystem(eqs, bcs_collected, domains, [t, x], [u(t, x)[i] for i in 1:n_comp], Symbolics.scalarize(params))
# Method of lines discretization
dx = 0.1
order = 2
discretization = MOLFiniteDifference([x => dx], t; approx_order = order)
# Convert the PDE problem into an ODE problem
prob = discretize(pdesys,discretization) #error occurs here
# Solve ODE problem
sol = solve(prob, Tsit5(), saveat=0.2)
The error I get from attempting discretization is:
ERROR: ArgumentError: invalid index: nothing of type Nothing
Stacktrace:
[1] to_index(i::Nothing)
@ Base .\indices.jl:300
[2] to_index(A::Vector{Symbolics.VarDomainPairing}, i::Nothing)
@ Base .\indices.jl:277
[3] to_indices
@ .\indices.jl:333 [inlined]
[4] to_indices
@ .\indices.jl:325 [inlined]
[5] getindex
@ .\abstractarray.jl:1241 [inlined]
[6] (::PDEBase.var"#48#57"{Vector{Symbolics.VarDomainPairing}})(x::SymbolicUtils.BasicSymbolic{Vector{Real}})
@ PDEBase \.julia\packages\PDEBase\rQehP\src\variable_map.jl:35
[7] iterate
@ .\generator.jl:47 [inlined]
[8] _collect(c::Vector{Any}, itr::Base.Generator{Vector{Any}, PDEBase.var"#48#57"{Vector{Symbolics.VarDomainPairing}}}, #unused#::Base.EltypeUnknown, isz::Base.HasShape{1})
@ Base .\array.jl:807
[9] collect_similar(cont::Vector{Any}, itr::Base.Generator{Vector{Any}, PDEBase.var"#48#57"{Vector{Symbolics.VarDomainPairing}}})
@ Base .\array.jl:716
[10] map(f::Function, A::Vector{Any})
@ Base .\abstractarray.jl:2933
[11] VariableMap(pdesys::PDESystem, disc::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
@ PDEBase \.julia\packages\PDEBase\rQehP\src\variable_map.jl:34
[12] symbolic_discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
@ PDEBase \.julia\packages\PDEBase\rQehP\src\symbolic_discretize.jl:15
[13] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}; analytic::Nothing, kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
@ PDEBase \.julia\packages\PDEBase\rQehP\src\discretization_state.jl:58
[14] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
@ PDEBase \.julia\packages\PDEBase\rQehP\src\discretization_state.jl:55
[15] top-level scope
@ \test_for_debug.jl:38