CompatHelper: bump compat for ContinuumArrays to 0.16, (keep existing compat)

[github-actions]

This pull request changes the compat entry for the ContinuumArrays package from 0.10, 0.11, 0.12 to 0.10, 0.11, 0.12, 0.16.
This keeps the compat entries for earlier versions.

Note: I have not tested your package with this new compat entry.
It is your responsibility to make sure that your package tests pass before you merge this pull request.

[jagot]

Closes #69, #71, #72 & #73

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 67.79%. Comparing base (4b817a5) to head (a1b977f).

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #70      +/-   ##
==========================================
- Coverage   67.98%   67.79%   -0.20%     
==========================================
  Files          24       24              
  Lines        1690     1621      -69     
==========================================
- Hits         1149     1099      -50     
+ Misses        541      522      -19     

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[jagot]

@dlfivefifty I finally got around fixing compat bounds. A lot of tests fail (related to diff and grammatrix). What do I need to do?

[dlfivefifty]

The changes are to avoid relying on @simplify which makes compile-time very slow. Some examples:

1. Overload grammatrix(::MyBasis) instead of @simplify *(::Adjoint{<:Any,<:MyBasis}, ::MyBasis) for creating the mass/gram matrix
2. Overload diff(::MyBasis; dims=1) instead of @simplify *(::Derivative, ::MyBasis) for creating the derivative

[jagot]

@dlfivefifty I seem to hitting a few snags:

• How do I implement the Laplacian A'D'D*B? I have specific formulae for the Laplacian, i.e. it is not the weak Laplacian formed from the multiplication of two gradient operators. Note that I need to consider both the left and right basis in, since I explicitly take the individual restrictions into account.
• How do I implement any other operator that mix derivative and potential operators, i.e. A'D'V*D*B, where V <: QuasiDiagonal.

In short, I need all arguments to the multiplication passed to my materialization routine. Incidentally, some of those that are implemented through the @materialize macro still work, e.g.

CompactBases.jl/src/fd_derivatives.jl

Line 222 in 4b817a5

@materialize function *(Ac::AdjointBasisOrRestricted{<:AbstractFiniteDifferences},

but not

CompactBases.jl/src/fd_derivatives.jl

Line 253 in 4b817a5

@materialize function *(Ac::AdjointBasisOrRestricted{<:AbstractFiniteDifferences},

Quick test example:

julia> N = 10
10

julia> ρ = 1.0
1.0

julia> R = StaggeredFiniteDifferences(N, ρ)
Staggered finite differences basis {Float64} on 0.0 .. 10.5 with 10 points spaced by ρ = 1.0

julia> r = axes(R, 1)
Inclusion(0.0 .. 10.5)

julia> D = Derivative(r)
Derivative(Inclusion(0.0 .. 10.5))

julia> ∇ = R'D*R
10×10 LinearAlgebra.Tridiagonal{Float64, Vector{Float64}}:
  0.0        0.666667    ⋅          ⋅          ⋅          ⋅          ⋅          ⋅          ⋅         ⋅
 -0.666667   0.0        0.533333    ⋅          ⋅          ⋅          ⋅          ⋅          ⋅         ⋅
   ⋅        -0.533333   0.0        0.514286    ⋅          ⋅          ⋅          ⋅          ⋅         ⋅
   ⋅          ⋅        -0.514286   0.0        0.507937    ⋅          ⋅          ⋅          ⋅         ⋅
   ⋅          ⋅          ⋅        -0.507937   0.0        0.505051    ⋅          ⋅          ⋅         ⋅
   ⋅          ⋅          ⋅          ⋅        -0.505051   0.0        0.503497    ⋅          ⋅         ⋅
   ⋅          ⋅          ⋅          ⋅          ⋅        -0.503497   0.0        0.502564    ⋅         ⋅
   ⋅          ⋅          ⋅          ⋅          ⋅          ⋅        -0.502564   0.0        0.501961   ⋅
   ⋅          ⋅          ⋅          ⋅          ⋅          ⋅          ⋅        -0.501961   0.0       0.501548
   ⋅          ⋅          ⋅          ⋅          ⋅          ⋅          ⋅          ⋅        -0.501548  0.0

julia> ∇² = R'D'D*R
ERROR: Overload diff(::StaggeredFiniteDifferences{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}})
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:35
 [2] diff_layout(#unused#::ContinuumArrays.BasisLayout, Vm::StaggeredFiniteDifferences{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, dims::Int64)
   @ ContinuumArrays ~/.julia/packages/ContinuumArrays/ZkEzA/src/bases/bases.jl:602
 [3] #diff#89
   @ ~/.julia/packages/QuasiArrays/5wpon/src/calculus.jl:50 [inlined]
 [4] diff
   @ ~/.julia/packages/QuasiArrays/5wpon/src/calculus.jl:50 [inlined]
 [5] mul
   @ ~/.julia/packages/ContinuumArrays/ZkEzA/src/operators.jl:139 [inlined]
 [6] mul
   @ ~/.julia/packages/ContinuumArrays/ZkEzA/src/operators.jl:42 [inlined]
 [7] *(A::QuasiArrays.QuasiAdjoint{Float64, StaggeredFiniteDifferences{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}, B::QuasiArrays.QuasiAdjoint{Float64, Derivative{Float64, IntervalSets.ClosedInterval{Float64}}})
   @ QuasiArrays ~/.julia/packages/QuasiArrays/5wpon/src/matmul.jl:23
 [8] *(::QuasiArrays.QuasiAdjoint{Float64, StaggeredFiniteDifferences{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}, ::QuasiArrays.QuasiAdjoint{Float64, Derivative{Float64, IntervalSets.ClosedInterval{Float64}}}, ::Derivative{Float64, IntervalSets.ClosedInterval{Float64}})
   @ Base ./operators.jl:578
 [9] top-level scope
   @ REPL[35]:1

[dlfivefifty]

Probably the best approach is to add a DerivativeStaggeredFiniteDifferences to represent D*R.

[jagot]

But then I would need such a proxy type for each basis, and also make it restriction-aware? That does not seem to be a scalable solution.

[dlfivefifty]

Just have diff return ApplyQuasiArray(*, D, P)

you might need to set simplifiable to be false