Aqua + typos CI

[ArnoStrouwen]

Minor amount of type piracy needs to be fixed.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (7b3920c) 57.06% compared to head (296678b) 57.64%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #77      +/-   ##
==========================================
+ Coverage   57.06%   57.64%   +0.58%     
==========================================
  Files          13       13              
  Lines        1055     1053       -2     
==========================================
+ Hits          602      607       +5     
+ Misses        453      446       -7     

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[ArnoStrouwen]

@AlCap23 does it make sense to upstream this function?

SymbolicNumericIntegration.jl/src/sparse.jl

Lines 124 to 128 in 7b3920c

	# This is needed to fix a bug/omission in DataDrivenSparse
	function DataDrivenSparse.active_set!(idx::BitMatrix, p::SoftThreshold,
	x::Matrix{ComplexF64}, λ::Float64)
	DataDrivenSparse.active_set!(idx, p, abs.(x), λ)
	end

[ArnoStrouwen]

@ChrisRackauckas If tests pass, I think this is good to go, the last remaining piracy can be made into an issue and fixed later.
EDIT: nevermind, this package has weird tests, it does not seem to fail if some integrals can no longer be solved.

[ArnoStrouwen]

@shahriariravanian is it safe to delete these functions?
https://github.com/SciML/SymbolicNumericIntegration.jl/pull/77/files#diff-5286ab18446ceac577bfe10dbc94bafeb42424a99a1a1556e26aa7dd8ec26267
Since it is type piracy, it is very hard to track down what the intended use of these lines is.

[shahriariravanian]

@ArnoStrouwen
We still need Base.signbit(z::Complex{T}) where {T <: Number} = signbit(real(z)). This is to prevent error messages when it tries to calculate abs(z) for when z is a complex number.

The problem arises because some of the derivatives in Symbolics have an abs in them. For example, expand_derivatives(Differential(x)(asec(x))) returns 1 / (abs(x)*sqrt(-1 + x^2)), which is the standard solution for real arguments but is meaningless for complex arguments. I think a better option would be to fix Symbolics to return 1 / (x^2 * sqrt(1 - 1/x^2)), which is what Mathematica does and works for complex values. If Symbolics is fixed, we can get rid of this signbit line.

[ChrisRackauckas]

That edit should happen in DiffRules.jl