ModelingToolkit.reorder_unknowns() returns the wrong permutation?

[gg2031]

Describe the bug 🐞

ModelingToolkit.reorder_unknowns() returns the wrong permutation.

Expected behavior

P * A * P' rather than P' * A * P.

Minimal Reproducible Example 👇

The issue is a math error not a code error, so apologies for not including a MRE and skipping the remaining sections.

ModelingToolkit.reorder_unknowns() calls ModelingToolkit.similarity_transform() for which I believe we should have T = P' and not T = P, i.e.,

similarity_transform(sys, P'; unitary = true)

rather than

ModelingToolkit.jl/src/linearization.jl

Line 816 in 091c445

similarity_transform(sys, P; unitary = true)

See:

ModelingToolkit.jl/src/linearization.jl

Lines 807 to 817 in 091c445

	function reorder_unknowns(sys::NamedTuple, old, new)
	nx = length(old)
	length(new) == nx || error("old and new must have the same length")
	perm = [findfirst(isequal(n), old) for n in new]
	issorted(perm) && return sys # shortcut return, no reordering
	P = zeros(Int, nx, nx)
	for i in 1:nx # Build permutation matrix
	P[i, perm[i]] = 1
	end
	similarity_transform(sys, P; unitary = true)
	end

ModelingToolkit.jl/src/linearization.jl

Lines 765 to 791 in 091c445

	"""
	(; Ã, B̃, C̃, D̃) = similarity_transform(sys, T; unitary=false)
	Perform a similarity transform `T : Tx̃ = x` on linear system represented by matrices in NamedTuple `sys` such that
	```
	Ã = T⁻¹AT
	B̃ = T⁻¹ B
	C̃ = CT
	D̃ = D
	```
	If `unitary=true`, `T` is assumed unitary and the matrix adjoint is used instead of the inverse.
	"""
	function similarity_transform(sys::NamedTuple, T; unitary = false)
	if unitary
	A = T'sys.A * T
	B = T'sys.B
	else
	Tf = lu(T)
	A = Tf \ sys.A * T
	B = Tf \ sys.B
	end
	C = sys.C * T
	D = sys.D
	(; A, B, C, D)
	end

Error & Stacktrace ⚠️

N/A

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

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• Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

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• Output of versioninfo()

N/A

Additional context

Add any other context about the problem here.