Rogue `true` in inverse of a matrix

[dpsanders]

julia> @variables a, b, c, d
(a, b, c, d)

julia> A = [a b; c d]
2×2 Matrix{Num}:
 a  b
 c  d

julia> inv(A)
2×2 Matrix{Num}:
                       (a^-1)*(true + (b*c*(a^-1)*((d - (b*c*(a^-1)))^-1)))  …  -b*(a^-1)*((d - (b*c*(a^-1)))^-1)
 -c*(a^-1)*((d - (b*c*(a^-1)))^-1)                                                          (d - (b*c*(a^-1)))^-1

Note the truein A[1, 1].

┆Issue is synchronized with this Trello card by Unito

[YingboMa]

It does equal to d/det(A) so at least it's not wrong :-). We might want to special case small inverses.

[dpsanders]

Maybe it should be returned in the form(1 / det(A)) * adj(A) with the det factored out?

[michakraus]

In Julia v1.7 this has a nasty side effect:

julia> inv(A)
ERROR: MethodError: no method matching checknonsingular(::Int64, ::Val{true})
Closest candidates are:
  checknonsingular(::Any) at /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.7/LinearAlgebra/src/factorization.jl:21
  checknonsingular(::Any, ::LinearAlgebra.RowMaximum) at /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.7/LinearAlgebra/src/factorization.jl:19
  checknonsingular(::Any, ::LinearAlgebra.NoPivot) at /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.7/LinearAlgebra/src/factorization.jl:20
Stacktrace:
 [1] sym_lu(A::Matrix{Num}; check::Bool)
   @ Symbolics ~/.julia/packages/Symbolics/1TCCw/src/linear_algebra.jl:49
 [2] #lu#25
   @ ~/.julia/packages/Symbolics/1TCCw/src/num.jl:174 [inlined]
 [3] lu
   @ ~/.julia/packages/Symbolics/1TCCw/src/num.jl:174 [inlined]
 [4] inv(A::Matrix{Num})
   @ LinearAlgebra /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.7/LinearAlgebra/src/dense.jl:874
 [5] top-level scope
   @ REPL[7]:1

(Julia v1.7.0-beta3.0, SymbolicUtils v0.13.4, Symbolics v3.2.0)

[ChrisRackauckas]

Yeah that's not good. @YingboMa you got this one?

[YingboMa]

That's not related to this issue. Could you open another issue?

[michakraus]

Is it not? As far as I can see, the problem comes from checknonsingular being called on the true that appears in the expression of the inverse, which maybe shouldn't be there in the first place?

[YingboMa]

That true is not related to this at all.

[michakraus]

Ok, then I'll open another issue (#357).

[Johan-Gronqvist]

I just had this issue, and in my case I have an upper triangular 2x2-matrix A for which inv seems to compute ldiv!(A, Matrix{Num}(I, (2, 2))). The type of I is UniformScaling{Bool} and I get the result I expect by using 1.0*I instead of I to replace the UniformScaling{Bool} by a UniformScaling{Float64}.

The code in triangular.jl from the LinearAlgebra stdlib calls (in this case)

Matrix{Num}(I, (2, 2))

which becomes a matrix containing true due to Num(true) evaluating to a value true.

I suggest that Num(true) should return one(Num) which is a "1" of some form instead of a symbolic expression with the content true.

Is there a reason to want to treat symbolic boolean expressions at all, such as piecewise defined functions?

I expect that the standard library calls Matrix{Num}(I, (2, 2)) with the expectation that it return a value with ones along the diagonal, and I would therefore expect Num(true) should return a value that represents the value 1 more clearly than true does.

[Johan-Gronqvist]

This seems to give me the behaviour I want, in the case I am looking at now:

import Symbolics: Num
Num(b :: Bool) = ifelse(b, one(Num), zero(Num))

[PhyX-Meow]

Does this get some improvement? Currently result of inverse matrix is basically unreadable.

[bowenszhu]

Does this get some improvement? Currently result of inverse matrix is basically unreadable.

Unfortunately no. See this related issue https://github.com/JuliaSymbolics/Symbolics.jl/issues/693.