lapack: posv: flaky test

[nsajko]

The test:

LinearAlgebra.jl/test/lapack.jl

Lines 676 to 689 in 9bc292d

	@testset "posv and some errors for friends" begin
	@testset for elty in (Float32, Float64, ComplexF32, ComplexF64)
	local n = 10
	A = rand(elty,n,n)/100
	A += real(diagm(0 => n*real(rand(elty,n))))
	if elty <: Complex
	A = A + A'
	else
	A = A + transpose(A)
	end
	B = rand(elty,n,n)
	D = copy(A)
	C = copy(B)
	D,C = LAPACK.posv!('U',D,C)

Observed in CI of PR JuliaLang/julia#56899:

https://buildkite.com/julialang/julia-master/builds/43437#019432a7-3343-4c56-b59b-6275b3cec3e9/862-916

LinearAlgebra/lapack                             (3) |         failed at 2025-01-04T11:14:05.793
Error During Test at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/stdlib/v1.12/LinearAlgebra/test/lapack.jl:677
  Got exception outside of a @test
  PosDefException: matrix is not positive definite; Factorization failed.
  Stacktrace:
    [1] chkposdef
      @ /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/stdlib/v1.12/LinearAlgebra/src/lapack.jl:54 [inlined]
    [2] posv!(uplo::Char, A::Matrix{Float32}, B::Matrix{Float32})
      @ LinearAlgebra.LAPACK /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/stdlib/v1.12/LinearAlgebra/src/lapack.jl:3273
    [3] macro expansion
      @ /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/stdlib/v1.12/LinearAlgebra/test/lapack.jl:689 [inlined]
    [4] macro expansion
      @ /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/stdlib/v1.12/Test/src/Test.jl:1853 [inlined]
    [5] macro expansion
      @ /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/stdlib/v1.12/LinearAlgebra/test/lapack.jl:677 [inlined]
    [6] macro expansion
      @ /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/stdlib/v1.12/Test/src/Test.jl:1764 [inlined]
    [7] top-level scope
      @ /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/stdlib/v1.12/LinearAlgebra/test/lapack.jl:677
    [8] include(mod::Module, _path::String)
      @ Base ./Base.jl:300
    [9] macro expansion
      @ /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/test/testdefs.jl:33 [inlined]
   [10] macro expansion
      @ /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/stdlib/v1.12/Test/src/Test.jl:1764 [inlined]
   [11] macro expansion
      @ /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/test/testdefs.jl:26 [inlined]
   [12] macro expansion
      @ ./timing.jl:611 [inlined]
   [13] runtests(name::String, path::String, isolate::Bool; seed::UInt128)
      @ Main /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/test/testdefs.jl:24
   [14] runtests
      @ /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/test/testdefs.jl:5 [inlined]
   [15] invokelatest(::Any, ::Any, ::Vararg{Any}; kwargs::@Kwargs{seed::UInt128})
      @ Base ./essentials.jl:1058
   [16] (::Distributed.var"#handle_msg##4#handle_msg##5"{Distributed.CallMsg{:call_fetch}})()
      @ Distributed /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/stdlib/v1.12/Distributed/src/process_messages.jl:287
   [17] run_work_thunk(thunk::Distributed.var"#handle_msg##4#handle_msg##5"{Distributed.CallMsg{:call_fetch}}, print_error::Bool)
      @ Distributed /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/stdlib/v1.12/Distributed/src/process_messages.jl:70
   [18] (::Distributed.var"#handle_msg##2#handle_msg##3"{Distributed.CallMsg{:call_fetch}, Distributed.MsgHeader, Sockets.TCPSocket})()
      @ Distributed /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-R17H3W25T9.0/build/default-honeycrisp-R17H3W25T9-0/julialang/julia-master/julia-640e80cd1d/share/julia/stdlib/v1.12/Distributed/src/process_messages.jl:287

[stevengj]

Seems like it should just do:

A = randn(elty,n,n)
A = A' * A