Error when inverting array view under certain conditions

[jmlawson]

Matrix inversion of an a view of an array seems to throw a contiguous columns error, but only when there are no zeros in the matrix view:

julia> x
2×2×2 Array{Float64, 3}:
[:, :, 1] =
 0.0  0.0
 0.0  0.0

[:, :, 2] =
 0.0  0.0
 0.0  0.0

julia> x[1,:,:]=[1 0; 0 1]
2×2 Matrix{Int64}:
 1  0
 0  1

julia> inv(@view x[1,:,:])
ERROR: matrix does not have contiguous columns
Stacktrace:
 [1] error(s::String)
   @ Base .\error.jl:33
 [2] _chkstride1(ok::Bool)
   @ LinearAlgebra C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\LinearAlgebra.jl:203
 [3] _chkstride1
   @ C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\LinearAlgebra.jl:204 [inlined]
 [4] chkstride1
   @ C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\LinearAlgebra.jl:202 [inlined]
 [5] trtrs!(uplo::Char, trans::Char, diag::Char, A::SubArray{Float64, 2, Array{Float64, 3}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}}, true}, B::Matrix{Float64})
   @ LinearAlgebra.LAPACK C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\lapack.jl:3412
 [6] ldiv!
   @ C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\triangular.jl:739 [inlined]
 [7] inv(A::LinearAlgebra.UpperTriangular{Float64, SubArray{Float64, 2, Array{Float64, 3}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}}, true}})
   @ LinearAlgebra C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\triangular.jl:821
 [8] inv(A::SubArray{Float64, 2, Array{Float64, 3}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}}, true})
   @ LinearAlgebra C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\dense.jl:811
 [9] top-level scope
   @ none:1

julia> x[1,:,:]=[1 .5; .5 1]
2×2 Matrix{Float64}:
 1.0  0.5
 0.5  1.0

julia> inv(@view x[1,:,:])
2×2 Matrix{Float64}:
  1.33333   -0.666667
 -0.666667   1.33333

Thanks for your help! Apologies if this is not truly a bug.

[andreasnoack]

This is a limitation in LAPACK that we use most linear algebra. We have generic fallbacks that could be used here but we'd have to change many signatures. I guess, we'd have to introduce a trait for LAPACK compatible strides.

[timholy]

If it helps, there's

julia> v = @view x[1,:,:]
2×2 view(::Array{Float64, 3}, 1, :, :) with eltype Float64:
 1.0  0.0
 0.0  1.0

julia> Base.iscontiguous(v)
false

julia> v isa Base.FastContiguousSubArray
false