Base.cond and Base.SparseMatrix.cond don't not always check if input matrix is square

[marcusps]

When attempting to compute the condition number of a rectangular matrix, Base.cond does not always fail, but when it fails it does not always fail for the right reasons:

julia> cond(randn(3,2))
1.6361841239391517

julia> cond(randn(3,2),1)
ERROR: DimensionMismatch("matrix is not square")
 in chksquare at ./linalg.jl:179
 in cond at linalg/dense.jl:511

julia> cond(randn(3,2),Inf)
ERROR: DimensionMismatch("matrix is not square")
 in chksquare at ./linalg.jl:179
 in cond at linalg/dense.jl:511

julia> cond(sprandn(3,2,.2))
ERROR: ArgumentError: 2-norm condition number is not implemented for sparse matrices, try cond(full(A), 2) instead
 in cond at sparse/linalg.jl:515
 in cond at sparse/linalg.jl:506

julia> cond(sprandn(3,2,.2),1)
ERROR: BoundsError: attempt to access 2x2 Array{Float64,2}:
 0.0        0.0     
 0.739339  -0.739339
  at index [1:3,1]
 in throw_boundserror at abstractarray.jl:153
 in normestinv at sparse/linalg.jl:570
 in cond at sparse/linalg.jl:508

julia> cond(sprandn(3,2,.2),Inf)
ERROR: DimensionMismatch("Q matrix size 2 and dense matrix has 3 rows")
 in qmult at sparse/spqr.jl:130
 in \ at sparse/spqr.jl:144
 in normestinv at sparse/linalg.jl:566
 in cond at sparse/linalg.jl:512

For rectangular matrices cond simply return Inf or raise an error (although I think ArgumentError would be more appropriate).

[andreasnoack]

It is pretty standard to allow the 2 condition number of rectangular matrices so I think the main thing we'll have to change is to add a chksquare in the sparse condition number function. Feel free to open a pr.

[marcusps]

Ah, just learned something about condition numbers after reading #1862.

I'll patch the sparse matrix implementation.

On Fri, Aug 21, 2015, 2:23 PM Andreas Noack [email protected]
wrote:

It is pretty standard to allow the 2 condition number of rectangular
matrices so I think the main thing we'll have to change is to add a
chksquare in the sparse condition number function. Feel free to open a pr.

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