Backports for v1.12 #624
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Backports for v1.12 #624
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The `issymmetric` check tracks an `offset` that it uses to go from (row, col) to (col, row). However, currently this doesn't account for the fact that if a column is empty, entries in `colptr` will be identical. E.g., in #605, we have ```julia julia> S = sparse([2, 3, 1], [1, 1, 3], [1, 1, 1], 3, 3) 3×3 SparseMatrixCSC{Int64, Int64} with 3 stored entries: ⋅ ⋅ 1 1 ⋅ ⋅ 1 ⋅ ⋅ julia> SparseArrays.getcolptr(S) 4-element Vector{Int64}: 1 3 3 4 ``` The offset `3` corresponds to rows in the third column, as the second column is empty. This PR checks for empty columns, in which case we may exit the call immediately. Fixes #605
The purpose of this PR is to not call `==` directly, and use `_iszero` instead. This is to help integration with [IntervalArithmetic.jl](https://github.com/JuliaIntervals/IntervalArithmetic.jl) since `==` for our `Interval` type does not always return a Boolean. Closes #609. I did not change two checks using `===` since this would break the behaviour for `-0.0`.
This improves performance: ```julia julia> using LinearAlgebra, SparseArrays julia> D = Diagonal(rand(3000)); julia> S = sprand(size(D,1), 0.01); julia> @Btime ldiv!($D, $S); 30.053 μs (0 allocations: 0 bytes) # master 1.585 μs (0 allocations: 0 bytes) # PR ```
This prevents us from being influenced by things like `LD_LIBRARY_PATH`, and ensures that we always load the correct `libsuitesparseconfig` that came with our JLL.
I find it worth pointing out explicitly in the docs that LDLt, which mathematically looks like a drop-in replacement for Cholesky that does away with the positive definiteness requirement, comes with the following caveats: * It fails for a lot of matrices (for example, `ldlt(Symmetric(sprandn(1000, 1000, p)))` basically never succeeds for any relevant sparsity `p`) due to the requirement that all leading principal minors be well-conditioned * In CHOLMOD, `ldlt` is significantly slower than `cholesky` as it does not have a supernodal implementation So I made some docstring edits to clarify the relationship and tradeoffs between `cholesky` and `ldlt`. Citation for these claims: pages 106-107 in the CHOLMOD user guide at https://github.com/DrTimothyAldenDavis/SuiteSparse/blob/v7.10.3/CHOLMOD/Doc/CHOLMOD_UserGuide.pdf
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## release-1.12 #624 +/- ##
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- Coverage 84.09% 83.87% -0.22%
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Files 12 12
Lines 9192 9187 -5
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- Hits 7730 7706 -24
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Included:
issymmetricfor matrices with empty columns #606v == zero(v)with_iszero#610ldiv!forDiagonaland a sparse vector #613eltypeinDiagonalldiv!/rdiv!#616libsuitesparseconfigfrom JLL #620