Clarify pros, cons and limitations of Cholesky and LDLt #621
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dkarrasch
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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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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:
ldlt(Symmetric(sprandn(1000, 1000, p)))basically never succeeds for any relevant sparsityp) due to the requirement that all leading principal minors be well-conditionedldltis significantly slower thancholeskyas it does not have a supernodal implementationSo I made some docstring edits to clarify the relationship and tradeoffs between
choleskyandldlt.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