@@ -1567,6 +1567,12 @@ using just `L` without accounting for `P` will give incorrect answers.
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To include the effects of permutation,
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it's typically preferable to extract "combined" factors like `PtL = F.PtL`
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(the equivalent of `P'*L`) and `LtP = F.UP` (the equivalent of `L'*P`).
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+ The complete list of supported factors is `:L, :PtL, :UP, :U`.
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+ The permutation vector is available as `F.p`, defined such that `L*L' == A[p, p]`,
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+
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+ The `L` component can be materialized as a sparse matrix using `sparse(F.L)`.
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+ Other components cannot be materialized directly, but can be reconstructed
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+ from `sparse(F.L)` and `F.p` if needed.
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When `check = true`, an error is thrown if the decomposition fails.
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When `check = false`, responsibility for checking the decomposition's
@@ -1744,6 +1750,11 @@ To include the effects of permutation, it is typically preferable to extract
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"combined" factors like `PtL = F.PtL` (the equivalent of
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`P'*L`) and `LtP = F.UP` (the equivalent of `L'*P`).
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The complete list of supported factors is `:L, :PtL, :D, :UP, :U, :LD, :DU, :PtLD, :DUP`.
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+ The permutation vector is available as `F.p`, defined such that `L*D*L' == A[p, p]`,
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+
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+ The `LD` component can be materialized as a sparse matrix using `sparse(F.LD)`,
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+ Other components cannot be materialized directly, but can be reconstructed from
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+ `sparse(F.LD)` and `F.p` if needed.
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Unlike the related Cholesky factorization, the ``LDL'`` factorization does not
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require `A` to be positive definite. However, it still requires all leading
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