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The inverse permutation has to be used in the second equation, and the rank has to be taken into account for rank-deficient cases. This doesn't make a difference in the simple example shown in the docstring, but it does in more complex cases.
dkarrasch
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Jun 22, 2021
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dkarrasch
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LGTM. How about actually adding a rank-deficient example? Something like
julia> X = [1.0, 2.0, 3.0, 4.0]; A = X*X';
julia> F = cholesky(A, Val(true), check = false);
julia> Ur = F.U[1:F.rank, :]; Lr = F.L[:, 1:F.rank]
julia> A[F.p, F.p] ≈ Ur' * Ur ≈ Lr * Lr'
true? To reduce the doctests, one could remove the full-rank case, since that one is covered in the non-pivoted case already?
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Good idea. Done. |
nalimilan
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Jun 22, 2021
KristofferC
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(cherry picked from commit 7409a1c)
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The inverse permutation has to be used in the second equation, and the rank has to be taken into account for rank-deficient cases.
This doesn't make a difference in the simple example shown in the docstring, but it does in more complex cases.
(These docs were introduced by #39964)