Clarify what sparse(F.LD) returns in the ldlt docstring

[ViralBShah]

Fixes #725.

F.LD means two different matrices depending on how you use it:

Use	What it is
F.LD \ b	solves with the product L*D (cholmod_solve with CHOLMOD_LD)
sparse(F.LD)	CHOLMOD's packed LDL' factor — L with its unit diagonal overwritten by diag(D)

so F.LD \ b and sparse(F.LD) \ b are different operations:

sparse(F.LD)           recovered L            recovered D
 7.0    0    0    0     1.0    0    0    0     7.0
 0.29  3.43  0    0     0.29  1.0   0    0          3.43
 0     0.29 4.71  0     0     0.29 1.0   0               4.71
 0.14 -0.08 0.23 5.58   0.14 -0.08 0.23 1.0                   5.58

L*D*L' == A[p,p]              : true
sparse(F.LD) == L*D           : false
F.LD \ b == (L*D) \ b         : true
F.LD \ b == sparse(F.LD) \ b  : false

The docstring said only that "the LD component can be materialized as a
sparse matrix using sparse(F.LD)", mentioning neither the packed layout nor
the divergence from F.LD \ b. Sitting next to F.PtL = P'*L and F.UP =
L'*P, which really are products, LD reads as L*D.

The internals already rely on the packed convention: sparse(::Factor) calls
getLd! on sparse(F.LD), which reads d off the diagonal and writes 1
back into it to recover L.

This documents both meanings and replaces the vague "can be reconstructed from
sparse(F.LD) and F.p if needed" with the actual recipe. The snippet is
verified on a 200×200 problem: diag(LD) == diag(F), L comes back as a
SparseMatrixCSC, and L*D*L' == A[F.p, F.p].

Docstring change only — no behavior change. Two alternatives I did not take:

• Renaming or aliasing the component. F.LD as an operator is consistent
  with PtL/UP; only sparse exposes the packed form, and changing either
  would break code.
• Making sparse(F.LD) return L*D. As the reporter notes, L is
  unrecoverable from L*D when D has a zero diagonal entry, and
  sparse(::Factor) depends on the packed layout. The packed form is strictly
  more informative — it just needed documenting.

🤖 Generated with Claude Code

https://claude.ai/code/session_01L8HenXTVrASo1sBZVGhpDQ

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 84.19%. Comparing base (53690b3) to head (930159b).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

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  Coverage   84.19%   84.19%           
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  Files          13       13           
  Lines        9403     9403           
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  Hits         7917     7917           
  Misses       1486     1486           

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