Define lq for sparse matrices as the adjoint of the sparse QR of the adjoint

[ViralBShah]

Fixes #114.

julia> A = sparse([1.0 0 1 0; 0 1 0 1]);

julia> lq(A)
ERROR: MethodError: no method matching lq!(::SparseMatrixCSC{Float64, Int64})

lq(A) now returns qr(A')', the AdjointQRSparse from #804, computed by SPQR on the sparse transpose, with tol and ordering passed through. It gets L, Q, prow and pcol properties so that A[F.prow, F.pcol] == F.L * F.Q, with F.L a lower triangular SparseMatrixCSC and F.Q the adjoint of the sparse Q; F \ b is the minimum-norm solution for a wide A and throws DimensionMismatch for a tall one, as dense lq does; F' is qr(A'), lq(A') reuses qr(A) without a copy, and rank and show work. qr also accepts adjoint and transpose wrappers of a SparseMatrixCSC directly, and the \ for a tall A' uses that instead of spelling the copy. The identity F.L * F.Q exposed a bug in the padded products with a sparse Q: they took the thin width from the number of stored Householder vectors, which SPQR keeps below the column count when the matrix is sparse enough, so qr(A).Q * qr(A).R threw DimensionMismatch for such an A. The width now comes from the column count that QRSparseQ records.

Tests in test/spqr.jl cover the factorization identity, properties, solves, tolerance, the tall error, the adjoint and transpose inputs and the thin product regression, for real and complex eltypes and both index types; spqr, linalg, Aqua, whitespace and the doctests pass on 1.14-DEV. docs/src/solvers.md lists lq. #831 will use lq for the wide \.

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[codecov]

Codecov Report

❌ Patch coverage is 96.77419% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 92.60%. Comparing base (88c6404) to head (8fb5d41).

Files with missing lines	Patch %	Lines
src/solvers/spqr.jl	96.66%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #833      +/-   ##
==========================================
+ Coverage   92.56%   92.60%   +0.04%     
==========================================
  Files          12       12              
  Lines        8699     8723      +24     
==========================================
+ Hits         8052     8078      +26     
+ Misses        647      645       -2     

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