Update NEWS.md and documentation for sparse QR. [ci skip]

NEWS.md

@@ -101,6 +101,8 @@ Library improvements
 
     * Large speedup in sparse ``\`` and splitting of Cholesky and LDLt factorizations into ``cholfact`` and ``ldltfact`` ([#10117])
 
+    * Add sparse least squares to ``\`` by adding ``qrfact`` for sparse matrices based on the SPQR library. ([#10180])
+
   * Other improvements
 
     * `assert`, `@assert` now throws an `AssertionError` exception type ([#9734]).

doc/stdlib/linalg.rst

@@ -21,7 +21,7 @@ Linear algebra functions in Julia are largely implemented by calling functions f
 .. function:: \\(A, B)
    :noindex:
 
-   Matrix division using a polyalgorithm. For input matrices ``A`` and ``B``, the result ``X`` is such that ``A*X == B`` when ``A`` is square.  The solver that is used depends upon the structure of ``A``.  A direct solver is used for upper- or lower triangular ``A``.  For Hermitian ``A`` (equivalent to symmetric ``A`` for non-complex ``A``) the ``BunchKaufman`` factorization is used.  Otherwise an LU factorization is used. For rectangular ``A`` the result is the minimum-norm least squares solution computed by a pivoted QR factorization of ``A`` and a rank estimate of A based on the R factor. For sparse, square ``A`` the LU factorization (from UMFPACK) is used.
+   Matrix division using a polyalgorithm. For input matrices ``A`` and ``B``, the result ``X`` is such that ``A*X == B`` when ``A`` is square.  The solver that is used depends upon the structure of ``A``.  A direct solver is used for upper- or lower triangular ``A``.  For Hermitian ``A`` (equivalent to symmetric ``A`` for non-complex ``A``) the ``BunchKaufman`` factorization is used.  Otherwise an LU factorization is used. For rectangular ``A`` the result is the minimum-norm least squares solution computed by a pivoted QR factorization of ``A`` and a rank estimate of A based on the R factor. When ``A`` is sparse, a similar polyalgorithm is used, but underdetermined systems are not supported.
 
 .. function:: dot(x, y)
               ⋅(x,y)
@@ -161,9 +161,13 @@ Linear algebra functions in Julia are largely implemented by calling functions f
    .. [Bischof1987] C Bischof and C Van Loan, The WY representation for products of Householder matrices, SIAM J Sci Stat Comput 8 (1987), s2-s13. doi:10.1137/0908009
    .. [Schreiber1989] R Schreiber and C Van Loan, A storage-efficient WY representation for products of Householder transformations, SIAM J Sci Stat Comput 10 (1989), 53-57. doi:10.1137/0910005
 
+.. function:: qrfact(A) -> SPQR.Factorization
+
+   Compute the QR factorization of a sparse matrix ``A``. A fill-reducing permutation is used. The main application of this type is to solve least squares problems with ``\``. The function calls the C library SPQR and a few additional functions from the library are wrapped but not exported.
+
 .. function:: qrfact!(A [,pivot=Val{false}])
 
-   ``qrfact!`` is the same as :func:`qrfact`, but saves space by overwriting the input ``A``, instead of creating a copy.
+   ``qrfact!`` is the same as :func:`qrfact` when A is a subtype of ``StridedMatrix``, but saves space by overwriting the input ``A``, instead of creating a copy.
 
 .. function:: full(QRCompactWYQ[, thin=true]) -> Matrix