From 482c5fb321695f7992d3bb718b7f64f2feaf61d5 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 19 Feb 2019 22:52:15 +0100
Subject: bug #899: remove "rank-revealing" qualifier for SparseQR and warn
 that it is not always rank-revealing.

---
 Eigen/src/SparseQR/SparseQR.h | 22 +++++++++++++++++-----
 1 file changed, 17 insertions(+), 5 deletions(-)

(limited to 'Eigen/src/SparseQR')

diff --git a/Eigen/src/SparseQR/SparseQR.h b/Eigen/src/SparseQR/SparseQR.h
index 1a28389e8..d1fb96f5c 100644
--- a/Eigen/src/SparseQR/SparseQR.h
+++ b/Eigen/src/SparseQR/SparseQR.h
@@ -41,15 +41,16 @@ namespace internal {
 /**
   * \ingroup SparseQR_Module
   * \class SparseQR
-  * \brief Sparse left-looking rank-revealing QR factorization
+  * \brief Sparse left-looking QR factorization with numerical column pivoting
   * 
-  * This class implements a left-looking rank-revealing QR decomposition 
-  * of sparse matrices. When a column has a norm less than a given tolerance
+  * This class implements a left-looking QR decomposition of sparse matrices
+  * with numerical column pivoting.
+  * When a column has a norm less than a given tolerance
   * it is implicitly permuted to the end. The QR factorization thus obtained is 
   * given by A*P = Q*R where R is upper triangular or trapezoidal. 
   * 
   * P is the column permutation which is the product of the fill-reducing and the
-  * rank-revealing permutations. Use colsPermutation() to get it.
+  * numerical permutations. Use colsPermutation() to get it.
   * 
   * Q is the orthogonal matrix represented as products of Householder reflectors. 
   * Use matrixQ() to get an expression and matrixQ().adjoint() to get the adjoint.
@@ -64,6 +65,17 @@ namespace internal {
   * 
   * \implsparsesolverconcept
   *
+  * The numerical pivoting strategy and default threshold are the same as in SuiteSparse QR, and
+  * detailed in the following paper:
+  * <i>
+  * Tim Davis, "Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing
+  * Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011.
+  * </i>
+  * Even though it is qualified as "rank-revealing", this strategy might fail for some 
+  * rank deficient problems. When this class is used to solve linear or least-square problems
+  * it is thus strongly recommended to check the accuracy of the computed solution. If it
+  * failed, it usually helps to increase the threshold with setPivotThreshold.
+  * 
   * \warning The input sparse matrix A must be in compressed mode (see SparseMatrix::makeCompressed()).
   * \warning For complex matrices matrixQ().transpose() will actually return the adjoint matrix.
   * 
@@ -331,7 +343,7 @@ void SparseQR<MatrixType,OrderingType>::analyzePattern(const MatrixType& mat)
   m_R.resize(m, n);
   m_Q.resize(m, diagSize);
   
-  // Allocate space for nonzero elements : rough estimation
+  // Allocate space for nonzero elements: rough estimation
   m_R.reserve(2*mat.nonZeros()); //FIXME Get a more accurate estimation through symbolic factorization with the etree
   m_Q.reserve(2*mat.nonZeros());
   m_hcoeffs.resize(diagSize);
-- 
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