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bug #899: remove "rank-revealing" qualifier for SparseQR and warn that it is not always rank-revealing.

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Gael Guennebaud 2019-02-19 22:52:15 +01:00
parent 9ac1634fdf
commit 482c5fb321
1 changed files with 17 additions and 5 deletions
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20
Eigen/src/SparseQR/SparseQR.h
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@ -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.
*