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Bug 236

Summary: qr_colpivoting_3 fails sometimes for rank 1 matrices.
Product: Eigen Reporter: Gael Guennebaud <gael.guennebaud>
Component: QRAssignee: Nobody <eigen.nobody>
Status: NEW ---    
Severity: Unknown    
Priority: ---    
Version: 3.0   
Hardware: All   
OS: All   

Description Gael Guennebaud 2011-03-25 15:05:27 UTC
Seed to reproduce: s1301044630

The problem happens when testing the rank of a rank 1 matrix. In ColPivHouseholderQR::rank(), line 202, there is like a factor 2 or 3 between premultiplied_threshold and the and the second biggest pivot which are both 1e-16 times smaller than the biggest. So nothing serious.

Nevertheless, if in the creation of a rank-one matrix (test/main.h, line 423), I remove the normalized(), then the "probably wrong negatives" go away.
Comment 1 Gael Guennebaud 2011-03-25 16:01:45 UTC
For the record, reflapack or mkl does no fails on this particular seed, but they fails on other matrices, e.g. with a rank 2 while Eigen passes. So I'd say even.

Here is the piece of code to call LAPACK from ColPivHouseholderQR (for complexes):

  int M = rows;
  int N = cols;
  int LDA = rows;
  int INFO = 0;
  VectorXd rwork(2*cols);
  VectorXi jpvt(cols);
  m_qr = matrix;
  zgeqpf_( &M, &N, &m_qr.real().coeffRef(0,0), &LDA,, &m_hCoeffs.real().coeffRef(0), &m_temp.real().coeffRef(0),, &INFO);
  m_maxpivot = internal::real(m_qr(0,0));
  m_nonzero_pivots = 0;
  for(Index k = 0; k < size; ++k)
  m_colsTranspositions = jpvt.cast<typename IntRowVectorType::Index>().array() - 1;
  for(Index k = 0; k < m_nonzero_pivots; ++k)
    m_colsPermutation.applyTranspositionOnTheRight(k, m_colsTranspositions.coeff(k));
  m_isInitialized = true;
  return *this;
Comment 2 Nobody 2019-12-04 10:35:11 UTC
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