mikity
Registered Member

Hi. I just started testing EIGEN. I'm interested in using the least squares solver provided by EIGEN.
I have successfully got correct solutions when system matrices are fullrank. However, when the specified system matrix is rank deficient, it seems that almost zero singular values are treated as nonzero values. I think, the better management of singular values should be that almost zero singular values are treated as exactly zero values. (I consistently use MatrixXf and VectorXf.) Here is an example, 4 2 6 2 1 3 The rank of this matrix is obviously 1. And JacobSVD returns its singular values as 8.3666 1.98603e16 This seems correct. However, when I gave a vector 5 2 to JacobSVD().solve(), it returns 6.01819e+014  2.14698e+015 3.14698e+015 This is too much bigger than I expected and this means that "1.98603e16" is treated as nonzero singular value. The expected behavior is that "1.98603e16" is treated as zero and thus its inverse is kept 0. If "1.98603e16" is treated as nonzero, its inverse is "1/1.98703e+16" and thus bigger numbers appear. By the way, in JacobSVD.h, I found the following statements. if(maxRemainingSingularValue == RealScalar(0)) { m_nonzeroSingularValues = i; break; } And I think RealScalar(0) should be replaced with an appropriate threshold. If double precision is used, any singular value is impossible to be precisely zero. Yesterday, I modified the statements in the end of JacobiSVD::compute() as follows and finally, it worked fine. The presented equation used for "tol" is (I think) the same equation used in Scilab, Octave and Matlab. /*** step 4. Sort singular values in descending order and compute the number of nonzero singular values ***/ Index pos; RealScalar maxSingularValue = m_singularValues.maxCoeff(&pos); double tol = std::max(m_rows,m_cols) * m_singularValues(pos) * precision; m_nonzeroSingularValues = m_diagSize; for(Index i = 0; i < m_diagSize; i++) { RealScalar maxRemainingSingularValue = m_singularValues.tail(m_diagSizei).maxCoeff(&pos); if(maxRemainingSingularValue < tol/*RealScalar(0)*/) { m_nonzeroSingularValues = i; break; } if(pos) { pos += i; std::swap(m_singularValues.coeffRef(i), m_singularValues.coeffRef(pos)); if(computeU()) m_matrixU.col(pos).swap(m_matrixU.col(i)); if(computeV()) m_matrixV.col(pos).swap(m_matrixV.col(i)); } } Thanks. 
ggael
Moderator

right, I think JacobiSVD should provide a setTolerance() function to let the user adjust its favorite tolerance value to consider what is a zero singularvalue.

mikity
Registered Member

Thanks, ggael. For me, EIGN is really great work and hope JacobiSVD().solve will improve its computational efficiency. For me, Lapack family seems too old fashion and I expect (and feel) EIGEN to be one of standard numerical libraries.

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