Dear all,
I am relatively new to libmesh and would like to report a problem using the SVD
routine of the DenseMatrix class for rectangular matrices. My example program
looks as follows:
#include <iostream>
#include <fstream>
#include <algorithm>
#include <math.h>
#include "libmesh/libmesh.h"
#include "libmesh/dense_vector.h"
#include "libmesh/dense_matrix.h"
#include <Eigen/SVD>
using namespace libMesh;
int main (int argc, char** argv)
{
LibMeshInit init (argc, argv);
{
std::cout << "## Libmesh DenseMatrix SVD" << std::endl;
DenseMatrix< Number > A( 3, 2 );
DenseMatrix< Number > U, VT;
DenseVector< Number > sigma;
A(0,0) = 2.0;
A(1,0) = 0.0;
A(2,0) = 0.0;
A(0,1) = 0.0;
A(1,1) = 1.0;
A(2,1) = 0.0;
std::cout << "A = " << std::endl << A << std::endl;
A.svd( sigma, U, VT );
std::cout << "U = " << std::endl << U << std::endl;
std::cout << "VT = " << std::endl << VT << std::endl;
std::cout << "sigma = " << std::endl << sigma << std::endl;
}
{
std::cout << "## Eigen SVD" << std::endl;
Eigen::MatrixXf A( 3, 2 );
A(0,0) = 2.0;
A(1,0) = 0.0;
A(2,0) = 0.0;
A(0,1) = 0.0;
A(1,1) = 1.0;
A(2,1) = 0.0;
std::cout << "A = " << std::endl << A << std::endl << std::endl;
Eigen::JacobiSVD< Eigen::MatrixXf > svd( A, Eigen::ComputeThinU |
Eigen::ComputeThinV );
std::cout << "U = " << std::endl << svd.matrixU() << std::endl << std::endl;
std::cout << "VT = " << std::endl << svd.matrixV() << std::endl <<
std::endl;
std::cout << "sigma = "<< std::endl << svd.singularValues() << std::endl;
}
return 0;
}
The output I get is:
## Libmesh DenseMatrix SVD
A =
2 0
0 1
0 0
U =
1 0
-0 1
VT =
1 0 1
0 -0 0
sigma =
2
1
## Eigen SVD
A =
2 0
0 1
0 0
U =
1 0
0 1
0 0
VT =
1 0
0 1
sigma =
2
1
Obviously, the SVD from the DenseMatrix class is wrong, whereas Eigen performs
well. It would be interesting to hear whether this is a known problem.
Best regards,
Jonas
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