VTK/Examples/Cxx/Math/EigenSymmetric

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At the moment, this is a pretty messy process, so here are some helper functions that will hopefully eventually be wrapped into a class/interface.

EigenSymmetric.cxx

#include <vtkMath.h>
 
/* allocate memory for an nrow x ncol matrix */
template<class TReal>
TReal **create_matrix ( long nrow, long ncol )
{
  typedef TReal* TRealPointer;
  TReal **m = new TRealPointer[nrow];
 
  TReal* block = ( TReal* ) calloc ( nrow*ncol, sizeof ( TReal ) );
  m[0] = block;
  for ( int row = 1; row < nrow; ++row )
  {
    m[ row ] = &block[ row * ncol ];
  }
  return m;
}
 
/* free a TReal matrix allocated with matrix() */
template<class TReal>
    void free_matrix ( TReal **m )
{
  free ( m[0] );
  delete[] m;
}
 
 
int main(int, char *[])
{
// Create this matrix
// 1 2 3
// 2 5 9
// 3 9 8
 
  double **a = create_matrix<double> ( 3,3 );
  a[0][0] = 1; a[0][1] = 2;  a[0][2] = 3;
  a[1][0] = 2; a[1][1] = 5;  a[1][2] = 9;
  a[2][0] = 3; a[2][1] = 9;  a[2][2] = 8;
 
  //create a matrix for the eigenvectors to be stored in
  double **w = create_matrix<double> ( 3,3 );
 
  //create a vector for the eigenvalues to be stored in
  double v[3];
 
  //compute the eigenvalues/vectors
  vtkMath::Jacobi ( a,v,w );
 
  //output eigen values
  std::cout << "Eigen values (decreasing order): " << std::endl;
  for ( int i=0; i<3; i++ )
    {
    std::cout << v[i] << " ";
    }
 
  //output eigenvectors
  std::cout << "Eigen vectors (same order as eigen values): " << std::endl;
  for ( int i=0; i<3; i++ )
    {
    //the columns of w are the eigenvectors
    std::cout << "Eigen vector " << i << " : " << w[0][i] << " " << w[1][i] << " " << w[2][i] << std::endl;
    }
 
  //clean up
  free_matrix ( w );
  free_matrix ( a );
 
  return EXIT_SUCCESS;
}

CMakeLists.txt

cmake_minimum_required(VERSION 2.8)
 
PROJECT(EigenSymmetric)
 
find_package(VTK REQUIRED)
include(${VTK_USE_FILE})
 
add_executable(EigenSymmetric MACOSX_BUNDLE EigenSymmetric.cxx)
 
if(VTK_LIBRARIES)
  target_link_libraries(EigenSymmetric ${VTK_LIBRARIES})
else()
  target_link_libraries(EigenSymmetric vtkHybrid vtkWidgets)
endif()

Download and Build EigenSymmetric

Click here to download EigenSymmetric. and its CMakeLists.txt file.

Once the tarball EigenSymmetric.tar has been downloaded and extracted,

cd EigenSymmetric/build 
  • If VTK is installed:
cmake ..
  • If VTK is not installed but compiled on your system, you will need to specify the path to your VTK build:
cmake -DVTK_DIR:PATH=/home/me/vtk_build ..

Build the project:

make

and run it:

./EigenSymmetric

WINDOWS USERS PLEASE NOTE: Be sure to add the VTK bin directory to your path. This will resolve the VTK dll's at run time.