EigenSymmetric

VTKExamples/Cxx/Math/EigenSymmetric

Description

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.

Code

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 3.3 FATAL_ERROR)

project(EigenSymmetric)

find_package(VTK COMPONENTS 
  vtkCommonCore QUIET)
if (NOT VTK_FOUND)
  message("Skipping EigenSymmetric: ${VTK_NOT_FOUND_MESSAGE}")
  return ()
endif()
message (STATUS "VTK_VERSION: ${VTK_VERSION}")
if (VTK_VERSION VERSION_LESS "8.90.0")
  # old system
  include(${VTK_USE_FILE})
  add_executable(EigenSymmetric MACOSX_BUNDLE EigenSymmetric.cxx )
  target_link_libraries(EigenSymmetric PRIVATE ${VTK_LIBRARIES})
else ()
  # include all components
  add_executable(EigenSymmetric MACOSX_BUNDLE EigenSymmetric.cxx )
  target_link_libraries(EigenSymmetric PRIVATE ${VTK_LIBRARIES})
  # vtk_module_autoinit is needed
  vtk_module_autoinit(
    TARGETS EigenSymmetric
    MODULES ${VTK_LIBRARIES}
    )
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

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