VTK/Examples/Cxx/Math/LeastSquares

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This example solves XM = Y (an interesting way to write Ax = b).

In particular, we are trying to solve

[1 4]     [-2]
[1 2] M = [6]
[2 3]     [1]

It currently does not work.

LeastSquares.cxx

#include <vtkSmartPointer.h>
#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 *[])
{
  
  // Solve XM = Y;
  
  int numberOfSamples = 3;
  int numberOfVariables = 2;
  double **x = create_matrix<double> (numberOfSamples, numberOfVariables);
  x[0][0] = 1; x[0][1] = 4;
  x[1][0] = 1; x[1][1] = 2;
  x[2][0] = 2; x[2][1] = 3;
  
  double **m = create_matrix<double> ( numberOfVariables, 1 );
  
  double **y = create_matrix<double> ( numberOfSamples, 1 );
  y[0][0] = -2;
  y[1][0] = 6;
  y[2][0] = 1;
  
  vtkMath::SolveLeastSquares(numberOfSamples, x, numberOfVariables, y, 1, m);
  
  std::cout << "Solution is: " << m[0][0] << " " << m[1][0] << std::endl;
  
  // Solution should be [3; -1];
  free_matrix(x);
  free_matrix(m);
  free_matrix(y);
  
  return EXIT_SUCCESS;
}

Please try the new VTKExamples website.

CMakeLists.txt

cmake_minimum_required(VERSION 2.8)

PROJECT(LeastSquares)

find_package(VTK REQUIRED)
include(${VTK_USE_FILE})

add_executable(LeastSquares MACOSX_BUNDLE LeastSquares.cxx)

if(VTK_LIBRARIES)
  target_link_libraries(LeastSquares ${VTK_LIBRARIES})
else()
  target_link_libraries(LeastSquares vtkHybrid vtkWidgets)
endif()

Download and Build LeastSquares

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

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

cd LeastSquares/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:

./LeastSquares

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.