# LeastSquares

VTKExamples/Cxx/Math/LeastSquares

### Description

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

In particular, we are trying to solve

    [4]     [-2](1)

    [2] M = [6](1)

    [3]     [1](2)

It currently does not work.

### Code

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;
    }

### 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 )

    target_link_libraries(LeastSquares ${VTK_LIBRARIES})

### 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.