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.

Question

If you have a question about this example, please use the VTK Discourse Forum

Code¶

LeastSquares.cxx

#include <vtkMath.h>

namespace {
/* 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;
}
} // namespace

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 3.12 FATAL_ERROR)

project(LeastSquares)

find_package(VTK COMPONENTS 
)

if (NOT VTK_FOUND)
  message(FATAL_ERROR "LeastSquares: Unable to find the VTK build folder.")
endif()

# Prevent a "command line is too long" failure in Windows.
set(CMAKE_NINJA_FORCE_RESPONSE_FILE "ON" CACHE BOOL "Force Ninja to use response files.")
add_executable(LeastSquares MACOSX_BUNDLE LeastSquares.cxx )
  target_link_libraries(LeastSquares PRIVATE ${VTK_LIBRARIES}
)
# vtk_module_autoinit is needed
vtk_module_autoinit(
  TARGETS LeastSquares
  MODULES ${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

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