LUFactorization

#include <vtkMath.h>

namespace {
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;
}

void OutputMatrix(double** a)
{
  std::cout << "[ " << a[0][0] << " " << a[0][1] << std::endl;
  std::cout << "  " << a[1][0] << " " << a[1][1] << " ]" << std::endl;
}
} // namespace

int main(int, char*[])
{
  // Create and populate matrix
  int n = 2;
  double** a = create_matrix<double>(n, n);
  a[0][0] = 4;
  a[0][1] = 3;
  a[1][0] = 6;
  a[1][1] = 3;

  //[4 3; 6 3] should decompose to [1 0; 1.5 1] * [4 3; 0 -1.5]

  std::cout << "a" << std::endl;
  OutputMatrix(a);

  // These values do not seem to change the result?
  int pivotIndices[2] = {0, 0};

  // Decompose matrix A into LU form
  vtkMath::LUFactorLinearSystem(a, pivotIndices, n);

  std::cout << "A decomposed into (unit lower triangular) L and U:"
            << std::endl;
  OutputMatrix(a);

  /* The resulting matrix,
   [6       3]
   [.66667  1]
   is a superposition of L and U, with L being a unit lower triangular matrix.
   That is, ones on the diagonal, zeros in the upper right triangle, and values
  in the lower left triangle.

  The diagonal of the resulting A is the diagonal of U. The upper right triangle
  of A is the upper right triangle of U. The lower left triangle of A is the
  lower left triangle of L (and remember, the diagonal of L is all 1's).
  */

  /*
  To show that the resulting interpretation of the output matrix A is correct,
  we form the matrices following the description above and show that they
  multiply to the original A matrix. octave:9> [1 0; .666667 1] * [6 3; 0 1] ans
  =

   6.0000   3.0000
   4.0000   3.0000
  */

  return EXIT_SUCCESS;
}

cmake_minimum_required(VERSION 3.12 FATAL_ERROR)

project(LUFactorization)

find_package(VTK COMPONENTS 
)

if (NOT VTK_FOUND)
  message(FATAL_ERROR "LUFactorization: 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(LUFactorization MACOSX_BUNDLE LUFactorization.cxx )
  target_link_libraries(LUFactorization PRIVATE ${VTK_LIBRARIES}
)
# vtk_module_autoinit is needed
vtk_module_autoinit(
  TARGETS LUFactorization
  MODULES ${VTK_LIBRARIES}
)

cd LUFactorization/build

cmake ..

cmake -DVTK_DIR:PATH=/home/me/vtk_build ..

make

./LUFactorization