# LUFactorization

VTKExamples/Cxx/Math/LUFactorization

Question

### Code¶

LUFactorization.cxx

#include <vtkMath.h>

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 = 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 );
delete[] m;
}

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

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


### CMakeLists.txt¶

cmake_minimum_required(VERSION 3.3 FATAL_ERROR)

project(LUFactorization)

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


cd LUFactorization/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:

./LUFactorization


WINDOWS USERS

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