# VTK/Examples/Cxx/Math/LUFactorization

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< VTK | Examples | Cxx

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## Contents

## 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[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;
}
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;
}
```

**Please try the new VTKExamples website.**

## CMakeLists.txt

```
cmake_minimum_required(VERSION 2.8)
PROJECT(LUFactorization)
find_package(VTK REQUIRED)
include(${VTK_USE_FILE})
add_executable(LUFactorization MACOSX_BUNDLE LUFactorization.cxx)
if(VTK_LIBRARIES)
target_link_libraries(LUFactorization ${VTK_LIBRARIES})
else()
target_link_libraries(LUFactorization vtkHybrid vtkWidgets)
endif()
```

## Download and Build LUFactorization

Click here to download LUFactorization. and its *CMakeLists.txt* file.

Once the tarball *LUFactorization.tar* has been downloaded and extracted,

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