# VTK/Examples/Cxx/Math/LeastSquares

< VTK‎ | Examples‎ | Cxx

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

In particular, we are trying to solve

```[1 4]     [-2]
[1 2] M = [6]
[2 3]     [1]
```

It currently does not work.

## 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;
}
```

# Please try the new VTKExamples website.

## CMakeLists.txt

```cmake_minimum_required(VERSION 2.8)

PROJECT(LeastSquares)

find_package(VTK REQUIRED)
include(\${VTK_USE_FILE})

if(VTK_LIBRARIES)
else()
endif()
```

```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.