# Boost C++ Libraries

...one of the most highly regarded and expertly designed C++ library projects in the world.

### Eigen Interoperability

```#include <boost/multiprecision/eigen.hpp>
```

which defines the traits classes and functions that the Eigen library needs all user-defined number types to provide.

For example the following code performs quad-precision matrix solving on complex numbers:

```#include <iostream>
#include <boost/multiprecision/cpp_complex.hpp>
#include <boost/multiprecision/eigen.hpp>
#include <Eigen/Dense>

int main()
{
using namespace Eigen;
//
// We want to solve Ax = b for x,
// define A and b first:
//
Matrix<complex_type, 2, 2> A, b;
A << complex_type(2, 3), complex_type(-1, -2), complex_type(-1, -4), complex_type(3, 6);
b << 1, 2, 3, 1;
std::cout << "Here is the matrix A:\n" << A << std::endl;
std::cout << "Here is the right hand side b:\n" << b << std::endl;
//
// Solve for x:
//
Matrix<complex_type, 2, 2> x = A.fullPivHouseholderQr().solve(b);
std::cout << "The solution is:\n" << x << std::endl;
//
// Compute the error in the solution by using the norms of Ax - b and b:
//
complex_type::value_type relative_error = (A*x - b).norm() / b.norm();
std::cout << "The relative error is: " << relative_error << std::endl;
return 0;
}
```

Which produces the following output:

```Here is the matrix A:
(2,3) (-1,-2)
(-1,-4)   (3,6)
Here is the right hand side b:
1 2
3 1
The solution is:
(0.6,-0.6)   (0.7,-0.7)
(0.64,-0.68) (0.58,-0.46)
The relative error is: 2.63132e-34
```