/**
* Example of a test. To be completed.
*
*/
bool testEigenDecomposition()
{
unsigned int nbok = 0;
unsigned int nb = 0;
typedef EigenDecomposition<2,double> Eigen2;
typedef Eigen2::Vector Vector2;
typedef Eigen2::Matrix Matrix2;
trace.beginBlock ( "Testing block ..." );
// [4 1]
// [1 2]
Matrix2 A;
A.setComponent( 0, 0, 4 );
A.setComponent( 0, 1, 1 );
A.setComponent( 1, 0, 1 );
A.setComponent( 1, 1, 2 );
Matrix2 P;
Vector2 v;
Eigen2::getEigenDecomposition( A, P, v );
trace.info() << "Input matrix: " << A << std::endl;
trace.info() << "Eigenvectors: " << P << std::endl;
trace.info() << "Eigenvalues: " << v << std::endl;
Vector2 V0 = P.column( 0 );
Vector2 V1 = P.column( 1 );
Vector2 V0_exp( 0.3826834323650898, -0.9238795325112868 );
Vector2 V1_exp( 0.9238795325112868, 0.3826834323650898);
double v0_exp = 1.585786437626905;
double v1_exp = 4.414213562373095;
double error_V0 = (V0-V0_exp).norm();
double error_V1 = (V1-V1_exp).norm();
double error_v0 = fabs( v[0] - v0_exp );
double error_v1 = fabs( v[1] - v1_exp );
trace.info() << "error_V0 = " << error_V0 << std::endl;
trace.info() << "error_V1 = " << error_V1 << std::endl;
trace.info() << "error_v0 = " << error_v0 << std::endl;
trace.info() << "error_v1 = " << error_v1 << std::endl;
double epsilon = 1e-10;
++nb, nbok += error_V0 < epsilon ? 1 : 0;
trace.info() << "(" << nbok << "/" << nb << ") "
<< "error_V0 < epsilon, i.e. " << error_V0 << " < " << epsilon << std::endl;
++nb, nbok += error_V1 < epsilon ? 1 : 0;
trace.info() << "(" << nbok << "/" << nb << ") "
<< "error_V1 < epsilon, i.e. " << error_V1 << " < " << epsilon << std::endl;
++nb, nbok += error_v0 < epsilon ? 1 : 0;
trace.info() << "(" << nbok << "/" << nb << ") "
<< "error_v0 < epsilon, i.e. " << error_v0 << " < " << epsilon << std::endl;
++nb, nbok += error_v1 < epsilon ? 1 : 0;
trace.info() << "(" << nbok << "/" << nb << ") "
<< "error_v1 < epsilon, i.e. " << error_v1 << " < " << epsilon << std::endl;
trace.endBlock();
return nbok == nb;
}
