// Test the eigenvalue finder. Set up a diagonal matrix and conjugate
// by a rotation. That way we obtain a symmetric matrix that can be
// diagonalized. Check if the eigenvalue finder reveals the original
// diagonal elements.
void testEigenvalues()
{
matrix3x3 Diagonal;
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
Diagonal.Set(i, j, 0.0);
Diagonal.Set(0, 0, randomizer.NextFloat());
Diagonal.Set(1, 1, Diagonal.Get(0,0)+fabs(randomizer.NextFloat()));
Diagonal.Set(2, 2, Diagonal.Get(1,1)+fabs(randomizer.NextFloat()));
// test the isDiagonal() method
VERIFY( Diagonal.isDiagonal() );
matrix3x3 rndRotation;
rndRotation.randomRotation(randomizer);
// check that rndRotation is really a rotation, i.e. that randomRotation() works
VERIFY( rndRotation.isOrthogonal() );
matrix3x3 toDiagonalize = rndRotation * Diagonal * rndRotation.inverse();
VERIFY( toDiagonalize.isSymmetric() );
vector3 eigenvals;
toDiagonalize.findEigenvectorsIfSymmetric(eigenvals);
for(unsigned int j=0; j<3; j++)
VERIFY( IsNegligible( eigenvals[j] - Diagonal.Get(j,j), Diagonal.Get(2,2) ) );
VERIFY( eigenvals[0] < eigenvals[1] && eigenvals[1] < eigenvals[2] );
}
/*! The axis of the rotation will be uniformly distributed on
the unit sphere and the angle will be uniformly distributed in
the interval 0..360 degrees. */
void matrix3x3::randomRotation(OBRandom &rnd)
{
double rotAngle;
vector3 v1;
v1.randomUnitVector(&rnd);
rotAngle = 360.0 * rnd.NextFloat();
this->RotAboutAxisByAngle(v1,rotAngle);
}
void pickRandom( double & d )
{
d = randomizer.NextFloat() * 2.0 - 1.0;
}