Default constructor without any initialization.

Construct a planar rotation from a cosine-sine pair (c, s).

Returns the adjoint transformation

Makes *this as a Givens rotation G such that applying \( G^* \) to the left of the vector \( V = \left ( \begin{array}{c} p \\ q \end{array} \right )\) yields: \( G^* V = \left ( \begin{array}{c} r \\ 0 \end{array} \right )\).

The value of r is returned if r is not null (the default is null). Also note that G is built such that the cosine is always real.

Example:

Vector2f v = Vector2f::Random();
JacobiRotation<float> G;
G.makeGivens(v.x(), v.y());
cout << "Here is the vector v:" << endl << v << endl;
v.applyOnTheLeft(0, 1, G.adjoint());
cout << "Here is the vector J' * v:" << endl << v << endl;

Output:

Here is the vector v:
  0.68
-0.211
Here is the vector J' * v:
0.712
    0

This function implements the continuous Givens rotation generation algorithm found in Anderson (2000), Discontinuous Plane Rotations and the Symmetric Eigenvalue Problem. LAPACK Working Note 150, University of Tennessee, UT-CS-00-454, December 4, 2000.

See also

MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()

Makes *this as a Jacobi rotation J such that applying J on both the right and left sides of the 2x2 selfadjoint matrix \( B = \left ( \begin{array}{cc} \text{this}_{pp} & \text{this}_{pq} \\ (\text{this}_{pq})^* & \text{this}_{qq} \end{array} \right )\) yields a diagonal matrix \( A = J^* B J \)

Example:

Matrix2f m = Matrix2f::Random();
m = (m + m.adjoint()).eval();
JacobiRotation<float> J;
J.makeJacobi(m, 0, 1);
cout << "Here is the matrix m:" << endl << m << endl;
m.applyOnTheLeft(0, 1, J.adjoint());
m.applyOnTheRight(0, 1, J);
cout << "Here is the matrix J' * m * J:" << endl << m << endl;

Output:

Here is the matrix m:
 1.36 0.355
0.355  1.19
Here is the matrix J' * m * J:
 1.64     0
    0 0.913

See also

JacobiRotation::makeJacobi(RealScalar, Scalar, RealScalar), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()

Makes *this as a Jacobi rotation J such that applying J on both the right and left sides of the selfadjoint 2x2 matrix \( B = \left ( \begin{array}{cc} x & y \\ \overline y & z \end{array} \right )\) yields a diagonal matrix \( A = J^* B J \)

See also

MatrixBase::makeJacobi(const MatrixBase<Derived>&, Index, Index), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()

Concatenates two planar rotation

Returns the transposed transformation