28 Numerics library [numerics]

28.9 Basic linear algebra algorithms [linalg]

28.9.13 BLAS 1 algorithms [linalg.algs.blas1] Givens rotations [linalg.algs.blas1.givens] Compute Givens rotation [linalg.algs.blas1.givens.lartg]

template<class Real> setup_givens_rotation_result<Real> setup_givens_rotation(Real a, Real b) noexcept; template<class Real> setup_givens_rotation_result<complex<Real>> setup_givens_rotation(complex<Real> a, complex<Real> b) noexcept;
These functions compute the Givens plane rotation represented by the two values c and s such that the 2 x 2 system of equations
holds, where c is always a real scalar, and .
That is, c and s represent a 2 x 2 matrix, that when multiplied by the right by the input vector whose components are a and b, produces a result vector whose first component r is the Euclidean norm of the input vector, and whose second component is zero.
[Note 1: 
These functions correspond to the LAPACK function xLARTG[bib].
— end note]
Returns: c, s, r, where c and s form the Givens plane rotation corresponding to the input a and b, and r is the Euclidean norm of the two-component vector formed by a and b.