[linalg.algs.blas1.givens.lartg]

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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

[\begin{matrix} c & s - ¯ ¯ ¯ s & c \end{matrix}] \cdot [\begin{matrix} a b \end{matrix}] = [\begin{matrix} r 0 \end{matrix}]

holds, where c is always a real scalar, and

c^{2} + | s |^{2} = 1

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.

28 Numerics library [numerics]

28.9 Basic linear algebra algorithms [linalg]

28.9.13 BLAS 1 algorithms [linalg.algs.blas1]

28.9.13.2 Givens rotations [linalg.algs.blas1.givens]

28.9.13.2.1 Compute Givens rotation [linalg.algs.blas1.givens.lartg]