# 28 Numerics library [numerics]

## 28.9 Basic linear algebra algorithms [linalg]

### 28.9.13 BLAS 1 algorithms [linalg.algs.blas1]

#### 28.9.13.2.1 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].
â€” 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.

#### 28.9.13.2.2 Apply a computed Givens rotation to vectors [linalg.algs.blas1.givens.rot]

```template<inout-vector InOutVec1, inout-vector InOutVec2, class Real> void apply_givens_rotation(InOutVec1 x, InOutVec2 y, Real c, Real s); template<class ExecutionPolicy, inout-vector InOutVec1, inout-vector InOutVec2, class Real> void apply_givens_rotation(ExecutionPolicy&& exec, InOutVec1 x, InOutVec2 y, Real c, Real s); template<inout-vector InOutVec1, inout-vector InOutVec2, class Real> void apply_givens_rotation(InOutVec1 x, InOutVec2 y, Real c, complex<Real> s); template<class ExecutionPolicy, inout-vector InOutVec1, inout-vector InOutVec2, class Real> void apply_givens_rotation(ExecutionPolicy&& exec, InOutVec1 x, InOutVec2 y, Real c, complex<Real> s); ```
[Note 1:
These functions correspond to the BLAS function xROT[bib].
â€” end note]
Mandates: compatible-static-extents<InOutVec1, InOutVec2>(0, 0) is true.
Preconditions: x.extent(0) equals y.extent(0).
Effects: Applies the plane rotation specified by c and s to the input vectors x and y, as if the rotation were a 2 x 2 matrix and the input vectors were successive rows of a matrix with two rows.