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| 1 |
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##### Compute Givens rotation <a id="linalg.algs.blas1.givens.lartg">[[linalg.algs.blas1.givens.lartg]]</a>
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``` cpp
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template<class Real>
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setup_givens_rotation_result<Real> setup_givens_rotation(Real a, Real b) noexcept;
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template<class Real>
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setup_givens_rotation_result<complex<Real>>
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setup_givens_rotation(complex<Real> a, complex<Real> b) noexcept;
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```
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These functions compute the Givens plane rotation represented by the two
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values c and s such that the 2 x 2 system of equations
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$$\left[ \begin{matrix}
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c & s \\
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-\overline{s} & c \\
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\end{matrix} \right]
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\cdot
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\left[ \begin{matrix}
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a \\
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b \\
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\end{matrix} \right]
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=
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\left[ \begin{matrix}
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r \\
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0 \\
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\end{matrix} \right]$$
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holds, where c is always a real scalar, and c² + |s|^2 = 1. That is, c
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and s represent a 2 x 2 matrix, that when multiplied by the right by the
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input vector whose components are a and b, produces a result vector
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whose first component r is the Euclidean norm of the input vector, and
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whose second component is zero.
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[*Note 1*: These functions correspond to the LAPACK function
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`xLARTG`. — *end note*]
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*Returns:* `c, s, r`, where `c` and `s` form the Givens plane rotation
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corresponding to the input `a` and `b`, and `r` is the Euclidean norm of
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the two-component vector formed by `a` and `b`.
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