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LAPACK
3.10.1
LAPACK: Linear Algebra PACKage
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subroutine clartg | ( | complex(wp) | f, |
complex(wp) | g, | ||
real(wp) | c, | ||
complex(wp) | s, | ||
complex(wp) | r | ||
) |
CLARTG generates a plane rotation with real cosine and complex sine.
CLARTG generates a plane rotation so that [ C S ] . [ F ] = [ R ] [ -conjg(S) C ] [ G ] [ 0 ] where C is real and C**2 + |S|**2 = 1. The mathematical formulas used for C and S are sgn(x) = { x / |x|, x != 0 { 1, x = 0 R = sgn(F) * sqrt(|F|**2 + |G|**2) C = |F| / sqrt(|F|**2 + |G|**2) S = sgn(F) * conjg(G) / sqrt(|F|**2 + |G|**2) When F and G are real, the formulas simplify to C = F/R and S = G/R, and the returned values of C, S, and R should be identical to those returned by CLARTG. The algorithm used to compute these quantities incorporates scaling to avoid overflow or underflow in computing the square root of the sum of squares. This is a faster version of the BLAS1 routine CROTG, except for the following differences: F and G are unchanged on return. If G=0, then C=1 and S=0. If F=0, then C=0 and S is chosen so that R is real. Below, wp=>sp stands for single precision from LA_CONSTANTS module.
[in] | F | F is COMPLEX(wp) The first component of vector to be rotated. |
[in] | G | G is COMPLEX(wp) The second component of vector to be rotated. |
[out] | C | C is REAL(wp) The cosine of the rotation. |
[out] | S | S is COMPLEX(wp) The sine of the rotation. |
[out] | R | R is COMPLEX(wp) The nonzero component of the rotated vector. |
Anderson E. (2017) Algorithm 978: Safe Scaling in the Level 1 BLAS ACM Trans Math Softw 44:1--28 https://doi.org/10.1145/3061665
Definition at line 117 of file clartg.f90.