LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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subroutine crotg | ( | complex(wp) | a, |
complex(wp) | b, | ||
real(wp) | c, | ||
complex(wp) | s | ||
) |
CROTG generates a Givens rotation with real cosine and complex sine.
The computation uses the formulas |x| = sqrt( Re(x)**2 + Im(x)**2 ) sgn(x) = x / |x| if x /= 0 = 1 if x = 0 c = |a| / sqrt(|a|**2 + |b|**2) s = sgn(a) * conjg(b) / sqrt(|a|**2 + |b|**2) r = sgn(a)*sqrt(|a|**2 + |b|**2) When a and b are real and r /= 0, the formulas simplify to c = a / r s = b / r the same as in SROTG when |a| > |b|. When |b| >= |a|, the sign of c and s will be different from those computed by SROTG if the signs of a and b are not the same.
[in,out] | A | A is COMPLEX On entry, the scalar a. On exit, the scalar r. |
[in] | B | B is COMPLEX The scalar b. |
[out] | C | C is REAL The scalar c. |
[out] | S | S is COMPLEX The scalar s. |
Based on the algorithm from 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