C Library Functions - zrotg (3)

NAME

zrotg(3f) - [BLAS:COMPLEX16_BLAS_LEVEL1] constructs a plane rotation

Synopsis
Definition
Options
A
Authors
Further Details
See Also

SYNOPSIS

subroutine zrotg( a, b, c, s )

      .. Scalar Arguments ..
      real(wp),intent(out)      :: c
      complex(wp),intent(in)    :: b
      complex(wp),intent(out)   :: s
      complex(wp),intent(inout) :: a
      ..

DEFINITION

ZROTG constructs a plane rotation
     [  c         s ] [ a ] = [ r ]
     [ -conjg(s)  c ] [ b ]   [ 0 ]
where c is real, s ic complex, and c**2 + conjg(s)*s = 1.

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)

When a and b are real and r /= 0, the formulas simplify to

    r = sgn(a)*sqrt(|a|**2 + |b|**2)
    c = a / r
    s = b / r

the same as in ZROTG when |a| > |b|. When |b| >= |a|, the sign of c and s will be different from those computed by ZROTG if the signs of a and b are not the same.

OPTIONS

A

A is DOUBLE COMPLEX On entry, the scalar a. On exit, the scalar r.

B

B is DOUBLE COMPLEX The scalar b.

C

C is DOUBLE PRECISION The scalar c.

S

S is DOUBLE PRECISION The scalar s.

AUTHORS

o Edward Anderson, Lockheed Martin

\par Contributors:

Weslley Pereira, University of Colorado Denver, USA

FURTHER DETAILS

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