zrotg(3f) - [BLAS:COMPLEX16_BLAS_LEVEL1] constructs a plane rotation
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
..
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.
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.
\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
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=wp), | intent(inout) | :: | a | |||
| complex(kind=wp), | intent(in) | :: | b | |||
| real(kind=wp), | intent(out) | :: | c | |||
| complex(kind=wp), | intent(out) | :: | s |
| Type | Visibility | Attributes | Name | Initial | |||
|---|---|---|---|---|---|---|---|
| real(kind=wp), | public | :: | abssq | ||||
| complex(kind=wp), | public, | parameter | :: | czero | = | 0.0_wp | |
| real(kind=wp), | public | :: | d | ||||
| complex(kind=wp), | public | :: | f | ||||
| real(kind=wp), | public | :: | f1 | ||||
| real(kind=wp), | public | :: | f2 | ||||
| complex(kind=wp), | public | :: | fs | ||||
| complex(kind=wp), | public | :: | g | ||||
| real(kind=wp), | public | :: | g1 | ||||
| real(kind=wp), | public | :: | g2 | ||||
| complex(kind=wp), | public | :: | gs | ||||
| real(kind=wp), | public | :: | h2 | ||||
| real(kind=wp), | public, | parameter | :: | one | = | 1.0_wp | |
| real(kind=wp), | public | :: | p | ||||
| complex(kind=wp), | public | :: | r | ||||
| real(kind=wp), | public, | parameter | :: | rtmax | = | sqrt(real(radix(0._wp), wp)**max(1-minexponent(0._wp), maxexponent(0._wp)-1)*epsilon(0._wp)) | |
| real(kind=wp), | public, | parameter | :: | rtmin | = | sqrt(real(radix(0._wp), wp)**max(minexponent(0._wp)-1, 1-maxexponent(0._wp))/epsilon(0._wp)) | |
| real(kind=wp), | public, | parameter | :: | safmax | = | real(radix(0._wp), wp)**max(1-minexponent(0._wp), maxexponent(0._wp)-1) | |
| real(kind=wp), | public, | parameter | :: | safmin | = | real(radix(0._wp), wp)**max(minexponent(0._wp)-1, 1-maxexponent(0._wp)) | |
| complex(kind=wp), | public | :: | t | ||||
| real(kind=wp), | public | :: | u | ||||
| real(kind=wp), | public | :: | uu | ||||
| real(kind=wp), | public | :: | v | ||||
| real(kind=wp), | public | :: | vv | ||||
| real(kind=wp), | public | :: | w | ||||
| integer, | public, | parameter | :: | wp | = | kind(1.d0) | |
| real(kind=wp), | public, | parameter | :: | zero | = | 0.0_wp |