LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ drotg()

 subroutine drotg ( real(wp) a, real(wp) b, real(wp) c, real(wp) s )

DROTG

Purpose:
``` The computation uses the formulas
sigma = sgn(a)    if |a| >  |b|
= sgn(b)    if |b| >= |a|
r = sigma*sqrt( a**2 + b**2 )
c = 1; s = 0      if r = 0
c = a/r; s = b/r  if r != 0
The subroutine also computes
z = s    if |a| > |b|,
= 1/c  if |b| >= |a| and c != 0
= 1    if c = 0
This allows c and s to be reconstructed from z as follows:
If z = 1, set c = 0, s = 1.
If |z| < 1, set c = sqrt(1 - z**2) and s = z.
If |z| > 1, set c = 1/z and s = sqrt( 1 - c**2).```
Parameters
 [in,out] A ``` A is DOUBLE PRECISION On entry, the scalar a. On exit, the scalar r.``` [in,out] B ``` B is DOUBLE PRECISION On entry, the scalar b. On exit, the scalar z.``` [out] C ``` C is DOUBLE PRECISION The scalar c.``` [out] S ``` S is DOUBLE PRECISION The scalar s.```
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```

Definition at line 92 of file drotg.f90.

93  integer, parameter :: wp = kind(1.d0)
94 !
95 ! -- Reference BLAS level1 routine --
96 ! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
97 ! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
98 !
99 ! .. Constants ..
100  real(wp), parameter :: zero = 0.0_wp
101  real(wp), parameter :: one = 1.0_wp
102 ! ..
103 ! .. Scaling constants ..
104  real(wp), parameter :: safmin = real(radix(0._wp),wp)**max( &
105  minexponent(0._wp)-1, &
106  1-maxexponent(0._wp) &
107  )
108  real(wp), parameter :: safmax = real(radix(0._wp),wp)**max( &
109  1-minexponent(0._wp), &
110  maxexponent(0._wp)-1 &
111  )
112 ! ..
113 ! .. Scalar Arguments ..
114  real(wp) :: a, b, c, s
115 ! ..
116 ! .. Local Scalars ..
117  real(wp) :: anorm, bnorm, scl, sigma, r, z
118 ! ..
119  anorm = abs(a)
120  bnorm = abs(b)
121  if( bnorm == zero ) then
122  c = one
123  s = zero
124  b = zero
125  else if( anorm == zero ) then
126  c = zero
127  s = one
128  a = b
129  b = one
130  else
131  scl = min( safmax, max( safmin, anorm, bnorm ) )
132  if( anorm > bnorm ) then
133  sigma = sign(one,a)
134  else
135  sigma = sign(one,b)
136  end if
137  r = sigma*( scl*sqrt((a/scl)**2 + (b/scl)**2) )
138  c = a/r
139  s = b/r
140  if( anorm > bnorm ) then
141  z = s
142  else if( c /= zero ) then
143  z = one/c
144  else
145  z = one
146  end if
147  a = r
148  b = z
149  end if
150  return
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