LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ drotg()

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

DROTG

Purpose:
``` DROTG constructs a plane rotation
[  c  s ] [ a ] = [ r ]
[ -s  c ] [ b ]   [ 0 ]
satisfying c**2 + s**2 = 1.

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).```
lartg: generate plane rotation, more accurate than BLAS rot,
lartgp: generate plane rotation, more accurate than BLAS rot
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 91 of file drotg.f90.

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