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.
Author
Edward Anderson, Lockheed Martin
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
Here is the caller graph for this function: