BLAS/SRC/drotg.f90(3)      Library Functions Manual      BLAS/SRC/drotg.f90(3)

NAME
       BLAS/SRC/drotg.f90

SYNOPSIS
   Functions/Subroutines
       subroutine drotg (a, b, c, s)
           DROTG

Function/Subroutine Documentation
   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).

       See also
           lartg:          generate plane rotation, more accurate than BLAS
           rot,

           lartgp:         generate plane rotation, more accurate than BLAS
           rot

       Parameters
           A

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

           B

                     B is DOUBLE PRECISION
                     On entry, the scalar b.
                     On exit, the scalar z.

           C

                     C is DOUBLE PRECISION
                     The scalar c.

           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 91 of file drotg.f90.

Author
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LAPACK                          Version 3.12.0           BLAS/SRC/drotg.f90(3)