C Library Functions - drotg (3)

NAME

drotg(3f) - [BLAS:SINGLE_BLAS_LEVEL1] constructs a plane rotation

Synopsis
Definition
Options
Authors
Further Details
See Also

SYNOPSIS

subroutine DROTG( a, b, c, s )

    .. Scalar Arguments ..
    real(wp),intent(inout) :: a, b
    real(wp),intent(out)   :: c, s

DEFINITION

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).

OPTIONS

A

On entry, the scalar a. On exit, the scalar r.

B

On entry, the scalar b. On exit, the scalar z.

C

The scalar c.

S

The scalar s.

AUTHORS

o Edward Anderson, Lockheed Martin

\par Contributors:

Weslley Pereira, University of Colorado Denver, USA

\ingroup single_blas_level1

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