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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