slartg.f90(3)

NAME
slartg.f90

SYNOPSIS

  Functions/Subroutines
subroutine slartg (f, g, c, s, r)
SLARTG generates a plane rotation with real cosine and real sine.

Function/Subroutine Documentation

  subroutine slartg (real(wp) f, real(wp) g, real(wp) c, real(wp) s, real(wp) r)

Purpose:

     SLARTG generates a plane rotation so that
        [  C  S  ]  .  [ F ]  =  [ R ]
        [ -S  C  ]     [ G ]     [ 0 ]
     where C**2 + S**2 = 1.
     The mathematical formulas used for C and S are
        R = sign(F) * sqrt(F**2 + G**2)
        C = F / R
        S = G / R
     Hence C >= 0. The algorithm used to compute these quantities
     incorporates scaling to avoid overflow or underflow in computing the
     square root of the sum of squares.
     This version is discontinuous in R at F = 0 but it returns the same
     C and S as SLARTG for complex inputs (F,0) and (G,0).
     This is a more accurate version of the BLAS1 routine SROTG,
     with the following other differences:
        F and G are unchanged on return.
        If G=0, then C=1 and S=0.
        If F=0 and (G .ne. 0), then C=0 and S=sign(1,G) without doing any
           floating point operations (saves work in SBDSQR when
           there are zeros on the diagonal).
     If F exceeds G in magnitude, C will be positive.
     Below, wp=>sp stands for single precision from LA_CONSTANTS module.

Parameters
    F

              F is REAL(wp)
              The first component of vector to be rotated.

    G

              G is REAL(wp)
              The second component of vector to be rotated.

    C

              C is REAL(wp)
              The cosine of the rotation.

    S

              S is REAL(wp)
              The sine of the rotation.

    R

              R is REAL(wp)
              The nonzero component of the rotated vector.

Author
    Edward Anderson, Lockheed Martin

Date
    July 2016

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 112 of file slartg.f90.

Author

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