rotg(3)

NAME
rotg - rotg: generate plane rotation (cf. lartg)

SYNOPSIS

  Functions
subroutine crotg (a, b, c, s)
CROTG generates a Givens rotation with real cosine and complex sine.
subroutine drotg (a, b, c, s)
DROTG
subroutine srotg (a, b, c, s)
SROTG
subroutine zrotg (a, b, c, s)
ZROTG generates a Givens rotation with real cosine and complex sine.

Detailed Description

Function Documentation

  subroutine crotg (complex(wp) a, complex(wp) b, real(wp) c, complex(wp) s)

CROTG generates a Givens rotation with real cosine and complex sine.

Purpose:

     CROTG constructs a plane rotation
        [  c         s ] [ a ] = [ r ]
        [ -conjg(s)  c ] [ b ]   [ 0 ]
     where c is real, s is complex, and c**2 + conjg(s)*s = 1.
     The computation uses the formulas
        |x| = sqrt( Re(x)**2 + Im(x)**2 )
        sgn(x) = x / |x|  if x /= 0
               = 1        if x  = 0
        c = |a| / sqrt(|a|**2 + |b|**2)
        s = sgn(a) * conjg(b) / sqrt(|a|**2 + |b|**2)
        r = sgn(a)*sqrt(|a|**2 + |b|**2)
     When a and b are real and r /= 0, the formulas simplify to
        c = a / r
        s = b / r
     the same as in SROTG when |a| > |b|.  When |b| >= |a|, the
     sign of c and s will be different from those computed by SROTG
     if the signs of a and b are not the same.

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

    lartgp: generate plane rotation, more accurate than BLAS rot

Parameters
    A

              A is COMPLEX
              On entry, the scalar a.
              On exit, the scalar r.

    B

              B is COMPLEX
              The scalar b.

    C

              C is REAL
              The scalar c.

    S

              S is COMPLEX
              The scalar s.

Author
    Weslley Pereira, University of Colorado Denver, USA

Date
    December 2021

Further Details:

     Based on the algorithm from
      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 88 of file crotg.f90.

  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.

  subroutine srotg (real(wp) a, real(wp) b, real(wp) c, real(wp) s)

SROTG

Purpose:

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

    B

              B is REAL
              On entry, the scalar b.
              On exit, the scalar z.

    C

              C is REAL
              The scalar c.

    S

              S is REAL
              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 srotg.f90.

  subroutine zrotg (complex(wp) a, complex(wp) b, real(wp) c, complex(wp) s)

ZROTG generates a Givens rotation with real cosine and complex sine.

Purpose:

     ZROTG constructs a plane rotation
        [  c         s ] [ a ] = [ r ]
        [ -conjg(s)  c ] [ b ]   [ 0 ]
     where c is real, s is complex, and c**2 + conjg(s)*s = 1.
     The computation uses the formulas
        |x| = sqrt( Re(x)**2 + Im(x)**2 )
        sgn(x) = x / |x|  if x /= 0
               = 1        if x  = 0
        c = |a| / sqrt(|a|**2 + |b|**2)
        s = sgn(a) * conjg(b) / sqrt(|a|**2 + |b|**2)
        r = sgn(a)*sqrt(|a|**2 + |b|**2)
     When a and b are real and r /= 0, the formulas simplify to
        c = a / r
        s = b / r
     the same as in DROTG when |a| > |b|.  When |b| >= |a|, the
     sign of c and s will be different from those computed by DROTG
     if the signs of a and b are not the same.

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

    B

              B is DOUBLE COMPLEX
              The scalar b.

    C

              C is DOUBLE PRECISION
              The scalar c.

    S

              S is DOUBLE COMPLEX
              The scalar s.

Author
    Weslley Pereira, University of Colorado Denver, USA

Date
    December 2021

Further Details:

     Based on the algorithm from
      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 88 of file zrotg.f90.

Author

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