rotg(3)

📦
version 3.12.1 · 9 versions
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✨ NAME ✨

rotg — bestie, this is rotg: it generates a plane rotation (cf. lartg). That's the whole assignment, and it ate. 💫

🎀 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 💅

Okay so the original page literally leaves this section empty — no cap, there is nothing under "Detailed Description." All the actual tea is in Function Documentation below, so keep scrolling bestie 🫶

🔥 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. Iconic behavior honestly.

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. That's it, that's the description — short and mysterious, main character energy fr fr.

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. Also just vibes in the description field. Slay.

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. The complex one. Obsessed.

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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