rotg - Man Page

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.

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.

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.

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.

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.