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rotg(3) Library Functions Manual 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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