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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