Library Functions Manual

NAME¶

lartg - lartg: generate plane rotation, more accurate than BLAS rot

SYNOPSIS¶

Functions¶

subroutine CLARTG (f, g, c, s, r)
CLARTG generates a plane rotation with real cosine and complex sine. subroutine DLARTG (f, g, c, s, r)
DLARTG generates a plane rotation with real cosine and real sine. subroutine SLARTG (f, g, c, s, r)
SLARTG generates a plane rotation with real cosine and real sine. subroutine ZLARTG (f, g, c, s, r)
ZLARTG generates a plane rotation with real cosine and complex sine.

Detailed Description¶

Function Documentation¶

subroutine CLARTG (complex(wp) f, complex(wp) g, real(wp) c, complex(wp) s, complex(wp) r)¶

CLARTG generates a plane rotation with real cosine and complex sine.

Purpose:

!>
!> CLARTG generates a plane rotation so that
!>
!>    [  C         S  ] . [ F ]  =  [ R ]
!>    [ -conjg(S)  C  ]   [ G ]     [ 0 ]
!>
!> where C is real and C**2 + |S|**2 = 1.
!>
!> The mathematical formulas used for C and S are
!>
!>    sgn(x) = {  x / |x|,   x != 0
!>             {  1,         x  = 0
!>
!>    R = sgn(F) * sqrt(|F|**2 + |G|**2)
!>
!>    C = |F| / sqrt(|F|**2 + |G|**2)
!>
!>    S = sgn(F) * conjg(G) / sqrt(|F|**2 + |G|**2)
!>
!> Special conditions:
!>    If G=0, then C=1 and S=0.
!>    If F=0, then C=0 and S is chosen so that R is real.
!>
!> When F and G are real, the formulas simplify to C = F/R and
!> S = G/R, and the returned values of C, S, and R should be
!> identical to those returned by SLARTG.
!>
!> The algorithm used to compute these quantities incorporates scaling
!> to avoid overflow or underflow in computing the square root of the
!> sum of squares.
!>
!> This is the same routine CROTG fom BLAS1, except that
!> F and G are unchanged on return.
!>
!> Below, wp=>sp stands for single precision from LA_CONSTANTS module.
!>

Parameters

!>          F is COMPLEX(wp)
!>          The first component of vector to be rotated.
!>

!>          G is COMPLEX(wp)
!>          The second component of vector to be rotated.
!>

!>          C is REAL(wp)
!>          The cosine of the rotation.
!>

!>          S is COMPLEX(wp)
!>          The sine of the rotation.
!>

!>          R is COMPLEX(wp)
!>          The nonzero component of the rotated vector.
!>

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 115 of file clartg.f90.

subroutine DLARTG (real(wp) f, real(wp) g, real(wp) c, real(wp) s, real(wp) r)¶

DLARTG generates a plane rotation with real cosine and real sine.

Purpose:

!>
!> DLARTG generates a plane rotation so that
!>
!>    [  C  S  ]  .  [ F ]  =  [ R ]
!>    [ -S  C  ]     [ G ]     [ 0 ]
!>
!> where C**2 + S**2 = 1.
!>
!> The mathematical formulas used for C and S are
!>    R = sign(F) * sqrt(F**2 + G**2)
!>    C = F / R
!>    S = G / R
!> Hence C >= 0. The algorithm used to compute these quantities
!> incorporates scaling to avoid overflow or underflow in computing the
!> square root of the sum of squares.
!>
!> This version is discontinuous in R at F = 0 but it returns the same
!> C and S as ZLARTG for complex inputs (F,0) and (G,0).
!>
!> This is a more accurate version of the BLAS1 routine DROTG,
!> with the following other differences:
!>    F and G are unchanged on return.
!>    If G=0, then C=1 and S=0.
!>    If F=0 and (G .ne. 0), then C=0 and S=sign(1,G) without doing any
!>       floating point operations (saves work in DBDSQR when
!>       there are zeros on the diagonal).
!>
!> Below, wp=>dp stands for double precision from LA_CONSTANTS module.
!>

Parameters

!>          F is REAL(wp)
!>          The first component of vector to be rotated.
!>

!>          G is REAL(wp)
!>          The second component of vector to be rotated.
!>

!>          C is REAL(wp)
!>          The cosine of the rotation.
!>

!>          S is REAL(wp)
!>          The sine of the rotation.
!>

!>          R is REAL(wp)
!>          The nonzero component of the rotated vector.
!>

Author

Edward Anderson, Lockheed Martin

Date

July 2016

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 110 of file dlartg.f90.

subroutine SLARTG (real(wp) f, real(wp) g, real(wp) c, real(wp) s, real(wp) r)¶

SLARTG generates a plane rotation with real cosine and real sine.

Purpose:

!>
!> SLARTG generates a plane rotation so that
!>
!>    [  C  S  ]  .  [ F ]  =  [ R ]
!>    [ -S  C  ]     [ G ]     [ 0 ]
!>
!> where C**2 + S**2 = 1.
!>
!> The mathematical formulas used for C and S are
!>    R = sign(F) * sqrt(F**2 + G**2)
!>    C = F / R
!>    S = G / R
!> Hence C >= 0. The algorithm used to compute these quantities
!> incorporates scaling to avoid overflow or underflow in computing the
!> square root of the sum of squares.
!>
!> This version is discontinuous in R at F = 0 but it returns the same
!> C and S as CLARTG for complex inputs (F,0) and (G,0).
!>
!> This is a more accurate version of the BLAS1 routine SROTG,
!> with the following other differences:
!>    F and G are unchanged on return.
!>    If G=0, then C=1 and S=0.
!>    If F=0 and (G .ne. 0), then C=0 and S=sign(1,G) without doing any
!>       floating point operations (saves work in SBDSQR when
!>       there are zeros on the diagonal).
!>
!> Below, wp=>sp stands for single precision from LA_CONSTANTS module.
!>

Parameters

!>          F is REAL(wp)
!>          The first component of vector to be rotated.
!>

!>          G is REAL(wp)
!>          The second component of vector to be rotated.
!>

!>          C is REAL(wp)
!>          The cosine of the rotation.
!>

!>          S is REAL(wp)
!>          The sine of the rotation.
!>

!>          R is REAL(wp)
!>          The nonzero component of the rotated vector.
!>

Author

Edward Anderson, Lockheed Martin

Date

July 2016

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 110 of file slartg.f90.

subroutine ZLARTG (complex(wp) f, complex(wp) g, real(wp) c, complex(wp) s, complex(wp) r)¶

ZLARTG generates a plane rotation with real cosine and complex sine.

Purpose:

!>
!> ZLARTG generates a plane rotation so that
!>
!>    [  C         S  ] . [ F ]  =  [ R ]
!>    [ -conjg(S)  C  ]   [ G ]     [ 0 ]
!>
!> where C is real and C**2 + |S|**2 = 1.
!>
!> The mathematical formulas used for C and S are
!>
!>    sgn(x) = {  x / |x|,   x != 0
!>             {  1,         x  = 0
!>
!>    R = sgn(F) * sqrt(|F|**2 + |G|**2)
!>
!>    C = |F| / sqrt(|F|**2 + |G|**2)
!>
!>    S = sgn(F) * conjg(G) / sqrt(|F|**2 + |G|**2)
!>
!> Special conditions:
!>    If G=0, then C=1 and S=0.
!>    If F=0, then C=0 and S is chosen so that R is real.
!>
!> When F and G are real, the formulas simplify to C = F/R and
!> S = G/R, and the returned values of C, S, and R should be
!> identical to those returned by DLARTG.
!>
!> The algorithm used to compute these quantities incorporates scaling
!> to avoid overflow or underflow in computing the square root of the
!> sum of squares.
!>
!> This is the same routine ZROTG fom BLAS1, except that
!> F and G are unchanged on return.
!>
!> Below, wp=>dp stands for double precision from LA_CONSTANTS module.
!>

Parameters

!>          F is COMPLEX(wp)
!>          The first component of vector to be rotated.
!>

!>          G is COMPLEX(wp)
!>          The second component of vector to be rotated.
!>

!>          C is REAL(wp)
!>          The cosine of the rotation.
!>

!>          S is COMPLEX(wp)
!>          The sine of the rotation.
!>

!>          R is COMPLEX(wp)
!>          The nonzero component of the rotated vector.
!>

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 115 of file zlartg.f90.

Author¶

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