.TH "lartg" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lartg \- lartg: generate plane rotation, more accurate than BLAS rot
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclartg\fP (f, g, c, s, r)"
.br
.RI "\fBCLARTG\fP generates a plane rotation with real cosine and complex sine\&. "
.ti -1c
.RI "subroutine \fBdlartg\fP (f, g, c, s, r)"
.br
.RI "\fBDLARTG\fP generates a plane rotation with real cosine and real sine\&. "
.ti -1c
.RI "subroutine \fBslartg\fP (f, g, c, s, r)"
.br
.RI "\fBSLARTG\fP generates a plane rotation with real cosine and real sine\&. "
.ti -1c
.RI "subroutine \fBzlartg\fP (f, g, c, s, r)"
.br
.RI "\fBZLARTG\fP generates a plane rotation with real cosine and complex sine\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine clartg (complex(wp) f, complex(wp) g, real(wp) c, complex(wp) s, complex(wp) r)"

.PP
\fBCLARTG\fP generates a plane rotation with real cosine and complex sine\&. 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIF\fP 
.PP
.nf
          F is COMPLEX(wp)
          The first component of vector to be rotated\&.
.fi
.PP
.br
\fIG\fP 
.PP
.nf
          G is COMPLEX(wp)
          The second component of vector to be rotated\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL(wp)
          The cosine of the rotation\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is COMPLEX(wp)
          The sine of the rotation\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          R is COMPLEX(wp)
          The nonzero component of the rotated vector\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Weslley Pereira, University of Colorado Denver, USA 
.RE
.PP
\fBDate\fP
.RS 4
December 2021 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
 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
.fi
.PP
 
.RE
.PP

.SS "subroutine dlartg (real(wp) f, real(wp) g, real(wp) c, real(wp) s, real(wp) r)"

.PP
\fBDLARTG\fP generates a plane rotation with real cosine and real sine\&. 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIF\fP 
.PP
.nf
          F is REAL(wp)
          The first component of vector to be rotated\&.
.fi
.PP
.br
\fIG\fP 
.PP
.nf
          G is REAL(wp)
          The second component of vector to be rotated\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL(wp)
          The cosine of the rotation\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is REAL(wp)
          The sine of the rotation\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          R is REAL(wp)
          The nonzero component of the rotated vector\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Edward Anderson, Lockheed Martin 
.RE
.PP
\fBDate\fP
.RS 4
July 2016 
.RE
.PP
\fBContributors:\fP
.RS 4
Weslley Pereira, University of Colorado Denver, USA 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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
.fi
.PP
 
.RE
.PP

.SS "subroutine slartg (real(wp) f, real(wp) g, real(wp) c, real(wp) s, real(wp) r)"

.PP
\fBSLARTG\fP generates a plane rotation with real cosine and real sine\&. 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIF\fP 
.PP
.nf
          F is REAL(wp)
          The first component of vector to be rotated\&.
.fi
.PP
.br
\fIG\fP 
.PP
.nf
          G is REAL(wp)
          The second component of vector to be rotated\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL(wp)
          The cosine of the rotation\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is REAL(wp)
          The sine of the rotation\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          R is REAL(wp)
          The nonzero component of the rotated vector\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Edward Anderson, Lockheed Martin 
.RE
.PP
\fBDate\fP
.RS 4
July 2016 
.RE
.PP
\fBContributors:\fP
.RS 4
Weslley Pereira, University of Colorado Denver, USA 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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
.fi
.PP
 
.RE
.PP

.SS "subroutine zlartg (complex(wp) f, complex(wp) g, real(wp) c, complex(wp) s, complex(wp) r)"

.PP
\fBZLARTG\fP generates a plane rotation with real cosine and complex sine\&. 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIF\fP 
.PP
.nf
          F is COMPLEX(wp)
          The first component of vector to be rotated\&.
.fi
.PP
.br
\fIG\fP 
.PP
.nf
          G is COMPLEX(wp)
          The second component of vector to be rotated\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL(wp)
          The cosine of the rotation\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is COMPLEX(wp)
          The sine of the rotation\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          R is COMPLEX(wp)
          The nonzero component of the rotated vector\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Weslley Pereira, University of Colorado Denver, USA 
.RE
.PP
\fBDate\fP
.RS 4
December 2021 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
 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
.fi
.PP
 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.