.TH "rotg" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
rotg \- rotg: generate plane rotation (cf\&. lartg)
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcrotg\fP (a, b, c, s)"
.br
.RI "\fBCROTG\fP generates a Givens rotation with real cosine and complex sine\&. "
.ti -1c
.RI "subroutine \fBdrotg\fP (a, b, c, s)"
.br
.RI "\fBDROTG\fP "
.ti -1c
.RI "subroutine \fBsrotg\fP (a, b, c, s)"
.br
.RI "\fBSROTG\fP "
.ti -1c
.RI "subroutine \fBzrotg\fP (a, b, c, s)"
.br
.RI "\fBZROTG\fP generates a Givens rotation with real cosine and complex sine\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine crotg (complex(wp) a, complex(wp) b, real(wp) c, complex(wp) s)"

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

.PP
.nf
 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\&.
.fi
.PP
.RE
.PP
\fBSee also\fP
.RS 4
\fBlartg:          generate plane rotation, more accurate than BLAS rot\fP, 
.PP
\fBlartgp:         generate plane rotation, more accurate than BLAS rot\fP 
.RE
.PP
\fBParameters\fP
.RS 4
\fIA\fP 
.PP
.nf
          A is COMPLEX
          On entry, the scalar a\&.
          On exit, the scalar r\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX
          The scalar b\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL
          The scalar c\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is COMPLEX
          The scalar s\&.
.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 drotg (real(wp) a, real(wp) b, real(wp) c, real(wp) s)"

.PP
\fBDROTG\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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)\&.
.fi
.PP
.RE
.PP
\fBSee also\fP
.RS 4
\fBlartg:          generate plane rotation, more accurate than BLAS rot\fP, 
.PP
\fBlartgp:         generate plane rotation, more accurate than BLAS rot\fP 
.RE
.PP
\fBParameters\fP
.RS 4
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION
          On entry, the scalar a\&.
          On exit, the scalar r\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION
          On entry, the scalar b\&.
          On exit, the scalar z\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION
          The scalar c\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is DOUBLE PRECISION
          The scalar s\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Edward Anderson, Lockheed Martin 
.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 srotg (real(wp) a, real(wp) b, real(wp) c, real(wp) s)"

.PP
\fBSROTG\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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)\&.
.fi
.PP
.RE
.PP
\fBSee also\fP
.RS 4
\fBlartg:          generate plane rotation, more accurate than BLAS rot\fP, 
.PP
\fBlartgp:         generate plane rotation, more accurate than BLAS rot\fP 
.RE
.PP
\fBParameters\fP
.RS 4
\fIA\fP 
.PP
.nf
          A is REAL
          On entry, the scalar a\&.
          On exit, the scalar r\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is REAL
          On entry, the scalar b\&.
          On exit, the scalar z\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL
          The scalar c\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is REAL
          The scalar s\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Edward Anderson, Lockheed Martin 
.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 zrotg (complex(wp) a, complex(wp) b, real(wp) c, complex(wp) s)"

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

.PP
.nf
 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\&.
.fi
.PP
.RE
.PP
\fBSee also\fP
.RS 4
\fBlartg:          generate plane rotation, more accurate than BLAS rot\fP, 
.PP
\fBlartgp:         generate plane rotation, more accurate than BLAS rot\fP 
.RE
.PP
\fBParameters\fP
.RS 4
\fIA\fP 
.PP
.nf
          A is DOUBLE COMPLEX
          On entry, the scalar a\&.
          On exit, the scalar r\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE COMPLEX
          The scalar b\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION
          The scalar c\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is DOUBLE COMPLEX
          The scalar s\&.
.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\&.