table of contents
| rotg(3) | LAPACK | 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
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
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
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
Author¶
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