ROTG[a,b,c,s]
computes a Givens rotation {c,s} for given scalars a and b.
ROTG
ROTG[a,b,c,s]
computes a Givens rotation {c,s} for given scalars a and b.
Details and Options
- To use ROTG, you first need to load the BLAS Package using Needs ["LinearAlgebra`BLAS`"].
- The following arguments must be given:
-
a input/output symbol scalar; the symbol value is modified in placeb input/output symbol scalar; the symbol value is modified in placec output symbol scalar; the symbol value is modified in places output symbol scalar; the symbol value is modified in place
- ROTG[a,b,c,s] computes {c,s} such that {{c,s},{-Conjugate [s],c}.{a,b}=={r,0}, where the signed radius r is given by rSign [b]Norm [{a,b}] if a==0 or a,b∈ with Abs [a]≤Abs [b], and by rSign [a]Norm [{a,b}] otherwise. In the degenerate case a==b==0, by convention c==1 and s==0.
- The scalars c and s can be viewed as the cosine and sine, respectively, of the angle of rotation and satisfy the conditions c∈ and c2+Abs [s]21.
- The scalar a is set to r. The scalar b is not modified if either a or b is complex. Otherwise, b is set to the value z given by:
-
- When given, the value z can be used to reconstruct c and s as follows:
-
c0 s1 if z1c sz if 0<Abs[z]<1c1 s0 if z==0
Examples
open all close allBasic Examples (1)
Load the BLAS package:
Compute a Givens rotation for given scalars:
Scope (3)
Real values:
Complex values:
Note that c is real-valued even when the inputs are complex:
Arbitrary-precision values:
Properties & Relations (1)
ROTG[a,b,c,s] satisfies the relation {{c,s},{-Conjugate [s],c}}.{a,b}={r,0} where r is the number saved in a:
The scalars c and s form a unit vector with c real:
Possible Issues (2)
All arguments must be symbols:
The first and the second arguments are modified and must be initialized to scalars:
Related Guides
Text
Wolfram Research (2017), ROTG, Wolfram Language function, https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROTG.html.
CMS
Wolfram Language. 2017. "ROTG." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROTG.html.
APA
Wolfram Language. (2017). ROTG. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROTG.html
BibTeX
@misc{reference.wolfram_2025_rotg, author="Wolfram Research", title="{ROTG}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROTG.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_rotg, organization={Wolfram Research}, title={ROTG}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROTG.html}, note=[Accessed: 17-November-2025]}