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ROT[x,y,c,s]

applies a Givens rotation {{c,s},{-Conjugate[s],c}} to the vectors x and y.

詳細とオプション
Details and Options Details and Options
例題  
例  
Scope  
Properties & Relations  
Possible Issues  
関連するガイド
引用書式
LinearAlgebra`BLAS`
LinearAlgebra`BLAS`

ROT

ROT[x,y,c,s]

applies a Givens rotation {{c,s},{-Conjugate[s],c}} to the vectors x and y.

詳細とオプション

  • To use ROT, you first need to load the BLAS Package using Needs["LinearAlgebra`BLAS`"].
  • The following arguments must be given:
  • xinput/output symbolvector; the symbol value is modified in place
    yinput/output symbolvector; the symbol value is modified in place
    cinput expressionreal-valued scalar
    sinput expressionscalar
  • ROT[x,y,c,s] is equivalent to {x,y}={{c,s},{-Conjugate[s],c}}.{x,y} where x and y are row vectors.
  • The vector arguments must be of the same length.

例題

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例  (1)

Load the BLAS package:

Wolfram Language code: Needs["LinearAlgebra`BLAS`"]

Apply a Givens rotation to two vectors:

Wolfram Language code: x = {1, 2, 3}; y = {-1, 2, 1}; {c, s} = {1, 2} / Sqrt[5]; ROT[x, y, c, s]; {x, y}

Scope  (4)

Real vectors:

Wolfram Language code: x = {1.2, 3.2, 6.7}; y = {2.2, 3., 4.5}; {c, s} = {2., 1.} / Sqrt[5.]; ROT[x, y, c, s]; {x, y}

Complex vectors:

Wolfram Language code: x = {2.3 - 0.3I, 2.I, 3.}; y = {-0.5I, 2.3, 4.1 + I}; {c, s} = {1., 2. + I} / Sqrt[{1., 2. + I}]; ROT[x, y, c, s]; {x, y}

Arbitrary-precision vectors:

Wolfram Language code: x = {1`20, 2, 3}; y = {-1`20, 2, 1}; {c, s} = {1, 2} / Sqrt[5]; ROT[x, y, c, s]; {x, y}

Symbolic vectors:

Wolfram Language code: x = {x1, x2}; y = {y1, y2}; Clear[c, s]; ROT[x, y, c, s]; {x, y}

Properties & Relations  (1)

ROT[x,y,c,s] is equivalent to {x,y}={{c,s},{-Conjugate[s],c}}.{x,y}:

Wolfram Language code: x = x1 = RandomReal[1, {5}]; y = y1 = RandomReal[1, {5}]; {c, s} = RandomReal[1, {2}]; {c, s} = {c, s} / Norm[{c, s}]; ROT[x, y, c, s]; {x, y} == {{c, s}, {-s, c}}.{x1, y1}

Possible Issues  (4)

If the first or second argument are not symbols, an error message is issued:

Wolfram Language code: x = {1, 2, 3}; {c, s} = {1, 2} / Sqrt[5]; ROT[x, {-1, 2, 1}, c, s]

If the first or second argument are not initialized, an error message is issued:

Wolfram Language code: Clear[x, y]; {c, s} = {1, 2} / Sqrt[5]; ROT[x, y, c, s]

The third argument c should be real.

Wolfram Language code: x = {1., 2, 3}; y = {-1., 2, 1}; {c, s} = {1. + I, 2. + I} / Norm[{1. + I, 2. + I}]; ROT[x, y, c, s]

The third and fourth arguments and should satisfy the relation to be a true Givens rotation. This condition is not checked.

Wolfram Language code: x = {1., 2, 3}; y = {-1., 2, 1}; ROT[x, y, 1., 2.] {x, y}
Wolfram Research (2017), ROT, Wolfram言語関数， https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROT.html.

テキスト

Wolfram Research (2017), ROT, Wolfram言語関数， https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROT.html.

CMS

Wolfram Language. 2017. "ROT." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROT.html.

APA

Wolfram Language. (2017). ROT. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROT.html

BibTeX

@misc{reference.wolfram_2026_rot, author="Wolfram Research", title="{ROT}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROT.html}", note=[Accessed: 17-July-2026]}

BibLaTeX

@online{reference.wolfram_2026_rot, organization={Wolfram Research}, title={ROT}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROT.html}, note=[Accessed: 17-July-2026]}