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.

Details and Options

  • 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.

Examples

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Basic Examples  (1)

Load the BLAS package:

Apply a Givens rotation to two vectors:

Scope  (4)

Real vectors:

Complex vectors:

Arbitrary-precision vectors:

Symbolic vectors:

Properties & Relations  (1)

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

Possible Issues  (4)

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

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

The third argument c should be real.

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

Wolfram Research (2017), ROT, Wolfram Language function, https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROT.html.

Text

Wolfram Research (2017), ROT, Wolfram Language function, 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_2024_rot, author="Wolfram Research", title="{ROT}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROT.html}", note=[Accessed: 22-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_rot, organization={Wolfram Research}, title={ROT}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROT.html}, note=[Accessed: 22-November-2024 ]}