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:
•  x input/output symbol vector; the symbol value is modified in place y input/output symbol vector; the symbol value is modified in place c input expression real-valued scalar s input expression scalar
• 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

open allclose all

## 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_2022_rot, author="Wolfram Research", title="{ROT}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROT.html}", note=[Accessed: 10-June-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_rot, organization={Wolfram Research}, title={ROT}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/ROT.html}, note=[Accessed: 10-June-2023 ]}