LinearAlgebra`BLAS`
LinearAlgebra`BLAS`

GER

GER[α,x,y,a]

computes the rank-one update a+αOuter[Times,x,y] and resets a to the result.

Details and Options

  • To use GER, you first need to load the BLAS Package using Needs["LinearAlgebra`BLAS`"].
  • The following arguments must be given:
  • αinput expressionscalar mutliple
    xinput expressionvector
    yinput expressionvector
    a
  • input/output symbol
    		• matrix; the symbol value is modified in place
  • Dimensions of the matrix and vector arguments must be such that the dot product and addition are well defined.

Examples

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Basic Examples  (1)

Load the BLAS package:

Apply a rank-one update to a matrix:

Scope  (4)

Real matrix and vectors:

Complex matrix and vectors:

Arbitrary-precision matrix and vectors:

Integer-symbolic matrix and vectors:

Properties & Relations  (1)

GER[α,x,y,a] is equivalent to a=a+αOuter[Times,x,y]:

This can also be expressed as a=a+αTranspose[{x}].{y}:

Possible Issues  (2)

The last argument must be a symbol:

The last argument must be initialized to a matrix:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2023_ger, author="Wolfram Research", title="{GER}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html}", note=[Accessed: 24-April-2024 ]}

BibLaTeX

@online{reference.wolfram_2023_ger, organization={Wolfram Research}, title={GER}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html}, note=[Accessed: 24-April-2024 ]}