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GER[α,x,y,a]

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

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`

GER

GER[α,x,y,a]

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

詳細とオプション

  • 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.

例題

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例  (1)

Load the BLAS package:

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

Apply a rank-one update to a matrix:

Wolfram Language code: a = {{1, 2}, {3, 4}}; GER[1 / 2, {1, 2}, {-2, 1}, a]; a

Scope  (4)

Real matrix and vectors:

Wolfram Language code: a = {{-2.1, 0., 3.2}, {4.3, 0.2, -0.3}, {4.1, 2.6, 0.}}; GER[1., {-1.2, 0., 2.3}, {3.1, 0.3, -0.9}, a]; a

Complex matrix and vectors:

Wolfram Language code: a = {{2.1 + 0.5I, 3.2 + I}, {4.1I, 3.8}}; GER[1.0, {3.2I, 2.3 - 0.4I}, {2.3, 3.4I}, a]; a

Arbitrary-precision matrix and vectors:

Wolfram Language code: a = {{1`20, 2}, {3, 4}}; GER[1`20 / 2, {1`20, 2}, {-2, 1}, a]; a

Integer-symbolic matrix and vectors:

Wolfram Language code: a = {{m11, m12}, {m21, m22}}; GER[α, {1, 2}, {-2, 1}, a]; a

Properties & Relations  (1)

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

Wolfram Language code: a = a1 = RandomReal[1, {5, 7}]; x = RandomReal[1, {5}]; y = RandomReal[1, {7}]; α = RandomReal[]; GER[α, x, y, a]; a == α Outer[Times, x, y] + a1

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

Wolfram Language code: a == α Transpose[{x}].{y} + a1

Possible Issues  (2)

The last argument must be a symbol:

Wolfram Language code: GER[1 / 2, {1, 2}, {-2, 1}, {{1, 2}, {3, 4}}]

The last argument must be initialized to a matrix:

Wolfram Language code: Clear[a]; GER[1 / 2, {1, 2}, {-2, 1}, a]
Wolfram Research (2017), GER, Wolfram言語関数， https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html.

テキスト

Wolfram Research (2017), GER, Wolfram言語関数， 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_2026_ger, author="Wolfram Research", title="{GER}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html}", note=[Accessed: 11-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_ger, organization={Wolfram Research}, title={GER}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html}, note=[Accessed: 11-August-2026]}