WOLFRAM

Wolfram言語 ＆ システムドキュメントセンター

GERC[α,x,y,a]

computes the rank-one update a+αOuter[Times,x,Conjugate[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`

GERC

GERC[α,x,y,a]

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

詳細とオプション

  • To use GERC, 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

すべて開く すべて閉じる

例  (1)

Load the BLAS package:

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

Apply rank-one update to a matrix:

Wolfram Language code: a = {{1, 2 I}, {3 - I, 4}}; GERC[1 / 2, {1, 1}, {-2 I, 1 + I}, 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.}}; GERC[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}}; GERC[1.0, {3.2I, -0.4I}, {2.3 + 2I, 3.4I}, a]; a

Arbitrary-precision matrix and vectors:

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

Integer-symbolic matrix and vectors:

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

Properties & Relations  (1)

  • GERC[α,x,y,a] is equivalent to a=a+αOuter[Times,x,Conjugate[y]]:
    • Wolfram Language code: a = a1 = RandomComplex[1 + I, {5, 7}]; x = RandomComplex[1 + I, {5}]; y = RandomComplex[1 + I, {7}]; α = RandomComplex[]; GERC[α, x, y, a]; a == α Outer[Times, x, Conjugate[y]] + a1

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

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

    Possible Issues  (2)

    The last argument must be a symbol:

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

    The last argument must be initialized to a matrix:

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

    テキスト

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

    CMS

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

    APA

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

    BibTeX

    @misc{reference.wolfram_2026_gerc, author="Wolfram Research", title="{GERC}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GERC.html}", note=[Accessed: 17-August-2026]}

    BibLaTeX

    @online{reference.wolfram_2026_gerc, organization={Wolfram Research}, title={GERC}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GERC.html}, note=[Accessed: 17-August-2026]}