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SYR[ul,α,x,a]

computes the symmetric rank-one update a+α Outer[Times,x,x] and resets the appropriate part of 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`

SYR

SYR[ul,α,x,a]

computes the symmetric rank-one update a+α Outer[Times,x,x] and resets the appropriate part of a to the result.

詳細とオプション

  • To use SYR, you first need to load the BLAS Package using Needs["LinearAlgebra`BLAS`"].
  • The following arguments must be given:
  • ulinput stringupper/lower triangular string
    αinput expressionscalar mutliple
    xinput expressionvector
    ainput/output symbolmatrix; the symbol value is modified in place
  • The upper/lower triangular string ul may be specified as:
  • "U"update the upper triangular part of a
    "L"update the lower triangular part of a
  • 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 symmetric rank-one update to the upper triangular part of a matrix:

Wolfram Language code: a = {{1, -2}, {-2, 3}}; SYR["U", 1, {1, 2}, 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.}}; SYR["U", 0.5, {-1.2, 0., 2.3}, a]; a

Complex matrix and vectors:

Wolfram Language code: a = {{2.1 + 0.5I, 3.2 + I}, {4.1I, 3.8}}; SYR["L", 1.0, {2.3, 3.4I}, a]; a

Arbitrary-precision matrix and vectors:

Wolfram Language code: a = {{1`20, -2}, {-2, 3}}; SYR["U", 1`20 / 2, {1`20, 2}, a]; a

Integer-symbolic matrix and vectors:

Wolfram Language code: a = {{m11, m12}, {m21, m22}}; SYR["U", α, {x1, x2}, a]; a

Properties & Relations  (1)

SYR["U",α,x,a] is equivalent to a=a+α Outer[Times,x,x] for the upper triangular part of a:

Wolfram Language code: a = a1 = RandomReal[1, {5, 5}]; x = RandomReal[1, {5}]; α = RandomReal[]; SYR["U", α, x, a]; a == UpperTriangularize[α Outer[Times, x, x]] + a1

The strictly lower triangular part of a is unchanged:

Wolfram Language code: LowerTriangularize[a, -1] == LowerTriangularize[a1, -1]

Possible Issues  (2)

The last argument must be a symbol:

Wolfram Language code: SYR["U", 1 / 2, {-2, 1}, {{1, 2}, {3, 4}}]

The last argument must be initialized to a matrix:

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

テキスト

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_syr, author="Wolfram Research", title="{SYR}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/SYR.html}", note=[Accessed: 18-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_syr, organization={Wolfram Research}, title={SYR}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/SYR.html}, note=[Accessed: 18-August-2026]}