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SYMV[ul,α,a,x,β,y]

computes the symmetric matrix-vector multiplication α a.x+β y and resets y 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`

SYMV

SYMV[ul,α,a,x,β,y]

computes the symmetric matrix-vector multiplication α a.x+β y and resets y to the result.

詳細とオプション

  • To use SYMV, 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
    ainput expressionsquare symmetric matrix
    xinput expressionvector
    βinput expressionscalar multiple
    yinput/output symbolvector; the symbol value is modified in place
  • The matrix is assumed symmetric, and only the upper or lower triangular part of a is used.
  • The upper/lower triangular string ul may be specified as:
  • "U"the upper triangular part of a is to be used
    "L"the lower triangular part of a is to be used
  • 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`"]

Compute a.x+2y and save it in y:

Wolfram Language code: y = {-2, 1}; a = {{1, 3}, {3, 4}}; x = {1, 2}; SYMV["U", 1, a, x, 2, y]; y

Scope  (4)

Real symmetric matrix and vectors:

Wolfram Language code: y = {2.3, 1.2, 3.9}; a = {{2.1, 0, 1.4}, {3.5, 2.4, 0.4}, {0, 2.7, 1.3}}; x = {0, 1.2, -1.3}; SYMV["U", 2, a, x, 1, y]; y

Complex symmetric matrix and vectors:

Wolfram Language code: y = {2.3 + 3.I, 1.2 I}; a = {{2.1, 1.4 I}, {1.4 I, 0.4}}; x = {1.2, -1.3 - 2.I}; SYMV["U", 2, a, x, 1, y]; y

Arbitrary-precision symmetric matrix and vectors:

Wolfram Language code: y = {-2`20, 1}; a = {{1`20, 3}, {3, 4}}; x = {1`20, 2}; SYMV["U", -1, a, x, 2, y]; y

Symbolic symmetric matrix and vectors:

Wolfram Language code: y = {y1, y2}; a = {{m11, m12}, {m12, m22}}; x = {x1, x2}; SYMV["U", α, a, x, β, y]; y

Properties & Relations  (3)

SYMV["U",α,a,x,β,y] is equivalent to y=α a.x+β y if a is symmetric:

Wolfram Language code: y = y1 = RandomReal[1, {5}]; a = RandomReal[1, {5, 5}]; a = (a + Transpose[a]) / 2.; (* symmetrize a *) x = RandomReal[1, {5}]; SYMV["U", 3, a, x, -2, y]; y == 3 a.x - 2 y1

For a symmetric matrix, using the upper or lower triangular part generally produces the same result:

Wolfram Language code: y = y1 = {v, w}; x = {s, t}; a = {{1, 2}, {2, 1}}; SYMV["U", α, a, x, β, y] y
Wolfram Language code: SYMV["L", α, a, x, β, y1] y1

SYMV works with a non-symmetric matrices:

Wolfram Language code: y = yU = yL = RandomReal[1, {5}]; x = RandomReal[1, {5}]; a = RandomReal[1, {5, 5}]; SYMV["U", 3, a, x, -2, yU]; yU

However, the upper and lower parts give different results:

Wolfram Language code: SYMV["L", 3, a, x, -2, yL]; yL

The effective computation of yU is the following:

Wolfram Language code: sa = Block[{lta = LowerTriangularize[a, -1]}, lta + Transpose[lta] + DiagonalMatrix[Diagonal[a]]]; yU == 3 sa.x - 2 y

Possible Issues  (2)

The last argument must be a symbol:

Wolfram Language code: a = {{1, 3}, {3, 4}}; x = {1, 2}; SYMV["U", 1, a, x, 2, {1, 2}]

The last argument must be initialized to a vector:

Wolfram Language code: Clear[y]; a = {{1, 3}, {3, 4}}; x = {1, 2}; SYMV["U", 1, a, x, 2, y]
Wolfram Research (2017), SYMV, Wolfram言語関数， https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/SYMV.html.

テキスト

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_symv, author="Wolfram Research", title="{SYMV}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/SYMV.html}", note=[Accessed: 11-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_symv, organization={Wolfram Research}, title={SYMV}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/SYMV.html}, note=[Accessed: 11-August-2026]}