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GEMV[ts,α,a,x,β,y]

computes the matrix-vector multiplication α opts[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`

GEMV

GEMV[ts,α,a,x,β,y]

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

詳細とオプション

  • To use GEMV, you first need to load the BLAS Package using Needs["LinearAlgebra`BLAS`"].
  • The following arguments must be given:
  • tsinput stringtransposition string
    αinput expressionscalar mutliple
    ainput expressionrectangular matrix
    xinput expressionvector
    βinput expressionscalar multiple
    yinput/output symbolvector; the symbol value is modified in place
  • The transposition string ts describes the operator opts and may be specified as:
  • "N"no transposition
    "T"transpose
    "C"conjugate transpose
  • 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`"]

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

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

Scope  (4)

Real 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}; GEMV["N", 2, a, x, 1, y]; y

Complex matrix and vectors:

Wolfram Language code: y = {2.3 + 3.I, 1.2 I, -3. + 2.I}; a = {{2.1, 0, 1.4 I}, {3.5 I, 2.4, 0.4 + I}, {0, 2.7, 1.3 I}}; x = {0, 1.2, -1.3 - 2.I}; GEMV["N", 2, a, x, 1, y]; y

Arbitrary-precision matrix and vectors:

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

Symbolic matrix and vectors:

Wolfram Language code: y = {y1, y2}; a = {{m11, m12}, {m21, m22}}; x = {x1, x2}; GEMV["N", α, a, x, β, y]; y

Properties & Relations  (3)

GEMV["N",α,a,x,β,y] is equivalent to y=α a.x+β y:

Wolfram Language code: y = y1 = RandomReal[1, {4}]; a = RandomReal[1, {4, 5}]; x = RandomReal[1, {5}]; GEMV["N", 3, a, x, -2, y]; y == 3 a.x - 2 y1

GEMV["T",α,a,x,β,y] is equivalent to y=α Transpose[a].x+β y:

Wolfram Language code: y = y1 = RandomReal[1, {5}]; a = RandomReal[1, {4, 5}]; x = RandomReal[1, {4}]; GEMV["T", 3, a, x, -2, y]; y == 3 Transpose[a].x - 2 y1

GEMV["C",α,a,x,β,y] is equivalent to y=α ConjugateTranspose[a].x+β y:

Wolfram Language code: y = y1 = RandomComplex[1 + I, {5}]; a = RandomComplex[1 + I, {4, 5}]; x = RandomComplex[1 + I, {4}]; GEMV["C", 3 + 2I, a, x, -2 + I, y]; y == (3 + 2I) ConjugateTranspose[a].x + (-2 + I) y1

Possible Issues  (2)

The last argument must be a symbol:

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

If the last argument is not a symbol initialized to a vector then an error message is issued:

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

テキスト

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_gemv, author="Wolfram Research", title="{GEMV}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GEMV.html}", note=[Accessed: 19-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_gemv, organization={Wolfram Research}, title={GEMV}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GEMV.html}, note=[Accessed: 19-August-2026]}