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TRMV[ul,ts,dg,a,b]

computes the triangular matrix-vector multiplication opts[a].b and resets b 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`

TRMV

TRMV[ul,ts,dg,a,b]

computes the triangular matrix-vector multiplication opts[a].b and resets b to the result.

詳細とオプション

  • To use TRMV, you first need to load the BLAS Package using Needs["LinearAlgebra`BLAS`"].
  • The following arguments must be given:
  • ul
  • input string
  • upper/lower triangular string
    • ts
  • input string
  • transposition string
    • dg
  • input string
    		• diagonal ones string
    ainput expressionrectangular matrix
    binput/output symbolvector; the symbol value is modified in place
  • 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
  • The transposition string ts describes the operator opts and may be specified as:
  • "N"no transposition
    "T"transpose
    "C"conjugate transpose
  • The diagonal ones string dg may be specified as:
  • "U"the main diagonal of a is assumed to contain only ones
    "N"the actual values of the main diagonal of a are used
  • Dimensions of the matrix and vector arguments must be such that the dot product is well defined.

例題

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例  (1)

Load the BLAS package:

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

Compute UpperTriangularize[a].b and save it in b:

Wolfram Language code: b = {-2, 1}; a = {{1, 3}, {2, 4}}; TRMV["U", "N", "N", a, b]; b

Scope  (4)

Real matrix and vectors:

Wolfram Language code: b = {2.3, 1.2, 3.9}; a = {{2.1, 0, 1.4}, {3.5, 2.4, 0.4}, {0, 2.7, 1.3}}; TRMV["U", "N", "N", a, b]; b

Complex matrix and vectors:

Wolfram Language code: b = {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}}; TRMV["U", "N", "N", a, b]; b

Arbitrary-precision matrix and vectors:

Wolfram Language code: b = {-2`20, 1}; a = {{1`20, 3}, {2, 4}}; TRMV["L", "N", "N", a, b]; b

Symbolic matrix and vectors:

Wolfram Language code: b = {x1, x2}; a = {{m11, m12}, {m21, m22}}; TRMV["L", "N", "U", a, b]; b

Properties & Relations  (4)

TRMV["U","N","N",a,b] is equivalent to b=UpperTriangularize[a].b:

Wolfram Language code: b = b1 = RandomReal[1, {5}]; a = RandomReal[1, {5, 5}]; TRMV["U", "N", "N", a, b]; b == UpperTriangularize[a].b1

TRMV["L","T","N",a,b] is equivalent to b=Transpose[LowerTriangularize[a]].b:

Wolfram Language code: b = bU = bL = RandomReal[1, {5}]; a = RandomReal[1, {5, 5}]; TRMV["L", "T", "N", a, bL]; bL == Transpose[LowerTriangularize[a]].b

Note this is not TRMV["U","N","N",a,b] as the lower triangular part is used for the transpose:

Wolfram Language code: TRMV["U", "N", "N", a, bU]; bL == bU

If dg="U", the diagonal values of a are assumed to be ones:

Wolfram Language code: b = {-2, 1}; a = {{3, 3}, {2, 4}}; TRMV["U", "N", "U", a, b]; b

The diagonal has been effectively replaced by ones:

Wolfram Language code: {{1, 3}, {0, 1}}.{-2, 1}

If a is a rectangular matrix then only the leading upper or lower triangular part of a is used:

Wolfram Language code: b = b1 = {1, 1}; a = {{3, 3}, {2, 4}, {-2, 3}}; TRMV["L", "N", "N", a, b]; b

The matrix a is effectively truncated to its upper left corner:

Wolfram Language code: {{3, 0}, {2, 4}}.b1

Possible Issues  (2)

The last argument must be a symbol:

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

The last argument must be initialized to a vector:

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

テキスト

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_trmv, author="Wolfram Research", title="{TRMV}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/TRMV.html}", note=[Accessed: 10-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_trmv, organization={Wolfram Research}, title={TRMV}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/TRMV.html}, note=[Accessed: 10-August-2026]}