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

solves the triangular system of linear equations opts[a].x==b and resets b to the result x.

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`

TRSV

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

solves the triangular system of linear equations opts[a].x==b and resets b to the result x.

詳細とオプション

  • To use TRSV, 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 Inverse[UpperTriangularize[a]].b and save it in b:

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

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}}; TRSV["U", "N", "N", a, b]; b

Arbitrary-precision matrix and vectors:

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

Symbolic matrix and vectors:

Wolfram Language code: b = {b1, b2}; a = {{m11, m12}, {m21, m22}}; TRSV["L", "N", "U", a, b]; b

Properties & Relations  (3)

For invertible matrices a, TRSV["U","N","N",a,b] is equivalent to b=Inverse[UpperTriangularize[a]].b:

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

For invertible matrices a, TRSV["L","T","N",a,b] is equivalent to b=Inverse[Transpose[LowerTriangularize[a]]].b:

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

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

Wolfram Language code: TRSV["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}}; TRSV["U", "N", "U", a, b]; b

The diagonal has been effectively replaced by ones:

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

Possible Issues  (3)

The last argument must be a symbol:

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

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}}; TRSV["L", "N", "N", a, b]; b

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

Wolfram Language code: Inverse[{{3, 0}, {2, 4}}].b1
Wolfram Research (2017), TRSV, Wolfram言語関数， https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/TRSV.html.

テキスト

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_trsv, author="Wolfram Research", title="{TRSV}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/TRSV.html}", note=[Accessed: 15-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_trsv, organization={Wolfram Research}, title={TRSV}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/TRSV.html}, note=[Accessed: 15-August-2026]}