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TRSM[sd,ul,ts,dg,α,a,b]

solves triangular systems of linear equations opts[a].x=α b or x.opts[a]==α b and resets b to the results 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`

TRSM

TRSM[sd,ul,ts,dg,α,a,b]

solves triangular systems of linear equations opts[a].x=α b or x.opts[a]==α b and resets b to the results x.

詳細とオプション

  • To use TRSM, you first need to load the BLAS Package using Needs["LinearAlgebra`BLAS`"].
  • The following arguments must be given:
  • sdinput stringleft/right side string
    ul
  • input string
    		• upper/lower triangular string
    tsinput stringtransposition string
    dginput stringdiagonal ones string
    αinput expressionscalar mutliple
    ainput expressionrectangular matrix
    binput/output symbolrectangular matrix; the symbol value is modified in place
  • The left/right side string sd may be specified as:
  • "L"a is on the left side of the dot product
    "R"a is on the right side of the dot product
  • 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 strings describe the operators 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 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 = {{1, 1}, {-2, 1}}; a = {{1, 3}, {2, 4}}; TRSM["L", "U", "N", "N", 1, a, b]; b

Scope  (4)

Real matrices:

Wolfram Language code: b = {{1., 0, 1.}, {2., 1., -2.}, {2.3, 1.2, 3.9}}; a = {{2.1, 0, 1.4}, {3.5, 2.4, 0.4}, {0, 2.7, 1.3}}; TRSM["L", "U", "N", "N", 2., a, b]; b

Complex matrices:

Wolfram Language code: b = {{2.3 + 3.I, 1.2 I}, {-3. + 2.I, 0.3I}}; a = {{2.1, 1.4 I}, {3.5 I, 0.4 + I}}; TRSM["R", "U", "N", "N", -1. + I, a, b]; b

Arbitrary-precision matrices:

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

Symbolic matrices:

Wolfram Language code: b = {{b11, b12}, {b21, b22}}; a = {{m11, m12}, {m21, m22}}; TRSM["R", "L", "N", "U", α, a, b]; b

Properties & Relations  (4)

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

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

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

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

Note this is not TRSM["L","U","T","N",α,a,L] as the lower triangular part is used for the transpose:

Wolfram Language code: TRSM["L", "U", "T", "N", 1, a, bL]; bL == bU

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

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

The diagonal in a has been effectively replaced by ones:

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

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

Wolfram Language code: b = {{1.5, 1}, {2, 2.5}}; a = {{3, 3, 2}, {2, 4, 2}}; TRSM["R", "L", "N", "N", 1, a, b]; b

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

Wolfram Language code: {{1.5, 1}, {2, 2.5}}.Inverse[{{3, 0}, {2, 4}}]

Possible Issues  (2)

The last argument must be a symbol:

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

The last argument must be initialized to a matrix:

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

テキスト

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_trsm, author="Wolfram Research", title="{TRSM}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/TRSM.html}", note=[Accessed: 12-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_trsm, organization={Wolfram Research}, title={TRSM}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/TRSM.html}, note=[Accessed: 12-August-2026]}