solves triangular systems of linear equations opts[a].x=α b or x.opts[a]==α b and resets b to the results x.
Details and Options
- To use TRSM, you first need to load the BLAS Package using Needs["LinearAlgebra`BLAS`"].
- The following arguments must be given:
sd input string left/right side string ul
- input string
upper/lower triangular string ts input string transposition string dg input string diagonal ones string α input expression scalar mutliple a input expression rectangular matrix b input/output symbol rectangular 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.
Examplesopen allclose all
Basic Examples (1)
Compute Inverse[UpperTriangularize[a]].b and save it in 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:
For invertible matrices a, TRSM["L","L","T","N",α,a,b] is equivalent to b=α 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:
If dg="U", the diagonal values of a are assumed to be ones:
The diagonal in a has been effectively replaced by ones:
If a is a rectangular matrix then only the leading upper or lower triangular part of a is used:
The matrix a is effectively truncated to its upper left corner:
Wolfram Research (2017), TRSM, Wolfram Language function, https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/TRSM.html.
Wolfram Language. 2017. "TRSM." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/TRSM.html.
Wolfram Language. (2017). TRSM. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/TRSM.html