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.

Details

• 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.

Examples

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Basic Examples(1)

Load the BLAS package:

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

 In:= Out= 