Inverse of a triangular matrix

General Usage Performance
1

Hello,

Is there an optimized way to inverse a triangular matrix? I searched with Google, no luck.

2

julia does provide specialized types UpperTriangular, UnitUpperTriangular, LowerTriangular, and UnitLowerTriangular. In the documentation it is stated that there are optimized functions for inv and det.

https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#LAPACK-functions

This is a small example of how this should work:

using LinearAlgebra
A = [1.0 2.0 3.0; 0.0 5.0 6.0; 0.0 0.0 9.0]
3×3 Array{Float64,2}:
 1.0  2.0  3.0
 0.0  5.0  6.0
 0.0  0.0  9.0

UTA = UpperTriangular(A)
3×3 UpperTriangular{Float64,Array{Float64,2}}:
 1.0  2.0  3.0
  ⋅   5.0  6.0
  ⋅    ⋅   9.0

inv(UTA)
3×3 UpperTriangular{Float64,Array{Float64,2}}:
 1.0  -0.4  -0.0666667
  ⋅    0.2  -0.133333
  ⋅     ⋅    0.111111
3

Ah nice, thanks!