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The Julia Language

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Julia is a high-level dynamic programming language designed to address the needs of high-performance numerical analysis and computational science. It provides a sophisticated compiler, distributed parallel execution, numerical accuracy, and an extensive mathematical function library.

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julia
sethaxen
sethaxen commented Feb 28, 2021

The current implementation of lyap for complex scalar arguments is incorrect. We can see this by comparing the result obtained using 1x1 matrices vs scalars:

julia> A = (1.0+2.0im)*ones(1,1);

julia> C = (3.0+4.0im)*ones(1,1);

julia> lyap(A, C)  # expected
1×1 Matrix{ComplexF64}:
 -1.5 - 2.0im

julia> lyap(A[1], C[1])  # wrong! 
-1.1 + 0.2im

julia> -C[1] / 2real(A[1])  
dash
Pluto.jl
JuMP.jl

Created by Jeff Bezanson, Stefan Karpinski, Viral B. Shah, Alan Edelman

Released February 14, 2012

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JuliaLang
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julialang.org
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