Fastest way to calculate eigenvectors of 4x4 matrix

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22

Big coupled systems are nothing new. Sounds like you may have a differential-algebraic equation (DAE)? There are solvers for this too.

Using a coupled solver, e.g. a DAE solver, lets you focus on formulating the continuous-time equations, and let the solver handle discretizing into time steps (often at high order accuracy, often with adaptive sizes).

23

Hi @Mason, thanks for your solution! But in latest Julia, I found expv has similar performance compared to expā€¦not sure whether I got the correct way to use itā€¦but if I ran this:

using ExponentialUtilities
using BenchmarkTools
using StaticArrays

A = rand(4, 4)
As = SMatrix{4, 4}(A)
v = rand(4)
vs = SVector{4}(v)
           
t = 1e-3

# calculate exp(t * A) * v
@btime expv($t, $A, $v)     
@btime expv($t, $As, $vs)
@btime exp($t*$As)*$vs

I got

  2.989 Ī¼s (27 allocations: 2.22 KiB)
4-element Vector{Float64}:
 0.6843916614773726
 0.6584018736208126
 0.9509576202197598
 0.6793439922385884

  213.225 ns (0 allocations: 0 bytes)
4-element SVector{4, Float64} with indices SOneTo(4):
 0.6843916614773728
 0.6584018736208129
 0.9509576202197598
 0.6793439922385885

  213.211 ns (0 allocations: 0 bytes)
4-element SVector{4, Float64} with indices SOneTo(4):
 0.6843916614773728
 0.6584018736208129
 0.9509576202197598
 0.6793439922385885

Is that normal (compared the second and third ones)? I am using Julia with the version of 1.11.5