import numpy as np
from scipy.linalg import expm, eigvals
rng=np.random.default_rng(7)
def edge(a): return np.max(np.real(eigvals(a)))
def gam(a,b,T):
 p=expm(b*T/2)@expm(a*T/2)
 return np.log(np.max(np.abs(eigvals(p))))/T
for i in range(20000):
 a=rng.normal(0,5,(2,2)); b=rng.normal(0,5,(2,2))
 ea,eb=edge(a),edge(b)
 if ea<=.2 or eb<=.2: continue
 av=edge((a+b)/2)
 vals=[gam(a,b,t) for t in [.01,.03,.1,.2,.5,1,2,5,10]]
 if av>0 and min(vals)<-.05:
  print('found',i,'edges',ea,eb,'avg',av,'comm',np.linalg.norm(a@b-b@a),'vals',vals)
  print(a);print(b);break
else: print('none')