python3 - <<'PY'
import math,random
ln2=math.log(2)
def f(x): return 0.0 if x<=0 else -x*math.log(x)/ln2
def H(x): return f(x)+f(1-x)
Q=[[0,0,.45],[0,.15,.15],[.15,.05,.05]]
def soft(z):
    m=max(z); e=[2**(x-m) for x in z]; s=sum(e); return [x/s for x in e]
def best(W,starts):
    bb=(-1e99,None)
    for l,m in starts:
        for it in range(80):
            wm=[sum(W[j][k]*m[k] for k in range(3)) for j in range(3)]
            l2=soft([-wm[j] for j in range(3)])
            wtl=[sum(W[j][k]*l2[j] for j in range(3)) for k in range(3)]
            m2=soft([-wtl[k] for k in range(3)])
            if max(abs(l2[i]-l[i])+abs(m2[i]-m[i]) for i in range(3))<1e-11: l,m=l2,m2;break
            l,m=l2,m2
        v=H(l[1])+H(m[1])-sum(W[j][k]*l[j]*m[k] for j in range(3) for k in range(3))
        if v>bb[0]: bb=(v,(l,m))
    return bb
def D(W,st):
    b=best(W,st); wq=sum(W[j][k]*Q[j][k] for j in range(3) for k in range(3))
    return wq+b[0],b[1]
W=[[0.0]*3 for _ in range(3)]
st=]
print('D0',D(W,st)[0])
random.seed(4)
bestD=1e9
for it in range(80):
    dv,lm=D(W,st); l,m=lm
    if dv<bestD: bestD=dv;bestW=[row[:] for row in W]
    g=[[Q[j][k]-l[j]*m[k] for k in range(3)] for j in range(3)]
    eta=1.0/(1+it*0.05)
    W=[[W[j][k]-eta*g[j][k] for k in range(3)] for j in range(3)]
    st=[(l,m)]+[(soft([random.gauss(0,2) for _ in range(3)]),soft([random.gauss(0,2) for _ in range(3)])) for _ in range(3)]
print('bestD',bestD)
print('W',bestW)
PY