import numpy as np
from lib import kappa
def best(R,n=1600,kmult=np.linspace(1,12,23)):
    k,L=kappa(R-2); d=R/n; u=-R/2+d*(np.arange(n)+.5)
    K=np.maximum(1-np.abs(u[:,None]-u[None,:]),0)*d*d
    S=u[:,None]+u[None,:]
    E=((np.abs(S-2)<d/2)|(np.abs(S+2)<d/2)).astype(float)*d/2
    a=-R+d*(np.arange(2*n-1)+1); out=np.abs(a)>=2
    B=None
    for km in kmult:
        z=np.linalg.solve(np.eye(n)*d-K+km*k*E,np.ones(n)); h=z/(z.sum()*d)
        gh=np.convolve(h,h)*d
        g0=(h.sum()*d)**2; gh0=np.sum(h*h)*d; inner=np.sum(gh*np.maximum(1-np.abs(a),0))*d
        gmax=max(gh[out].max(),0) if out.any() else 0.
        tot=(gh0-inner+k*gmax)/g0
        if B is None or tot<B[0]: B=(tot,km,gmax,np.abs(h-h[::-1]).max())
    return B,k
for R in [2.0,2.02,2.05,2.1,2.2,2.3]:
    (t,km,gm,asym),k=best(R)
    print(f"R={R} kappa={k:.3f} m={t:.6f} simple>={1-t:.4%} gain={0.0677147-t:+.6f} gmax={gm:.2e} asym={asym:.1e}")