"""Scientific summary of the proved rotation bound; plots are not certification."""
from pathlib import Path
from fractions import Fraction
import json
import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt


def main():
    root=Path(__file__).parent
    cert=json.loads((root/'ROTATION_BOUND_CERTIFICATE.json').read_text())
    pars=cert['parameters']
    r,t,d,g=[float(Fraction(pars[k])) for k in ('r','t','delta','kappa')]
    a=1+r
    w=np.sqrt(a*a-t*t)
    C,S=np.cos(np.pi/8),np.sin(np.pi/8)
    A,H=2*(t*S-w*C),2*(t*C+w*S)
    eta0=(1-t)/2
    q=lambda z:A*A*z*z/(4*a*(A*A+(z+H)**2))
    reward=lambda eta:q(4*eta/3)+q(2*eta/3)
    derivative=float(cert['packing_reward_derivative_at_eta0'][0])
    plt.rcParams.update({'font.size':10,'axes.spines.top':False,
                         'axes.spines.right':False,'figure.facecolor':'white'})
    fig,axes=plt.subplots(1,3,figsize=(13.2,4.2),constrained_layout=True)
    ax=axes[0]
    angles=np.linspace(0,2*np.pi,1000)
    ax.fill(np.cos(angles),np.sin(angles),color='#edf2f7')
    for rotation,color,alpha in [(0,'#1591a2',.75),(np.pi/6,'#d48332',.55)]:
        for k in range(4):
            phi=np.pi/4+k*np.pi/2+rotation
            u=np.array([np.cos(phi),np.sin(phi)])
            v=np.array([-np.sin(phi),np.cos(phi)])
            ss=np.linspace(t,1,100)
            zz=np.sqrt(a*a-ss*ss)
            pts=np.r_[ss[:,None]*u+zz[:,None]*v,ss[::-1,None]*u-zz[::-1,None]*v]
            ax.fill(pts[:,0],pts[:,1],color=color,alpha=alpha)
    ax.plot(np.cos(angles),np.sin(angles),color='#1e3a5f',lw=1.2)
    ax.set(xlim=(-1.18,1.18),ylim=(-1.18,1.18),aspect='equal',
           title='A. Average over all cap rotations')
    ax.set_xticks([-1,0,1]);ax.set_yticks([-1,0,1])
    ax.text(.5,.53,r'Point membership $\leq 2\arccos t$',transform=ax.transAxes,
            ha='center',fontsize=10)
    ax.text(.5,.41,'Two example orientations shown',transform=ax.transAxes,
            ha='center',fontsize=8,color='#526276')
    ax.text(.5,-.1,'Cap regions; no candidate barrier shown',transform=ax.transAxes,
            ha='center',fontsize=8,color='#526276')
    ax=axes[1]
    vals=[1.076457,d*1e6]
    ax.bar([0,1],vals,color=['#94a3b8','#1591a2'],width=.58)
    ax.set_xticks([0,1],['Published parameter\nchoice (2026)','Rotation certificate\nhere'])
    ax.set(ylabel=r'Excess above $\pi$, in units of $10^{-6}$',ylim=(0,9.7),
           title='B. Complete-barrier lower bound')
    for x,y in enumerate(vals):ax.text(x,y+.14,f'{y:.7f}',ha='center',fontsize=9)
    ax.text(.04,.96,f'Excess ratio: {vals[1]/vals[0]:.3f}'+r'$\times$',
            transform=ax.transAxes,va='top')
    ax=axes[2]
    x=np.linspace(0,1,501)
    U=np.pi*eta0*x
    nonlinear=g*reward(eta0-U/np.pi)/d
    linear=np.maximum(0,g*(reward(eta0)-derivative*U/np.pi)/d)
    ax.plot(x,nonlinear,color='#1591a2',lw=2.5,label='Nonlinear robust gain')
    ax.plot(x,linear,color='#d48332',lw=1.8,ls='--',label='Linear corollary (with zero)')
    ax.set(xlabel=r'Missed-line measure $U/(\pi\eta_0)$',
           ylabel=r'Gain over $L\geq\pi-U/2$, divided by $d$',ylim=(-.02,1.12),
           title='C. Robustness to incomplete coverage')
    ax.grid(alpha=.17);ax.legend(fontsize=8,loc='upper right')
    fig.suptitle(r'Rotation-averaged disk opacity: $L>\pi+'+f'{d*1e6:.7f}'+r'\times10^{-6}$',
                 fontsize=16,fontweight='bold')
    for suffix in ('png','pdf'):
        fig.savefig(root/'figures'/f'disk_bound.{suffix}',dpi=180,bbox_inches='tight')
    plt.close(fig)


if __name__=='__main__':
    main()