"""Finite checks for coherent sparse-repair refusal. Synthetic, not hardware."""
from itertools import product, combinations
from fractions import Fraction
from math import comb, gcd
import json
from pathlib import Path
import numpy as np


def vectors(p,n):
    return np.array(list(product(range(p),repeat=n)),dtype=int)


def rank_mod(A,p):
    A=np.array(A,dtype=int).copy()%p
    m,n=A.shape
    row=0
    for j in range(n):
        pivot=next((i for i in range(row,m) if A[i,j]),None)
        if pivot is None: continue
        A[[row,pivot]]=A[[pivot,row]]
        A[row]=(A[row]*pow(int(A[row,j]),-1,p))%p
        for i in range(m):
            if i!=row and A[i,j]: A[i]=(A[i]-A[i,j]*A[row])%p
        row+=1
        if row==m: break
    return row


def rank_q(A):
    A=[[Fraction(int(x)) for x in row] for row in A]
    m=len(A); n=len(A[0]) if m else 0; row=0
    for j in range(n):
        pivot=next((i for i in range(row,m) if A[i][j]),None)
        if pivot is None: continue
        A[row],A[pivot]=A[pivot],A[row]
        den=A[row][j]
        A[row]=[x/den for x in A[row]]
        for i in range(row+1,m):
            if A[i][j]:
                a=A[i][j]; A[i]=[x-a*y for x,y in zip(A[i],A[row])]
        row+=1
        if row==m: break
    return row


def rank_z(A):
    """Exact integer elimination, normalizing rows by their gcd."""
    A=[[int(x) for x in row] for row in A]
    m=len(A); n=len(A[0]) if m else 0; row=0
    for j in range(n):
        pivot=next((i for i in range(row,m) if A[i][j]),None)
        if pivot is None: continue
        A[row],A[pivot]=A[pivot],A[row]
        den=A[row][j]
        for i in range(row+1,m):
            if A[i][j]:
                z=A[i][j]
                A[i]=[den*x-z*y for x,y in zip(A[i],A[row])]
                g=0
                for x in A[i]: g=gcd(g,abs(x))
                if g>1: A[i]=[x//g for x in A[i]]
        row+=1
        if row==m: break
    return row


def repair_distance(B,s,p):
    for k in range(B.shape[1]+1):
        for S in combinations(range(B.shape[1]),k):
            C=B[:,S]
            if rank_mod(C,p)==rank_mod(np.column_stack([C,s]),p): return k
    return None


def run():
    out={}
    B=np.array([[1,0,1,0,0,0],[0,1,1,0,0,0],
                [0,0,0,1,0,1],[0,0,0,0,1,1]],dtype=int)
    G=vectors(2,4)
    legal=np.array(sorted({(0,0,0,0),*[tuple(B[:,j]) for j in range(6)]}),dtype=int)
    evals=(-1.)**(legal@G.T%2)
    counts={}
    for D in range(1,5):
        deficient=0
        total=0
        for inds in combinations(range(16),D):
            total+=1
            if rank_q(evals[:,inds])<D: deficient+=1
        counts[str(D)]={'total_alphabets':total,'nonzero_refusal_alphabets':deficient}
    out['exact_rational_alphabet_scan']=counts
    A=np.array([[0,0,0,0],[1,0,0,0],[0,0,1,0],[1,0,1,0]])
    mu=np.full(4,.25)
    c=np.array([1.,-1.,-1.,1.])
    v=c/2
    probs=[]
    for s in G:
        state=np.sqrt(mu)*((-1.)**(A@s%2))
        prob=abs(np.vdot(v,state))**2
        probs.append({'s':s.tolist(),'distance':repair_distance(B,s,2),'prob':prob})
    out['binary_block_dictionary']={'B':B.tolist(),'rank':rank_mod(B,2),'legal_count':len(legal),'probabilities':probs}
    rng=np.random.default_rng(20261024)
    mu=rng.dirichlet(np.ones(4))
    Z=np.sum(1/mu)
    v=(c/np.sqrt(mu))/np.sqrt(Z)
    maxerr=0
    for s in G:
        state=np.sqrt(mu)*((-1.)**(A@s%2))
        prob=abs(np.vdot(v,state))**2
        predicted=(abs(np.prod(1-(-1.)**(np.array([s[0],s[2]]))))**2)/Z
        maxerr=max(maxerr,abs(prob-predicted))
    out['nonuniform_cube']={'mu':mu.tolist(),'Z':float(Z),'success_on_1111':float(16/Z),'uniform_success':1.0,'formula_max_error':maxerr}
    # Every nonzero 2-bit covector in each block: exact average success 4/9.
    nonzero=[a for a in vectors(2,2) if np.any(a)]
    alt=[s for s in G if np.any(s[:2]) and np.any(s[2:])]
    rates=[]
    for s in alt:
        rates.append(sum(int((a@s[:2])%2)*int((b@s[2:])%2) for a in nonzero for b in nonzero)/9)
    out['random_block_queries']={'alternatives':len(alt),'min_success':min(rates),'max_success':max(rates),'exact_rate':'4/9'}
    # General p uniform cube formula and one-sided soundness.
    p=3;n=3;t=2
    A=np.array([[e[0],e[1],0] for e in product((0,1),repeat=t)])
    v=np.array([(-1.)**sum(e) for e in product((0,1),repeat=t)])/2
    maxerr=0; maxlegal=0
    for s in vectors(p,n):
        state=np.exp(2j*np.pi*(A@s%p)/p)/2
        prob=abs(np.vdot(v,state))**2
        pred=float(np.prod(np.sin(np.pi*s[:t]/p)**2))
        maxerr=max(maxerr,abs(prob-pred))
        if np.count_nonzero(s)<=t-1: maxlegal=max(maxlegal,prob)
    out['ternary_cube']={'max_formula_error':maxerr,'max_legal_refusal_roundoff':maxlegal,'alternative_success_when_both_selected_nonzero':9/16}
    # A target-dependent optimum based on a general signed witness is Cauchy exact.
    c=np.array([1+2j,-2+1j,0.5-1j,-1j])
    mu=np.abs(c)/np.sum(np.abs(c))
    out['l1_witness_amplitudes']={'cauchy_gap':float(np.sum(np.abs(c)**2/mu)-np.sum(np.abs(c))**2)}
    identity_scans={}
    chars=vectors(2,4)
    for k,max_D in [(1,3),(2,7)]:
        legal=chars[np.count_nonzero(chars,axis=1)<=k]
        full=(-1)**((legal@chars.T)%2)
        by_D={}
        for D in range(1,max_D+1):
            deficient=0
            for inds in combinations(range(16),D):
                deficient+=int(rank_z(full[:,inds])<D)
            by_D[str(D)]={'total':comb(16,D),'rank_deficient':deficient}
        cube=np.array([list(e)+[0]*(4-k-1) for e in product((0,1),repeat=k+1)])
        cube_matrix=(-1)**((legal@cube.T)%2)
        identity_scans[str(k)]={'n':4,'k':k,'alphabets':by_D,'threshold_cube_modes':len(cube),'threshold_cube_rank':rank_z(cube_matrix)}
    out['identity_sparse_ball_exact_scans']=identity_scans
    prime_checks=[]
    for p in [2,3,5,7]:
        n=3;t=2
        A=np.array([[e[0],e[1],0] for e in product((0,1),repeat=t)])
        c=np.array([(-1.)**sum(e) for e in product((0,1),repeat=t)])
        mu=rng.dirichlet(np.ones(4)); Z=np.sum(1/mu)
        v=(c/np.sqrt(mu))/np.sqrt(Z)
        maxerr=0;maxlegal=0;tested=0
        for s in vectors(p,n):
            state=np.sqrt(mu)*np.exp(2j*np.pi*(A@s%p)/p)
            prob=abs(np.vdot(v,state))**2
            pred=float(np.prod(4*np.sin(np.pi*s[:t]/p)**2))/Z
            maxerr=max(maxerr,abs(prob-pred));tested+=1
            if np.count_nonzero(s)<=1:maxlegal=max(maxlegal,prob)
        prime_checks.append({'p':p,'n':n,'tested_all_syndromes':tested,'formula_max_error':maxerr,'legal_refusal_max_roundoff':maxlegal})
    out['all_small_prime_syndromes']=prime_checks
    assert all(counts[str(D)]['nonzero_refusal_alphabets']==0 for D in [1,2,3])
    assert counts['4']['nonzero_refusal_alphabets']==36
    assert all(row['rank_deficient']==0 for scan in identity_scans.values() for row in scan['alphabets'].values())
    assert all(scan['threshold_cube_rank']==scan['threshold_cube_modes']-1 for scan in identity_scans.values())
    assert all(row['prob']==0 for row in probs if row['distance']<=1)
    assert max(abs(rate-4/9) for rate in rates)<1e-12
    assert out['nonuniform_cube']['formula_max_error']<1e-12
    assert all(row['formula_max_error']<1e-12 and row['legal_refusal_max_roundoff']<1e-12 for row in prime_checks)
    assert abs(out['l1_witness_amplitudes']['cauchy_gap'])<1e-12
    Path('research/refusal_test_results.json').write_text(json.dumps(out,indent=2))
    print(json.dumps({k:v for k,v in out.items() if k!='binary_block_dictionary'},indent=2))

if __name__=='__main__': run()