import sys, time, collections
from system import ERRDIMS, ERRORDER, err_offsets
from solve import echelon, nullspace_mod, check_vec
from gauge import gauge_errors, plus_eigen_basis

def analyze(S, p, t, blocks_order=("E3","E25","E2","b","a"), verbose=False):
    """Column order: nu, then error blocks in blocks_order. Report projection dims
    onto successive tails."""
    idx = {}
    for r in S.rows:
        for c in r:
            if c[0]=="nu" and c not in idx:
                idx[c]=len(idx)
    N=len(idx)
    off={}
    o=N
    for n in blocks_order:
        off[n]=o
        for i in range(ERRDIMS[n]):
            idx[("err",n,i)]=o+i
        o+=ERRDIMS[n]
    tot=o
    rows=[{idx[c]: int(v)%p for c,v in r.items() if int(v)%p} for r in S.rows]
    piv=echelon(rows,p,verbose=verbose)
    res={}
    for j,n in enumerate(blocks_order):
        tail=blocks_order[j:]
        start=off[n]
        ntail=tot-start
        npiv=sum(1 for c in piv if c>=start)
        res[tail]=ntail-npiv
    # gauge vectors projected
    G=[]
    for w in plus_eigen_basis(t):
        g=gauge_errors(S.rels,w,t)
        eo,_=err_offsets()
        vec=[0]*(tot-N)
        for n in ERRORDER:
            for i in range(ERRDIMS[n]):
                vec[off[n]-N+i]=int(g[eo[n]+i])%p
        G.append(vec)
    cons={c-N:{cc-N:v for cc,v in r.items()} for c,r in piv.items() if c>=N}
    bad=[check_vec(cons,g,p) for g in G]
    # gauge rank on each tail
    gr={}
    for j,n in enumerate(blocks_order):
        start=off[n]-N
        sub=[{i-start:g[i] for i in range(start,len(g)) if g[i]} for g in G]
        pv=echelon(sub,p)
        gr[blocks_order[j:]]=len(pv)
    return res, gr, bad, piv, N, off