"""subblock.py -- extract the "fully active" 9x9 sub-block M_{S->S^c} (both source and
target sectors fully active, i.e. every party involved) from the full bigraduated
cluster map. This is Corollary "sub-block witnesses" specialized to V=S, T=S^c."""
import numpy as np


def fully_active_block(C, s0, s1):
    others = [k for k in range(4) if k not in (s0, s1)]
    c0, c1 = others
    M = np.zeros((9, 9))
    rows = [(i, j) for i in [1, 2, 3] for j in [1, 2, 3]]
    cols = [(i, j) for i in [1, 2, 3] for j in [1, 2, 3]]
    for ri, (ia, ib) in enumerate(rows):
        for ci, (ic, idd) in enumerate(cols):
            idx = [0, 0, 0, 0]
            idx[s0] = ia
            idx[s1] = ib
            idx[c0] = ic
            idx[c1] = idd
            M[ri, ci] = C[tuple(idx)]
    return M / 3.0  # same normalization convention as cluster.cluster_map


def nuc(M):
    return np.linalg.svd(M, compute_uv=False).sum()