"""Check for item 2 of 06-ilang-source/08-typical-or-forced (role: check).

One field object (N_f = 1, n = 1/|X|) of class F with r = 2 internal places on a ring (D = 1)
or a square torus (D = 2) of side L. Own contract h = sum_a sum_x |x+a><x| (x) h_a with Bloch
matrix h(k) = -2t sum_mu cos k_mu + Delta |2><2| + lam sin k_1 sigma_1 (lowest state at k_0 = 0),
coupled operator Phi_x = |x><x| (x) phi, source at x_s = 0.
chi_0(x, x_s) of (3.6) is computed from the eigenvectors of h and compared with the Bloch formula
(8.8) and with the large-distance forms (8.10), (8.11), (8.13). All values are reported as chi/(2n).
"""
from pathlib import Path

import matplotlib
import numpy as np

matplotlib.use("Agg")
import matplotlib.pyplot as plt  # noqa: E402

OUT = Path(__file__).parent / "output"
OUT.mkdir(exist_ok=True)
T, DELTA = 1.0, 1.5
SX = np.array([[0, 1], [1, 0]], complex)
P2 = np.diag([0, 1]).astype(complex)
PHI_LR = np.array([[1.0, 0.3], [0.3, -0.5]], complex)
LOG = []


def log(s=""):
    print(s)
    LOG.append(s)


def blocks(D, lam):
    """Hopping blocks h_a of h = sum_a sum_x |x+a><x| (x) h_a, h(k) = sum_a exp(-i k.a) h_a."""
    b = {(0,) * D: DELTA * P2}
    for mu in range(D):
        e = np.zeros(D, int)
        e[mu] = 1
        hp = -T * np.eye(2, dtype=complex) + (0.5j * lam * SX if mu == 0 else 0)
        b[tuple(e)] = hp
        b[tuple(-e)] = hp.conj().T
    return b


def h_bloch(k, blk):
    return sum(np.exp(-1j * np.dot(k, a)) * M for a, M in blk.items())


def lowest(blk, k):
    ev, W = np.linalg.eigh(h_bloch(k, blk))
    return ev[0], W[:, 0]


def grid(L, D):
    return np.array(np.unravel_index(np.arange(L ** D), (L,) * D)).T


def chi_direct(L, D, blk, phi):
    """chi_0(x, 0) of (3.6) from the full diagonalization of h on |X| x r places."""
    n, xs = L ** D, grid(L, D)
    H = np.zeros((2 * n, 2 * n), complex)
    for a, M in blk.items():
        tgt = np.ravel_multi_index(((xs + np.array(a)) % L).T, (L,) * D)
        for s in range(n):
            H[2 * tgt[s]:2 * tgt[s] + 2, 2 * s:2 * s + 2] += M
    assert np.allclose(H, H.conj().T)
    e, U = np.linalg.eigh(H)
    assert e[1] - e[0] > 1e-8, "lowest eigenvector not unique"
    Ur = U.reshape(n, 2, -1)
    amp = np.einsum("xo,op,xpm->xm", Ur[:, :, 0].conj(), phi, Ur)  # <u_0|phi_x|u_m>
    chi = 2 * np.real(amp[:, 1:] * amp[0, 1:].conj()) @ (1 / (e[1:] - e[0]))
    return chi.reshape((L,) * D)


def chi_bloch(L, D, blk, phi):
    """(8.8) with k_0 = 0: chi(d) = (2n/|X|) sum_q cos(q.d) S_L(q)."""
    e0, w0 = lowest(blk, np.zeros(D))
    S = np.empty(L ** D)
    for i, k in enumerate(2 * np.pi * grid(L, D) / L):
        ev, W = np.linalg.eigh(h_bloch(k, blk))
        m2 = np.abs(W.conj().T @ phi @ w0) ** 2
        keep = ev - e0 > 1e-12  # drops only (k_0, l = 0)
        S[i] = np.sum(m2[keep] / (ev[keep] - e0))
    return 2 / L ** D * np.real(np.fft.ifftn(S.reshape((L,) * D)))


def band_data(D, blk, phi, eps=1e-3):
    """phibar = <w0|phi|w0>; A = Hessian/2 of the lowest band at k_0; C = Hessian/2 of |F(q)|^2."""
    _, w0 = lowest(blk, np.zeros(D))
    phibar = np.real(w0.conj() @ phi @ w0)
    E = lambda q: lowest(blk, q)[0]  # noqa: E731
    F2 = lambda q: abs(w0.conj() @ phi @ lowest(blk, q)[1]) ** 2  # noqa: E731
    A, C = np.zeros((D, D)), np.zeros((D, D))
    for mu in range(D):
        for nu in range(D):
            em, en = np.eye(D)[mu] * eps, np.eye(D)[nu] * eps
            for f, Mat in ((E, A), (F2, C)):
                Mat[mu, nu] = (f(em + en) - f(em - en) - f(en - em) + f(-em - en)) / (8 * eps ** 2)
    return phibar, A, C


def pred_lattice(L, D, ratio):
    """(1/|X|) sum_{q != 0} cos(q.d) ratio(qhat), qhat_mu = 2 sin(q_mu/2): lattice form of chi/(2n)."""
    qh = 2 * np.sin(np.pi * grid(L, D) / L)
    val = np.array([ratio(v) if np.any(v != 0) else 0.0 for v in qh])
    return np.real(np.fft.ifftn(val.reshape((L,) * D)))


def osc(c):
    """Omega(d) = max - min of c over graph distances d..L/2."""
    return np.array([c[i:].max() - c[i:].min() for i in range(len(c))])


rows_ring, rows_torus = [], []
fig, ax = plt.subplots(1, 2, figsize=(11, 4.2))
log("Check of item 2: chi_0(x, x_s) of (3.6) for one field object (N_f = 1), r = 2, x_s = 0.")
log(f"t = {T}, Delta = {DELTA}; all values are chi/(2n), n = 1/|X|.")

# ---------------- rings ----------------
ring = {"LR": (0.5, PHI_LR), "phibar0": (0.5, SX), "sector": (0.0, SX)}
styles = {"LR": "-", "phibar0": "--", "sector": ":"}
for name, (lam, phi) in ring.items():
    blk = blocks(1, lam)
    phibar, A, C = band_data(1, blk, phi)
    a = A[0, 0]
    log(f"\n[ring] member {name}: lam = {lam}, phibar = {phibar:.6f}, A = {a:.6f} "
        f"(analytic t - lam^2/Delta = {T - lam ** 2 / DELTA:.6f}), C = {C[0, 0]:.6f}")
    for L in (40, 80, 160):
        chi = chi_direct(L, 1, blk, phi)
        err = np.max(np.abs(chi - chi_bloch(L, 1, blk, phi))) * L / 2
        c = chi[: L // 2 + 1] * L / 2
        d = np.arange(L // 2 + 1)
        om = osc(c)
        msg = f"  L = {L:4d}: max |direct - Bloch (8.8)| = {err:.2e}; Omega(L/4) = {om[L // 4]:.3e}"
        if name == "LR":
            p = pred_lattice(L, 1, lambda q: phibar ** 2 / (a * q[0] ** 2))[: L // 2 + 1]
            sel = slice(6, L // 2 - 5)
            r = (c[sel] - c[-1]) / (p[sel] - p[-1])
            msg += (f"; (chi(d)-chi(L/2))/(pred(d)-pred(L/2)) over 6<=d<=L/2-6: "
                    f"max|ratio-1| = {np.max(np.abs(r - 1)):.2e}; slope -(chi(12)-chi(8))/4 = "
                    f"{-(c[12] - c[8]) / 4:.4f} vs phibar^2/(2A)(1-20/L) = "
                    f"{phibar ** 2 / (2 * a) * (1 - 20 / L):.4f}")
        elif name == "phibar0":
            kap = np.arccosh((4 * T ** 2 + 2 * T * DELTA - lam ** 2) / (4 * T ** 2 + lam ** 2))
            fit = -np.polyfit(d[4:15], np.log(np.abs(c[4:15] - c[-1])), 1)[0]
            msg += (f"; chi(L/2)/(2n) = {c[-1]:.3e} (O(1/L) constant); fitted decay rate of "
                    f"|chi(d)-chi(L/2)| (4<=d<=14) = {fit:.5f} vs nearest zero of det(h(k)-e0): {kap:.5f}")
        else:
            kap = np.arccosh(1 + DELTA / (2 * T))
            ex = np.cosh(kap * (L / 2 - d)) / (2 * T * np.sinh(kap) * np.sinh(kap * L / 2))
            msg += f"; max|chi/(2n) - exact (8.13)| = {np.max(np.abs(c - ex)):.2e} (kappa = {kap:.5f})"
        log(msg)
        for di in d:
            rows_ring.append((name, L, di, c[di], om[di]))
        if L in (40, 160):
            ax[0].semilogy(d[:-1], om[:-1], styles[name], label=f"{name}, L={L}")

# ---------------- tori ----------------
torus = {"LR": (0.5, PHI_LR), "phibar0": (0.5, SX)}
for name, (lam, phi) in torus.items():
    blk = blocks(2, lam)
    phibar, A, C = band_data(2, blk, phi)
    a1, a2 = A[0, 0], A[1, 1]
    log(f"\n[torus] member {name}: lam = {lam}, phibar = {phibar:.6f}, A = diag({a1:.6f}, {a2:.6f}) "
        f"(offdiag {A[0, 1]:.1e}), C = [[{C[0, 0]:.6f}, {C[0, 1]:.1e}], [., {C[1, 1]:.1e}]]")
    for L in (20, 32):
        chi = chi_direct(L, 2, blk, phi)
        err = np.max(np.abs(chi - chi_bloch(L, 2, blk, phi))) * L ** 2 / 2
        c = chi * L ** 2 / 2
        if name == "LR":
            p = pred_lattice(L, 2, lambda q: phibar ** 2 / (a1 * q[0] ** 2 + a2 * q[1] ** 2))
        else:
            p = pred_lattice(L, 2, lambda q: (q @ C @ q) / (a1 * q[0] ** 2 + a2 * q[1] ** 2))
        log(f"  L = {L}: max |direct - Bloch (8.8)| = {err:.2e}")
        for axis in (0, 1):
            d = np.arange(L // 2 + 1)
            cd = c[d, 0] if axis == 0 else c[0, d]
            pd = p[d, 0] if axis == 0 else p[0, d]
            for di in d:
                rows_torus.append((name, L, axis + 1, di, cd[di], pd[di]))
            if name == "LR":
                ref = L // 2
                s = ", ".join(f"d={di}: {(cd[di] - cd[ref]) / (pd[di] - pd[ref]):.4f}" for di in (3, 5, 7))
                log(f"    axis {axis + 1}: (chi(d)-chi(L/2))/(pred(d)-pred(L/2)), "
                    f"pred = lattice form of phibar^2/(q^T A q): {s}")
            else:
                cc, pc = c[L // 2, L // 2], p[L // 2, L // 2]  # far corner as reference
                k_inf = (-C[0, 0] / (2 * np.pi * np.sqrt(a1 * a2)) if axis == 0
                         else C[0, 0] * np.sqrt(a2) / (2 * np.pi * a1 ** 1.5))
                s = ", ".join(f"d={di}: {di ** 2 * (cd[di] - cc):+.5f} (pred {di ** 2 * (pd[di] - pc):+.5f})"
                              for di in (4, 6, 8, 10))
                log(f"    axis {axis + 1}: d^2 (chi(d)-chi(corner))/(2n), pred = lattice form of "
                    f"q^T C q/(q^T A q): {s}; L -> infinity value of d^2 chi/(2n) = -C11 d^2 (d/dd1)^2 G_A = {k_inf:+.5f}")
                if L == 32:
                    dd = d[2:]
                    ln = ax[1].plot(dd, dd ** 2 * (cd[2:] - cc), "o", label=f"direct, axis {axis + 1}")
                    ax[1].plot(dd, dd ** 2 * (pd[2:] - pc), "-", color=ln[0].get_color(),
                               label=f"lattice form of (8.11), axis {axis + 1}")
                    ax[1].axhline(k_inf, ls=":", color=ln[0].get_color())

ax[0].set_xlabel("graph distance d from the source (ring)")
ax[0].set_ylabel("Omega(d)/(2n) = max-min of chi/(2n) beyond d")
ax[0].legend(fontsize=7)
ax[1].set_xlabel("d along axis (torus L=32, member phibar0)")
ax[1].set_ylabel("d^2 (chi(d) - chi(corner))/(2n)")
ax[1].legend(fontsize=7)
fig.tight_layout()
fig.savefig(OUT / "decay.png", dpi=120)
np.savetxt(OUT / "chi_ring.csv", np.array(rows_ring, dtype=object), fmt="%s", delimiter=",",
           header="member,L,d,chi_over_2n,Omega_over_2n", comments="")
np.savetxt(OUT / "chi_torus.csv", np.array(rows_torus, dtype=object), fmt="%s", delimiter=",",
           header="member,L,axis,d,chi_over_2n,lattice_pred_over_2n", comments="")
(OUT / "check_log.txt").write_text("\n".join(LOG) + "\n", encoding="utf-8")

Check of item 2: chi_0(x, x_s) of (3.6) for one field object (N_f = 1), r = 2, x_s = 0.
t = 1.0, Delta = 1.5; all values are chi/(2n), n = 1/|X|.

[ring] member LR: lam = 0.5, phibar = 1.000000, A = 0.833333 (analytic t - lam^2/Delta = 0.833333), C = -0.101111
  L =   40: max |direct - Bloch (8.8)| = 1.12e-13; Omega(L/4) = 1.500e+00; (chi(d)-chi(L/2))/(pred(d)-pred(L/2)) over 6<=d<=L/2-6: max|ratio-1| = 4.75e-05; slope -(chi(12)-chi(8))/4 = 0.3000 vs phibar^2/(2A)(1-20/L) = 0.3000
  L =   80: max |direct - Bloch (8.8)| = 2.56e-13; Omega(L/4) = 3.000e+00; (chi(d)-chi(L/2))/(pred(d)-pred(L/2)) over 6<=d<=L/2-6: max|ratio-1| = 1.62e-05; slope -(chi(12)-chi(8))/4 = 0.4500 vs phibar^2/(2A)(1-20/L) = 0.4500
  L =  160: max |direct - Bloch (8.8)| = 5.95e-12; Omega(L/4) = 6.000e+00; (chi(d)-chi(L/2))/(pred(d)-pred(L/2)) over 6<=d<=L/2-6: max|ratio-1| = 6.85e-06; slope -(chi(12)-chi(8))/4 = 0.5250 vs phibar^2/(2A)(1-20/L) = 0.5250

[ring] member phibar0: lam = 0.5, phibar = 0.000000, A = 0.833333 (analytic t - lam^2/Delta = 0.833333), C = 0.111111
  L =   40: max |direct - Bloch (8.8)| = 4.30e-15; Omega(L/4) = 1.190e-05; chi(L/2)/(2n) = -3.333e-03 (O(1/L) constant); fitted decay rate of |chi(d)-chi(L/2)| (4<=d<=14) = 1.03774 vs nearest zero of det(h(k)-e0): 1.03749
  L =   80: max |direct - Bloch (8.8)| = 4.86e-15; Omega(L/4) = 3.714e-10; chi(L/2)/(2n) = -1.667e-03 (O(1/L) constant); fitted decay rate of |chi(d)-chi(L/2)| (4<=d<=14) = 1.03749 vs nearest zero of det(h(k)-e0): 1.03749
  L =  160: max |direct - Bloch (8.8)| = 2.35e-13; Omega(L/4) = 2.316e-15; chi(L/2)/(2n) = -8.333e-04 (O(1/L) constant); fitted decay rate of |chi(d)-chi(L/2)| (4<=d<=14) = 1.03749 vs nearest zero of det(h(k)-e0): 1.03749

[ring] member sector: lam = 0.0, phibar = 0.000000, A = 1.000000 (analytic t - lam^2/Delta = 1.000000), C = 0.000000
  L =   40: max |direct - Bloch (8.8)| = 3.28e-14; Omega(L/4) = 3.229e-06; max|chi/(2n) - exact (8.13)| = 3.28e-14 (kappa = 1.15881)
  L =   80: max |direct - Bloch (8.8)| = 1.84e-14; Omega(L/4) = 2.996e-11; max|chi/(2n) - exact (8.13)| = 1.83e-14 (kappa = 1.15881)
  L =  160: max |direct - Bloch (8.8)| = 1.89e-13; Omega(L/4) = 2.704e-16; max|chi/(2n) - exact (8.13)| = 1.89e-13 (kappa = 1.15881)

[torus] member LR: lam = 0.5, phibar = 1.000000, A = diag(0.833333, 1.000000) (offdiag 0.0e+00), C = [[-0.101111, 0.0e+00], [., 0.0e+00]]
  L = 20: max |direct - Bloch (8.8)| = 2.62e-14
    axis 1: (chi(d)-chi(L/2))/(pred(d)-pred(L/2)), pred = lattice form of phibar^2/(q^T A q): d=3: 1.0145, d=5: 1.0100, d=7: 1.0077
    axis 2: (chi(d)-chi(L/2))/(pred(d)-pred(L/2)), pred = lattice form of phibar^2/(q^T A q): d=3: 0.9783, d=5: 0.9847, d=7: 0.9875
  L = 32: max |direct - Bloch (8.8)| = 4.40e-14
    axis 1: (chi(d)-chi(L/2))/(pred(d)-pred(L/2)), pred = lattice form of phibar^2/(q^T A q): d=3: 1.0106, d=5: 1.0065, d=7: 1.0044
    axis 2: (chi(d)-chi(L/2))/(pred(d)-pred(L/2)), pred = lattice form of phibar^2/(q^T A q): d=3: 0.9842, d=5: 0.9901, d=7: 0.9927

[torus] member phibar0: lam = 0.5, phibar = 0.000000, A = diag(0.833333, 1.000000) (offdiag 0.0e+00), C = [[0.111111, 0.0e+00], [., 0.0e+00]]
  L = 20: max |direct - Bloch (8.8)| = 1.03e-14
    axis 1: d^2 (chi(d)-chi(corner))/(2n), pred = lattice form of q^T C q/(q^T A q): d=4: +0.00103 (pred -0.02040), d=6: -0.01708 (pred -0.01999), d=8: -0.02343 (pred -0.02235), d=10: -0.03209 (pred -0.02994); L -> infinity value of d^2 chi/(2n) = -C11 d^2 (d/dd1)^2 G_A = -0.01937
    axis 2: d^2 (chi(d)-chi(corner))/(2n), pred = lattice form of q^T C q/(q^T A q): d=4: +0.03249 (pred +0.02664), d=6: +0.02626 (pred +0.02756), d=8: +0.03012 (pred +0.03253), d=10: +0.04140 (pred +0.04457); L -> infinity value of d^2 chi/(2n) = -C11 d^2 (d/dd1)^2 G_A = +0.02325
  L = 32: max |direct - Bloch (8.8)| = 1.29e-14
    axis 1: d^2 (chi(d)-chi(corner))/(2n), pred = lattice form of q^T C q/(q^T A q): d=4: +0.00101 (pred -0.02056), d=6: -0.01627 (pred -0.01952), d=8: -0.01971 (pred -0.01931), d=10: -0.02059 (pred -0.01976); L -> infinity value of d^2 chi/(2n) = -C11 d^2 (d/dd1)^2 G_A = -0.01937
    axis 2: d^2 (chi(d)-chi(corner))/(2n), pred = lattice form of q^T C q/(q^T A q): d=4: +0.03191 (pred +0.02590), d=6: +0.02417 (pred +0.02508), d=8: +0.02412 (pred +0.02569), d=10: +0.02605 (pred +0.02738); L -> infinity value of d^2 chi/(2n) = -C11 d^2 (d/dd1)^2 G_A = +0.02325

member,L,d,chi_over_2n,Omega_over_2n
LR,40,0,3.9321437683959335,5.9294437685334564
LR,40,1,3.3926989262758225,5.389998926413345
LR,40,2,2.853841056244801,4.851141056382324
LR,40,3,2.334560899442846,4.331860899580369
LR,40,4,1.8415876831617874,3.83888768329931
LR,40,5,1.3773058588356821,3.3746058589732053
LR,40,6,0.9425603390220681,2.939860339159591
LR,40,7,0.5376505121755382,2.534950512313061
LR,40,8,0.16268246435901068,2.1599824644965335
LR,40,9,-0.18230621362341606,1.8149937865141068
LR,40,10,-0.49730220175105194,1.499997798386471
LR,40,11,-0.7823007801740507,1.2149992199634723
LR,40,12,-1.0373002764488777,0.9599997236886453
LR,40,13,-1.2623000979576602,0.7349999021798628
LR,40,14,-1.457300034710713,0.53999996542681
LR,40,15,-1.6223000122998563,0.37499998783766664
LR,40,16,-1.7573000043593598,0.2399999957781631
LR,40,17,-1.8623000015474416,0.13499999859008138
LR,40,18,-1.9373000005559375,0.05999999958158542
LR,40,19,-1.982300000218353,0.014999999919169893
LR,40,20,-1.997300000137523,0.0
LR,80,0,7.930793768395934,11.929443768396059
LR,80,1,7.38384892627581,11.382498926275936
LR,80,2,6.822491056244784,10.82114105624491
LR,80,3,6.2657108994428405,10.264360899442966
LR,80,4,5.720237683161806,9.718887683161931
LR,80,5,5.188455858835707,9.187105858835832
LR,80,6,4.671210339022121,8.669860339022247
LR,80,7,4.168800512175607,8.167450512175732
LR,80,8,3.681332464359104,7.679982464359229
LR,80,9,3.2088437863766996,7.2074937863768245
LR,80,10,2.751347798249067,6.749997798249192
LR,80,11,2.3088492198260933,6.3074992198262185
LR,80,12,1.8813497235513026,5.879999723551428
LR,80,13,1.468849902042574,5.467499902042699
LR,80,14,1.0713499652896235,5.069999965289749
LR,80,15,0.6888499877007371,4.687499987700862
LR,80,16,0.32134999564194033,4.319999995642066
LR,80,17,-0.031150001544154204,3.967499998455971
LR,80,18,-0.3686500005470766,3.6299999994530485
LR,80,19,-0.6911500001937729,3.3074999998063523
LR,80,20,-0.9986500000685838,2.9999999999315414
LR,80,21,-1.2911500000242249,2.7074999999759006
LR,80,22,-1.5686500000085082,2.429999999991617
LR,80,23,-1.8311500000029566,2.167499999997169
LR,80,24,-2.0786500000009966,1.9199999999991286
LR,80,25,-2.3111500000002967,1.6874999999998286
LR,80,26,-2.5286500000000576,1.4700000000000677
LR,80,27,-2.7311499999999835,1.2675000000001417
LR,80,28,-2.9186499999999778,1.0800000000001475
LR,80,29,-3.0911499999999936,0.9075000000001316
LR,80,30,-3.2486500000000125,0.7500000000001128
LR,80,31,-3.3911500000000387,0.6075000000000865
LR,80,32,-3.5186500000000756,0.4800000000000497
LR,80,33,-3.631150000000107,0.36750000000001837
LR,80,34,-3.728650000000138,0.26999999999998714
LR,80,35,-3.8111500000001546,0.1874999999999707
LR,80,36,-3.8786500000001722,0.11999999999995303
LR,80,37,-3.931150000000157,0.06749999999996836
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sector,80,29,9.301099387210021e-16,1.060891825777066e-15
sector,80,30,2.1507860596681194e-16,3.458604930228759e-16
sector,80,31,-1.3078188705606397e-16,2.9883322379131716e-16
sector,80,32,-1.0842021724855044e-16,2.7647155398380363e-16
sector,80,33,8.40256683676266e-18,2.3527187142935446e-16
sector,80,34,-2.710505431213761e-18,2.3527187142935446e-16
sector,80,35,-5.719166459861036e-17,2.3527187142935446e-16
sector,80,36,-6.722053469410127e-17,2.3527187142935446e-16
sector,80,37,-5.421010862427522e-18,1.734723475976807e-16
sector,80,38,1.6805133673525319e-16,6.396792817664476e-17
sector,80,39,1.566672139241554e-16,5.2583805365546965e-17
sector,80,40,1.0408340855860843e-16,0.0
sector,160,0,0.3481553119112064,0.3481553119112066
sector,160,1,0.1092717958448834,0.10927179584488357
sector,160,2,0.0342959735458846,0.03429597354588477
sector,160,3,0.010764111565711729,0.010764111565711894
sector,160,4,0.0033784169341067086,0.003378416934106874
sector,160,5,0.0010603477036615853,0.0010603477036617505
sector,160,6,0.0003328000287087043,0.00033280002870886966
sector,160,7,0.00010445239681864131,0.00010445239681880665
sector,160,8,3.2783360156212566e-05,3.278336015637791e-05
sector,160,9,1.028936372806581e-05,1.0289363728231151e-05
sector,160,10,3.2294128919250695e-06,3.2294128920904103e-06
sector,160,11,1.0135813936377807e-06,1.0135813938031216e-06
sector,160,12,3.1812198569576133e-07,3.1812198586110216e-07
sector,160,13,9.984555593011042e-08,9.984555609545125e-08
sector,160,14,3.133746001029395e-08,3.133746017563478e-08
sector,160,15,9.83555440705556e-09,9.83555457239639e-09
sector,160,16,3.086980659159147e-09,3.0869808244999783e-09
sector,160,17,9.688777227344e-10,9.688778880752313e-10
sector,160,18,3.0409131376168963e-10,3.0409147910252093e-10
sector,160,19,9.544195945718204e-11,9.544212479801334e-11
sector,160,20,2.995541314998462e-11,2.9955578490815926e-11
sector,160,21,9.401812553315458e-12,9.401977894146762e-12
sector,160,22,2.9509603311286825e-12,2.9511256719599865e-12
sector,160,23,9.26168321722931e-13,9.263336625542351e-13
sector,160,24,2.906865286672611e-13,2.908518694985651e-13
sector,160,25,9.128684136730514e-14,9.145218219860918e-14
sector,160,26,2.8679315866586563e-14,2.88446566978906e-14
sector,160,27,9.062303858720089e-15,9.227644690024128e-15
sector,160,28,2.724871109999194e-15,2.8902119413032334e-15
sector,160,29,8.394435320469018e-16,1.0047843633509412e-15
sector,160,30,3.016792544940916e-16,4.67020085798131e-16
sector,160,31,1.111307226797642e-16,2.813504637599884e-16
sector,160,32,0.0,2.813504637599884e-16
sector,160,33,9.75781955236954e-18,2.813504637599884e-16
sector,160,34,1.1600963245594897e-16,2.813504637599884e-16
sector,160,35,-3.957337929572091e-17,2.7042373874040793e-16
sector,160,36,-1.0489656018797255e-16,2.7042373874040793e-16
sector,160,37,-1.111307226797642e-17,2.7042373874040793e-16
sector,160,38,4.526544070126981e-17,2.7042373874040793e-16
sector,160,39,5.854691731421724e-17,2.7042373874040793e-16
sector,160,40,2.7376104855258987e-17,2.7042373874040793e-16
sector,160,41,2.4936649967166602e-17,2.7042373874040793e-16
sector,160,42,8.660064852727967e-17,2.7042373874040793e-16
sector,160,43,9.893344823930228e-18,2.7042373874040793e-16
sector,160,44,-1.328147661294743e-17,2.7042373874040793e-16
sector,160,45,-2.4259023609363162e-17,2.7042373874040793e-16
sector,160,46,-1.4162390878091902e-17,2.7042373874040793e-16
sector,160,47,1.0842021724855044e-17,2.7042373874040793e-16
sector,160,48,2.1955093992831465e-17,2.7042373874040793e-16
sector,160,49,-6.213833701057547e-17,2.7042373874040793e-16
sector,160,50,-4.0488174878755556e-17,2.7042373874040793e-16
sector,160,51,-2.1311348952918197e-17,2.7042373874040793e-16
sector,160,52,-1.638161719989817e-17,2.7042373874040793e-16
sector,160,53,2.668153783851046e-18,2.7042373874040793e-16
sector,160,54,6.696642480992498e-17,2.7042373874040793e-16
sector,160,55,1.050829074363685e-16,2.7042373874040793e-16
sector,160,56,5.488773498207866e-18,2.573624906937466e-16
sector,160,57,-5.797093491008432e-17,2.573624906937466e-16
sector,160,58,-1.6534083130403943e-16,2.573624906937466e-16
sector,160,59,-1.1201163694490868e-16,2.0403329633461587e-16
sector,160,60,2.89346454782069e-17,1.83772268236293e-16
sector,160,61,6.349358972618235e-17,1.83772268236293e-16
sector,160,62,5.746271514173174e-17,1.83772268236293e-16
sector,160,63,1.9922214919421144e-17,1.83772268236293e-16
sector,160,64,9.486769009248164e-18,1.83772268236293e-16
sector,160,65,5.651403824080692e-17,1.83772268236293e-16
sector,160,66,-2.642742795433417e-17,1.83772268236293e-16
sector,160,67,7.155734338404329e-17,1.83772268236293e-16
sector,160,68,9.202165938970719e-17,1.83772268236293e-16
sector,160,69,5.949559421514206e-17,1.736078728692414e-16
sector,160,70,8.185726402265558e-17,1.736078728692414e-16
sector,160,71,-9.175060884658581e-17,1.4026865606531214e-16
sector,160,72,3.3881317890172014e-17,1.191267137018448e-16
sector,160,73,4.8518047218726323e-17,1.191267137018448e-16
sector,160,74,-4.2012834183813297e-17,1.009663273127126e-16
sector,160,75,-1.0842021724855044e-17,1.009663273127126e-16
sector,160,76,-1.4907779871675686e-18,1.009663273127126e-16
sector,160,77,-7.060866648311848e-17,1.009663273127126e-16
sector,160,78,-6.816921159502609e-17,9.852687242462022e-17
sector,160,79,-2.2090619264392153e-17,5.244828009398628e-17
sector,160,80,3.0357660829594124e-17,0.0

member,L,axis,d,chi_over_2n,lattice_pred_over_2n
LR,20,1,0,0.5688328827060117,0.5757469225778707
LR,20,1,1,0.29946220439568694,0.29379341799811226
LR,20,1,2,0.17600535903625827,0.1717589222847163
LR,20,1,3,0.10500609679378184,0.10231777099315278
LR,20,1,4,0.057963021633844564,0.05618647404081099
LR,20,1,5,0.024549581040927086,0.023284138839156823
LR,20,1,6,0.00027040700537074477,-0.00070388275841623
LR,20,1,7,-0.017134921258405315,-0.01794134480627634
LR,20,1,8,-0.02890467976063648,-0.029615934487158116
LR,20,1,9,-0.03573135536417715,-0.036393840387363714
LR,20,1,10,-0.03797033167382227,-0.038617811781505175
LR,20,2,0,0.5688328827060117,0.5757469225778707
LR,20,2,1,0.3020386495212501,0.3119580779853708
LR,20,2,2,0.1837977939599422,0.18991527306911948
LR,20,2,3,0.11608318263536088,0.11967446123649661
LR,20,2,4,0.07102819965388464,0.07325106448734632
LR,20,2,5,0.03888017457002738,0.040353672951359
LR,20,2,6,0.015448320541873865,0.016491832310272316
LR,20,2,7,-0.0013769082079536433,-0.0005884364112234614
LR,20,2,8,-0.01276175213627436,-0.012123280855082012
LR,20,2,9,-0.019366131987478694,-0.018807075014367226
LR,20,2,10,-0.021532171548798263,-0.02099801320363807
LR,32,1,0,0.6507234511350054,0.6577355754612638
LR,32,1,1,0.3809481734433833,0.3753799452198417
LR,32,1,2,0.2562666828147108,0.2521280739117587
LR,32,1,3,0.1831904147771513,0.18062156317576777
LR,32,1,4,0.13316476004359698,0.13152312211370776
LR,32,1,5,0.0957896387131431,0.09467772386524886
LR,32,1,6,0.06647591439634476,0.06567650839637991
LR,32,1,7,0.042847993616517796,0.04224047872501025
LR,32,1,8,0.0235276582645424,0.023042558275798264
LR,32,1,9,0.007650805255384788,0.007246450325801672
LR,32,1,10,-0.005353695174272785,-0.005703370297844831
LR,32,1,11,-0.01587678905898846,-0.016188803906223966
LR,32,1,12,-0.024191531019844385,-0.024477498080572993
LR,32,1,13,-0.030489513989209852,-0.030757735453382992
LR,32,1,14,-0.03490298933150975,-0.03515972413365913
LR,32,1,15,-0.03751849215097419,-0.037768770842226185
LR,32,1,16,-0.03838503426310662,-0.03863322993001972
LR,32,2,0,0.6507234511350054,0.6577355754612638
LR,32,2,1,0.3835040149650625,0.3935201166796646
LR,32,2,2,0.2639799970139178,0.2701898312683035
LR,32,2,3,0.19410145851393873,0.19777760728133464
LR,32,2,4,0.145963236400425,0.14825986264829044
LR,32,2,5,0.10975736883085956,0.11128919972109609
LR,32,2,6,0.08121922265168495,0.08230030705982389
LR,32,2,7,0.05814377466082835,0.05894227671251387
LR,32,2,8,0.03924264518936533,0.03985471940523591
LR,32,2,9,0.023699067113269783,0.02418330931384087
LR,32,2,10,0.010966595613487088,0.011360818529044553
LR,32,2,11,0.0006667715435866118,0.0009966762596469135
LR,32,2,12,-0.00746755961080449,-0.007183622733528964
LR,32,2,13,-0.013625588103910445,-0.013373849935116065
LR,32,2,14,-0.017938911534560745,-0.017708476385422386
LR,32,2,15,-0.020494150958131396,-0.02027587189711899
LR,32,2,16,-0.02134056731739653,-0.021126240870760413
phibar0,20,1,0,0.222392079025308,0.06265616726789026
phibar0,20,1,1,0.05194736983965655,-0.017768731379630035
phibar0,20,1,2,0.012015042666759517,-0.005843689352582487
phibar0,20,1,3,0.0022509553739743482,-0.0025899769088617353
phibar0,20,1,4,-0.00012128624857638822,-0.0014698807192820964
phibar0,20,1,5,-0.0006214170471566358,-0.0009904766480704262
phibar0,20,1,6,-0.0006601206289822344,-0.0007500601720292163
phibar0,20,1,7,-0.00060592686282907,-0.0006180952814096391
phibar0,20,1,8,-0.0005518136575621882,-0.0005440745247648135
phibar0,20,1,9,-0.0005178765041200058,-0.000505991373585249
phibar0,20,1,10,-0.0005066209163133493,-0.0004942145474588757
phibar0,20,2,0,0.222392079025308,0.06265616726789026
phibar0,20,2,1,0.0528176577282949,0.01856608364065338
phibar0,20,2,2,0.014388016473049499,0.00657357953859853
phibar0,20,2,3,0.004643948189436581,0.002842313499600023
phibar0,20,2,4,0.0018446364761663411,0.0014701295723567288
phibar0,20,2,5,0.000912125585637499,0.0008714040994440011
phibar0,20,2,6,0.000543687923863849,0.0005708744576126005
phibar0,20,2,7,0.000372573358546593,0.00040605525913891465
phibar0,20,2,8,0.00028488383567632533,0.0003134723336908887
phibar0,20,2,9,0.00024149261197710354,0.0002657132329008419
phibar0,20,2,10,0.00022824638376151127,0.00025091599777078054
phibar0,32,1,0,0.22248314517304082,0.06274552828774162
phibar0,32,1,1,0.05203963123859086,-0.01767814829529352
phibar0,32,1,2,0.01211087043985202,-0.005749469176087435
phibar0,32,1,3,0.0023526745361542424,-0.002489778879913143
phibar0,32,1,4,-1.1387978674517367e-05,-0.0013614455709885292
phibar0,32,1,5,-0.0005010224054856073,-0.0008715735402020184
phibar0,32,1,6,-0.000526735268857711,-0.0006183523285598423
phibar0,32,1,7,-0.000456625060248717,-0.0004708997689510622
phibar0,32,1,8,-0.00038284372695828844,-0.0003779781586373959
phibar0,32,1,9,-0.0003240856103080963,-0.0003162533040298166
phibar0,32,1,10,-0.00028067830607842755,-0.00027382004928712026
phibar0,32,1,11,-0.00024941747635801075,-0.00024408150845245136
phibar0,32,1,12,-0.00022724050709881417,-0.00022316127174074822
phibar0,32,1,13,-0.0002118888425096118,-0.0002086937426536027
phibar0,32,1,14,-0.00020184529267134666,-0.0001992152433935193
phibar0,32,1,15,-0.00019616159529317118,-0.00019384255206119846
phibar0,32,1,16,-0.00019432154977595074,-0.00019210150723882047
phibar0,32,2,0,0.22248314517304082,0.06274552828774162
phibar0,32,2,1,0.052907726784753584,0.01865442627313965
phibar0,32,2,2,0.014475079626098812,0.0066588467997439095
phibar0,32,2,3,0.004725945672311243,0.002922380233407243
phibar0,32,2,4,0.0019193997072542016,0.0015427312911913036
phibar0,32,2,5,0.0009772819470400176,0.0009340248982216155
phibar0,32,2,6,0.0005965088445436992,0.0006205714310329925
phibar0,32,2,7,0.0004097383611367165,0.0004391867305881472
phibar0,32,2,8,0.00030211574616729087,0.00032527695735986857
phibar0,32,2,9,0.00023298043202893979,0.0002496467929788803
phibar0,32,2,10,0.0001856807593158509,0.00019757084139507137
phibar0,32,2,11,0.00015230126116346605,0.00016097025101053297
phibar0,32,2,12,0.00012857652589805274,0.00013513412941764885
phibar0,32,2,13,0.00011200454315916112,0.00011720471036665052
phibar0,32,2,14,0.00010105826597337273,0.00010542210350046262
phibar0,32,2,15,9.481828659943964e-05,9.872820321022037e-05
phibar0,32,2,16,9.279033162332785e-05,9.655639752598045e-05