"""Check (ii) of 08-ilang-propagation/02-grip-weight.

Ring of three oscillator cells. The total contract C = H + mu F(q_0) is compressed
to the M lowest levels of 1/2(p^2 + q^2) in every cell, C_M = Pi C Pi.
 - (G2) grip F = F0 + F1 q + F2 q^2: lowest eigenvalue of C_M (with and without the
   body) for increasing M against the exact uncompressed value (2.6).
 - (G) grip F = F0 + theta f, f = sin q + b (1 - cos q): the first and second Taylor
   coefficients in theta of the eigenvalue of C_M connected to the lowest one, for
   increasing M, against the uncompressed values mu <f> and -mu^2 S of (2.9);
   and the lowest eigenvalue at theta = 0.1 against the second-order expression.
Output: output/compression.json.
"""
import json
import os
import threading
import time
from pathlib import Path

import numpy as np
import scipy.sparse as sp
import scipy.sparse.linalg as sla
from scipy import integrate

WALL_LIMIT_S = 1200
threading.Timer(WALL_LIMIT_S, lambda: os._exit(3)).start()
T0 = time.time()
OUT = Path(__file__).parent / "output"
OUT.mkdir(exist_ok=True)

KAPPA, MH = 1.0, 1.0
MS = [4, 6, 8, 10, 12, 16, 20, 24]
G2 = (1.0, 0.5, 0.2)
F0G, B, THETA = 1.0, 0.5, 0.1

# uncompressed 3-ring: K = (m^2 + 2 kappa) 1 - kappa (adjacency of the triangle)
K = (MH**2 + 2 * KAPPA) * np.eye(3) - KAPPA * (np.ones((3, 3)) - np.eye(3))
wk = np.sqrt(np.linalg.eigvalsh(K))
G0 = np.linalg.inv(K)[0, 0]
w0 = 0.5 * np.mean(1 / wk)


def exact_g2(mu, F):
    F0, F1, F2 = F
    Kp = K.copy()
    Kp[0, 0] += 2 * mu * F2
    J = np.array([mu * F1, 0, 0])
    return mu * F0 + 0.5 * np.sum(np.sqrt(np.linalg.eigvalsh(Kp))) - 0.5 * J @ np.linalg.solve(Kp, J)


def cell_ops(M, Mbig=None):
    n = np.arange(M)
    q = np.diag(np.sqrt((n[:-1] + 1) / 2), 1)
    q = q + q.T
    q2 = np.diag(n + 0.5) + np.diag(np.sqrt((n[:-2] + 1) * (n[:-2] + 2)) / 2, 2)
    q2 = np.triu(q2) + np.triu(q2, 1).T
    p2 = np.diag(n + 0.5) - np.diag(np.sqrt((n[:-2] + 1) * (n[:-2] + 2)) / 2, 2)
    p2 = np.triu(p2) + np.triu(p2, 1).T
    return q, q2, p2


def compressed_function(M, fun, extra=60):
    """Pi fun(q) Pi on the M lowest levels, from a much larger truncation."""
    Mb = M + extra
    qb, _, _ = cell_ops(Mb)
    lam, U = np.linalg.eigh(qb)
    return ((U * fun(lam)) @ U.T)[:M, :M]


def field_contract(M):
    q, q2, p2 = cell_ops(M)
    I = sp.identity(M, format="csr")
    def on(op, x):
        mats = [I, I, I]
        mats[x] = sp.csr_matrix(op)
        return sp.kron(sp.kron(mats[0], mats[1]), mats[2], format="csr")
    H = sum(on(0.5 * p2 + 0.5 * (MH**2 + 2 * KAPPA) * q2, x) for x in range(3))
    for (x, y) in [(0, 1), (1, 2), (2, 0)]:
        mats = [I, I, I]
        mats[x] = sp.csr_matrix(q)
        mats[y] = sp.csr_matrix(q)
        H = H - KAPPA * sp.kron(sp.kron(mats[0], mats[1]), mats[2], format="csr")
    return H, on


def lowest(A, v0=None):
    vals, vecs = sla.eigsh(A, k=1, which="SA", tol=1e-13, v0=v0, maxiter=200000)
    return vals[0], vecs[:, 0]


def main():
    res = dict(parameters=dict(kappa_h=KAPPA, m_h=MH, G2_grip=G2, G_grip=dict(F0=F0G, b=B, theta=THETA)),
               field=dict(omega=wk.tolist(), G0=G0, w0=w0))
    # analytic (M -> infinity) Taylor coefficients for f = sin q + b (1 - cos q)
    c = lambda tau: np.sum(np.exp(-wk * tau) / wk) / 6.0
    S_int, _ = integrate.quad(lambda t: np.sinh(c(t)) + B**2 * (np.cosh(c(t)) - 1), 0, np.inf, epsabs=1e-14, limit=400)
    T_int, _ = integrate.quad(lambda t: 1 - np.exp(-c(t)), 0, np.inf, epsabs=1e-14, limit=400)
    Sf = np.exp(-w0) * S_int
    Tf = B * np.exp(-w0) * T_int
    rows_g2, rows_g = [], []
    E_field_exact = 0.5 * np.sum(wk)
    for M in MS:
        H, on = field_contract(M)
        q, q2, _ = cell_ops(M)
        E_f, Om = lowest(H)
        row = dict(M=M, E_field=E_f, E_field_exact=E_field_exact)
        for mu in (+0.75, -0.75):
            F0, F1, F2 = G2
            V = on(F0 * np.eye(M) + F1 * q + F2 * q2, 0) * mu
            E_b, _ = lowest(H + V, v0=Om)
            row[f"E_body_mu{mu:+}"] = E_b
            row[f"E_body_exact_mu{mu:+}"] = exact_g2(mu, G2)
            row[f"cost_mu{mu:+}"] = E_b - E_f
            row[f"cost_exact_mu{mu:+}"] = exact_g2(mu, G2) - E_field_exact
        rows_g2.append(row)
        # (G): Taylor coefficients by Rayleigh-Schroedinger on the finite matrix
        mu = 0.75
        fM = compressed_function(M, lambda x: np.sin(x) + B * (1 - np.cos(x)))
        V = on(fM, 0) * mu
        VO = V @ Om
        E1 = Om @ VO
        rhs = VO - E1 * Om
        A = sla.LinearOperator(H.shape, matvec=lambda x: H @ x - E_f * x + Om * (Om @ x), dtype=float)
        sol, info = sla.cg(A, rhs, rtol=1e-13, atol=0, maxiter=20000)
        E2 = -rhs @ sol
        Eth, _ = lowest(H + on(F0G * np.eye(M), 0) * mu + THETA * V, v0=Om)
        rows_g.append(dict(M=M, E1=E1, E1_exact=mu * B * (1 - np.exp(-w0 / 2)), E2=E2, E2_exact=-mu**2 * Sf,
                           cg_info=int(info), E_theta=Eth,
                           E_theta_2nd_order=E_field_exact + mu * F0G + THETA * mu * B * (1 - np.exp(-w0 / 2))
                           - THETA**2 * mu**2 * Sf))
        print(f"M={M} done at {time.time() - T0:.1f}s", flush=True)
    res["G2"] = rows_g2
    res["G"] = rows_g
    res["G_weight_coefficient_T"] = Tf
    res["runtime_s"] = time.time() - T0
    with open(OUT / "compression.json", "w") as fh:
        json.dump(res, fh, indent=1)
    print(json.dumps(res, indent=1))
    os._exit(0)


if __name__ == "__main__":
    main()

"""Check (i) of 08-ilang-propagation/02-grip-weight.

For (G2) grips F(q) = F0 + F1 q + F2 q^2 on rings and cubic tori, compute the
weighing ratios rho_mark and rho_bond from the exact lowest eigenvalue of the
uncompressed quadratic total contract
    E = sum_i s mu_i F0 + 1/2 Tr sqrt(K') - 1/2 J^T K'^{-1} J ,
obtained by numerical linear algebra (eigvalsh, solve) with finite differences in
s (grip scaling) and g_s (source strength), and compare them with the formulas
of the derivation: (2.15) exact G2 mark ratio, (2.16) exact G2 bond ratio,
(2.14) order-mu^2 ratio, (2.17)-(2.18) smooth-grip limit, (2.19) square-grip deviation.
Outputs: output/g2_mark.csv, output/g2_bond.csv, output/g2_summary.json.
"""
import itertools
import json
import os
import threading
import time
from pathlib import Path

import numpy as np
from scipy import integrate

WALL_LIMIT_S = 1500
threading.Timer(WALL_LIMIT_S, lambda: os._exit(3)).start()
T0 = time.time()

OUT = Path(__file__).parent / "output"
OUT.mkdir(exist_ok=True)

KAPPA, MH = 1.0, 0.3
# Model D levels: M_k = m + 2 pi k/(N lambda0) with m = 0.5, N = 4, lambda0 = 2 pi
M_LEVEL = {0: 0.5, 1: 0.75}
GRIPS = {
    "square": (1.0, 0.6, 0.09),   # F0 (1 + 0.3 q)^2 : 4 F0 F2 = F1^2
    "generic": (1.0, 0.6, 0.15),  # 4 F0 F2 / F1^2 = 1.667
    "linear": (1.0, 0.6, 0.0),    # control
}
GRAPHS = [("ring", 1, 40), ("ring", 1, 80), ("cubic", 3, 8), ("cubic", 3, 12)]
LEVELS = [(0, +1), (0, -1), (1, +1), (1, -1)]
PAIRS = [((0, +1), (0, +1)), ((1, -1), (1, -1)), ((0, +1), (1, +1)), ((0, +1), (0, -1))]


class Graph:
    def __init__(self, D, L):
        self.D, self.L = D, L
        self.coords = np.array(list(itertools.product(range(L), repeat=D)))
        self.N = len(self.coords)
        idx = {tuple(c): i for i, c in enumerate(self.coords)}
        self.idx = idx
        K = np.eye(self.N) * (MH**2 + 2 * D * KAPPA)
        for i, c in enumerate(self.coords):
            for d in range(D):
                for sgn in (+1, -1):
                    c2 = c.copy()
                    c2[d] = (c2[d] + sgn) % L
                    K[i, idx[tuple(c2)]] -= KAPPA
        self.K = K
        ks = 2 * np.pi * self.coords / L  # momenta
        self.ks = ks
        self.w2 = MH**2 + KAPPA * np.sum(4 * np.sin(ks / 2) ** 2, axis=1)
        self.w = np.sqrt(self.w2)
        self.trK = 0.5 * np.sum(self.w)

    def site(self, c):
        return self.idx[tuple(np.mod(c, self.L))]

    def G(self, r):  # Green function K^{-1} at separation r (Fourier sum)
        return np.mean(np.cos(self.ks @ np.asarray(r, float)) / self.w2)

    def w0(self):
        return np.mean(1 / (2 * self.w))

    def J2(self, r):  # int_0^inf c_r(tau)^2 dtau, c_r(tau) = (1/2N) sum_k cos(k.r) e^{-w_k tau}/w_k
        a = np.cos(self.ks @ np.asarray(r, float)) / self.w
        W = self.w[:, None] + self.w[None, :]
        return float(np.sum((a[:, None] * a[None, :]) / W) / (4 * self.N**2))

    def g(self, nu, r=None):
        if r is None:
            return np.mean(1 / (self.w2 + nu**2))
        return np.mean(np.cos(self.ks @ np.asarray(r, float)) / (self.w2 + nu**2))


def energy(gr, bodies, s, gsrc, src):
    """Exact lowest eigenvalue of 1/2 p^2 + 1/2 q K q + sum_i s mu_i F(q_{x_i}) + g q_src."""
    Kp = gr.K.copy()
    J = np.zeros(gr.N)
    c = 0.0
    for (x, mu, F) in bodies:
        F0, F1, F2 = F
        Kp[x, x] += 2 * s * mu * F2
        J[x] += s * mu * F1
        c += s * mu * F0
    J[src] += gsrc
    ev = np.linalg.eigvalsh(Kp)
    if ev.min() <= 0:
        raise ValueError("no lowest eigenvector: K' not positive")
    return c + 0.5 * np.sum(np.sqrt(ev)) - 0.5 * J @ np.linalg.solve(Kp, J)


def classical(gr, bodies, s, gsrc, src):
    """g-odd part only needs the classical term; used for central differences in g."""
    Kp = gr.K.copy()
    J = np.zeros(gr.N)
    for (x, mu, F) in bodies:
        Kp[x, x] += 2 * s * mu * F[2]
        J[x] += s * mu * F[1]
    J[src] += gsrc
    return -0.5 * J @ np.linalg.solve(Kp, J)


def dweight(gr, bodies, s, src):
    # linear coefficient in g of the exact eigenvalue: E is exactly quadratic in g and the
    # trace term is g-independent (same K'), so the central difference with g = 1 is exact
    return (classical(gr, bodies, s, 1.0, src) - classical(gr, bodies, s, -1.0, src)) / 2


def dds(f, h=1e-2):
    return (8 * (f(h) - f(-h)) - (f(2 * h) - f(-2 * h))) / (12 * h)


def zeta_mark(gr, mu, F):
    F0, F1, F2 = F
    if F2 == 0:
        return 0.0
    G0, t = gr.G(np.zeros(gr.D)), 2 * mu * F2

    def chi(x):
        return (x - np.log1p(x)) / x**2 if abs(x) > 1e-6 else 0.5 - x / 3 + x**2 / 4

    def integrand(nu):
        g = gr.g(nu)
        return g**2 * (1 + t * G0) * chi(t * g)

    val, _ = integrate.quad(integrand, 0, np.inf, epsabs=1e-14, epsrel=1e-11, limit=400)
    return 4 * F2**2 / (np.pi * G0) * val


def zbond(gr, r, a1, a2):
    if a1 == 0 or a2 == 0:
        return 0.0

    def integrand(nu):
        g, gr_ = gr.g(nu), gr.g(nu, r)
        return np.log1p(-a1 * a2 * gr_**2 / ((1 + a1 * g) * (1 + a2 * g)))

    val, _ = integrate.quad(integrand, 0, np.inf, epsabs=1e-15, epsrel=1e-11, limit=400)
    return val / (2 * np.pi)


def main():
    mark_rows, bond_rows, graph_info = [], [], []
    for (name, D, L) in GRAPHS:
        gr = Graph(D, L)
        zero = np.zeros(D, int)
        e1 = np.eye(D, dtype=int)[0]
        e2 = np.eye(D, dtype=int)[1] if D > 1 else e1
        src = gr.site(zero)
        anti = np.full(D, L // 2)
        G0, w0 = gr.G(zero), gr.w0()
        J20 = gr.J2(zero)
        graph_info.append(dict(graph=name, L=L, N=gr.N, G0=G0, w0=w0, J2_0=J20,
                               J2_over_G0=J20 / G0, ell=np.sqrt(KAPPA) / MH))
        dists = [1, 5, 10] if (D == 1 and L == 40) else [1, 5, 20] if D == 1 else [1, 2, 3] if L == 8 else [1, 3, 5]
        phi = lambda c: -gr.G(np.asarray(c))  # made field per unit g_s
        for gname, F in GRIPS.items():
            F0, F1, F2 = F
            for (k, sg) in LEVELS:
                mu = sg * M_LEVEL[k]
                xb0 = gr.site(anti)
                cost = lambda s: energy(gr, [(xb0, mu, F)], s, 0, src) - gr.trK
                C1 = dds(cost)
                Cmark = cost(1.0) - C1
                meanF = F0 + F2 * w0
                zeta = zeta_mark(gr, mu, F)
                rho_exact = 4 * F2 * meanF / (F1**2 + zeta)
                rho_mu2 = 4 * F2 * meanF / (F1**2 + 4 * F2**2 * J20 / G0)
                rho_lead = 4 * F0 * F2 / F1**2
                Wref = {}
                for xc in [anti] + [d * e1 for d in dists]:
                    x = gr.site(xc)
                    W = dweight(gr, [(x, mu, F)], 1.0, src)
                    W1 = dds(lambda s: dweight(gr, [(x, mu, F)], s, src))
                    Wref[tuple(xc)] = (W, W1)
                Wa, W1a = Wref[tuple(anti)]
                for d in dists:
                    W, W1 = Wref[tuple(d * e1)]
                    dWmark, dW1 = (W - W1) - (Wa - W1a), W1 - W1a
                    rho_num = (dWmark / Cmark) / (dW1 / C1)
                    mark_rows.append(dict(graph=name, L=L, grip=gname, k=k, sigma=sg, d=d,
                                          C1=C1, C1_formula=mu * meanF, Cmark=Cmark,
                                          rho_num=rho_num, rho_exact=rho_exact,
                                          rho_mu2=rho_mu2, rho_lead=rho_lead,
                                          dev_exact=rho_num - rho_exact))
            # bonds
            Fd = F
            mu_r = M_LEVEL[0]
            x_ref = gr.site(anti)
            C1r = dds(lambda s: energy(gr, [(x_ref, mu_r, Fd)], s, 0, src) - gr.trK)
            W1_cache = {}

            def W1_at(xs):
                if xs not in W1_cache:
                    W1_cache[xs] = dds(lambda s: dweight(gr, [(xs, mu_r, Fd)], s, src))
                return W1_cache[xs]
            W1_ref = W1_at(x_ref)
            mid_d = [4, 8, 12] if D == 1 else dists
            seps = [2, 4]
            for (p1, p2) in PAIRS:
                mu1, mu2 = p1[1] * M_LEVEL[p1[0]], p2[1] * M_LEVEL[p2[0]]
                for r in seps:
                    rvec = r * e2
                    def pair_sites(mc):
                        return gr.site(np.asarray(mc) - rvec // 2), gr.site(np.asarray(mc) + rvec // 2)
                    # bond profile U = E_pair - E_1 - E_2 + E_0 (no source), at s = 1
                    xa, xbb = pair_sites(anti)
                    try:
                        Ep = energy(gr, [(xa, mu1, Fd), (xbb, mu2, Fd)], 1.0, 0, src)
                    except ValueError:
                        continue
                    E1 = energy(gr, [(xa, mu1, Fd)], 1.0, 0, src)
                    E2 = energy(gr, [(xbb, mu2, Fd)], 1.0, 0, src)
                    U = Ep - E1 - E2 + gr.trK

                    def Wbond(mc):
                        x1, x2 = pair_sites(mc)
                        return (dweight(gr, [(x1, mu1, Fd), (x2, mu2, Fd)], 1.0, src)
                                - dweight(gr, [(x1, mu1, Fd)], 1.0, src)
                                - dweight(gr, [(x2, mu2, Fd)], 1.0, src))
                    Wb_ref = Wbond(anti)
                    # single-body C1 weight per unit at the midpoint (level independent): C1r, W1_at
                    # formulas
                    Gr, J2r = gr.G(rvec), gr.J2(rvec)
                    a1, a2 = 2 * mu1 * F2, 2 * mu2 * F2
                    v = np.array([mu1 * F1, mu2 * F1])
                    D1, D2 = 1 + a1 * G0, 1 + a2 * G0
                    Del = G0**2 - Gr**2
                    B = np.array([[G0 + a2 * Del, Gr], [Gr, G0 + a1 * Del]]) / (D1 * D2 - a1 * a2 * Gr**2)
                    Mm = B - np.diag([G0 / D1, G0 / D2])
                    Ucl = -0.5 * v @ Mm @ v
                    Zb = zbond(gr, rvec, a1, a2)
                    wts = v * (Mm @ v) / (v @ Mm @ v)
                    meanF = F0 + F2 * w0
                    for d in mid_d:
                        mc = d * e1
                        x1c, x2c = np.asarray(mc) - rvec // 2, np.asarray(mc) + rvec // 2
                        if gr.site(x1c) == src or gr.site(x2c) == src:
                            continue
                        Wb = Wbond(mc)
                        xm = gr.site(mc)
                        W1m = W1_at(xm)
                        rho_num = ((Wb - Wb_ref) / U) / ((W1m - W1_ref) / C1r)
                        a1c, a2c = anti - rvec // 2, anti + rvec // 2
                        dphi = np.array([phi(x1c) - phi(a1c), phi(x2c) - phi(a2c)])
                        dphibar = phi(mc) - phi(anti)
                        mf = dphi.sum() / (2 * dphibar)
                        mw = (wts @ dphi) / dphibar
                        zb = F1**2 * Zb / Ucl if F2 != 0 else 0.0
                        rho_exact = 4 * F2 * meanF / (F1**2 + zb) * mw
                        rho_mu2 = 4 * F2 * meanF * Gr / (F1**2 * Gr + 4 * F2**2 * J2r) * mf
                        bond_rows.append(dict(graph=name, L=L, grip=gname, pair=f"{p1}{p2}", r=r, d=d,
                                              U=U, U_formula=Ucl + Zb, rho_num=rho_num,
                                              rho_exact=rho_exact, rho_mu2=rho_mu2,
                                              rho_lead_times_mf=4 * F0 * F2 / F1**2 * mf, mf=mf,
                                              J2r_over_Gr=J2r / Gr, dev_exact=rho_num - rho_exact,
                                              dev_mu2=rho_num - rho_mu2))
        print(f"{name} L={L} done at {time.time() - T0:.1f}s", flush=True)

    import csv
    for fname, rows in (("g2_mark.csv", mark_rows), ("g2_bond.csv", bond_rows)):
        with open(OUT / fname, "w", newline="") as fh:
            wr = csv.DictWriter(fh, fieldnames=list(rows[0].keys()))
            wr.writeheader()
            for row in rows:
                wr.writerow({k: (f"{v:.12g}" if isinstance(v, float) else v) for k, v in row.items()})

    def mx(rows, key, cond=lambda r: True):
        vals = [abs(r[key]) for r in rows if cond(r)]
        return max(vals) if vals else None

    summary = dict(
        parameters=dict(kappa_h=KAPPA, m_h=MH, M_levels=M_LEVEL, grips=GRIPS),
        graphs=graph_info,
        max_abs_C1_minus_formula=max(abs(r["C1"] - r["C1_formula"]) for r in mark_rows),
        max_abs_rho_mark_num_minus_exact=mx(mark_rows, "dev_exact"),
        max_abs_bond_U_minus_formula=max(abs(r["U"] - r["U_formula"]) for r in bond_rows),
        max_abs_rho_bond_num_minus_exact=mx(bond_rows, "dev_exact"),
        max_abs_rho_bond_num_minus_mu2=mx(bond_rows, "dev_mu2"),
        rho_mark_square_by_level={f"{r['graph']}{r['L']} k={r['k']} s={r['sigma']}": r["rho_num"]
                                  for r in mark_rows if r["grip"] == "square" and r["d"] == 1},
        rho_mark_generic_by_level={f"{r['graph']}{r['L']} k={r['k']} s={r['sigma']}": r["rho_num"]
                                   for r in mark_rows if r["grip"] == "generic" and r["d"] == 1},
        square_deviation_prediction={f"{g['graph']}{g['L']}": 0.09 * (g["w0"] - g["J2_over_G0"]) for g in graph_info},
        square_bond_deviation={f"{r['graph']}{r['L']} r={r['r']} d={r['d']}":
                               dict(rho_over_mf_minus_1=r["rho_num"] / r["mf"] - 1,
                                    prediction_2_19=0.09 * (next(g["w0"] for g in graph_info if g["graph"] == r["graph"] and g["L"] == r["L"]) - r["J2r_over_Gr"]))
                               for r in bond_rows if r["grip"] == "square" and r["pair"] == "(0, 1)(0, 1)"},
        max_abs_rho_linear=max(abs(r["rho_num"]) for r in mark_rows + bond_rows if r["grip"] == "linear"),
        max_distance_spread_rho_mark=max(
            max(r["rho_num"] for r in mark_rows if (r["graph"], r["L"], r["grip"], r["k"], r["sigma"]) == key)
            - min(r["rho_num"] for r in mark_rows if (r["graph"], r["L"], r["grip"], r["k"], r["sigma"]) == key)
            for key in {(r["graph"], r["L"], r["grip"], r["k"], r["sigma"]) for r in mark_rows}),
        runtime_s=time.time() - T0,
    )
    with open(OUT / "g2_summary.json", "w") as fh:
        json.dump(summary, fh, indent=1)
    print(json.dumps(summary, indent=1))
    os._exit(0)


if __name__ == "__main__":
    main()

{
 "parameters": {
  "kappa_h": 1.0,
  "m_h": 1.0,
  "G2_grip": [
   1.0,
   0.5,
   0.2
  ],
  "G_grip": {
   "F0": 1.0,
   "b": 0.5,
   "theta": 0.1
  }
 },
 "field": {
  "omega": [
   0.9999999999999996,
   2.0,
   2.0
  ],
  "G0": 0.5,
  "w0": 0.3333333333333334
 },
 "G2": [
  {
   "M": 4,
   "E_field": 2.5229411498752925,
   "E_field_exact": 2.5,
   "E_body_mu+0.75": 3.2939749766591997,
   "E_body_exact_mu+0.75": 3.267777025021477,
   "cost_mu+0.75": 0.7710338267839072,
   "cost_exact_mu+0.75": 0.767777025021477,
   "E_body_mu-0.75": 1.6753286736452642,
   "E_body_exact_mu-0.75": 1.656726183178957,
   "cost_mu-0.75": -0.8476124762300283,
   "cost_exact_mu-0.75": -0.843273816821043
  },
  {
   "M": 6,
   "E_field": 2.5017491024326044,
   "E_field_exact": 2.5,
   "E_body_mu+0.75": 3.2699458084591178,
   "E_body_exact_mu+0.75": 3.267777025021477,
   "cost_mu+0.75": 0.7681967060265134,
   "cost_exact_mu+0.75": 0.767777025021477,
   "E_body_mu-0.75": 1.658083843740656,
   "E_body_exact_mu-0.75": 1.656726183178957,
   "cost_mu-0.75": -0.8436652586919484,
   "cost_exact_mu-0.75": -0.843273816821043
  },
  {
   "M": 8,
   "E_field": 2.5001244991775686,
   "E_field_exact": 2.5,
   "E_body_mu+0.75": 3.2679475656745893,
   "E_body_exact_mu+0.75": 3.267777025021477,
   "cost_mu+0.75": 0.7678230664970207,
   "cost_exact_mu+0.75": 0.767777025021477,
   "E_body_mu-0.75": 1.656819742470056,
   "E_body_exact_mu-0.75": 1.656726183178957,
   "cost_mu-0.75": -0.8433047567075127,
   "cost_exact_mu-0.75": -0.843273816821043
  },
  {
   "M": 10,
   "E_field": 2.5000085877039133,
   "E_field_exact": 2.5,
   "E_body_mu+0.75": 3.267790182692385,
   "E_body_exact_mu+0.75": 3.267777025021477,
   "cost_mu+0.75": 0.7677815949884716,
   "cost_exact_mu+0.75": 0.767777025021477,
   "E_body_mu-0.75": 1.656732463974447,
   "E_body_exact_mu-0.75": 1.656726183178957,
   "cost_mu-0.75": -0.8432761237294664,
   "cost_exact_mu-0.75": -0.843273816821043
  },
  {
   "M": 12,
   "E_field": 2.5000005825247573,
   "E_field_exact": 2.5,
   "E_body_mu+0.75": 3.2677780330818713,
   "E_body_exact_mu+0.75": 3.267777025021477,
   "cost_mu+0.75": 0.767777450557114,
   "cost_exact_mu+0.75": 0.767777025021477,
   "E_body_mu-0.75": 1.6567265990326816,
   "E_body_exact_mu-0.75": 1.656726183178957,
   "cost_mu-0.75": -0.8432739834920757,
   "cost_exact_mu-0.75": -0.843273816821043
  },
  {
   "M": 16,
   "E_field": 2.500000002602074,
   "E_field_exact": 2.5,
   "E_body_mu+0.75": 3.267777030900761,
   "E_body_exact_mu+0.75": 3.267777025021477,
   "cost_mu+0.75": 0.7677770282986871,
   "cost_exact_mu+0.75": 0.767777025021477,
   "E_body_mu-0.75": 1.6567261849604649,
   "E_body_exact_mu-0.75": 1.656726183178957,
   "cost_mu-0.75": -0.8432738176416092,
   "cost_exact_mu-0.75": -0.843273816821043
  },
  {
   "M": 20,
   "E_field": 2.5000000000113354,
   "E_field_exact": 2.5,
   "E_body_mu+0.75": 3.2677770250557403,
   "E_body_exact_mu+0.75": 3.267777025021477,
   "cost_mu+0.75": 0.7677770250444049,
   "cost_exact_mu+0.75": 0.767777025021477,
   "E_body_mu-0.75": 1.6567261831864524,
   "E_body_exact_mu-0.75": 1.656726183178957,
   "cost_mu-0.75": -0.843273816824883,
   "cost_exact_mu-0.75": -0.843273816821043
  },
  {
   "M": 24,
   "E_field": 2.50000000000006,
   "E_field_exact": 2.5,
   "E_body_mu+0.75": 3.267777025021679,
   "E_body_exact_mu+0.75": 3.267777025021477,
   "cost_mu+0.75": 0.7677770250216192,
   "cost_exact_mu+0.75": 0.767777025021477,
   "E_body_mu-0.75": 1.6567261831789881,
   "E_body_exact_mu-0.75": 1.656726183178957,
   "cost_mu-0.75": -0.8432738168210718,
   "cost_exact_mu-0.75": -0.843273816821043
  }
 ],
 "G": [
  {
   "M": 4,
   "E1": 0.062141933889909316,
   "E1_exact": 0.05756935316601974,
   "E2": -0.10395847580868413,
   "E2_exact": -0.10333095416625977,
   "cg_info": 0,
   "E_theta": 3.27812873150405,
   "E_theta_2nd_order": 3.2547236257749392
  },
  {
   "M": 6,
   "E1": 0.058099077216148036,
   "E1_exact": 0.05756935316601974,
   "E2": -0.10317834426416711,
   "E2_exact": -0.10333095416625977,
   "cg_info": 0,
   "E_theta": 3.2565410700540247,
   "E_theta_2nd_order": 3.2547236257749392
  },
  {
   "M": 8,
   "E1": 0.057622017405937524,
   "E1_exact": 0.05756935316601974,
   "E2": -0.1032893678001503,
   "E2_exact": -0.10333095416625977,
   "cg_info": 0,
   "E_theta": 3.2548678003233373,
   "E_theta_2nd_order": 3.2547236257749392
  },
  {
   "M": 10,
   "E1": 0.05757417615874387,
   "E1_exact": 0.05756935316601974,
   "E2": -0.10332454764359597,
   "E2_exact": -0.10333095416625977,
   "cg_info": 0,
   "E_theta": 3.2547467662826244,
   "E_theta_2nd_order": 3.2547236257749392
  },
  {
   "M": 12,
   "E1": 0.05756977381909598,
   "E1_exact": 0.05756935316601974,
   "E2": -0.10333015388423028,
   "E2_exact": -0.10333095416625977,
   "cg_info": 0,
   "E_theta": 3.2547382650050256,
   "E_theta_2nd_order": 3.2547236257749392
  },
  {
   "M": 16,
   "E1": 0.05756935608869652,
   "E1_exact": 0.05756935316601974,
   "E2": -0.1033309448084939,
   "E2_exact": -0.10333095416625977,
   "cg_info": 0,
   "E_theta": 3.254737635183718,
   "E_theta_2nd_order": 3.2547236257749392
  },
  {
   "M": 20,
   "E1": 0.057569353184781374,
   "E1_exact": 0.05756935316601974,
   "E2": -0.1033309540761183,
   "E2_exact": -0.10333095416625977,
   "cg_info": 0,
   "E_theta": 3.2547376322019193,
   "E_theta_2nd_order": 3.2547236257749392
  },
  {
   "M": 24,
   "E1": 0.057569353166133354,
   "E1_exact": 0.05756935316601974,
   "E2": -0.10333095416548013,
   "E2_exact": -0.10333095416625977,
   "cg_info": 0,
   "E_theta": 3.2547376321877377,
   "E_theta_2nd_order": 3.2547236257749392
  }
 ],
 "G_weight_coefficient_T": 0.08299858683910247,
 "runtime_s": 1.325458288192749
}

graph,L,grip,pair,r,d,U,U_formula,rho_num,rho_exact,rho_mu2,rho_lead_times_mf,mf,J2r_over_Gr,dev_exact,dev_mu2
ring,40,square,"(0, 1)(0, 1)",2,4,-0.0579822588057,-0.0579822588057,1.0899673822,1.0899673822,1.09039105584,1.045,1.045,0.0363461563664,1.10800257858e-13,-0.000423673643432
ring,40,square,"(0, 1)(0, 1)",2,8,-0.0579822588057,-0.0579822588057,1.0899673822,1.0899673822,1.09039105584,1.045,1.045,0.0363461563664,1.91402449445e-13,-0.000423673643351
ring,40,square,"(0, 1)(0, 1)",2,12,-0.0579822588057,-0.0579822588057,1.0899673822,1.0899673822,1.09039105584,1.045,1.045,0.0363461563664,1.0684786389e-12,-0.000423673642474
ring,40,square,"(0, 1)(0, 1)",4,4,-0.032805725039,-0.032805725039,1.23761462991,1.23761462991,1.23774081874,1.18405,1.18405,0.0159925711997,2.76889622342e-13,-0.000126188834053
ring,40,square,"(0, 1)(0, 1)",4,8,-0.032805725039,-0.032805725039,1.23761462991,1.23761462991,1.23774081874,1.18405,1.18405,0.0159925711997,1.46549439251e-13,-0.000126188834183
ring,40,square,"(0, 1)(0, 1)",4,12,-0.032805725039,-0.032805725039,1.23761462991,1.23761462991,1.23774081874,1.18405,1.18405,0.0159925711997,7.93143328792e-13,-0.000126188833537
ring,40,square,"(1, -1)(1, -1)",2,4,-0.361375437432,-0.361375437432,1.09116431841,1.09116431841,1.09039105584,1.045,1.045,0.0363461563664,5.95079541199e-14,0.000773262571648
ring,40,square,"(1, -1)(1, -1)",2,8,-0.361375437432,-0.361375437432,1.09116431841,1.09116431841,1.09039105584,1.045,1.045,0.0363461563664,4.04121180964e-14,0.000773262571629
ring,40,square,"(1, -1)(1, -1)",2,12,-0.361375437432,-0.361375437432,1.09116431841,1.09116431841,1.09039105584,1.045,1.045,0.0363461563664,7.85149723015e-13,0.000773262572374
ring,40,square,"(1, -1)(1, -1)",4,4,-0.183123925773,-0.183123925773,1.23798424027,1.23798424027,1.23774081874,1.18405,1.18405,0.0159925711997,8.61533067109e-14,0.000243421527062
ring,40,square,"(1, -1)(1, -1)",4,8,-0.183123925773,-0.183123925773,1.23798424027,1.23798424027,1.23774081874,1.18405,1.18405,0.0159925711997,6.75015598972e-14,0.000243421527043
ring,40,square,"(1, -1)(1, -1)",4,12,-0.183123925773,-0.183123925773,1.23798424027,1.23798424027,1.23774081874,1.18405,1.18405,0.0159925711997,9.34807786734e-13,0.000243421527911
ring,40,square,"(0, 1)(1, 1)",2,4,-0.0805929973798,-0.0805929973798,1.09498491838,1.09498491838,1.09039105584,1.045,1.045,0.0363461563664,4.79616346638e-14,0.0045938625384
ring,40,square,"(0, 1)(1, 1)",2,8,-0.0805929973798,-0.0805929973798,1.09518633249,1.09518633249,1.09039105584,1.045,1.045,0.0363461563664,7.83817455385e-14,0.00479527665039
ring,40,square,"(0, 1)(1, 1)",2,12,-0.0805929973798,-0.0805929973798,1.09591301398,1.09591301398,1.09039105584,1.045,1.045,0.0363461563664,7.38298311376e-13,0.00552195814421
ring,40,square,"(0, 1)(1, 1)",4,4,-0.045868298456,-0.045868298456,1.24323932992,1.24323932992,1.23774081874,1.18405,1.18405,0.0159925711997,6.99440505514e-14,0.00549851117308
ring,40,square,"(0, 1)(1, 1)",4,8,-0.045868298456,-0.045868298456,1.24346200935,1.24346200935,1.23774081874,1.18405,1.18405,0.0159925711997,4.37427871702e-14,0.0057211906104
ring,40,square,"(0, 1)(1, 1)",4,12,-0.045868298456,-0.045868298456,1.24426541396,1.24426541396,1.23774081874,1.18405,1.18405,0.0159925711997,1.00386365887e-12,0.00652459522113
ring,40,square,"(0, 1)(0, -1)",2,4,0.0841629051102,0.0841629051102,1.06391117114,1.06391117114,1.09039105584,1.045,1.045,0.0363461563664,1.71196390397e-13,-0.0264798847043
ring,40,square,"(0, 1)(0, -1)",2,8,0.0841629051102,0.0841629051102,1.06286605252,1.06286605252,1.09039105584,1.045,1.045,0.0363461563664,1.43884903991e-13,-0.0275250033223
ring,40,square,"(0, 1)(0, -1)",2,12,0.0841629051102,0.0841629051102,1.05909537155,1.05909537155,1.09039105584,1.045,1.045,0.0363461563664,9.98534588348e-13,-0.0312956842853
ring,40,square,"(0, 1)(0, -1)",4,4,0.0461752638956,0.0461752638956,1.20703721431,1.20703721431,1.23774081874,1.18405,1.18405,0.0159925711997,-8.81517081552e-14,-0.0307036044333
ring,40,square,"(0, 1)(0, -1)",4,8,0.0461752638956,0.0461752638956,1.20582689497,1.20582689497,1.23774081874,1.18405,1.18405,0.0159925711997,-3.33066907388e-14,-0.0319139237721
ring,40,square,"(0, 1)(0, -1)",4,12,0.0461752638956,0.0461752638956,1.20146018672,1.20146018672,1.23774081874,1.18405,1.18405,0.0159925711997,9.31699162265e-13,-0.0362806320211
ring,40,generic,"(0, 1)(0, 1)",2,4,-0.047806912573,-0.047806912573,1.85757238547,1.85757238535,1.86075300889,1.74166666667,1.045,0.0363461563664,1.22694743254e-10,-0.0031806234173
ring,40,generic,"(0, 1)(0, 1)",2,8,-0.047806912573,-0.047806912573,1.85757238547,1.85757238535,1.86075300889,1.74166666667,1.045,0.0363461563664,1.23531851415e-10,-0.00318062341647
ring,40,generic,"(0, 1)(0, 1)",2,12,-0.047806912573,-0.047806912573,1.85757238547,1.85757238535,1.86075300889,1.74166666667,1.045,0.0363461563664,1.21875620707e-10,-0.00318062341812
ring,40,generic,"(0, 1)(0, 1)",4,4,-0.0273404997657,-0.0273404997657,2.11809165253,2.11809165239,2.11903429268,1.97341666667,1.18405,0.0159925711997,1.40370826074e-10,-0.000942640149121
ring,40,generic,"(0, 1)(0, 1)",4,8,-0.0273404997657,-0.0273404997657,2.11809165253,2.11809165239,2.11903429268,1.97341666667,1.18405,0.0159925711997,1.41409550736e-10,-0.000942640148082
ring,40,generic,"(0, 1)(0, 1)",4,12,-0.0273404997657,-0.0273404997657,2.11809165253,2.11809165239,2.11903429268,1.97341666667,1.18405,0.0159925711997,1.39632749807e-10,-0.00094264014986
ring,40,generic,"(1, -1)(1, -1)",2,4,-0.690087068278,-0.690087068278,1.86749070389,1.86749070377,1.86075300889,1.74166666667,1.045,0.0363461563664,1.23355103909e-10,0.00673769500495
ring,40,generic,"(1, -1)(1, -1)",2,8,-0.690087068278,-0.690087068278,1.86749070389,1.86749070377,1.86075300889,1.74166666667,1.045,0.0363461563664,1.24163124227e-10,0.00673769500576
ring,40,generic,"(1, -1)(1, -1)",2,12,-0.690087068278,-0.690087068278,1.86749070389,1.86749070377,1.86075300889,1.74166666667,1.045,0.0363461563664,1.22413634784e-10,0.00673769500401
ring,40,generic,"(1, -1)(1, -1)",4,4,-0.311424540081,-0.311424540081,2.12122047754,2.1212204774,2.11903429268,1.97341666667,1.18405,0.0159925711997,1.40083944444e-10,0.00218618485929
ring,40,generic,"(1, -1)(1, -1)",4,8,-0.311424540081,-0.311424540081,2.12122047754,2.1212204774,2.11903429268,1.97341666667,1.18405,0.0159925711997,1.41005873644e-10,0.00218618486021
ring,40,generic,"(1, -1)(1, -1)",4,12,-0.311424540081,-0.311424540081,2.12122047754,2.1212204774,2.11903429268,1.97341666667,1.18405,0.0159925711997,1.390074722e-10,0.00218618485821
ring,40,generic,"(0, 1)(1, 1)",2,4,-0.0640918592678,-0.0640918592679,1.86941861627,1.86941861614,1.86075300889,1.74166666667,1.045,0.0363461563664,1.2373702063e-10,0.00866560737842
ring,40,generic,"(0, 1)(1, 1)",2,8,-0.0640918592678,-0.0640918592679,1.86991158747,1.86991158734,1.86075300889,1.74166666667,1.045,0.0363461563664,1.2458278853e-10,0.00915857857907
ring,40,generic,"(0, 1)(1, 1)",2,12,-0.0640918592678,-0.0640918592679,1.87169017708,1.87169017696,1.86075300889,1.74166666667,1.045,0.0363461563664,1.22805321467e-10,0.0109371681908
ring,40,generic,"(0, 1)(1, 1)",4,4,-0.0369303233381,-0.0369303233381,2.13147887334,2.1314788732,2.11903429268,1.97341666667,1.18405,0.0159925711997,1.41521905306e-10,0.0124445806552
ring,40,generic,"(0, 1)(1, 1)",4,8,-0.0369303233381,-0.0369303233381,2.13201373902,2.13201373888,2.11903429268,1.97341666667,1.18405,0.0159925711997,1.42674316805e-10,0.012979446338
ring,40,generic,"(0, 1)(1, 1)",4,12,-0.0369303233381,-0.0369303233381,2.13394347963,2.13394347949,2.11903429268,1.97341666667,1.18405,0.0159925711997,1.40496947409e-10,0.0149091869505
ring,40,generic,"(0, 1)(0, -1)",2,4,0.0890522100612,0.0890522100612,1.78454957825,1.78454957813,1.86075300889,1.74166666667,1.045,0.0363461563664,1.17800658117e-10,-0.0762034306375
ring,40,generic,"(0, 1)(0, -1)",2,8,0.0890522100612,0.0890522100612,1.78152238331,1.78152238319,1.86075300889,1.74166666667,1.045,0.0363461563664,1.18376641822e-10,-0.0792306255746
ring,40,generic,"(0, 1)(0, -1)",2,12,0.0890522100612,0.0890522100612,1.77060057393,1.77060057381,1.86075300889,1.74166666667,1.045,0.0363461563664,1.15920384403e-10,-0.0901524349579
ring,40,generic,"(0, 1)(0, -1)",4,4,0.0486455877985,0.0486455877985,2.02910201454,2.02910201441,2.11903429268,1.97341666667,1.18405,0.0159925711997,1.33757449561e-10,-0.0899322781423
ring,40,generic,"(0, 1)(0, -1)",4,8,0.0486455877985,0.0486455877985,2.02554977193,2.0255497718,2.11903429268,1.97341666667,1.18405,0.0159925711997,1.34378286276e-10,-0.0934845207491
ring,40,generic,"(0, 1)(0, -1)",4,12,0.0486455877985,0.0486455877985,2.01273364432,2.01273364419,2.11903429268,1.97341666667,1.18405,0.0159925711997,1.3167289481e-10,-0.106300648365
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ring,80,linear,"(1, -1)(1, -1)",4,8,-0.100977250092,-0.100977250092,2.42966539786e-14,0,0,0,1.18405,0.0159925411218,2.42966539786e-14,2.42966539786e-14
ring,80,linear,"(1, -1)(1, -1)",4,12,-0.100977250092,-0.100977250092,1.80754088343e-13,0,0,0,1.18405,0.0159925411218,1.80754088343e-13,1.80754088343e-13
ring,80,linear,"(0, 1)(1, 1)",2,4,-0.12238876996,-0.12238876996,1.5160284309e-14,0,0,0,1.045,0.0363463403641,1.5160284309e-14,1.5160284309e-14
ring,80,linear,"(0, 1)(1, 1)",2,8,-0.12238876996,-0.12238876996,0,0,0,0,1.045,0.0363463403641,0,0
ring,80,linear,"(0, 1)(1, 1)",2,12,-0.12238876996,-0.12238876996,4.97105815339e-14,0,0,0,1.045,0.0363463403641,4.97105815339e-14,4.97105815339e-14
ring,80,linear,"(0, 1)(1, 1)",4,4,-0.0673181667281,-0.0673181667281,-2.75623748981e-15,0,0,0,1.18405,0.0159925411218,-2.75623748981e-15,-2.75623748981e-15
ring,80,linear,"(0, 1)(1, 1)",4,8,-0.0673181667281,-0.0673181667281,-2.73337357259e-14,0,0,0,1.18405,0.0159925411218,-2.73337357259e-14,-2.73337357259e-14
ring,80,linear,"(0, 1)(1, 1)",4,12,-0.0673181667281,-0.0673181667281,-2.41005451124e-13,0,0,0,1.18405,0.0159925411218,-2.41005451124e-13,-2.41005451124e-13
ring,80,linear,"(0, 1)(0, -1)",2,4,0.0815925133066,0.0815925133066,-2.27404264634e-15,0,0,0,1.045,0.0363463403641,-2.27404264634e-15,-2.27404264634e-15
ring,80,linear,"(0, 1)(0, -1)",2,8,0.0815925133066,0.0815925133066,-0,0,0,0,1.045,0.0363463403641,-0,-0
ring,80,linear,"(0, 1)(0, -1)",2,12,0.0815925133066,0.0815925133066,1.24276453835e-13,0,0,0,1.045,0.0363463403641,1.24276453835e-13,1.24276453835e-13
ring,80,linear,"(0, 1)(0, -1)",4,4,0.0448787778188,0.0448787778188,2.06717811736e-14,0,0,0,1.18405,0.0159925411218,2.06717811736e-14,2.06717811736e-14
ring,80,linear,"(0, 1)(0, -1)",4,8,0.0448787778188,0.0448787778188,-2.73337357259e-14,0,0,0,1.18405,0.0159925411218,-2.73337357259e-14,-2.73337357259e-14
ring,80,linear,"(0, 1)(0, -1)",4,12,0.0448787778188,0.0448787778188,-0,0,0,0,1.18405,0.0159925411218,-0,-0
cubic,8,square,"(0, 1)(0, 1)",2,1,-0.00306716266437,-0.00306716266436,0.522621617717,0.522621617715,0.52262217366,0.512356520282,0.512356520282,0.00190430718275,2.57938115311e-12,-5.55943227898e-07
cubic,8,square,"(0, 1)(0, 1)",2,2,-0.00306716266437,-0.00306716266436,0.70485820957,0.704858209569,0.704858959372,0.691013703425,0.691013703425,0.00190430718275,1.19093623852e-12,-7.49801253197e-07
cubic,8,square,"(0, 1)(0, 1)",2,3,-0.00306716266437,-0.00306716266436,0.800800476142,0.800800476141,0.800801328003,0.785071515391,0.785071515391,0.00190430718275,1.63435931455e-12,-8.51860692208e-07
cubic,8,square,"(0, 1)(0, 1)",4,1,-0.00181884682081,-0.0018188468208,0.232248194324,0.232248194324,0.232248245294,0.22766241425,0.22766241425,0.000739061403917,-3.87107013111e-13,-5.0970208304e-08
cubic,8,square,"(0, 1)(0, 1)",4,2,-0.00181884682081,-0.0018188468208,0.372776419293,0.372776419293,0.372776501103,0.365415885529,0.365415885529,0.000739061403917,-1.51600954013e-13,-8.18106797307e-08
cubic,8,square,"(0, 1)(0, 1)",4,3,-0.00181884682081,-0.0018188468208,0.446216183988,0.44621618399,0.446216281918,0.43740556959,0.43740556959,0.000739061403917,-1.94089189165e-12,-9.79297598569e-08
cubic,8,square,"(1, -1)(1, -1)",2,1,-0.00774985198166,-0.00774985198174,0.522623042977,0.522623042968,0.52262217366,0.512356520282,0.512356520282,0.00190430718275,9.05842068022e-12,8.6931651444e-07
cubic,8,square,"(1, -1)(1, -1)",2,2,-0.00774985198166,-0.00774985198174,0.704860131816,0.704860131804,0.704858959372,0.691013703425,0.691013703425,0.00190430718275,1.18358656209e-11,1.17244419673e-06
cubic,8,square,"(1, -1)(1, -1)",2,3,-0.00774985198166,-0.00774985198174,0.800802660036,0.800802660022,0.800801328003,0.785071515391,0.785071515391,0.00190430718275,1.4233170198e-11,1.33203304209e-06
cubic,8,square,"(1, -1)(1, -1)",4,1,-0.00458051599435,-0.0045805159945,0.232248325506,0.232248325497,0.232248245294,0.22766241425,0.22766241425,0.000739061403917,9.4722008015e-12,8.02120553034e-08
cubic,8,square,"(1, -1)(1, -1)",4,2,-0.00458051599435,-0.0045805159945,0.372776629849,0.372776629835,0.372776501103,0.365415885529,0.365415885529,0.000739061403917,1.48422940605e-11,1.28746227401e-07
cubic,8,square,"(1, -1)(1, -1)",4,3,-0.00458051599435,-0.0045805159945,0.446216436026,0.446216436011,0.446216281918,0.43740556959,0.43740556959,0.000739061403917,1.56631929649e-11,1.54108101558e-07
cubic,8,square,"(0, 1)(1, 1)",2,1,-0.00454947978562,-0.0045494797856,0.522621482181,0.522621482181,0.52262217366,0.512356520282,0.512356520282,0.00190430718275,9.50350909079e-14,-6.9147885573e-07
cubic,8,square,"(0, 1)(1, 1)",2,2,-0.00454947978562,-0.0045494797856,0.704858026775,0.704858026776,0.704858959372,0.691013703425,0.691013703425,0.00190430718275,-1.24755761277e-12,-9.3259683609e-07
cubic,8,square,"(0, 1)(1, 1)",2,3,-0.00454947978562,-0.0045494797856,0.800800268465,0.800800268467,0.800801328003,0.785071515391,0.785071515391,0.00190430718275,-1.32582833601e-12,-1.05953781315e-06
cubic,8,square,"(0, 1)(1, 1)",4,1,-0.00269870324166,-0.00269870324174,0.232248181947,0.232248181939,0.232248245294,0.22766241425,0.22766241425,0.000739061403917,7.8097806e-12,-6.33468738298e-08
cubic,8,square,"(0, 1)(1, 1)",4,2,-0.00269870324166,-0.00269870324174,0.372776399427,0.372776399414,0.372776501103,0.365415885529,0.365415885529,0.000739061403917,1.31516464386e-11,-1.01676044084e-07
cubic,8,square,"(0, 1)(1, 1)",4,3,-0.00269870324166,-0.00269870324174,0.44621616021,0.446216160196,0.446216281918,0.43740556959,0.43740556959,0.000739061403917,1.43293155119e-11,-1.21708404577e-07
cubic,8,square,"(0, 1)(0, -1)",2,1,0.00321189184319,0.00321189184323,0.52262218461,0.5226221846,0.52262217366,0.512356520282,0.512356520282,0.00190430718275,9.87210313497e-12,1.09498148326e-08
cubic,8,square,"(0, 1)(0, -1)",2,2,0.00321189184319,0.00321189184323,0.70485897414,0.704858974126,0.704858959372,0.691013703425,0.691013703425,0.00190430718275,1.33409949754e-11,1.47680090379e-08
cubic,8,square,"(0, 1)(0, -1)",2,3,0.00321189184319,0.00321189184323,0.800801344783,0.800801344766,0.800801328003,0.785071515391,0.785071515391,0.00190430718275,1.6499024369e-11,1.67795090045e-08
cubic,8,square,"(0, 1)(0, -1)",4,1,0.00190220071545,0.00190220071548,0.232248246356,0.23224824635,0.232248245294,0.22766241425,0.22766241425,0.000739061403917,5.92020876766e-12,1.06151007429e-09
cubic,8,square,"(0, 1)(0, -1)",4,2,0.00190220071545,0.00190220071548,0.372776502806,0.372776502798,0.372776501103,0.365415885529,0.365415885529,0.000739061403917,8.88200624161e-12,1.70318587012e-09
cubic,8,square,"(0, 1)(0, -1)",4,3,0.00190220071545,0.00190220071548,0.446216283957,0.446216283946,0.446216281918,0.43740556959,0.43740556959,0.000739061403917,1.08882902694e-11,2.03898276041e-09
cubic,8,generic,"(0, 1)(0, 1)",2,1,-0.00297795933363,-0.00297795933378,0.882267719594,0.88226771955,0.882272016688,0.853927533803,0.512356520282,0.00190430718275,4.36812808147e-11,-4.29709380034e-06
cubic,8,generic,"(0, 1)(0, 1)",2,2,-0.00297795933363,-0.00297795933378,1.18991182935,1.18991182929,1.18991762483,1.15168950571,0.691013703425,0.00190430718275,5.99229554865e-11,-5.79547652046e-06
cubic,8,generic,"(0, 1)(0, 1)",2,3,-0.00297795933363,-0.00297795933378,1.35187750753,1.35187750746,1.35188409186,1.30845252565,0.785071515391,0.00190430718275,6.86477541478e-11,-6.58433127887e-06
cubic,8,generic,"(0, 1)(0, 1)",4,1,-0.00176706115224,-0.00176706115228,0.392145839568,0.392145839559,0.392146233043,0.379437357083,0.22766241425,0.000739061403917,8.98342511491e-12,-3.93475025229e-07
cubic,8,generic,"(0, 1)(0, 1)",4,2,-0.00176706115224,-0.00176706115228,0.629424578904,0.629424578893,0.629425210466,0.609026475882,0.365415885529,0.000739061403917,1.06777919839e-11,-6.31561766551e-07
cubic,8,generic,"(0, 1)(0, 1)",4,3,-0.00176706115224,-0.00176706115228,0.753425965735,0.753425965721,0.753426721718,0.729009282649,0.43740556959,0.000739061403917,1.41450184898e-11,-7.5598283189e-07
cubic,8,generic,"(1, -1)(1, -1)",2,1,-0.00813626588297,-0.00813626588293,0.882278926331,0.882278926335,0.882272016688,0.853927533803,0.512356520282,0.00190430718275,-4.53004300738e-12,6.90964321803e-06
cubic,8,generic,"(1, -1)(1, -1)",2,2,-0.00813626588297,-0.00813626588293,1.18992694384,1.18992694385,1.18991762483,1.15168950571,0.691013703425,0.00190430718275,-6.65045796211e-12,9.31901456003e-06
cubic,8,generic,"(1, -1)(1, -1)",2,3,-0.00813626588297,-0.00813626588293,1.35189467934,1.35189467934,1.35188409186,1.30845252565,0.785071515391,0.00190430718275,-8.35731484017e-12,1.05874779217e-05
cubic,8,generic,"(1, -1)(1, -1)",4,1,-0.00480109330908,-0.00480109330883,0.392146872438,0.392146872459,0.392146233043,0.379437357083,0.22766241425,0.000739061403917,-2.14531725717e-11,6.39395069224e-07
cubic,8,generic,"(1, -1)(1, -1)",4,2,-0.00480109330908,-0.00480109330883,0.629426236744,0.629426236779,0.629425210466,0.609026475882,0.365415885529,0.000739061403917,-3.46428441489e-11,1.02627861809e-06
cubic,8,generic,"(1, -1)(1, -1)",4,3,-0.00480109330908,-0.00480109330883,0.753427950179,0.753427950222,0.753426721718,0.729009282649,0.43740556959,0.000739061403917,-4.28771462779e-11,1.22846183281e-06
cubic,8,generic,"(0, 1)(1, 1)",2,1,-0.00438579808554,-0.00438579808555,0.882266688988,0.882266688985,0.882272016688,0.853927533803,0.512356520282,0.00190430718275,2.8583801992e-12,-5.32769941819e-06
cubic,8,generic,"(0, 1)(1, 1)",2,2,-0.00438579808554,-0.00438579808555,1.18991043938,1.18991043937,1.18991762483,1.15168950571,0.691013703425,0.00190430718275,3.83626463929e-12,-7.18545225764e-06
cubic,8,generic,"(0, 1)(1, 1)",2,3,-0.00438579808554,-0.00438579808555,1.35187592835,1.35187592835,1.35188409186,1.30845252565,0.785071515391,0.00190430718275,6.0051963402e-12,-8.16350345412e-06
cubic,8,generic,"(0, 1)(1, 1)",4,1,-0.00260373311448,-0.00260373311436,0.392145745683,0.392145745703,0.392146233043,0.379437357083,0.22766241425,0.000739061403917,-1.96089255944e-11,-4.87359364199e-07
cubic,8,generic,"(0, 1)(1, 1)",4,2,-0.00260373311448,-0.00260373311436,0.629424428215,0.629424428247,0.629425210466,0.609026475882,0.365415885529,0.000739061403917,-3.20791171404e-11,-7.82250298093e-07
cubic,8,generic,"(0, 1)(1, 1)",4,3,-0.00260373311448,-0.00260373311436,0.753425785359,0.753425785396,0.753426721718,0.729009282649,0.43740556959,0.000739061403917,-3.74494879551e-11,-9.36358554249e-07
cubic,8,generic,"(0, 1)(0, -1)",2,1,0.00321583720074,0.0032158372006,0.88227215919,0.88227215923,0.882272016688,0.853927533803,0.512356520282,0.00190430718275,-4.01332300726e-11,1.4250268332e-07
cubic,8,generic,"(0, 1)(0, -1)",2,2,0.00321583720074,0.0032158372006,1.18991781702,1.18991781708,1.18991762483,1.15168950571,0.691013703425,0.00190430718275,-5.51862999743e-11,1.92191883075e-07
cubic,8,generic,"(0, 1)(0, -1)",2,3,0.00321583720074,0.0032158372006,1.35188431021,1.35188431027,1.35188409186,1.30845252565,0.785071515391,0.00190430718275,-6.1863403289e-11,2.18353050085e-07
cubic,8,generic,"(0, 1)(0, -1)",4,1,0.00190411012693,0.00190411012678,0.392146246772,0.392146246803,0.392146233043,0.379437357083,0.22766241425,0.000739061403917,-3.10989567431e-11,1.37294072777e-08
cubic,8,generic,"(0, 1)(0, -1)",4,2,0.00190411012693,0.00190411012678,0.629425232504,0.629425232552,0.629425210466,0.609026475882,0.365415885529,0.000739061403917,-4.82828221848e-11,2.20384002159e-08
cubic,8,generic,"(0, 1)(0, -1)",4,3,0.00190411012693,0.00190411012678,0.753426748094,0.753426748155,0.753426721718,0.729009282649,0.43740556959,0.000739061403917,-6.10513861687e-11,2.63768746844e-08
cubic,8,linear,"(0, 1)(0, 1)",2,1,-0.0032096755549,-0.00320967555488,1.79282824768e-13,0,0,0,0.512356520282,0.00190430718275,1.79282824768e-13,1.79282824768e-13
cubic,8,linear,"(0, 1)(0, 1)",2,2,-0.0032096755549,-0.00320967555488,6.96897522284e-13,0,0,0,0.691013703425,0.00190430718275,6.96897522284e-13,6.96897522284e-13
cubic,8,linear,"(0, 1)(0, 1)",2,3,-0.0032096755549,-0.00320967555488,-2.01497823978e-12,0,0,0,0.785071515391,0.00190430718275,-2.01497823978e-12,-2.01497823978e-12
cubic,8,linear,"(0, 1)(0, 1)",4,1,-0.00190112812345,-0.00190112812352,7.06260991532e-13,0,0,0,0.22766241425,0.000739061403917,7.06260991532e-13,7.06260991532e-13
cubic,8,linear,"(0, 1)(0, 1)",4,2,-0.00190112812345,-0.00190112812352,5.88286216472e-13,0,0,0,0.365415885529,0.000739061403917,5.88286216472e-13,5.88286216472e-13
cubic,8,linear,"(0, 1)(0, 1)",4,3,-0.00190112812345,-0.00190112812352,-6.80377752567e-13,0,0,0,0.43740556959,0.000739061403917,-6.80377752567e-13,-6.80377752567e-13
cubic,8,linear,"(1, -1)(1, -1)",2,1,-0.00722176999841,-0.00722176999848,2.39043766361e-13,0,0,0,0.512356520282,0.00190430718275,2.39043766361e-13,2.39043766361e-13
cubic,8,linear,"(1, -1)(1, -1)",2,2,-0.00722176999841,-0.00722176999848,3.09732232131e-13,0,0,0,0.691013703425,0.00190430718275,3.09732232131e-13,3.09732232131e-13
cubic,8,linear,"(1, -1)(1, -1)",2,3,-0.00722176999841,-0.00722176999848,1.07465506123e-12,0,0,0,0.785071515391,0.00190430718275,1.07465506123e-12,1.07465506123e-12
cubic,8,linear,"(1, -1)(1, -1)",4,1,-0.00427753827785,-0.00427753827793,0,0,0,0,0.22766241425,0.000739061403917,0,0
cubic,8,linear,"(1, -1)(1, -1)",4,2,-0.00427753827785,-0.00427753827793,5.22921081298e-13,0,0,0,0.365415885529,0.000739061403917,5.22921081298e-13,5.22921081298e-13
cubic,8,linear,"(1, -1)(1, -1)",4,3,-0.00427753827785,-0.00427753827793,-1.20956044898e-12,0,0,0,0.43740556959,0.000739061403917,-1.20956044898e-12,-1.20956044898e-12
cubic,8,linear,"(0, 1)(1, 1)",2,1,-0.00481451333224,-0.00481451333232,-3.98406277271e-14,0,0,0,0.512356520282,0.00190430718275,-3.98406277271e-14,-3.98406277271e-14
cubic,8,linear,"(0, 1)(1, 1)",2,2,-0.00481451333224,-0.00481451333232,3.4844876115e-13,0,0,0,0.691013703425,0.00190430718275,3.4844876115e-13,3.4844876115e-13
cubic,8,linear,"(0, 1)(1, 1)",2,3,-0.00481451333224,-0.00481451333232,0,0,0,0,0.785071515391,0.00190430718275,0,0
cubic,8,linear,"(0, 1)(1, 1)",4,1,-0.00285169218523,-0.00285169218529,-2.01788854719e-13,0,0,0,0.22766241425,0.000739061403917,-2.01788854719e-13,-2.01788854719e-13
cubic,8,linear,"(0, 1)(1, 1)",4,2,-0.00285169218523,-0.00285169218529,-7.84381621947e-13,0,0,0,0.365415885529,0.000739061403917,-7.84381621947e-13,-7.84381621947e-13
cubic,8,linear,"(0, 1)(1, 1)",4,3,-0.00285169218523,-0.00285169218529,-3.62868134695e-12,0,0,0,0.43740556959,0.000739061403917,-3.62868134695e-12,-3.62868134695e-12
cubic,8,linear,"(0, 1)(0, -1)",2,1,0.0032096755549,0.00320967555488,-2.39043766357e-13,0,0,0,0.512356520282,0.00190430718275,-2.39043766357e-13,-2.39043766357e-13
cubic,8,linear,"(0, 1)(0, -1)",2,2,0.0032096755549,0.00320967555488,-1.04534628343e-12,0,0,0,0.691013703425,0.00190430718275,-1.04534628343e-12,-1.04534628343e-12
cubic,8,linear,"(0, 1)(0, -1)",2,3,0.0032096755549,0.00320967555488,4.02995647956e-13,0,0,0,0.785071515391,0.00190430718275,4.02995647956e-13,4.02995647956e-13
cubic,8,linear,"(0, 1)(0, -1)",4,1,0.00190112812356,0.00190112812352,2.01788854711e-13,0,0,0,0.22766241425,0.000739061403917,2.01788854711e-13,2.01788854711e-13
cubic,8,linear,"(0, 1)(0, -1)",4,2,0.00190112812356,0.00190112812352,5.88286216437e-13,0,0,0,0.365415885529,0.000739061403917,5.88286216437e-13,5.88286216437e-13
cubic,8,linear,"(0, 1)(0, -1)",4,3,0.00190112812356,0.00190112812352,2.04113325758e-12,0,0,0,0.43740556959,0.000739061403917,2.04113325758e-12,2.04113325758e-12
cubic,12,square,"(0, 1)(0, 1)",2,1,-0.00226667704555,-0.00226667704585,0.548255150999,0.548255150939,0.548255619431,0.537515366176,0.537515366176,0.0018072395231,5.95750115906e-11,-4.68432184375e-07
cubic,12,square,"(0, 1)(0, 1)",2,3,-0.00226667704555,-0.00226667704585,0.857202713253,0.857202713157,0.857203445649,0.840410946363,0.840410946363,0.0018072395231,9.59883283969e-11,-7.32395820657e-07
cubic,12,square,"(0, 1)(0, 1)",2,5,-0.00226667704555,-0.00226667704585,0.931902646249,0.93190264614,0.931903442464,0.913647580368,0.913647580368,0.0018072395231,1.09446895991e-10,-7.96214508436e-07
cubic,12,square,"(0, 1)(0, 1)",4,1,-0.0007254477282,-0.000725447728414,0.272613477832,0.272613477757,0.272613492564,0.267237362133,0.267237362133,0.000324158845092,7.52132245374e-11,-1.47317014143e-08
cubic,12,square,"(0, 1)(0, 1)",4,3,-0.0007254477282,-0.000725447728414,0.600618236806,0.600618236645,0.600618269268,0.588773653199,0.588773653199,0.000324158845092,1.61304858359e-10,-3.2461084376e-08
cubic,12,square,"(0, 1)(0, 1)",4,5,-0.0007254477282,-0.000725447728414,0.720057623866,0.720057623689,0.720057662799,0.705857617613,0.705857617613,0.000324158845092,1.76641701266e-10,-3.89330599981e-08
cubic,12,square,"(1, -1)(1, -1)",2,1,-0.00569227263622,-0.00569227263669,0.548256350698,0.548256350665,0.548255619431,0.537515366176,0.537515366176,0.0018072395231,3.28677085548e-11,7.31266873166e-07
cubic,12,square,"(1, -1)(1, -1)",2,3,-0.00569227263622,-0.00569227263669,0.857204588992,0.857204588941,0.857203445649,0.840410946363,0.840410946363,0.0018072395231,5.1588622263e-11,1.14334367141e-06
cubic,12,square,"(1, -1)(1, -1)",2,5,-0.00569227263622,-0.00569227263669,0.93190468544,0.931904685387,0.931903442464,0.913647580368,0.913647580368,0.0018072395231,5.31966692918e-11,1.24297613768e-06
cubic,12,square,"(1, -1)(1, -1)",4,1,-0.00181440364076,-0.00181440364023,0.27261351575,0.272613515836,0.272613492564,0.267237362133,0.267237362133,0.000324158845092,-8.62636073684e-11,2.3186184972e-08
cubic,12,square,"(1, -1)(1, -1)",4,3,-0.00181440364076,-0.00181440364023,0.600618320354,0.600618320541,0.600618269268,0.588773653199,0.588773653199,0.000324158845092,-1.8739665375e-10,5.10861395409e-08
cubic,12,square,"(1, -1)(1, -1)",4,5,-0.00181440364076,-0.00181440364023,0.720057724026,0.720057724269,0.720057662799,0.705857617613,0.705857617613,0.000324158845092,-2.42785347382e-10,6.12270441014e-08
cubic,12,square,"(0, 1)(1, 1)",2,1,-0.00336405513417,-0.00336405513421,0.548255036607,0.548255036613,0.548255619431,0.537515366176,0.537515366176,0.0018072395231,-5.58020296637e-12,-5.82824075002e-07
cubic,12,square,"(0, 1)(1, 1)",2,3,-0.00336405513417,-0.00336405513421,0.857202534397,0.857202534406,0.857203445649,0.840410946363,0.840410946363,0.0018072395231,-8.77753425499e-12,-9.11251643254e-07
cubic,12,square,"(0, 1)(1, 1)",2,5,-0.00336405513417,-0.00336405513421,0.931902451809,0.931902451812,0.931903442464,0.913647580368,0.913647580368,0.0018072395231,-2.59614552078e-12,-9.90654661082e-07
cubic,12,square,"(0, 1)(1, 1)",4,1,-0.00107707310826,-0.00107707310846,0.272613474201,0.272613474157,0.272613492564,0.267237362133,0.267237362133,0.000324158845092,4.4395320753e-11,-1.83626729378e-08
cubic,12,square,"(0, 1)(1, 1)",4,3,-0.00107707310826,-0.00107707310846,0.600618228808,0.600618228713,0.600618269268,0.588773653199,0.588773653199,0.000324158845092,9.44846423323e-11,-4.04597131354e-08
cubic,12,square,"(0, 1)(1, 1)",4,5,-0.00107707310826,-0.00107707310846,0.720057614287,0.72005761418,0.720057662799,0.705857617613,0.705857617613,0.000324158845092,1.07454267706e-10,-4.85113811344e-08
cubic,12,square,"(0, 1)(0, -1)",2,1,0.00236790944518,0.00236790944431,0.548255628201,0.548255628414,0.548255619431,0.537515366176,0.537515366176,0.0018072395231,-2.13481343714e-10,8.76946082418e-09
cubic,12,square,"(0, 1)(0, -1)",2,3,0.00236790944518,0.00236790944431,0.85720345936,0.857203459694,0.857203445649,0.840410946363,0.840410946363,0.0018072395231,-3.33442939926e-10,1.37114818388e-08
cubic,12,square,"(0, 1)(0, -1)",2,5,0.00236790944518,0.00236790944431,0.93190345737,0.931903457733,0.931903442464,0.913647580368,0.913647580368,0.0018072395231,-3.6216618593e-10,1.49066872179e-08
cubic,12,square,"(0, 1)(0, -1)",4,1,0.000756633529363,0.000756633529344,0.272613492851,0.272613492865,0.272613492564,0.267237362133,0.267237362133,0.000324158845092,-1.36184952204e-11,2.87436630053e-10
cubic,12,square,"(0, 1)(0, -1)",4,3,0.000756633529363,0.000756633529344,0.600618269902,0.600618269931,0.600618269268,0.588773653199,0.588773653199,0.000324158845092,-2.85039769565e-11,6.34776453623e-10
cubic,12,square,"(0, 1)(0, -1)",4,5,0.000756633529363,0.000756633529344,0.720057663561,0.720057663594,0.720057662799,0.705857617613,0.705857617613,0.000324158845092,-3.33789662577e-11,7.61802065874e-10
cubic,12,generic,"(0, 1)(0, 1)",2,1,-0.00220406521612,-0.0022040652163,0.925518904843,0.925518904728,0.92552252753,0.895858943627,0.537515366176,0.0018072395231,1.15170095683e-10,-3.62268719944e-06
cubic,12,generic,"(0, 1)(0, 1)",2,3,-0.00220406521612,-0.0022040652163,1.44705857291,1.44705857273,1.44706423702,1.40068491061,0.840410946363,0.0018072395231,1.8044588046e-10,-5.66410928338e-06
cubic,12,generic,"(0, 1)(0, 1)",2,5,-0.00220406521612,-0.0022040652163,1.57316080841,1.57316080823,1.57316696613,1.52274596728,0.913647580368,0.0018072395231,1.83244752705e-10,-6.15771442192e-06
cubic,12,generic,"(0, 1)(0, 1)",4,1,-0.000705954016667,-0.000705954016476,0.460313973538,0.460313973641,0.460314087994,0.445395603556,0.267237362133,0.000324158845092,-1.03798858397e-10,-1.14455897204e-07
cubic,12,generic,"(0, 1)(0, 1)",4,3,-0.000705954016667,-0.000705954016476,1.01415736801,1.01415736825,1.01415762019,0.981289421999,0.588773653199,0.000324158845092,-2.39572583993e-10,-2.52178531168e-07
cubic,12,generic,"(0, 1)(0, 1)",4,5,-0.000705954016667,-0.000705954016476,1.2158334528,1.21583345306,1.2158337551,1.17642936269,0.705857617613,0.000324158845092,-2.5660384928e-10,-3.02296329968e-07
cubic,12,generic,"(1, -1)(1, -1)",2,1,-0.00596013675113,-0.00596013675127,0.925528335261,0.925528335199,0.92552252753,0.895858943627,0.537515366176,0.0018072395231,6.1768701265e-11,5.80773075154e-06
cubic,12,generic,"(1, -1)(1, -1)",2,3,-0.00596013675113,-0.00596013675127,1.44707331747,1.44707331737,1.44706423702,1.40068491061,0.840410946363,0.0018072395231,9.46467348939e-11,9.08044637837e-06
cubic,12,generic,"(1, -1)(1, -1)",2,5,-0.00596013675113,-0.00596013675127,1.57317683789,1.57317683778,1.57316696613,1.52274596728,0.913647580368,0.0018072395231,1.10255138352e-10,9.87175867295e-06
cubic,12,generic,"(1, -1)(1, -1)",4,1,-0.00189599627674,-0.00189599627761,0.460314273689,0.46031427346,0.460314087994,0.445395603556,0.267237362133,0.000324158845092,2.29404606422e-10,1.85695627763e-07
cubic,12,generic,"(1, -1)(1, -1)",4,3,-0.00189599627674,-0.00189599627761,1.01415802931,1.01415802881,1.01415762019,0.981289421999,0.588773653199,0.000324158845092,5.01588992563e-10,4.09118201761e-07
cubic,12,generic,"(1, -1)(1, -1)",4,5,-0.00189599627674,-0.00189599627761,1.21583424557,1.21583424497,1.2158337551,1.17642936269,0.705857617613,0.000324158845092,6.01918515031e-10,4.90476333548e-07
cubic,12,generic,"(0, 1)(1, 1)",2,1,-0.00324902967486,-0.00324902967548,0.925518034677,0.925518034461,0.92552252753,0.895858943627,0.537515366176,0.0018072395231,2.16121454066e-10,-4.49285254955e-06
cubic,12,generic,"(0, 1)(1, 1)",2,3,-0.00324902967486,-0.00324902967548,1.44705721239,1.44705721206,1.44706423702,1.40068491061,0.840410946363,0.0018072395231,3.34691163673e-10,-7.02462558255e-06
cubic,12,generic,"(0, 1)(1, 1)",2,5,-0.00324902967486,-0.00324902967548,1.57315932934,1.57315932899,1.57316696613,1.52274596728,0.913647580368,0.0018072395231,3.59544172213e-10,-7.6367827182e-06
cubic,12,generic,"(0, 1)(1, 1)",4,1,-0.00104129051988,-0.00104129052003,0.460313946424,0.460313946337,0.460314087994,0.445395603556,0.267237362133,0.000324158845092,8.7471807575e-11,-1.41569135748e-07
cubic,12,generic,"(0, 1)(1, 1)",4,3,-0.00104129051988,-0.00104129052003,1.01415730828,1.01415730809,1.01415762019,0.981289421999,0.588773653199,0.000324158845092,1.89010807006e-10,-3.11906863892e-07
cubic,12,generic,"(0, 1)(1, 1)",4,5,-0.00104129051988,-0.00104129052003,1.2158333812,1.21583338094,1.2158337551,1.17642936269,0.705857617613,0.000324158845092,2.62084354219e-10,-3.73897406813e-07
cubic,12,generic,"(0, 1)(0, -1)",2,1,0.00237057672621,0.0023705767259,0.925522644491,0.925522644569,0.92552252753,0.895858943627,0.537515366176,0.0018072395231,-7.81074094292e-11,1.16960799934e-07
cubic,12,generic,"(0, 1)(0, -1)",2,3,0.00237057672621,0.0023705767259,1.44706441989,1.44706442001,1.44706423702,1.40068491061,0.840410946363,0.0018072395231,-1.24036780846e-10,1.82867529785e-07
cubic,12,generic,"(0, 1)(0, -1)",2,5,0.00237057672621,0.0023705767259,1.57316716493,1.57316716507,1.57316696613,1.52274596728,0.913647580368,0.0018072395231,-1.34712463407e-10,1.98803441043e-07
cubic,12,generic,"(0, 1)(0, -1)",4,1,0.000757268159305,0.000757268160478,0.460314092652,0.460314091918,0.460314087994,0.445395603556,0.267237362133,0.000324158845092,7.34070637609e-10,4.65884220091e-09
cubic,12,generic,"(0, 1)(0, -1)",4,3,0.000757268159305,0.000757268160478,1.01415763045,1.01415762884,1.01415762019,0.981289421999,0.588773653199,0.000324158845092,1.61668300969e-09,1.0263685235e-08
cubic,12,generic,"(0, 1)(0, -1)",4,5,0.000757268159305,0.000757268160478,1.21583376738,1.21583376546,1.2158337551,1.17642936269,0.705857617613,0.000324158845092,1.91310856046e-09,1.22796601776e-08
cubic,12,linear,"(0, 1)(0, 1)",2,1,-0.00236641093579,-0.00236641093671,0,0,0,0,0.537515366176,0.0018072395231,0,0
cubic,12,linear,"(0, 1)(0, 1)",2,3,-0.00236641093579,-0.00236641093671,-4.18041793155e-12,0,0,0,0.840410946363,0.0018072395231,-4.18041793155e-12,-4.18041793155e-12
cubic,12,linear,"(0, 1)(0, 1)",2,5,-0.00236641093579,-0.00236641093671,1.4737853093e-12,0,0,0,0.913647580368,0.0018072395231,1.4737853093e-12,1.4737853093e-12
cubic,12,linear,"(0, 1)(0, 1)",4,1,-0.000756276984248,-0.00075627698487,-1.68760251635e-12,0,0,0,0.267237362133,0.000324158845092,-1.68760251635e-12,-1.68760251635e-12
cubic,12,linear,"(0, 1)(0, 1)",4,3,-0.000756276984248,-0.00075627698487,-2.90680881195e-12,0,0,0,0.588773653199,0.000324158845092,-2.90680881195e-12,-2.90680881195e-12
cubic,12,linear,"(0, 1)(0, 1)",4,5,-0.000756276984248,-0.00075627698487,1.84460547951e-11,0,0,0,0.705857617613,0.000324158845092,1.84460547951e-11,1.84460547951e-11
cubic,12,linear,"(1, -1)(1, -1)",2,1,-0.0053244246069,-0.00532442460759,0,0,0,0,0.537515366176,0.0018072395231,0,0
cubic,12,linear,"(1, -1)(1, -1)",2,3,-0.0053244246069,-0.00532442460759,0,0,0,0,0.840410946363,0.0018072395231,0,0
cubic,12,linear,"(1, -1)(1, -1)",2,5,-0.0053244246069,-0.00532442460759,-1.31003138571e-12,0,0,0,0.913647580368,0.0018072395231,-1.31003138571e-12,-1.31003138571e-12
cubic,12,linear,"(1, -1)(1, -1)",4,1,-0.00170162321547,-0.00170162321596,-2.1429873212e-13,0,0,0,0.267237362133,0.000324158845092,-2.1429873212e-13,-2.1429873212e-13
cubic,12,linear,"(1, -1)(1, -1)",4,3,-0.00170162321547,-0.00170162321596,2.58383005369e-12,0,0,0,0.588773653199,0.000324158845092,2.58383005369e-12,2.58383005369e-12
cubic,12,linear,"(1, -1)(1, -1)",4,5,-0.00170162321547,-0.00170162321596,-4.09912328561e-12,0,0,0,0.705857617613,0.000324158845092,-4.09912328561e-12,-4.09912328561e-12
cubic,12,linear,"(0, 1)(1, 1)",2,1,-0.0035496164046,-0.00354961640506,0,0,0,0,0.537515366176,0.0018072395231,0,0
cubic,12,linear,"(0, 1)(1, 1)",2,3,-0.0035496164046,-0.00354961640506,-2.1676241121e-12,0,0,0,0.840410946363,0.0018072395231,-2.1676241121e-12,-2.1676241121e-12
cubic,12,linear,"(0, 1)(1, 1)",2,5,-0.0035496164046,-0.00354961640506,9.8252353928e-13,0,0,0,0.913647580368,0.0018072395231,9.8252353928e-13,9.8252353928e-13
cubic,12,linear,"(0, 1)(1, 1)",4,1,-0.00113441547683,-0.00113441547731,-4.82172147336e-13,0,0,0,0.267237362133,0.000324158845092,-4.82172147336e-13,-4.82172147336e-13
cubic,12,linear,"(0, 1)(1, 1)",4,3,-0.00113441547683,-0.00113441547731,-4.84468135131e-12,0,0,0,0.588773653199,0.000324158845092,-4.84468135131e-12,-4.84468135131e-12
cubic,12,linear,"(0, 1)(1, 1)",4,5,-0.00113441547683,-0.00113441547731,1.84460547877e-11,0,0,0,0.705857617613,0.000324158845092,1.84460547877e-11,1.84460547877e-11
cubic,12,linear,"(0, 1)(0, -1)",2,1,0.00236641093761,0.00236641093671,-2.31144784593e-13,0,0,0,0.537515366176,0.0018072395231,-2.31144784593e-13,-2.31144784593e-13
cubic,12,linear,"(0, 1)(0, -1)",2,3,0.00236641093761,0.00236641093671,4.64490880926e-13,0,0,0,0.840410946363,0.0018072395231,4.64490880926e-13,4.64490880926e-13
cubic,12,linear,"(0, 1)(0, -1)",2,5,0.00236641093761,0.00236641093671,1.47378530816e-12,0,0,0,0.913647580368,0.0018072395231,1.47378530816e-12,1.47378530816e-12
cubic,12,linear,"(0, 1)(0, -1)",4,1,0.000756276985612,0.00075627698487,1.20543036665e-12,0,0,0,0.267237362133,0.000324158845092,1.20543036665e-12,1.20543036665e-12
cubic,12,linear,"(0, 1)(0, -1)",4,3,0.000756276985612,0.00075627698487,8.72042642013e-12,0,0,0,0.588773653199,0.000324158845092,8.72042642013e-12,8.72042642013e-12
cubic,12,linear,"(0, 1)(0, -1)",4,5,0.000756276985612,0.00075627698487,-9.22302738092e-12,0,0,0,0.705857617613,0.000324158845092,-9.22302738092e-12,-9.22302738092e-12

graph,L,grip,k,sigma,d,C1,C1_formula,Cmark,rho_num,rho_exact,rho_mu2,rho_lead,dev_exact
ring,40,square,0,1,1,0.523424829168,0.523424829179,-0.0652630432208,1.03605018957,1.03605018957,1.03680478561,1,4.81881201608e-12
ring,40,square,0,1,5,0.523424829168,0.523424829179,-0.0652630432208,1.03605018957,1.03605018957,1.03680478561,1,4.54147830453e-12
ring,40,square,0,1,10,0.523424829168,0.523424829179,-0.0652630432208,1.03605018957,1.03605018957,1.03680478561,1,3.26028093411e-12
ring,40,square,0,-1,1,-0.523424829168,-0.523424829179,-0.0878631862926,1.03764191087,1.03764191087,1.03680478561,1,-3.62065932791e-12
ring,40,square,0,-1,5,-0.523424829168,-0.523424829179,-0.0878631862926,1.03764191087,1.03764191087,1.03680478561,1,-3.34199334873e-12
ring,40,square,0,-1,10,-0.523424829168,-0.523424829179,-0.0878631862926,1.03764191087,1.03764191087,1.03680478561,1,-2.01660910193e-12
ring,40,square,1,1,1,0.785137243694,0.785137243768,-0.137979576612,1.03569894357,1.03569894357,1.03680478561,1,1.89515070304e-12
ring,40,square,1,1,5,0.785137243694,0.785137243768,-0.137979576612,1.03569894357,1.03569894357,1.03680478561,1,2.40274466989e-12
ring,40,square,1,1,10,0.785137243694,0.785137243768,-0.137979576612,1.03569894357,1.03569894357,1.03680478561,1,4.33830749103e-12
ring,40,square,1,-1,1,-0.785137243694,-0.785137243768,-0.21645665226,1.03809774135,1.03809774135,1.03680478561,1,4.20108392518e-12
ring,40,square,1,-1,5,-0.785137243694,-0.785137243768,-0.21645665226,1.03809774135,1.03809774135,1.03680478561,1,3.68771679859e-12
ring,40,square,1,-1,10,-0.785137243694,-0.785137243768,-0.21645665226,1.03809774135,1.03809774135,1.03680478561,1,1.73283609683e-12
ring,40,generic,0,1,1,0.539041381919,0.539041381964,-0.061265193279,1.74410710345,1.74410710337,1.74971635162,1.66666666667,8.01465560585e-11
ring,40,generic,0,1,5,0.539041381919,0.539041381964,-0.061265193279,1.74410710345,1.74410710337,1.74971635162,1.66666666667,8.01312349807e-11
ring,40,generic,0,1,10,0.539041381919,0.539041381964,-0.061265193279,1.74410710345,1.74410710337,1.74971635162,1.66666666667,7.93292098678e-11
ring,40,generic,0,-1,1,-0.539041381919,-0.539041381964,-0.100797366354,1.75642148532,1.75642148519,1.74971635162,1.66666666667,1.31652022617e-10
ring,40,generic,0,-1,5,-0.539041381919,-0.539041381964,-0.100797366354,1.75642148532,1.75642148519,1.74971635162,1.66666666667,1.31660682356e-10
ring,40,generic,0,-1,10,-0.539041381919,-0.539041381964,-0.100797366354,1.75642148532,1.75642148519,1.74971635162,1.66666666667,1.32351685167e-10
ring,40,generic,1,1,1,0.808562072604,0.808562072946,-0.125595934791,1.74161103217,1.74161103171,1.74971635162,1.66666666667,4.53704629422e-10
ring,40,generic,1,1,5,0.808562072604,0.808562072946,-0.125595934791,1.74161103217,1.74161103171,1.74971635162,1.66666666667,4.53422410729e-10
ring,40,generic,1,1,10,0.808562072604,0.808562072946,-0.125595934791,1.74161103217,1.74161103171,1.74971635162,1.66666666667,4.5405412763e-10
ring,40,generic,1,-1,1,-0.808562072604,-0.808562072946,-0.270751600514,1.76034338797,1.76034338735,1.74971635162,1.66666666667,6.224611937e-10
ring,40,generic,1,-1,5,-0.808562072604,-0.808562072946,-0.270751600514,1.76034338797,1.76034338735,1.74971635162,1.66666666667,6.22740747858e-10
ring,40,generic,1,-1,10,-0.808562072604,-0.808562072946,-0.270751600514,1.76034338797,1.76034338735,1.74971635162,1.66666666667,6.22024431962e-10
ring,40,linear,0,1,1,0.5,0.5,-0.0741711794292,6.37006348614e-14,0,0,0,6.37006348614e-14
ring,40,linear,0,1,5,0.5,0.5,-0.0741711794292,1.71396742814e-12,0,0,0,1.71396742814e-12
ring,40,linear,0,1,10,0.5,0.5,-0.0741711794292,8.78413430338e-12,0,0,0,8.78413430338e-12
ring,40,linear,0,-1,1,-0.5,-0.5,-0.0741711794295,-6.37006348611e-14,0,0,0,-6.37006348611e-14
ring,40,linear,0,-1,5,-0.5,-0.5,-0.0741711794295,-1.71396742813e-12,0,0,0,-1.71396742813e-12
ring,40,linear,0,-1,10,-0.5,-0.5,-0.0741711794295,-8.78413430334e-12,0,0,0,-8.78413430334e-12
ring,40,linear,1,1,1,0.75,0.75,-0.166885153716,-8.1891133134e-14,0,0,0,-8.1891133134e-14
ring,40,linear,1,1,5,0.75,0.75,-0.166885153716,-5.3417118016e-13,0,0,0,-5.3417118016e-13
ring,40,linear,1,1,10,0.75,0.75,-0.166885153716,-1.18239948225e-13,0,0,0,-1.18239948225e-13
ring,40,linear,1,-1,1,-0.75,-0.75,-0.166885153716,8.1891133134e-14,0,0,0,8.1891133134e-14
ring,40,linear,1,-1,5,-0.75,-0.75,-0.166885153716,5.3417118016e-13,0,0,0,5.3417118016e-13
ring,40,linear,1,-1,10,-0.75,-0.75,-0.166885153716,1.18239948225e-13,0,0,0,1.18239948225e-13
ring,80,square,0,1,1,0.523424796402,0.523424796412,-0.0652623164737,1.03605007008,1.03605007008,1.03680465762,1,2.97406543837e-12
ring,80,square,0,1,5,0.523424796402,0.523424796412,-0.0652623164737,1.03605007008,1.03605007008,1.03680465762,1,3.55426799103e-12
ring,80,square,0,1,20,0.523424796402,0.523424796412,-0.0652623164737,1.03605007016,1.03605007008,1.03680465762,1,8.11892775232e-11
ring,80,square,0,-1,1,-0.523424796402,-0.523424796412,-0.0878618669942,1.03764177268,1.03764177268,1.03680465762,1,-2.15161222172e-12
ring,80,square,0,-1,5,-0.523424796402,-0.523424796412,-0.0878618669942,1.03764177268,1.03764177268,1.03680465762,1,-2.73381317584e-12
ring,80,square,0,-1,20,-0.523424796402,-0.523424796412,-0.0878618669942,1.0376417726,1.03764177268,1.03680465762,1,-8.06184008439e-11
ring,80,square,1,1,1,0.785137194545,0.785137194619,-0.137978133286,1.03569882782,1.03569882782,1.03680465762,1,-1.98530081263e-12
ring,80,square,1,1,5,0.785137194545,0.785137194619,-0.137978133286,1.03569882782,1.03569882782,1.03680465762,1,-2.24464891119e-12
ring,80,square,1,1,20,0.785137194545,0.785137194619,-0.137978133286,1.03569882778,1.03569882782,1.03680465762,1,-4.00715016724e-11
ring,80,square,1,-1,1,-0.785137194545,-0.785137194619,-0.216453091796,1.03809759722,1.03809759721,1.03680465762,1,8.05822075733e-12
ring,80,square,1,-1,5,-0.785137194545,-0.785137194619,-0.216453091796,1.03809759722,1.03809759721,1.03680465762,1,8.32356406022e-12
ring,80,square,1,-1,20,-0.785137194545,-0.785137194619,-0.216453091796,1.03809759726,1.03809759721,1.03680465762,1,4.65676386341e-11
ring,80,generic,0,1,1,0.539041327309,0.539041327354,-0.0612645701901,1.74410669844,1.74410669836,1.74971588361,1.66666666667,7.48980877319e-11
ring,80,generic,0,1,5,0.539041327309,0.539041327354,-0.0612645701901,1.74410669844,1.74410669836,1.74971588361,1.66666666667,7.41025019124e-11
ring,80,generic,0,1,20,0.539041327309,0.539041327354,-0.0612645701901,1.74410669834,1.74410669836,1.74971588361,1.66666666667,-1.90154558766e-11
ring,80,generic,0,-1,1,-0.539041327309,-0.539041327354,-0.100795667565,1.75642093091,1.75642093078,1.74971588361,1.66666666667,1.35886413233e-10
ring,80,generic,0,-1,5,-0.539041327309,-0.539041327354,-0.100795667565,1.75642093091,1.75642093078,1.74971588361,1.66666666667,1.36671118867e-10
ring,80,generic,0,-1,20,-0.539041327309,-0.539041327354,-0.100795667565,1.75642093101,1.75642093078,1.74971588361,1.66666666667,2.2949420142e-10
ring,80,generic,1,1,1,0.808561990688,0.808561991031,-0.12559477229,1.74161065288,1.74161065242,1.74971588361,1.66666666667,4.62855753725e-10
ring,80,generic,1,1,5,0.808561990688,0.808561991031,-0.12559477229,1.74161065288,1.74161065242,1.74971588361,1.66666666667,4.63101779147e-10
ring,80,generic,1,1,20,0.808561990688,0.808561991031,-0.12559477229,1.74161065288,1.74161065242,1.74971588361,1.66666666667,4.6264725384e-10
ring,80,generic,1,-1,1,-0.808561990688,-0.808561991031,-0.270746138055,1.76034277619,1.76034277558,1.74971588361,1.66666666667,6.15627770983e-10
ring,80,generic,1,-1,5,-0.808561990688,-0.808561991031,-0.270746138055,1.76034277619,1.76034277558,1.74971588361,1.66666666667,6.15381967606e-10
ring,80,generic,1,-1,20,-0.808561990688,-0.808561991031,-0.270746138055,1.76034277619,1.76034277558,1.74971588361,1.66666666667,6.1603411261e-10
ring,80,linear,0,1,1,0.5,0.5,-0.0741702264716,-1.25856300368e-13,0,0,0,-1.25856300368e-13
ring,80,linear,0,1,5,0.5,0.5,-0.0741702264716,-1.60335119936e-12,0,0,0,-1.60335119936e-12
ring,80,linear,0,1,20,0.5,0.5,-0.0741702264716,-1.34248909008e-10,0,0,0,-1.34248909008e-10
ring,80,linear,0,-1,1,-0.5,-0.5,-0.0741702264709,1.25856300369e-13,0,0,0,1.25856300369e-13
ring,80,linear,0,-1,5,-0.5,-0.5,-0.0741702264709,1.60335119938e-12,0,0,0,1.60335119938e-12
ring,80,linear,0,-1,20,-0.5,-0.5,-0.0741702264709,1.3424890901e-10,0,0,0,1.3424890901e-10
ring,80,linear,1,1,1,0.75,0.75,-0.16688300956,-1.33642003641e-13,0,0,0,-1.33642003641e-13
ring,80,linear,1,1,5,0.75,0.75,-0.16688300956,-6.21651534109e-13,0,0,0,-6.21651534109e-13
ring,80,linear,1,1,20,0.75,0.75,-0.16688300956,1.77842293235e-12,0,0,0,1.77842293235e-12
ring,80,linear,1,-1,1,-0.75,-0.75,-0.16688300956,1.33642003641e-13,0,0,0,1.33642003641e-13
ring,80,linear,1,-1,5,-0.75,-0.75,-0.16688300956,6.21651534109e-13,0,0,0,6.21651534109e-13
ring,80,linear,1,-1,20,-0.75,-0.75,-0.16688300956,-1.77842293235e-12,0,0,0,-1.77842293235e-12
cubic,8,square,0,1,1,0.510105487055,0.510105487052,-0.0105490577419,1.01557930122,1.01557930153,1.01563152709,1,-3.09808179111e-10
cubic,8,square,0,1,2,0.510105487055,0.510105487052,-0.0105490577419,1.01557930125,1.01557930153,1.01563152709,1,-2.84684498197e-10
cubic,8,square,0,1,3,0.510105487055,0.510105487052,-0.0105490577419,1.01557930123,1.01557930153,1.01563152709,1,-3.08854719577e-10
cubic,8,square,0,-1,1,-0.510105487055,-0.510105487052,-0.0110104550009,1.01568455663,1.0156845563,1.01563152709,1,3.2444114062e-10
cubic,8,square,0,-1,2,-0.510105487055,-0.510105487052,-0.0110104550009,1.0156845566,1.0156845563,1.01563152709,1,2.99460234388e-10
cubic,8,square,0,-1,3,-0.510105487055,-0.510105487052,-0.0110104550009,1.01568455663,1.0156845563,1.01563152709,1,3.24628324222e-10
cubic,8,square,1,1,1,0.765158230581,0.765158230577,-0.0234893181268,1.01555348238,1.01555348254,1.01563152709,1,-1.59666502242e-10
cubic,8,square,1,1,2,0.765158230581,0.765158230577,-0.0234893181268,1.01555348238,1.01555348254,1.01563152709,1,-1.56310520083e-10
cubic,8,square,1,1,3,0.765158230581,0.765158230577,-0.0234893181268,1.01555348235,1.01555348254,1.01563152709,1,-1.87907023275e-10
cubic,8,square,1,-1,1,-0.765158230581,-0.765158230577,-0.0250474295282,1.0157113803,1.01571138014,1.01563152709,1,1.6205614628e-10
cubic,8,square,1,-1,2,-0.765158230581,-0.765158230577,-0.0250474295282,1.0157113803,1.01571138014,1.01563152709,1,1.58517865501e-10
cubic,8,square,1,-1,3,-0.765158230581,-0.765158230577,-0.0250474295282,1.01571138033,1.01571138014,1.01563152709,1,1.90439219949e-10
cubic,8,generic,0,1,1,0.516842478419,0.516842478419,-0.0104883378408,1.7010973828,1.70109738272,1.70149717469,1.66666666667,8.31605895257e-11
cubic,8,generic,0,1,2,0.516842478419,0.516842478419,-0.0104883378408,1.70109738281,1.70109738272,1.70149717469,1.66666666667,9.68722879691e-11
cubic,8,generic,0,1,3,0.516842478419,0.516842478419,-0.0104883378408,1.70109738281,1.70109738272,1.70149717469,1.66666666667,9.06954511493e-11
cubic,8,generic,0,-1,1,-0.516842478419,-0.516842478419,-0.0112608041566,1.70190739814,1.7019073982,1.70149717469,1.66666666667,-6.50470788344e-11
cubic,8,generic,0,-1,2,-0.516842478419,-0.516842478419,-0.0112608041566,1.70190739812,1.7019073982,1.70149717469,1.66666666667,-7.85329579145e-11
cubic,8,generic,0,-1,3,-0.516842478419,-0.516842478419,-0.0112608041566,1.70190739813,1.7019073982,1.70149717469,1.66666666667,-7.25439708305e-11
cubic,8,generic,1,1,1,0.775263717636,0.775263717629,-0.0232010255271,1.70090123491,1.70090123539,1.70149717469,1.66666666667,-4.82060391604e-10
cubic,8,generic,1,1,2,0.775263717636,0.775263717629,-0.0232010255271,1.70090123491,1.70090123539,1.70149717469,1.66666666667,-4.80391726398e-10
cubic,8,generic,1,1,3,0.775263717636,0.775263717629,-0.0232010255271,1.70090123491,1.70090123539,1.70149717469,1.66666666667,-4.81626072357e-10
cubic,8,generic,1,-1,1,-0.775263717636,-0.775263717629,-0.0258122628641,1.70211659558,1.70211659509,1.70149717469,1.66666666667,4.85283369045e-10
cubic,8,generic,1,-1,2,-0.775263717636,-0.775263717629,-0.0258122628641,1.70211659557,1.70211659509,1.70149717469,1.66666666667,4.83718398669e-10
cubic,8,generic,1,-1,3,-0.775263717636,-0.775263717629,-0.0258122628641,1.70211659558,1.70211659509,1.70149717469,1.66666666667,4.84490225716e-10
cubic,8,linear,0,1,1,0.5,0.5,-0.0107264462812,-1.29646474273e-11,0,0,0,-1.29646474273e-11
cubic,8,linear,0,1,2,0.5,0.5,-0.0107264462812,-1.7946846594e-11,0,0,0,-1.7946846594e-11
cubic,8,linear,0,1,3,0.5,0.5,-0.0107264462812,-1.72441450027e-11,0,0,0,-1.72441450027e-11
cubic,8,linear,0,-1,1,-0.5,-0.5,-0.0107264462821,1.29646474262e-11,0,0,0,1.29646474262e-11
cubic,8,linear,0,-1,2,-0.5,-0.5,-0.0107264462821,1.79468465924e-11,0,0,0,1.79468465924e-11
cubic,8,linear,0,-1,3,-0.5,-0.5,-0.0107264462821,1.72441450012e-11,0,0,0,1.72441450012e-11
cubic,8,linear,1,1,1,0.750000000007,0.75,-0.0241345041406,-2.81645788848e-12,0,0,0,-2.81645788848e-12
cubic,8,linear,1,1,2,0.750000000007,0.75,-0.0241345041406,-1.08755602257e-11,0,0,0,-1.08755602257e-11
cubic,8,linear,1,1,3,0.750000000007,0.75,-0.0241345041406,-4.21992499369e-11,0,0,0,-4.21992499369e-11
cubic,8,linear,1,-1,1,-0.750000000007,-0.75,-0.0241345041268,2.81645789009e-12,0,0,0,2.81645789009e-12
cubic,8,linear,1,-1,2,-0.750000000007,-0.75,-0.0241345041268,1.0875560232e-11,0,0,0,1.0875560232e-11
cubic,8,linear,1,-1,3,-0.750000000007,-0.75,-0.0241345041268,4.2199249961e-11,0,0,0,4.2199249961e-11
cubic,12,square,0,1,1,0.510073598408,0.510073598419,-0.0101701801808,1.01540702315,1.01540702218,1.01545751295,1,9.77886660536e-10
cubic,12,square,0,1,3,0.510073598408,0.510073598419,-0.0101701801808,1.01540702309,1.01540702218,1.01545751295,1,9.1485263809e-10
cubic,12,square,0,1,5,0.510073598408,0.510073598419,-0.0101701801808,1.01540702303,1.01540702218,1.01545751295,1,8.49205594733e-10
cubic,12,square,0,-1,1,-0.510073598408,-0.510073598419,-0.0105983046066,1.01550876154,1.01550876264,1.01545751295,1,-1.09597175779e-09
cubic,12,square,0,-1,3,-0.510073598408,-0.510073598419,-0.0105983046066,1.01550876161,1.01550876264,1.01545751295,1,-1.03271458052e-09
cubic,12,square,0,-1,5,-0.510073598408,-0.510073598419,-0.0105983046066,1.01550876167,1.01550876264,1.01545751295,1,-9.66339452901e-10
cubic,12,square,1,1,1,0.765110397629,0.765110397628,-0.022654141957,1.01538205434,1.01538205438,1.01545751295,1,-3.8357539367e-11
cubic,12,square,1,1,3,0.765110397629,0.765110397628,-0.022654141957,1.01538205434,1.01538205438,1.01545751295,1,-3.93685084532e-11
cubic,12,square,1,1,5,0.765110397629,0.765110397628,-0.022654141957,1.01538205435,1.01538205438,1.01545751295,1,-2.94826385527e-11
cubic,12,square,1,-1,1,-0.765110397629,-0.765110397628,-0.0240998328086,1.01553467935,1.01553467932,1.01545751295,1,2.90227841759e-11
cubic,12,square,1,-1,3,-0.765110397629,-0.765110397628,-0.0240998328086,1.01553467935,1.01553467932,1.01545751295,1,3.04687386432e-11
cubic,12,square,1,-1,5,-0.765110397629,-0.765110397628,-0.0240998328086,1.01553467934,1.01553467932,1.01545751295,1,2.02398098281e-11
cubic,12,generic,0,1,1,0.51678933072,0.516789330698,-0.0101185442659,1.70042566404,1.70042566774,1.70081206232,1.66666666667,-3.70420494278e-09
cubic,12,generic,0,1,3,0.51678933072,0.516789330698,-0.0101185442659,1.7004256641,1.70042566774,1.70081206232,1.66666666667,-3.64538421671e-09
cubic,12,generic,0,1,5,0.51678933072,0.516789330698,-0.0101185442659,1.70042566414,1.70042566774,1.70081206232,1.66666666667,-3.60949981015e-09
cubic,12,generic,0,-1,1,-0.51678933072,-0.516789330698,-0.0108353898031,1.70120830568,1.70120830209,1.70081206232,1.66666666667,3.58803187162e-09
cubic,12,generic,0,-1,3,-0.51678933072,-0.516789330698,-0.0108353898031,1.70120830562,1.70120830209,1.70081206232,1.66666666667,3.52887119526e-09
cubic,12,generic,0,-1,5,-0.51678933072,-0.516789330698,-0.0108353898031,1.70120830558,1.70120830209,1.70081206232,1.66666666667,3.49371065411e-09
cubic,12,generic,1,1,1,0.775183996094,0.775183996047,-0.0223964339983,1.70023600847,1.70023601197,1.70081206232,1.66666666667,-3.50453110975e-09
cubic,12,generic,1,1,3,0.775183996094,0.775183996047,-0.0223964339983,1.70023600845,1.70023601197,1.70081206232,1.66666666667,-3.51791507036e-09
cubic,12,generic,1,1,5,0.775183996094,0.775183996047,-0.0223964339983,1.70023600839,1.70023601197,1.70081206232,1.66666666667,-3.57953533481e-09
cubic,12,generic,1,-1,1,-0.775183996094,-0.775183996047,-0.0248193715967,1.70141027678,1.70141027347,1.70081206232,1.66666666667,3.30496496836e-09
cubic,12,generic,1,-1,3,-0.775183996094,-0.775183996047,-0.0248193715967,1.70141027679,1.70141027347,1.70081206232,1.66666666667,3.3182550041e-09
cubic,12,generic,1,-1,5,-0.775183996094,-0.775183996047,-0.0248193715967,1.70141027685,1.70141027347,1.70081206232,1.66666666667,3.37941985507e-09
cubic,12,linear,0,1,1,0.500000000011,0.5,-0.010332106101,1.35995599407e-11,0,0,0,1.35995599407e-11
cubic,12,linear,0,1,3,0.500000000011,0.5,-0.010332106101,2.92590715862e-11,0,0,0,2.92590715862e-11
cubic,12,linear,0,1,5,0.500000000011,0.5,-0.010332106101,9.13594738511e-11,0,0,0,9.13594738511e-11
cubic,12,linear,0,-1,1,-0.500000000011,-0.5,-0.0103321060792,-1.35995599695e-11,0,0,0,-1.35995599695e-11
cubic,12,linear,0,-1,3,-0.500000000011,-0.5,-0.0103321060792,-2.92590716481e-11,0,0,0,-2.92590716481e-11
cubic,12,linear,0,-1,5,-0.500000000011,-0.5,-0.0103321060792,-9.13594740441e-11,0,0,0,-9.13594740441e-11
cubic,12,linear,1,1,1,0.750000000024,0.75,-0.0232472387259,-1.00659868133e-12,0,0,0,-1.00659868133e-12
cubic,12,linear,1,1,3,0.750000000024,0.75,-0.0232472387259,9.39286788556e-12,0,0,0,9.39286788556e-12
cubic,12,linear,1,1,5,0.750000000024,0.75,-0.0232472387259,-5.91037158617e-11,0,0,0,-5.91037158617e-11
cubic,12,linear,1,-1,1,-0.750000000024,-0.75,-0.023247238678,1.0065986834e-12,0,0,0,1.0065986834e-12
cubic,12,linear,1,-1,3,-0.750000000024,-0.75,-0.023247238678,-9.39286790492e-12,0,0,0,-9.39286790492e-12
cubic,12,linear,1,-1,5,-0.750000000024,-0.75,-0.023247238678,5.91037159835e-11,0,0,0,5.91037159835e-11

{
 "parameters": {
  "kappa_h": 1.0,
  "m_h": 0.3,
  "M_levels": {
   "0": 0.5,
   "1": 0.75
  },
  "grips": {
   "square": [
    1.0,
    0.6,
    0.09
   ],
   "generic": [
    1.0,
    0.6,
    0.15
   ],
   "linear": [
    1.0,
    0.6,
    0.0
   ]
  }
 },
 "graphs": [
  {
   "graph": "ring",
   "L": 40,
   "N": 40,
   "G0": 1.6482484317631325,
   "w0": 0.5205517595233952,
   "J2_0": 0.1774302269608021,
   "J2_over_G0": 0.10764774504957657,
   "ell": 3.3333333333333335
  },
  {
   "graph": "ring",
   "L": 80,
   "N": 80,
   "G0": 1.6482272549165387,
   "w0": 0.5205510313875381,
   "J2_0": 0.17742907231156824,
   "J2_over_G0": 0.10764842759535166,
   "ell": 3.3333333333333335
  },
  {
   "graph": "cubic",
   "L": 8,
   "N": 512,
   "G0": 0.2383654729250418,
   "w0": 0.22456637892382791,
   "J2_0": 0.011942017505383932,
   "J2_over_G0": 0.05009961115106343,
   "ell": 3.3333333333333335
  },
  {
   "graph": "cubic",
   "L": 12,
   "N": 1728,
   "G0": 0.22960235754516248,
   "w0": 0.22385774263575145,
   "J2_0": 0.01178190850229115,
   "J2_over_G0": 0.051314405602188404,
   "ell": 3.3333333333333335
  }
 ],
 "max_abs_C1_minus_formula": 3.4289604489146086e-10,
 "max_abs_rho_mark_num_minus_exact": 3.704204942778233e-09,
 "max_abs_bond_U_minus_formula": 1.173335842548362e-12,
 "max_abs_rho_bond_num_minus_exact": 1.913108560458454e-09,
 "max_abs_rho_bond_num_minus_mu2": 0.1063006483652984,
 "rho_mark_square_by_level": {
  "ring40 k=0 s=1": 1.0360501895749457,
  "ring40 k=0 s=-1": 1.0376419108708703,
  "ring40 k=1 s=1": 1.035698943567965,
  "ring40 k=1 s=-1": 1.0380977413541779,
  "ring80 k=0 s=1": 1.0360500700805226,
  "ring80 k=0 s=-1": 1.0376417726813787,
  "ring80 k=1 s=1": 1.035698827815264,
  "ring80 k=1 s=-1": 1.0380975972166337,
  "cubic8 k=0 s=1": 1.0155793012249723,
  "cubic8 k=0 s=-1": 1.0156845566259873,
  "cubic8 k=1 s=1": 1.0155534823810877,
  "cubic8 k=1 s=-1": 1.015711380304419,
  "cubic12 k=0 s=1": 1.0154070231541465,
  "cubic12 k=0 s=-1": 1.0155087615439349,
  "cubic12 k=1 s=1": 1.0153820543415208,
  "cubic12 k=1 s=-1": 1.0155346793487507
 },
 "rho_mark_generic_by_level": {
  "ring40 k=0 s=1": 1.744107103454471,
  "ring40 k=0 s=-1": 1.756421485320555,
  "ring40 k=1 s=1": 1.7416110321669154,
  "ring40 k=1 s=-1": 1.7603433879717885,
  "ring80 k=0 s=1": 1.744106698436927,
  "ring80 k=0 s=-1": 1.7564209309114982,
  "ring80 k=1 s=1": 1.7416106528828887,
  "ring80 k=1 s=-1": 1.7603427761910968,
  "cubic8 k=0 s=1": 1.7010973827998532,
  "cubic8 k=0 s=-1": 1.7019073981351815,
  "cubic8 k=1 s=1": 1.7009012349119788,
  "cubic8 k=1 s=-1": 1.7021165955759672,
  "cubic12 k=0 s=1": 1.7004256640403947,
  "cubic12 k=0 s=-1": 1.7012083056774314,
  "cubic12 k=1 s=1": 1.7002360084666222,
  "cubic12 k=1 s=-1": 1.7014102767792856
 },
 "square_deviation_prediction": {
  "ring40": 0.03716136130264367,
  "ring80": 0.03716123434129678,
  "cubic8": 0.015702009099548803,
  "cubic12": 0.015528900333020675
 },
 "square_bond_deviation": {
  "ring40 r=2 d=4": {
   "rho_over_mf_minus_1": 0.0430309877476569,
   "prediction_2_19": 0.04357850428413369
  },
  "ring40 r=2 d=8": {
   "rho_over_mf_minus_1": 0.04303098774773417,
   "prediction_2_19": 0.04357850428413369
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  "ring40 r=2 d=12": {
   "rho_over_mf_minus_1": 0.0430309877485735,
   "prediction_2_19": 0.04357850428413369
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  "ring40 r=4 d=4": {
   "rho_over_mf_minus_1": 0.045238486472983785,
   "prediction_2_19": 0.04541032694913632
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  "ring40 r=4 d=8": {
   "rho_over_mf_minus_1": 0.04523848647287387,
   "prediction_2_19": 0.04541032694913632
  },
  "ring40 r=4 d=12": {
   "rho_over_mf_minus_1": 0.04523848647341966,
   "prediction_2_19": 0.04541032694913632
  },
  "ring80 r=2 d=4": {
   "rho_over_mf_minus_1": 0.04303091512566981,
   "prediction_2_19": 0.04357842219210909
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  "ring80 r=2 d=8": {
   "rho_over_mf_minus_1": 0.04303091512554458,
   "prediction_2_19": 0.04357842219210909
  },
  "ring80 r=2 d=12": {
   "rho_over_mf_minus_1": 0.04303091512576618,
   "prediction_2_19": 0.04357842219210909
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  "ring80 r=4 d=4": {
   "rho_over_mf_minus_1": 0.045238429068053865,
   "prediction_2_19": 0.045410264123918125
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  "ring80 r=4 d=8": {
   "rho_over_mf_minus_1": 0.04523842906776765,
   "prediction_2_19": 0.045410264123918125
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  "ring80 r=4 d=12": {
   "rho_over_mf_minus_1": 0.045238429067910424,
   "prediction_2_19": 0.045410264123918125
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  "cubic8 r=2 d=1": {
   "rho_over_mf_minus_1": 0.020035067436624088,
   "prediction_2_19": 0.020039586456697164
  },
  "cubic8 r=2 d=2": {
   "rho_over_mf_minus_1": 0.02003506743331296,
   "prediction_2_19": 0.020039586456697164
  },
  "cubic8 r=2 d=3": {
   "rho_over_mf_minus_1": 0.02003506743367156,
   "prediction_2_19": 0.020039586456697164
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  "cubic8 r=4 d=1": {
   "rho_over_mf_minus_1": 0.020142894861607807,
   "prediction_2_19": 0.02014445857679201
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  "cubic8 r=4 d=2": {
   "rho_over_mf_minus_1": 0.020142894862893446,
   "prediction_2_19": 0.02014445857679201
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  "cubic8 r=4 d=3": {
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   "prediction_2_19": 0.02014445857679201
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  "cubic12 r=2 d=1": {
   "rho_over_mf_minus_1": 0.019980423814522252,
   "prediction_2_19": 0.019984545280138433
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  "cubic12 r=2 d=3": {
   "rho_over_mf_minus_1": 0.019980423817904214,
   "prediction_2_19": 0.019984545280138433
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  "cubic12 r=2 d=5": {
   "rho_over_mf_minus_1": 0.01998042382347931,
   "prediction_2_19": 0.019984545280138433
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  "cubic12 r=4 d=1": {
   "rho_over_mf_minus_1": 0.020117380503231308,
   "prediction_2_19": 0.02011802254115932
  },
  "cubic12 r=4 d=3": {
   "rho_over_mf_minus_1": 0.020117380495751513,
   "prediction_2_19": 0.02011802254115932
  },
  "cubic12 r=4 d=5": {
   "rho_over_mf_minus_1": 0.02011738047203515,
   "prediction_2_19": 0.02011802254115932
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 },
 "max_abs_rho_linear": 1.342489090096755e-10,
 "max_distance_spread_rho_mark": 1.3412305270930614e-10,
 "runtime_s": 342.85846519470215
}