###############################################################################
# This file is part of SWIFT.
# Copyright (c) 2015 Bert Vandenbroucke (bert.vandenbroucke@ugent.be)
#                    Matthieu Schaller (schaller@strw.leidenuniv.nl)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################

# Computes the analytical solution of the 3D Sedov blast wave.
# The script works for a given initial box and dumped energy and computes the solution at a later time t.

# Parameters
rho_0 = 1.0  # Background Density
P_0 = 1.0e-6  # Background Pressure
E_0 = 1.0  # Energy of the explosion
gas_gamma = 5.0 / 3.0  # Gas polytropic index


# ---------------------------------------------------------------
# Don't touch anything after this.
# ---------------------------------------------------------------

import matplotlib

matplotlib.use("Agg")
from pylab import *
from numpy import power
from scipy import stats
import h5py

style.use("../../../tools/stylesheets/mnras.mplstyle")

snap = int(sys.argv[1])

# Read the simulation data
sim = h5py.File("sedov_%04d.hdf5" % snap, "r")
boxSize = sim["/Header"].attrs["BoxSize"][0]
time = sim["/Header"].attrs["Time"][0]
scheme = sim["/HydroScheme"].attrs["Scheme"]
kernel = sim["/HydroScheme"].attrs["Kernel function"]
neighbours = sim["/HydroScheme"].attrs["Kernel target N_ngb"]
eta = sim["/HydroScheme"].attrs["Kernel eta"]
git = sim["Code"].attrs["Git Revision"]

pos = sim["/PartType0/Coordinates"][:, :]
x = pos[:, 0] - boxSize / 2
y = pos[:, 1] - boxSize / 2
z = pos[:, 2] - boxSize / 2
vel = sim["/PartType0/Velocities"][:, :]
r = sqrt(x ** 2 + y ** 2 + z ** 2)
v_r = (x * vel[:, 0] + y * vel[:, 1] + z * vel[:, 2]) / r
u = sim["/PartType0/InternalEnergies"][:]
S = sim["/PartType0/Entropies"][:]
P = sim["/PartType0/Pressures"][:]
rho = sim["/PartType0/Densities"][:]

try:
    diffusion = sim["/PartType0/DiffusionParameters"][:]
    plot_diffusion = True
except:
    plot_diffusion = False

try:
    viscosity = sim["/PartType0/ViscosityParameters"][:]
    plot_viscosity = True
except:
    plot_viscosity = False

# Bin the data
r_bin_edge = np.arange(0.0, 0.5, 0.01)
r_bin = 0.5 * (r_bin_edge[1:] + r_bin_edge[:-1])
rho_bin, _, _ = stats.binned_statistic(r, rho, statistic="mean", bins=r_bin_edge)
v_bin, _, _ = stats.binned_statistic(r, v_r, statistic="mean", bins=r_bin_edge)
P_bin, _, _ = stats.binned_statistic(r, P, statistic="mean", bins=r_bin_edge)
S_bin, _, _ = stats.binned_statistic(r, S, statistic="mean", bins=r_bin_edge)
u_bin, _, _ = stats.binned_statistic(r, u, statistic="mean", bins=r_bin_edge)
rho2_bin, _, _ = stats.binned_statistic(r, rho ** 2, statistic="mean", bins=r_bin_edge)
v2_bin, _, _ = stats.binned_statistic(r, v_r ** 2, statistic="mean", bins=r_bin_edge)
P2_bin, _, _ = stats.binned_statistic(r, P ** 2, statistic="mean", bins=r_bin_edge)
S2_bin, _, _ = stats.binned_statistic(r, S ** 2, statistic="mean", bins=r_bin_edge)
u2_bin, _, _ = stats.binned_statistic(r, u ** 2, statistic="mean", bins=r_bin_edge)
rho_sigma_bin = np.sqrt(rho2_bin - rho_bin ** 2)
v_sigma_bin = np.sqrt(v2_bin - v_bin ** 2)
P_sigma_bin = np.sqrt(P2_bin - P_bin ** 2)
S_sigma_bin = np.sqrt(S2_bin - S_bin ** 2)
u_sigma_bin = np.sqrt(u2_bin - u_bin ** 2)

if plot_diffusion:
    alpha_diff_bin, _, _ = stats.binned_statistic(
        r, diffusion, statistic="mean", bins=r_bin_edge
    )
    alpha2_diff_bin, _, _ = stats.binned_statistic(
        r, diffusion ** 2, statistic="mean", bins=r_bin_edge
    )
    alpha_diff_sigma_bin = np.sqrt(alpha2_diff_bin - alpha_diff_bin ** 2)

if plot_viscosity:
    alpha_visc_bin, _, _ = stats.binned_statistic(
        r, viscosity, statistic="mean", bins=r_bin_edge
    )
    alpha2_visc_bin, _, _ = stats.binned_statistic(
        r, viscosity ** 2, statistic="mean", bins=r_bin_edge
    )
    alpha_visc_sigma_bin = np.sqrt(alpha2_visc_bin - alpha_visc_bin ** 2)


# Now, work our the solution....

from scipy.special import gamma as Gamma


def calc_a(g, nu=3):
    """ 
    exponents of the polynomials of the sedov solution
    g - the polytropic gamma
    nu - the dimension
    """
    a = [0] * 8

    a[0] = 2.0 / (nu + 2)
    a[2] = (1 - g) / (2 * (g - 1) + nu)
    a[3] = nu / (2 * (g - 1) + nu)
    a[5] = 2 / (g - 2)
    a[6] = g / (2 * (g - 1) + nu)

    a[1] = (((nu + 2) * g) / (2.0 + nu * (g - 1.0))) * (
        (2.0 * nu * (2.0 - g)) / (g * (nu + 2.0) ** 2) - a[2]
    )
    a[4] = a[1] * (nu + 2) / (2 - g)
    a[7] = (2 + nu * (g - 1)) * a[1] / (nu * (2 - g))
    return a


def calc_beta(v, g, nu=3):
    """ 
    beta values for the sedov solution (coefficients of the polynomials of the similarity variables) 
    v - the similarity variable
    g - the polytropic gamma
    nu- the dimension
    """

    beta = (
        (nu + 2)
        * (g + 1)
        * array(
            (
                0.25,
                (g / (g - 1)) * 0.5,
                -(2 + nu * (g - 1))
                / 2.0
                / ((nu + 2) * (g + 1) - 2 * (2 + nu * (g - 1))),
                -0.5 / (g - 1),
            ),
            dtype=float64,
        )
    )

    beta = outer(beta, v)

    beta += (g + 1) * array(
        (
            0.0,
            -1.0 / (g - 1),
            (nu + 2) / ((nu + 2) * (g + 1) - 2.0 * (2 + nu * (g - 1))),
            1.0 / (g - 1),
        ),
        dtype=float64,
    ).reshape((4, 1))

    return beta


def sedov(t, E0, rho0, g, n=1000, nu=3):
    """ 
    solve the sedov problem
    t - the time
    E0 - the initial energy
    rho0 - the initial density
    n - number of points (10000)
    nu - the dimension
    g - the polytropic gas gamma
    """
    # the similarity variable
    v_min = 2.0 / ((nu + 2) * g)
    v_max = 4.0 / ((nu + 2) * (g + 1))

    v = v_min + arange(n) * (v_max - v_min) / (n - 1.0)

    a = calc_a(g, nu)
    beta = calc_beta(v, g=g, nu=nu)
    lbeta = log(beta)

    r = exp(-a[0] * lbeta[0] - a[2] * lbeta[1] - a[1] * lbeta[2])
    rho = ((g + 1.0) / (g - 1.0)) * exp(
        a[3] * lbeta[1] + a[5] * lbeta[3] + a[4] * lbeta[2]
    )
    p = exp(nu * a[0] * lbeta[0] + (a[5] + 1) * lbeta[3] + (a[4] - 2 * a[1]) * lbeta[2])
    u = beta[0] * r * 4.0 / ((g + 1) * (nu + 2))
    p *= 8.0 / ((g + 1) * (nu + 2) * (nu + 2))

    # we have to take extra care at v=v_min, since this can be a special point.
    # It is not a singularity, however, the gradients of our variables (wrt v) are.
    # r -> 0, u -> 0, rho -> 0, p-> constant

    u[0] = 0.0
    rho[0] = 0.0
    r[0] = 0.0
    p[0] = p[1]

    # volume of an n-sphere
    vol = (pi ** (nu / 2.0) / Gamma(nu / 2.0 + 1)) * power(r, nu)

    # note we choose to evaluate the integral in this way because the
    # volumes of the first few elements (i.e near v=vmin) are shrinking
    # very slowly, so we dramatically improve the error convergence by
    # finding the volumes exactly. This is most important for the
    # pressure integral, as this is on the order of the volume.

    # (dimensionless) energy of the model solution
    de = rho * u * u * 0.5 + p / (g - 1)
    # integrate (trapezium rule)
    q = inner(de[1:] + de[:-1], diff(vol)) * 0.5

    # the factor to convert to this particular problem
    fac = (q * (t ** nu) * rho0 / E0) ** (-1.0 / (nu + 2))

    # shock speed
    shock_speed = fac * (2.0 / (nu + 2))
    rho_s = ((g + 1) / (g - 1)) * rho0
    r_s = shock_speed * t * (nu + 2) / 2.0
    p_s = (2.0 * rho0 * shock_speed * shock_speed) / (g + 1)
    u_s = (2.0 * shock_speed) / (g + 1)

    r *= fac * t
    u *= fac
    p *= fac * fac * rho0
    rho *= rho0
    return r, p, rho, u, r_s, p_s, rho_s, u_s, shock_speed


# The main properties of the solution
r_s, P_s, rho_s, v_s, r_shock, _, _, _, _ = sedov(time, E_0, rho_0, gas_gamma, 1000, 3)

# Append points for after the shock
r_s = np.insert(r_s, np.size(r_s), [r_shock, r_shock * 1.5])
rho_s = np.insert(rho_s, np.size(rho_s), [rho_0, rho_0])
P_s = np.insert(P_s, np.size(P_s), [P_0, P_0])
v_s = np.insert(v_s, np.size(v_s), [0, 0])

# Additional arrays
u_s = P_s / (rho_s * (gas_gamma - 1.0))  # internal energy
s_s = P_s / rho_s ** gas_gamma  # entropic function


# Plot the interesting quantities
figure(figsize=(7, 7 / 1.6))

line_color = "C4"
binned_color = "C2"
binned_marker_size = 4

scatter_props = dict(
    marker=".",
    ms=1,
    markeredgecolor="none",
    alpha=0.2,
    zorder=-1,
    rasterized=True,
    linestyle="none",
)

errorbar_props = dict(color=binned_color, ms=binned_marker_size, fmt=".", lw=1.2)

# Velocity profile --------------------------------
subplot(231)
plot(r, v_r, **scatter_props)
plot(r_s, v_s, "--", color=line_color, alpha=0.8, lw=1.2)
errorbar(r_bin, v_bin, yerr=v_sigma_bin, **errorbar_props)
xlabel("Radius $r$")
ylabel("Radialvelocity $v_r$")
xlim(0, 1.3 * r_shock)
ylim(-0.2, 3.8)

# Density profile --------------------------------
subplot(232)
plot(r, rho, **scatter_props)
plot(r_s, rho_s, "--", color=line_color, alpha=0.8, lw=1.2)
errorbar(r_bin, rho_bin, yerr=rho_sigma_bin, **errorbar_props)
xlabel("Radius $r$")
ylabel("Density $\\rho$")
xlim(0, 1.3 * r_shock)
ylim(-0.2, 5.2)

# Pressure profile --------------------------------
subplot(233)
plot(r, P, **scatter_props)
plot(r_s, P_s, "--", color=line_color, alpha=0.8, lw=1.2)
errorbar(r_bin, P_bin, yerr=P_sigma_bin, **errorbar_props)
xlabel("Radius $r$")
ylabel("Pressure $P$")
xlim(0, 1.3 * r_shock)
ylim(-1, 12.5)

# Internal energy profile -------------------------
subplot(234)
plot(r, u, **scatter_props)
plot(r_s, u_s, "--", color=line_color, alpha=0.8, lw=1.2)
errorbar(r_bin, u_bin, yerr=u_sigma_bin, **errorbar_props)
xlabel("Radius $r$")
ylabel("Internal Energy $u$")
xlim(0, 1.3 * r_shock)
ylim(-2, 22)

# Entropy profile ---------------------------------
subplot(235)
xlabel("Radius $r$")
if plot_diffusion or plot_viscosity:
    if plot_diffusion:
        plot(r, diffusion, **scatter_props)
        errorbar(
            r_bin,
            alpha_diff_bin,
            yerr=alpha_diff_sigma_bin,
            **errorbar_props,
            label="Diffusion",
        )

    if plot_viscosity:
        plot(r, viscosity, **scatter_props)
        errorbar(
            r_bin,
            alpha_visc_bin,
            yerr=alpha_visc_sigma_bin,
            label="Viscosity",
            color="C4",
            ms=binned_marker_size,
            fmt=".",
            lw=1.2,
        )

    ylabel(r"Rate Coefficient $\alpha$", labelpad=0)
    legend()
else:
    plot(r, S, **scatter_props)
    plot(r_s, s_s, "--", color=line_color, alpha=0.8, lw=1.2)
    errorbar(r_bin, S_bin, yerr=S_sigma_bin, **errorbar_props)
    ylabel("Entropy $S$", labelpad=0)
    ylim(-5, 50)

xlim(0, 1.3 * r_shock)
# Information -------------------------------------
subplot(236, frameon=False)

text_fontsize = 5

text(
    -0.45,
    0.9,
    "Sedov blast with  $\\gamma=%.3f$ in 3D at $t=%.2f$" % (gas_gamma, time),
    fontsize=text_fontsize,
)
text(-0.45, 0.8, "Background $\\rho_0=%.2f$" % (rho_0), fontsize=text_fontsize)
text(-0.45, 0.7, "Energy injected $E_0=%.2f$" % (E_0), fontsize=text_fontsize)
plot([-0.45, 0.1], [0.62, 0.62], "k-", lw=1)
text(-0.45, 0.5, "SWIFT %s" % git.decode("utf-8"), fontsize=text_fontsize)
text(-0.45, 0.4, scheme.decode("utf-8"), fontsize=text_fontsize)
text(-0.45, 0.3, kernel.decode("utf-8"), fontsize=text_fontsize)
text(
    -0.45,
    0.2,
    "$%.2f$ neighbours ($\\eta=%.3f$)" % (neighbours, eta),
    fontsize=text_fontsize,
)
xlim(-0.5, 0.5)
ylim(0, 1)
xticks([])
yticks([])

tight_layout()

savefig("Sedov.png")