#!/usr/bin/env python3

# Copyright 2019 Jean-Luc Vay, Maxence Thevenet, Remi Lehe
#
#
# This file is part of WarpX.
#
# License: BSD-3-Clause-LBNL
#
# This is a script that analyses the simulation results from
# the script `inputs.multi.rt`. This simulates a 3D periodic plasma wave.
# The electric field in the simulation is given (in theory) by:
# $$ E_x = \epsilon \,\frac{m_e c^2 k_x}{q_e}\sin(k_x x)\cos(k_y y)\cos(k_z z)\sin( \omega_p t)$$
# $$ E_y = \epsilon \,\frac{m_e c^2 k_y}{q_e}\cos(k_x x)\sin(k_y y)\cos(k_z z)\sin( \omega_p t)$$
# $$ E_z = \epsilon \,\frac{m_e c^2 k_z}{q_e}\cos(k_x x)\cos(k_y y)\sin(k_z z)\sin( \omega_p t)$$
import os
import re
import sys

import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1.axes_divider import make_axes_locatable
import yt

yt.funcs.mylog.setLevel(50)

import numpy as np
from scipy.constants import c, e, epsilon_0, m_e

sys.path.insert(1, '../../../../warpx/Regression/Checksum/')
import checksumAPI

# this will be the name of the plot file
fn = sys.argv[1]

# Parse test name and check if current correction (psatd.current_correction=1) is applied
current_correction = True if re.search( 'current_correction', fn ) else False

# Parse test name and check if Vay current deposition (algo.current_deposition=vay) is used
vay_deposition = True if re.search( 'Vay_deposition', fn ) else False

# Parameters (these parameters must match the parameters in `inputs.multi.rt`)
epsilon = 0.01
n = 4.e24
n_osc_x = 2
n_osc_z = 2
xmin = -20e-6; xmax = 20.e-6; Nx = 128
zmin = -20e-6; zmax = 20.e-6; Nz = 128

# Wave vector of the wave
kx = 2.*np.pi*n_osc_x/(xmax-xmin)
kz = 2.*np.pi*n_osc_z/(zmax-zmin)
# Plasma frequency
wp = np.sqrt((n*e**2)/(m_e*epsilon_0))

k = {'Ex':kx, 'Ez':kz}
cos = {'Ex': (0,1,1), 'Ez':(1,1,0)}

def get_contribution( is_cos, k ):
    du = (xmax-xmin)/Nx
    u = xmin + du*( 0.5 + np.arange(Nx) )
    if is_cos == 1:
        return( np.cos(k*u) )
    else:
        return( np.sin(k*u) )

def get_theoretical_field( field, t ):
    amplitude = epsilon * (m_e*c**2*k[field])/e * np.sin(wp*t)
    cos_flag = cos[field]
    x_contribution = get_contribution( cos_flag[0], kx )
    z_contribution = get_contribution( cos_flag[2], kz )

    E = amplitude * x_contribution[:, np.newaxis ] \
                  * z_contribution[np.newaxis, :]

    return( E )

# Read the file
ds = yt.load(fn)
t0 = ds.current_time.to_value()
data = ds.covering_grid(level = 0, left_edge = ds.domain_left_edge, dims = ds.domain_dimensions)
edge = np.array([(ds.domain_left_edge[1]).item(), (ds.domain_right_edge[1]).item(), \
                 (ds.domain_left_edge[0]).item(), (ds.domain_right_edge[0]).item()])

# Check the validity of the fields
error_rel = 0
for field in ['Ex', 'Ez']:
    E_sim = data[('mesh',field)].to_ndarray()[:,:,0]
    E_th = get_theoretical_field(field, t0)
    max_error = abs(E_sim-E_th).max()/abs(E_th).max()
    print('%s: Max error: %.2e' %(field,max_error))
    error_rel = max( error_rel, max_error )

# Plot the last field from the loop (Ez at iteration 40)
fig, (ax1, ax2) = plt.subplots(1, 2, dpi = 100)
# First plot
vmin = E_sim.min()
vmax = E_sim.max()
cax1 = make_axes_locatable(ax1).append_axes('right', size = '5%', pad = '5%')
im1 = ax1.imshow(E_sim, origin = 'lower', extent = edge, vmin = vmin, vmax = vmax)
cb1 = fig.colorbar(im1, cax = cax1)
ax1.set_xlabel(r'$z$')
ax1.set_ylabel(r'$x$')
ax1.set_title(r'$E_z$ (sim)')
# Second plot
vmin = E_th.min()
vmax = E_th.max()
cax2 = make_axes_locatable(ax2).append_axes('right', size = '5%', pad = '5%')
im2 = ax2.imshow(E_th, origin = 'lower', extent = edge, vmin = vmin, vmax = vmax)
cb2 = fig.colorbar(im2, cax = cax2)
ax2.set_xlabel(r'$z$')
ax2.set_ylabel(r'$x$')
ax2.set_title(r'$E_z$ (theory)')
# Save figure
fig.tight_layout()
fig.savefig('Langmuir_multi_2d_analysis.png', dpi = 200)

tolerance_rel = 0.05

print("error_rel    : " + str(error_rel))
print("tolerance_rel: " + str(tolerance_rel))

assert( error_rel < tolerance_rel )

# Check relative L-infinity spatial norm of rho/epsilon_0 - div(E)
# with current correction (and periodic single box option) or with Vay current deposition
if current_correction:
    tolerance = 1e-9
elif vay_deposition:
    tolerance = 1e-3
if current_correction or vay_deposition:
    rho  = data[('boxlib','rho')].to_ndarray()
    divE = data[('boxlib','divE')].to_ndarray()
    error_rel = np.amax( np.abs( divE - rho/epsilon_0 ) ) / np.amax( np.abs( rho/epsilon_0 ) )
    print("Check charge conservation:")
    print("error_rel = {}".format(error_rel))
    print("tolerance = {}".format(tolerance))
    assert( error_rel < tolerance )

test_name = os.path.split(os.getcwd())[1]
checksumAPI.evaluate_checksum(test_name, fn)