#!/usr/bin/env python3

# Copyright 2019 Andrew Myers, Jean-Luc Vay, Maxence Thevenet
# Remi Lehe, Weiqun Zhang, Luca Fedeli
#
# This file is part of WarpX.
#
# License: BSD-3-Clause-LBNL

# This file is part of the WarpX automated test suite. Its purpose is to test the
# injection of a Gaussian laser pulse from an antenna in a 2D simulation.
# In order to avoid privileged directions, the laser is injected at
# approximately 27 degrees with respect to the x axis. Moreover the polarization axis is neither
# parallel nor perpendicular to the xz plane. Finally moving window along the
# x axis is enabled.
# The test calculates the envelope of each component of the laser pulse at the end of
# the simulation and it compares it with theory. It also checks that the
# central frequency of the Fourier transform is the expected one.

import yt
import sys
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import numpy as np
import os
from scipy.signal import hilbert
from mpl_toolkits.axes_grid1 import make_axes_locatable
sys.path.insert(1, '../../../../warpx/Regression/Checksum/')
import checksumAPI

# Maximum acceptable error for this test
relative_error_threshold = 0.05

# A small number
small_num = 1.0e-8

# Physical parameters
um = 1.e-6
fs = 1.e-15
c = 299792458

# Parameters of the gaussian beam
wavelength = 1.*um
w0 = 5.*um
tt = 10.*fs
x_c = 10.*um
t_c = 24.*fs
# foc_dist = 13.109*um (not actually used)
E_max = 4e12

# laser direction
dir_vector = np.array([2.,0,1.0])
dir_vector /= np.linalg.norm(dir_vector)

rot_angle = np.arctan(dir_vector[2]/dir_vector[0])

# polarization vector
pol_vector = np.array([1.0,1.0,-2.0])
pol_vector /= np.linalg.norm(pol_vector)

# Calculates the envelope of a Gaussian beam
def gauss_env(T,XX,ZZ):
    '''Function to compute the theory for the envelope
    '''

    Z =  np.cos(rot_angle)*(XX-x_c) + np.sin(rot_angle)*ZZ
    X = -np.sin(rot_angle)*(XX-x_c) + np.cos(rot_angle)*ZZ

    inv_tau2 = 1./tt/tt
    inv_w_2 = 1.0/(w0*w0)
    exp_arg = - (X*X)*inv_w_2 - inv_tau2 / c/c * (Z-T*c)*(Z-T*c)
    return E_max * np.real(np.exp(exp_arg))

# Checks envelope and central frequency for a given laser component
def check_component(data, component, t_env_theory, coeff, X,Z,dx,dz):
    print("*** Checking " + component + " ***")
    field = data['boxlib', component].v.squeeze()
    env = abs(hilbert(field))

    env_theory = t_env_theory*np.abs(coeff)

    # Plot results
    fig = plt.figure(figsize=(12,6))

    ax1 = fig.add_subplot(221, aspect='equal')
    ax1.set_title('PIC field')
    p1 = ax1.pcolormesh(X,Z,field)
    cax1 = make_axes_locatable(ax1).append_axes('right', size='5%', pad=0.05)
    fig.colorbar(p1, cax=cax1, orientation='vertical')

    ax2 = fig.add_subplot(222, aspect='equal')
    ax2.set_title('PIC envelope')
    p2 = ax2.pcolormesh(X,Z,env)
    cax2 = make_axes_locatable(ax2).append_axes('right', size='5%', pad=0.05)
    fig.colorbar(p2, cax=cax2, orientation='vertical')

    ax3 = fig.add_subplot(223, aspect='equal')
    ax3.set_title('Theory envelope')
    p3 = ax3.pcolormesh(X,Z,env_theory)
    cax3 = make_axes_locatable(ax3).append_axes('right', size='5%', pad=0.05)
    fig.colorbar(p3, cax=cax3, orientation='vertical')

    ax4 = fig.add_subplot(224, aspect='equal')
    ax4.set_title('Difference')
    p4 = ax4.pcolormesh(X,Z,env-env_theory)
    cax4 = make_axes_locatable(ax4).append_axes('right', size='5%', pad=0.05)
    fig.colorbar(p4, cax=cax4, orientation='vertical')

    plt.tight_layout()
    plt.savefig("plt_" + component + ".png", bbox_inches='tight')

    if(np.abs(coeff) < small_num):
        is_field_zero = np.sum(np.abs(env)) < small_num
        if is_field_zero :
            print("[OK] Field component expected to be 0 is ~ 0")
        else :
            print("[FAIL] Field component expected to be 0 is NOT ~ 0")
        assert(is_field_zero)
        print("******\n")
        return

    relative_error_env = np.sum(np.abs(env-env_theory)) / np.sum(np.abs(env_theory))
    is_env_ok = relative_error_env < relative_error_threshold
    if is_env_ok :
        print("[OK] Relative error envelope: {:6.3f} %".format(relative_error_env*100))
    else :
        print("[FAIL] Relative error envelope: {:6.3f} %".format(relative_error_env*100))
    assert(is_env_ok)

    fft_field = np.fft.fft2(field)

    freq_rows = np.fft.fftfreq(fft_field.shape[0],dx/c)
    freq_cols = np.fft.fftfreq(fft_field.shape[1],dz/c)

    pos_max = np.unravel_index(np.abs(fft_field).argmax(), fft_field.shape)

    freq = np.sqrt((freq_rows[pos_max[0]])**2 + (freq_cols[pos_max[1]]**2))
    exp_freq = c/wavelength

    relative_error_freq = np.abs(freq-exp_freq)/exp_freq
    is_freq_ok = relative_error_freq < relative_error_threshold
    if is_freq_ok :
        print("[OK] Relative error frequency: {:6.3f} %".format(relative_error_freq*100))
    else :
        print("[FAIL] Relative error frequency: {:6.3f} %".format(relative_error_freq*100))
    assert(is_freq_ok)

    print("******\n")

def check_laser(filename):
    ds = yt.load(filename)

    # yt 4.0+ has rounding issues with our domain data:
    # RuntimeError: yt attempted to read outside the boundaries
    # of a non-periodic domain along dimension 0.
    if 'force_periodicity' in dir(ds): ds.force_periodicity()

    x = np.linspace(
        ds.domain_left_edge[0].v,
        ds.domain_right_edge[0].v,
        ds.domain_dimensions[0])

    dx = (ds.domain_right_edge[0].v-ds.domain_left_edge[0].v)/(ds.domain_dimensions[0]-1)

    z = np.linspace(
        ds.domain_left_edge[1].v,
        ds.domain_right_edge[1].v,
        ds.domain_dimensions[1])

    dz = (ds.domain_right_edge[1].v-ds.domain_left_edge[1].v)/(ds.domain_dimensions[1]-1)

    X, Z = np.meshgrid(x, z, indexing='ij')

    # Compute the theory for envelope
    env_theory = gauss_env(+t_c-ds.current_time.to_value(),X,Z)+gauss_env(-t_c+ds.current_time.to_value(),X,Z)

    # Read laser field in PIC simulation, and compute envelope
    all_data_level_0 = ds.covering_grid(level=0, left_edge=ds.domain_left_edge, dims=ds.domain_dimensions)

    b_vector = np.cross(dir_vector, pol_vector)

    components = ["Ex", "Ey", "Ez", "Bx", "By", "Bz"]
    coeffs = [
        pol_vector[0],
        pol_vector[1],
        pol_vector[2],
        b_vector[0],
        b_vector[1],
        b_vector[2]]

    field_facts = [1, 1, 1, 1/c, 1/c, 1/c]

    for comp, coeff, field_fact in zip(components, coeffs, field_facts):
        check_component(all_data_level_0, comp, field_fact*env_theory, coeff, X, Z, dx, dz)

def main():
    filename_end = sys.argv[1]

    check_laser(filename_end)

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

if __name__ == "__main__":
    main()