#!/usr/bin/env python3

# Copyright 2020 Neil Zaim
#
# This file is part of WarpX.
#
# License: BSD-3-Clause-LBNL

## In this test, we check that leveling thinning works as expected on two simple cases. Each case
## corresponds to a different particle species.

import yt
import numpy as np
import os
import sys
from scipy.special import erf
sys.path.insert(1, '../../../../warpx/Regression/Checksum/')
import checksumAPI

fn_final = sys.argv[1]
fn0 = fn_final[:-4] + '0000'

ds0 = yt.load(fn0)
ds = yt.load(fn_final)

ad0 = ds0.all_data()
ad = ds.all_data()

numcells = 16*16
t_r = 1.3 # target ratio
relative_tol = 1.e-13 # tolerance for machine precision errors


#### Tests for first species ####
# Particles are present in all simulation cells and all have the same weight

ppc = 400.
numparts_init = numcells*ppc

w0 = ad0['resampled_part1','particle_weight'].to_ndarray() # weights before resampling
w = ad['resampled_part1','particle_weight'].to_ndarray() # weights after resampling

# Renormalize weights for easier calculations
w0 = w0*ppc
w = w*ppc

# Check that initial number of particles is indeed as expected
assert(w0.shape[0] == numparts_init)
# Check that all initial particles have the same weight
assert(np.unique(w0).shape[0] == 1)
# Check that this weight is 1 (to machine precision)
assert(abs(w0[0] - 1) < relative_tol)

# Check that the number of particles after resampling is as expected
numparts_final = w.shape[0]
expected_numparts_final = numparts_init/t_r**2
error = np.abs(numparts_final - expected_numparts_final)
std_numparts_final = np.sqrt(numparts_init/t_r**2*(1.-1./t_r**2))
# 5 sigma test that has an intrinsic probability to fail of 1 over ~2 millions
print("difference between expected and actual final number of particles (1st species): " + str(error))
print("tolerance: " + str(5*std_numparts_final))
assert(error<5*std_numparts_final)

# Check that the final weight is the same for all particles (to machine precision) and is as
# expected
final_weight = t_r**2
assert(np.amax(np.abs(w-final_weight)) < relative_tol*final_weight )


#### Tests for second species ####
# Particles are only present in a single cell and have a gaussian weight distribution
# Using a single cell makes the analysis easier because leveling thinning is done separately in
# each cell

ppc = 100000.
numparts_init = ppc

w0 = ad0['resampled_part2','particle_weight'].to_ndarray() # weights before resampling
w = ad['resampled_part2','particle_weight'].to_ndarray() # weights after resampling

# Renormalize and sort weights for easier calculations
w0 = np.sort(w0)*ppc
w = np.sort(w)*ppc

## First we verify that the initial distribution is as expected

# Check that the mean initial weight is as expected
mean_initial_weight = np.average(w0)
expected_mean_initial_weight = 2.*np.sqrt(2.)
error = np.abs(mean_initial_weight - expected_mean_initial_weight)
expected_std_initial_weight = 1./np.sqrt(2.)
std_mean_initial_weight = expected_std_initial_weight/np.sqrt(numparts_init)
# 5 sigma test that has an intrinsic probability to fail of 1 over ~2 millions
print("difference between expected and actual mean initial weight (2nd species): " + str(error))
print("tolerance: " + str(5*std_mean_initial_weight))
assert(error<5*std_mean_initial_weight)

# Check that the initial weight variance is as expected
variance_initial_weight = np.var(w0)
expected_variance_initial_weight = 0.5
error = np.abs(variance_initial_weight - expected_variance_initial_weight)
std_variance_initial_weight = expected_variance_initial_weight*np.sqrt(2./numparts_init)
# 5 sigma test that has an intrinsic probability to fail of 1 over ~2 millions
print("difference between expected and actual variance of initial weight (2nd species): " + str(error))
print("tolerance: " + str(5*std_variance_initial_weight))

## Next we verify that the resampling worked as expected

# Check that the level weight value is as expected from the initial distribution
level_weight = w[0]
assert(np.abs(level_weight - mean_initial_weight*t_r) < level_weight*relative_tol)

# Check that the number of particles at the level weight is the same as predicted from analytic
# calculations
numparts_leveled = np.argmax(w > level_weight) # This returns the first index for which
# w > level_weight, which thus corresponds to the number of particles at the level weight
expected_numparts_leveled = numparts_init/(2.*t_r)*(1+erf(expected_mean_initial_weight*(t_r-1.)) \
                            -1./(np.sqrt(np.pi)*expected_mean_initial_weight)* \
                            np.exp(-(expected_mean_initial_weight*(t_r-1.))**2))
error = np.abs(numparts_leveled - expected_numparts_leveled)
std_numparts_leveled = np.sqrt(expected_numparts_leveled - numparts_init/np.sqrt(np.pi)/(t_r* \
                       expected_mean_initial_weight)**2*(np.sqrt(np.pi)/4.* \
                       (2.*expected_mean_initial_weight**2+1.)*(1.-erf(expected_mean_initial_weight* \
                       (t_r-1.)))-0.5*np.exp(-(expected_mean_initial_weight*(t_r-1.))**2* \
                       (expected_mean_initial_weight*(t_r+1.)))))
# 5 sigma test that has an intrinsic probability to fail of 1 over ~2 millions
print("difference between expected and actual number of leveled particles (2nd species): " + str(error))
print("tolerance: " + str(5*std_numparts_leveled))

numparts_unaffected = w.shape[0] - numparts_leveled
numparts_unaffected_anticipated = w0.shape[0] - np.argmax(w0 > level_weight)
# Check that number of particles with weight higher than level weight is the same before and after
# resampling
assert(numparts_unaffected == numparts_unaffected_anticipated)
# Check that particles with weight higher than level weight are unaffected by resampling.
assert(np.all(w[-numparts_unaffected:] == w0[-numparts_unaffected:]))

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