#!/usr/bin/env python
# Copyright (c) 2019, Anthony Latorre <tlatorre at uchicago>
#
# This program is free software: you can redistribute it and/or modify it
# under the terms of the GNU 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 General Public License along with
# this program. If not, see <https://www.gnu.org/licenses/>.
"""
Script to reprocess ZDAB files from SNO. We reprocess the files since the only
files I have access to right now were done for LETA and in those files the PMT
style banks are missing from the ZDAB file. They also might have the charge
stored in counts above pedestal instead of being normalized by the high half
point (although I'm not 100% sure about this). To reprocess a single file:

    $ ./zdab-reprocess FILENAME

and to batch reprocess:

    $ ./zdab-reprocess FILENAME FILENAME ...

You can also specify a minimum nhit value to reprocess. For example:

    $ ./zdab-reprocess --min-nhit 100 SNOCR_00000100004_000_p2.xzdab

will only reprocess events with an nhit greater than 100. One thing to note is
that this nhit value is just the total number of PMT bundles and so includes
channels with bad calibration, OWLs, and FEC/D hits.

By default, the reprocessed files will be stored in the current working
directory with _reprocessed appended to the name, but this can be changed by
passing a different suffix on the command line. For example:

    $ 
#!/usr/bin/env python
# Copyright (c) 2019, Anthony Latorre <tlatorre at uchicago>
#
# This program is free software: you can redistribute it and/or modify it
# under the terms of the GNU 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 General Public License along with
# this program. If not, see <https://www.gnu.org/licenses/>.

from __future__ import print_function, division
import numpy as np
from scipy.stats import iqr
import nlopt
from scipy.stats import poisson
import sys
from math import exp
import emcee
from scipy.optimize import brentq
from scipy.stats import truncnorm
from matplotlib.lines import Line2D
from sddm.plot import despine
from sddm.dc import *
from sddm.plot_energy import *
from sddm import printoptions

try:
    from emcee import moves
except ImportError:
    print("emcee version 2.2.1 is required",file=sys.stderr)
    sys.exit(1)

def radius_cut(ev):
    ev['radius_cut'] = np.digitize((ev.r/PSUP_RADIUS)**3,(0.9,))
    return ev

def udotr_cut(ev):
    ev['udotr_cut'] = np.digitize(ev.udotr,(-0.5,))
    return ev

def psi_cut(ev):
    ev['psi_cut'] = np.digitize(ev.psi,(6.0,))
    return ev

def cos_theta_cut(ev):
    ev['cos_theta_cut'] = np.digitize(ev.cos_theta,(-0.5,))
    return ev

def z_cut(ev):
    ev['z_cut'] = np.digitize(ev.z,(0.0,))
    return ev

# Constraint to enforce the fact that P(r,psi,z,udotr|muon) all add up to 1.0.
# In the likelihood function we set the last possibility for r and udotr equal
# to 1.0 minus the others. Therefore, we need to enforce the fact that the
# others must add up to less than 1.
muon_r_psi_z_udotr = Constraint(range(11,26))

# Constraint to enforce the fact that P(z,udotr|noise) all add up to 1.0. In
# the likelihood function we set the last possibility for r and udotr equal to
# 1.0 minus the others. Therefore, we need to enforce the fact that the others
# must add up to less than 1.
noise_z_udotr = Constraint(range(28,31))

# Constraint to enforce the fact that P(r,z,udotr|neck) all add up to 1.0. In
# the likelihood function we set the last possibility for r and udotr equal to
# 1.0 minus the others. Therefore, we need to enforce the fact that the others
# must add up to less than 1.
neck_r_z_udotr = Constraint(range(31,38))

# Constraint to enforce the fact that P(r,udotr|flasher) all add up to 1.0. In
# the likelihood function we set the last possibility for r and udotr equal to
# 1.0 minus the others. Therefore, we need to enforce the fact that the others
# must add up to less than 1
flasher_r_udotr = Constraint(range(39,42))

# Constraint to enforce the fact that P(r,udotr|breakdown) all add up to 1.0.
# In the likelihood function we set the last possibility for r and udotr equal
# to 1.0 minus the others. Therefore, we need to enforce the fact that the
# others must add up to less than 1.
breakdown_r_udotr = Constraint(range(44,47))

def make_nll(data, sacrifice, constraints, fitted_fraction):
    def nll(x, grad=None, fill_value=1e9):
        if grad is not None and grad.size > 0:
            raise Exception("nll got passed grad!")

        nll = 0.0
        # Here we explicitly return a crazy high value if one of the
        # constraints is violated. When using nlopt it should respect all the
        # constraints, *but* later when we do the Metropolis Hastings algorithm
        # we don't have any way to add the constraints explicitly.
        for constraint in constraints:
            if constraint(x) > 0:
                nll += fill_value + 1e4*constraint(x)**2

        if (x <= 0).any() or (x[6:] >= 1).any():
            nll += fill_value + 1e4*np.sum((x[x < 0])**2) + 1e4*np.sum((x[6:][x[6:] > 1]-1)**2)

        if nll:
            return nll

        (mu_signal, mu_muon, mu_noise, mu_neck, mu_flasher, mu_breakdown,
         contamination_muon, contamination_noise, contamination_neck, contamination_flasher, contamination_breakdown,
         p_r_psi_z_udotr_muon_lolololo, # 11
         p_r_psi_z_udotr_muon_lololohi,
         p_r_psi_z_udotr_muon_lolohilo,
         p_r_psi_z_udotr_muon_lolohihi,
         p_r_psi_z_udotr_muon_lohilolo,
         p_r_psi_z_udotr_muon_lohilohi,
         p_r_psi_z_udotr_muon_lohihilo,
         p_r_psi_z_udotr_muon_lohihihi,
         p_r_psi_z_udotr_muon_hilololo,
         p_r_psi_z_udotr_muon_hilolohi,
         p_r_psi_z_udotr_muon_hilohilo,
         p_r_psi_z_udotr_muon_hilohihi,
         p_r_psi_z_udotr_muon_hihilolo,
         p_r_psi_z_udotr_muon_hihilohi,
         p_r_psi_z_udotr_muon_hihihilo,
         p_r_noise_lo, p_psi_noise_lo, # 26, 27
         p_z_udotr_noise_lolo, # 28
         p_z_udotr_noise_lohi,
         p_z_udotr_noise_hilo,
         p_r_z_udotr_neck_lololo, # 31
         p_r_z_udotr_neck_lolohi,
         p_r_z_udotr_neck_lohilo,
         p_r_z_udotr_neck_lohihi,
         p_r_z_udotr_neck_hilolo,
         p_r_z_udotr_neck_hilohi,
         p_r_z_udotr_neck_hihilo,
         p_psi_neck_lo, # 38
         p_r_udotr_flasher_lolo, p_r_udotr_flasher_lohi, p_r_udotr_flasher_hilo, # 39, ..., 41
         p_psi_flasher_lo, p_z_flasher_lo,
         p_r_udotr_breakdown_lolo, p_r_udotr_breakdown_lohi, p_r_udotr_breakdown_hilo, # 44, ..., 46
         p_psi_breakdown_lo, p_z_breakdown_lo,
         p_neck_given_muon) = x

        p_r_udotr_flasher_hihi = 1-p_r_udotr_flasher_lolo-p_r_udotr_flasher_lohi-p_r_udotr_flasher_hilo
        p_r_udotr_breakdown_hihi = 1-p_r_udotr_breakdown_lolo-p_r_udotr_breakdown_lohi-p_r_udotr_breakdown_hilo
        p_r_psi_z_udotr_muon_hihihihi = 1 - \
            p_r_psi_z_udotr_muon_lolololo - \
            p_r_psi_z_udotr_muon_lololohi - \
            p_r_psi_z_udotr_muon_lolohilo - \
            p_r_psi_z_udotr_muon_lolohihi - \
            p_r_psi_z_udotr_muon_lohilolo - \
            p_r_psi_z_udotr_muon_lohilohi - \
            p_r_psi_z_udotr_muon_lohihilo - \
            p_r_psi_z_udotr_muon_lohihihi - \
            p_r_psi_z_udotr_muon_hilololo - \
            p_r_psi_z_udotr_muon_hilolohi - \
            p_r_psi_z_udotr_muon_hilohilo - \
            p_r_psi_z_udotr_muon_hilohihi - \
            p_r_psi_z_udotr_muon_hihilolo - \
            p_r_psi_z_udotr_muon_hihilohi - \
            p_r_psi_z_udotr_muon_hihihilo
        p_r_z_udotr_neck_hihihi = 1 - p_r_z_udotr_neck_lololo - p_r_z_udotr_neck_lolohi - p_r_z_udotr_neck_lohilo - p_r_z_udotr_neck_lohihi - p_r_z_udotr_neck_hilolo - p_r_z_udotr_neck_hilohi - p_r_z_udotr_neck_hihilo
        p_z_udotr_noise_hihi = 1 - p_z_udotr_noise_lolo - p_z_udotr_noise_lohi - p_z_udotr_noise_hilo

        # Muon events
        # first 6 parameters are the mean number of signal and bgs
        p_muon = np.array([\
            [[[p_r_psi_z_udotr_muon_lolololo, p_r_psi_z_udotr_muon_lololohi], \
              [p_r_psi_z_udotr_muon_lolohilo, p_r_psi_z_udotr_muon_lolohihi]], \
             [[p_r_psi_z_udotr_muon_lohilolo, p_r_psi_z_udotr_muon_lohilohi], \
              [p_r_psi_z_udotr_muon_lohihilo, p_r_psi_z_udotr_muon_lohihihi]]], \
            [[[p_r_psi_z_udotr_muon_hilololo, p_r_psi_z_udotr_muon_hilolohi], \
              [p_r_psi_z_udotr_muon_hilohilo, p_r_psi_z_udotr_muon_hilohihi]], \
             [[p_r_psi_z_udotr_muon_hihilolo, p_r_psi_z_udotr_muon_hihilohi], \
              [p_r_psi_z_udotr_muon_hihihilo, p_r_psi_z_udotr_muon_hihihihi]]]])
        expected_muon = p_muon*contamination_muon*mu_muon*fitted_fraction['muon'] + sacrifice['muon']*mu_signal

        nll -= fast_poisson_logpmf(data['muon'],expected_muon).sum()

        # Noise events
        p_r_noise = np.array([p_r_noise_lo,1-p_r_noise_lo])
        p_psi_noise = np.array([p_psi_noise_lo,1-p_psi_noise_lo])
        p_z_udotr_noise = np.array([\
            [p_z_udotr_noise_lolo,p_z_udotr_noise_lohi],
            [p_z_udotr_noise_hilo,p_z_udotr_noise_hihi]])
        p_noise = p_r_noise[:,np.newaxis,np.newaxis,np.newaxis]*p_psi_noise[:,np.newaxis,np.newaxis]*p_z_udotr_noise
        expected_noise = p_noise*contamination_noise*mu_noise*fitted_fraction['noise'] + sacrifice['noise']*mu_signal

        nll -= fast_poisson_logpmf(data['noise'],expected_noise).sum()

        # Neck events
        # FIXME: for now assume parameterized same as muon
        p_r_z_udotr_neck = np.array([\
            [[p_r_z_udotr_neck_lololo, p_r_z_udotr_neck_lolohi], \
             [p_r_z_udotr_neck_lohilo, p_r_z_udotr_neck_lohihi]], \
            [[p_r_z_udotr_neck_hilolo, p_r_z_udotr_neck_hilohi], \
             [p_r_z_udotr_neck_hihilo, p_r_z_udotr_neck_hihihi]]])
        p_psi_neck = np.array([p_psi_neck_lo,1-p_psi_neck_lo])
        p_neck = p_r_z_udotr_neck[:,np.newaxis,:,:]*p_psi_neck[:,np.newaxis,np.newaxis]
        expected_neck = p_neck*contamination_neck*mu_neck*fitted_fraction['neck'] + sacrifice['neck']*mu_signal
        # FIXME: pdf should be different for muon given neck
        expected_neck += p_muon*p_neck_given_muon*mu_muon*fitted_fraction['neck']

        nll -= fast_poisson_logpmf(data['neck'],expected_neck).sum()

        # Flasher events
        p_r_udotr_flasher = np.array([\
            [p_r_udotr_flasher_lolo,p_r_udotr_flasher_lohi], \
            [p_r_udotr_flasher_hilo,p_r_udotr_flasher_hihi]])
        p_psi_flasher = np.array([p_psi_flasher_lo,1-p_psi_flasher_lo])
        p_z_flasher = np.array([p_z_flasher_lo,1-p_z_flasher_lo])
        p_flasher = p_r_udotr_flasher[:,np.newaxis,np.newaxis,:]*p_psi_flasher[:,np.newaxis,np.newaxis]*p_z_flasher[:,np.newaxis]
        expected_flasher = p_flasher*contamination_flasher*mu_flasher*fitted_fraction['flasher'] + sacrifice['flasher']*mu_signal

        nll -= fast_poisson_logpmf(data['flasher'],expected_flasher).sum()

        # Breakdown events
        p_r_udotr_breakdown = np.array([\
            [p_r_udotr_breakdown_lolo,p_r_udotr_breakdown_lohi], \
            [p_r_udotr_breakdown_hilo,p_r_udotr_breakdown_hihi]])
        p_psi_breakdown = np.array([p_psi_breakdown_lo,1-p_psi_breakdown_lo])
        p_z_breakdown = np.array([p_z_breakdown_lo,1-p_z_breakdown_lo])
        p_breakdown = p_r_udotr_breakdown[:,np.newaxis,np.newaxis,:]*p_psi_breakdown[:,np.newaxis,np.newaxis]*p_z_breakdown[:,np.newaxis]
        expected_breakdown = p_breakdown*contamination_breakdown*mu_breakdown*fitted_fraction['breakdown'] + sacrifice['breakdown']*mu_signal

        nll -= fast_poisson_logpmf(data['breakdown'],expected_breakdown).sum()

        # Signal like events
        expected_signal = np.zeros_like(expected_muon)
        expected_signal += mu_signal*sacrifice['signal']
        expected_signal += p_muon*(1-contamination_muon)*mu_muon
        expected_signal += p_neck*(1-contamination_neck)*mu_neck
        expected_signal += p_noise*(1-contamination_noise)*mu_noise
        expected_signal += p_flasher*(1-contamination_flasher)*mu_flasher
        expected_signal += p_breakdown*(1-contamination_breakdown)*mu_breakdown

        nll -= fast_poisson_logpmf(data['signal'],expected_signal).sum()

        if not np.isfinite(nll):
            print("x = ", x)
            print("p_r_z_udotr_neck = ", p_r_z_udotr_neck)
            print("expected_muon = ", expected_muon)
            print("expected_noise = ", expected_noise)
            print("expected_neck = ", expected_neck)
            print("expected_flasher = ", expected_flasher)
            print("expected_breakdown = ", expected_breakdown)
            print("nll is not finite!")
            sys.exit(0)

        return nll
    return nll

if __name__ == '__main__':
    import argparse
    import numpy as np
    import pandas as pd
    import sys
    import h5py
    from sddm import setup_matplotlib

    parser = argparse.ArgumentParser("plot fit results")
    parser.add_argument("filenames", nargs='+', help="input files")
    parser.add_argument("--steps", type=int, default=100000, help="number of steps in the MCMC chain")
    parser.add_argument("--save", action="store_true", default=False, help="save plots")
    parser.add_argument("--mc", nargs='+', required=True, help="atmospheric MC files")
    parser.add_argument("--nhit-thresh", type=int, default=None, help="nhit threshold to apply to events before processing (should only be used for testing to speed things up)")
    args = parser.parse_args()

    setup_matplotlib(args.save)

    import matplotlib.pyplot as plt

    # Loop over runs to prevent using too much memory
    evs = []
    rhdr = pd.concat([read_hdf(filename, "rhdr").assign(filename=filename) for filename in args.filenames],ignore_index=True)
    for run, df in rhdr.groupby('run'):
        evs.append(get_events(df.filename.values, merge_fits=True, nhit_thresh=args.nhit_thresh))
    ev = pd.concat(evs)

    ev = ev[ev.prompt]
    ev = ev[ev.nhit_cal > 100]

    # Note: Technically we want to know the fitted fraction only for events
    # which *would* reconstruct above 20 MeV. However, there is no way to know
    # if the energy is above 20 MeV without fitting it. However, since I only
    # skip fitting events based on the gtid, there shouldn't be any correlation
    # with energy and so the fitted fraction here should be correct.
    fitted_fraction = {}
    for bg in ['signal','muon','noise','neck','flasher','breakdown']:
        if np.count_nonzero(ev[bg]):
            fitted_fraction[bg] = np.count_nonzero(ev[bg] & ~np.isnan(ev.fmin))/np.count_nonzero(ev[bg])
            print("Fitted fraction for %s: %.0f %%" % (bg,fitted_fraction[bg]*100))
        else:
            print_warning("Warning: No %s events in sample!" % bg)
            sys.exit(1)

    ev = ev[~np.isnan(ev.fmin)]
    ev = ev[ev.ke > 20]

    # figure out bins for high level variables
    ev = radius_cut(ev)
    ev = psi_cut(ev)
    ev = cos_theta_cut(ev)
    ev = z_cut(ev)
    ev = udotr_cut(ev)

    data = {}
    for bg in ['signal','muon','noise','neck','flasher','breakdown']:
        data[bg] = np.zeros((2,2,2,2),dtype=int)
        for _, row in ev[ev[bg]].iterrows():
            data[bg][row.radius_cut][row.psi_cut][row.z_cut][row.udotr_cut] += 1

    ev_mc = get_events(args.mc, merge_fits=True, apply_nhit_trigger=False)

    ev_mc = ev_mc[ev_mc.prompt]
    ev_mc = ev_mc[ev_mc.nhit_cal > 100]
    ev_mc = ev_mc[~np.isnan(ev_mc.fmin)]
    ev_mc = ev_mc[ev_mc.ke > 20]

    # figure out bins for high level variables
    ev_mc = radius_cut(ev_mc)
    ev_mc = psi_cut(ev_mc)
    ev_mc = cos_theta_cut(ev_mc)
    ev_mc = z_cut(ev_mc)
    ev_mc = udotr_cut(ev_mc)

    # FIXME: Double check that what I'm calculating here matches with what I
    # expect
    sacrifice = {}
    for bg in ['signal','muon','noise','neck','flasher','breakdown']:
        sacrifice[bg] = np.zeros((2,2,2,2),dtype=float)
        for _, row in ev_mc[ev_mc[bg]].iterrows():
            sacrifice[bg][row.radius_cut][row.psi_cut][row.z_cut][row.udotr_cut] += 1

        sacrifice[bg] /= len(ev_mc)

    constraints = [flasher_r_udotr, breakdown_r_udotr,muon_r_psi_z_udotr,neck_r_z_udotr,noise_z_udotr]
    nll = make_nll(data,sacrifice,constraints,fitted_fraction)

    x0 = []
    for bg in ['signal','muon','noise','neck','flasher','breakdown']:
        x0.append(data[bg].sum())

    # contamination
    x0 += [0.99]*5

    if data['muon'].sum() > 0:
        # P(r,psi,z,udotr|muon)
        x0 += [data['muon'][0,0,0,0].sum()/data['muon'].sum()]
        x0 += [data['muon'][0,0,0,1].sum()/data['muon'].sum()]
        x0 += [data['muon'][0,0,1,0].sum()/data['muon'].sum()]
        x0 += [data['muon'][0,0,1,1].sum()/data['muon'].sum()]
        x0 += [data['muon'][0,1,0,0].sum()/data['muon'].sum()]
        x0 += [data['muon'][0,1,0,1].sum()/data['muon'].sum()]
        x0 += [data['muon'][0,1,1,0].sum()/data['muon'].sum()]
        x0 += [data['muon'][0,1,1,1].sum()/data['muon'].sum()]
        x0 += [data['muon'][1,0,0,0].sum()/data['muon'].sum()]
        x0 += [data['muon'][1,0,0,1].sum()/data['muon'].sum()]
        x0 += [data['muon'][1,0,1,0].sum()/data['muon'].sum()]
        x0 += [data['muon'][1,0,1,1].sum()/data['muon'].sum()]
        x0 += [data['muon'][1,1,0,0].sum()/data['muon'].sum()]
        x0 += [data['muon'][1,1,0,1].sum()/data['muon'].sum()]
        x0 += [data['muon'][1,1,1,0].sum()/data['muon'].sum()]
    else:
        x0 += [0.1]*15

    if data['noise'].sum() > 0:
        # P(r|noise)
        x0 += [data['noise'][0].sum()/data['noise'].sum()]
        # P(psi|noise)
        x0 += [data['noise'][:,0].sum()/data['noise'].sum()]
        # P(z,udotr|noise)
        x0 += [data['noise'][:,:,0,0].sum()/data['noise'].sum()]
        x0 += [data['noise'][:,:,0,1].sum()/data['noise'].sum()]
        x0 += [data['noise'][:,:,1,0].sum()/data['noise'].sum()]
    else:
        x0 += [0.1]*5

    if data['neck'].sum() > 0:
        # P(r,z,udotr|neck)
        x0 += [data['neck'][0,:,0,0].sum()/data['neck'].sum()]
        x0 += [data['neck'][0,:,0,1].sum()/data['neck'].sum()]
        x0 += [data['neck'][0,:,1,0].sum()/data['neck'].sum()]
        x0 += [data['neck'][0,:,1,1].sum()/data['neck'].sum()]
        x0 += [data['neck'][1,:,0,0].sum()/data['neck'].sum()]
        x0 += [data['neck'][1,:,0,1].sum()/data['neck'].sum()]
        x0 += [data['neck'][1,:,1,0].sum()/data['neck'].sum()]
        # P(psi|neck)
        x0 += [data['neck'][:,0].sum()/data['neck'].sum()]
    else:
        x0 += [0.1]*8

    if data['flasher'].sum() > 0:
        # P(r,udotr|flasher)
        x0 += [data['flasher'][0,:,:,0].sum()/data['flasher'].sum()]
        x0 += [data['flasher'][0,:,:,1].sum()/data['flasher'].sum()]
        x0 += [data['flasher'][1,:,:,0].sum()/data['flasher'].sum()]
        # P(psi|flasher)
        x0 += [data['flasher'][:,0].sum()/data['flasher'].sum()]
        # P(z|flasher)
        x0 += [data['flasher'][:,:,0].sum()/data['flasher'].sum()]
    else:
        x0 += [0.1]*5

    if data['breakdown'].sum() > 0:
        # P(r,udotr|breakdown)
        x0 += [data['breakdown'][0,:,:,0].sum()/data['breakdown'].sum()]
        x0 += [data['breakdown'][0,:,:,1].sum()/data['breakdown'].sum()]
        x0 += [data['breakdown'][1,:,:,0].sum()/data['breakdown'].sum()]
        # P(psi|breakdown)
        x0 += [data['breakdown'][:,0].sum()/data['breakdown'].sum()]
        # P(z|breakdown)
        x0 += [data['breakdown'][:,:,0].sum()/data['breakdown'].sum()]
    else:
        x0 += [0.1]*5

    # P(neck|muon)
    x0 += [EPSILON]

    x0 = np.array(x0)

    # Use the COBYLA algorithm here because it is the only derivative free
    # minimization routine which honors inequality constraints
    # Edit: SBPLX seems to work better
    opt = nlopt.opt(nlopt.LN_SBPLX, len(x0))
    opt.set_min_objective(nll)
    # set lower bounds to 1e-10 to prevent nans if we predict something should
    # be 0 but observe an event.
    low = np.ones_like(x0)*EPSILON
    high = np.array([1e9]*6 + [1-EPSILON]*(len(x0)-6))
    x0[x0 < low] = low[x0 < low]
    x0[x0 > high] = high[x0 > high]
    opt.set_lower_bounds(low)
    opt.set_upper_bounds(high)
    opt.set_ftol_abs(1e-10)
    opt.set_initial_step([1]*6 + [0.01]*(len(x0)-6))
    #for constraint in constraints:
        #opt.add_inequality_constraint(constraint,0)

    xopt = opt.optimize(x0)
    nll_xopt = nll(xopt)
    print("nll(xopt) = ", nll(xopt))

    while True:
        xopt = opt.optimize(xopt)
        if not nll(xopt) < nll_xopt - 1e-10:
            break
        nll_xopt = nll(xopt)
        print("nll(xopt) = ", nll(xopt))
        #print("n = ", opt.get_numevals())

    stepsizes = estimate_errors(nll,xopt,low,high,constraints)
    with printoptions(precision=3, suppress=True):
        print("Errors: ", stepsizes)

    #samples = metropolis_hastings(nll,xopt,stepsizes,100000)
    #print("nll(xopt) = %.2g" % nll(xopt))

    pos = np.empty((10, len(x0)),dtype=np.double)
    for i in range(pos.shape[0]):
        pos[i] = xopt + np.random.randn(len(x0))*stepsizes
        pos[i,:6] = np.clip(pos[i,:6],EPSILON,1e9)
        pos[i,6:] = np.clip(pos[i,6:],EPSILON,1-EPSILON)

        for constraint in constraints:
            if constraint(pos[i]) >= 0:
                pos[i] = constraint.renormalize_no_fix(pos[i])

    nwalkers, ndim = pos.shape

    proposal = get_proposal_func(stepsizes*0.5,low,high)
    sampler = emcee.EnsembleSampler(nwalkers, ndim, lambda x, grad, fill_value: -nll(x,grad,fill_value), moves=emcee.moves.MHMove(proposal),args=[None,np.inf])
    with np.errstate(invalid='ignore'):
        sampler.run_mcmc(pos, args.steps)

    print("Mean acceptance fraction: {0:.3f}".format(np.mean(sampler.acceptance_fraction)))

    try:
        print("autocorrelation time: ", sampler.get_autocorr_time(quiet=True))
    except Exception as e:
        print(e)

    # Plot walker positions as a function of step number for the expected
    # number of events
    fig, axes = plt.subplots(6, num=1, sharex=True)
    samples = sampler.get_chain()
    labels = ["Signal","Muon","Noise","Neck","Flasher","Breakdown"]
    for i, bg in enumerate(['signal','muon','noise','neck','flasher','breakdown']):
        ax = axes[i]
        ax.plot(samples[:,:,i], "k", alpha=0.3)
        ax.set_xlim(0, len(samples))
        ax.set_ylabel(labels[i], rotation=0)
        ax.yaxis.set_label_coords(-0.1, 0.5)
        despine(ax=ax,trim=True)
    plt.subplots_adjust(left=0.2)
    fig.tight_layout()

    # Plot walker positions as a function of step number for the background cut
    # efficiencies
    fig, axes = plt.subplots(5, num=2, sharex=True)
    samples = sampler.get_chain()
    tag_labels = ['M','N','Ne','F','B']
    for i, bg in enumerate(['muon','noise','neck','flasher','breakdown']):
        ax = axes[i]
        ax.plot(samples[:,:,6+i], "k", alpha=0.3)
        ax.set_xlim(0, len(samples))
        ax.set_ylabel(r"$P(\mathrm{%s}\mid\mathrm{%s})$" % (tag_labels[i],bg), rotation=0)
        ax.yaxis.set_label_coords(-0.1, 0.5)
        despine(ax=ax,trim=True)
    plt.subplots_adjust(left=0.2)
    fig.tight_layout()

    samples = sampler.chain.reshape((-1,len(x0)))

    plt.figure(3)
    for i, bg in enumerate(['signal','muon','noise','neck','flasher','breakdown']):
        ax = plt.subplot(3,2,i+1)
        plt.hist(samples[:,i],bins=100,histtype='step')
        plt.title(bg.capitalize())
        despine(ax=ax,left=True,trim=True)
        ax.get_yaxis().set_visible(False)
    plt.legend()
    plt.tight_layout()

    plt.figure(4)
    for i, bg in enumerate(['muon','noise','neck','flasher','breakdown']):
        ax = plt.subplot(3,2,i+1)
        plt.hist(samples[:,6+i],bins=100,histtype='step')
        plt.title(bg.capitalize())
        despine(ax=ax,left=True,trim=True)
        ax.get_yaxis().set_visible(False)
    plt.legend()
    plt.tight_layout()

    (mu_signal, mu_muon, mu_noise, mu_neck, mu_flasher, mu_breakdown,
     contamination_muon, contamination_noise, contamination_neck, contamination_flasher, contamination_breakdown,
     p_r_psi_z_udotr_muon_lolololo, # 11
     p_r_psi_z_udotr_muon_lololohi,
     p_r_psi_z_udotr_muon_lolohilo,
     p_r_psi_z_udotr_muon_lolohihi,
     p_r_psi_z_udotr_muon_lohilolo,
     p_r_psi_z_udotr_muon_lohilohi,
     p_r_psi_z_udotr_muon_lohihilo,
     p_r_psi_z_udotr_muon_lohihihi,
     p_r_psi_z_udotr_muon_hilololo,
     p_r_psi_z_udotr_muon_hilolohi,
     p_r_psi_z_udotr_muon_hilohilo,
     p_r_psi_z_udotr_muon_hilohihi,
     p_r_psi_z_udotr_muon_hihilolo,
     p_r_psi_z_udotr_muon_hihilohi,
     p_r_psi_z_udotr_muon_hihihilo,
     p_r_noise_lo, p_psi_noise_lo, # 26, 27
     p_z_udotr_noise_lolo, # 28
     p_z_udotr_noise_lohi,
     p_z_udotr_noise_hilo,
     p_r_z_udotr_neck_lololo, # 31
     p_r_z_udotr_neck_lolohi,
     p_r_z_udotr_neck_lohilo,
     p_r_z_udotr_neck_lohihi,
     p_r_z_udotr_neck_hilolo,
     p_r_z_udotr_neck_hilohi,
     p_r_z_udotr_neck_hihilo,
     p_psi_neck_lo, # 38
     p_r_udotr_flasher_lolo, p_r_udotr_flasher_lohi, p_r_udotr_flasher_hilo, # 39, ..., 41
     p_psi_flasher_lo, p_z_flasher_lo,
     p_r_udotr_breakdown_lolo, p_r_udotr_breakdown_lohi, p_r_udotr_breakdown_hilo, # 44, ..., 46
     p_psi_breakdown_lo, p_z_breakdown_lo,
     p_neck_given_muon) = samples.T

    p_r_muon_lo = p_r_psi_z_udotr_muon_lolololo + \
                  p_r_psi_z_udotr_muon_lololohi + \
                  p_r_psi_z_udotr_muon_lolohilo + \
                  p_r_psi_z_udotr_muon_lolohihi + \
                  p_r_psi_z_udotr_muon_lohilolo + \
                  p_r_psi_z_udotr_muon_lohilohi + \
                  p_r_psi_z_udotr_muon_lohihilo + \
                  p_r_psi_z_udotr_muon_lohihihi

    p_psi_muon_lo = p_r_psi_z_udotr_muon_lolololo + \
                    p_r_psi_z_udotr_muon_lololohi + \
                    p_r_psi_z_udotr_muon_lolohilo + \
                    p_r_psi_z_udotr_muon_lolohihi + \
                    p_r_psi_z_udotr_muon_hilololo + \
                    p_r_psi_z_udotr_muon_hilolohi + \
                    p_r_psi_z_udotr_muon_hilohilo + \
                    p_r_psi_z_udotr_muon_hilohihi

    p_r = [sacrifice['signal'][0].sum(), p_r_muon_lo, p_r_noise_lo, \
        p_r_z_udotr_neck_lololo + p_r_z_udotr_neck_lolohi + p_r_z_udotr_neck_lohilo + p_r_z_udotr_neck_lohihi, \
        p_r_udotr_flasher_lolo + p_r_udotr_flasher_lohi, \
        p_r_udotr_breakdown_lolo + p_r_udotr_breakdown_lohi]

    p_psi = [sacrifice['signal'][:,0].sum(), \
        p_psi_muon_lo, \
        p_psi_noise_lo, \
        p_psi_neck_lo, \
        p_psi_flasher_lo, \
        p_psi_breakdown_lo]

    ylim_max = 0
    fig = plt.figure(5)
    axes = []
    for i, bg in enumerate(['signal','muon','noise','neck','flasher','breakdown']):
        axes.append(plt.subplot(3,2,i+1))
        if i == 0:
            plt.hist(samples[:,i],bins=100,histtype='step',label="After DC cuts")
            plt.hist(samples[:,i]*p_r[i],bins=100,histtype='step',linestyle=':',label="+ radius cut")
            plt.hist(samples[:,i]*p_r[i]*p_psi[i],bins=100,histtype='step',linestyle='--',label=r"+ $\psi$ cut")
        else:
            plt.hist(samples[:,i]*(1-samples[:,5+i]),bins=100,histtype='step')
            plt.hist(samples[:,i]*(1-samples[:,5+i])*p_r[i],bins=100,histtype='step',linestyle=':')
            plt.hist(samples[:,i]*(1-samples[:,5+i])*p_r[i]*p_psi[i],bins=100,histtype='step',linestyle='--')
        plt.title(bg.capitalize())
    xlim_max = max(ax.get_xlim()[1] for ax in axes)
    for ax in axes:
        ax.set_xlim((0,xlim_max))
        despine(ax=ax,left=True,trim=True)
        ax.get_yaxis().set_visible(False)
    # Create new legend handles but use the colors from the existing ones
    handles, labels = axes[0].get_legend_handles_labels()
    new_handles = [Line2D([], [], c=h.get_edgecolor()) for h in handles]
    fig.legend(new_handles,labels,loc='upper right')
    plt.legend()
    plt.tight_layout()

    if args.save:
        plt.figure(1)
        plt.savefig("dc_walker_pos_num_events.pdf")
        plt.savefig("dc_walker_pos_num_events.eps")
        plt.figure(2)
        plt.savefig("dc_walker_pos_cut_eff.pdf")
        plt.savefig("dc_walker_pos_cut_eff.eps")
        plt.figure(3)
        plt.savefig("dc_num_events.pdf")
        plt.savefig("dc_num_events.eps")
        plt.figure(4)
        plt.savefig("dc_cut_eff.pdf")
        plt.savefig("dc_cut_eff.eps")
        plt.figure(5)
        plt.savefig("dc_num_events_after_cuts.pdf")
        plt.savefig("dc_num_events_after_cuts.eps")
    else:
        plt.figure(3)
        plt.suptitle("Expected number of events")
        plt.figure(4)
        plt.suptitle("Probability of correctly tagging background")
        plt.figure(5)
        plt.suptitle("Expected number of Backgrounds after cuts")

        plt.show()