src/proton.h

#!/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, norm
import contextlib
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 *

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

# from https://stackoverflow.com/questions/2891790/how-to-pretty-print-a-numpy-array-without-scientific-notation-and-with-given-pre
@contextlib.contextmanager
def printoptions(*args, **kwargs):
    original = np.get_printoptions()
    np.set_printoptions(*args, **kwargs)
    try:
        yield
    finally: 
        np.set_printoptions(**original)

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

def fit(data, sacrifice, steps):
    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,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, 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)

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

    return samples

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("-n", type=int, default=10, help="number of fits to run")
    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]

    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))
        elif bg != 'signal':
            print_warning("Warning: No %s events in sample, assuming 10%% fitted fraction" % bg)
            fitted_fraction[bg] = 0.1
        else:
            print_warning("Warning: No signal events in sample, assuming 100%% fitted fraction")
            fitted_fraction[bg] = 1.0

    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)

    ev['noise'] = ev.dc & (DC_JUNK | DC_CRATE_ISOTROPY | DC_QVNHIT | DC_ITC | DC_ESUM) != 0
    ev['neck'] = ((ev.dc & DC_NECK) != 0) & ~ev.noise
    ev['flasher'] = ((ev.dc & DC_FLASHER) != 0) & ~(ev.noise | ev.neck) & (ev.nhit < 1000)
    ev['breakdown'] = ((ev.dc & (DC_FLASHER | DC_BREAKDOWN)) != 0) & ~(ev.noise | ev.neck) & (ev.nhit >= 1000)
    ev['muon'] = ((ev.dc & DC_MUON) != 0) & ~(ev.noise | ev.neck | ev.flasher | ev.breakdown)
    ev['signal'] = ~(ev.noise | ev.neck | ev.flasher | ev.breakdown | ev.muon)

    ev_mc = get_events(args.mc, merge_fits=True)
    ev_mc = ev_mc[ev_mc.prompt]
    ev_mc = ev_mc[ev_mc.nhit_cal > 100]

    # 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)

    ev_mc['noise'] = ev_mc.dc & (DC_JUNK | DC_CRATE_ISOTROPY | DC_QVNHIT | DC_ITC | DC_ESUM) != 0
    ev_mc['neck'] = ((ev_mc.dc & DC_NECK) != 0) & ~ev_mc.noise
    ev_mc['flasher'] = ((ev_mc.dc & DC_FLASHER) != 0) & ~(ev_mc.noise | ev_mc.neck) & (ev_mc.nhit < 1000)
    ev_mc['breakdown'] = ((ev_mc.dc & (DC_FLASHER | DC_BREAKDOWN)) != 0) & ~(ev_mc.noise | ev_mc.neck) & (ev_mc.nhit >= 1000)
    ev_mc['muon'] = ((ev_mc.dc & DC_MUON) != 0) & ~(ev_mc.noise | ev_mc.neck | ev_mc.flasher | ev_mc.breakdown)
    ev_mc['signal'] = ~(ev_mc.noise | ev_mc.neck | ev_mc.flasher | ev_mc.breakdown | ev_mc.muon)

    contamination_pull = {}

    nbg = {}
    for bg in ['signal','muon','noise','neck','flasher','breakdown']:
        nbg[bg] = 100
        contamination_pull[bg] = []

    for i in range(args.n):
        data = {}
        for bg in ['signal','muon','noise','neck','flasher','breakdown']:
            data[bg] = np.zeros((2,2,2,2),dtype=int)
            if bg == 'signal':
                for bg2 in ['signal','muon','noise','neck','flasher','breakdown']:
                    if bg2 == 'signal':
                        for _, row in ev_mc[ev_mc[bg2]].sample(n=nbg[bg2],replace=True).iterrows():
                            data[bg][row.radius_cut][row.psi_cut][row.z_cut][row.udotr_cut] += 1
                    else:
                        for _, row in ev[ev[bg2]].sample(n=nbg[bg2],replace=True).iterrows():
                            data[bg][row.radius_cut][row.psi_cut][row.z_cut][row.udotr_cut] += 1
            else:
                for _, row in ev[ev[bg]].iterrows():
                    data[bg][row.radius_cut][row.psi_cut][row.z_cut][row.udotr_cut] += 1

        # 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)

        samples = fit(data, sacrifice, args.steps)

        (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

        for i, bg in enumerate(['signal','muon','noise','neck','flasher','breakdown']):
            if i == 0:
                contamination = samples[:,i]
            else:
                contamination = samples[:,i]*(1-samples[:,5+i])
            mean = np.mean(contamination)
            std = np.std(contamination)
            contamination_pull[bg].append((mean - nbg[bg])/std)

    bins = np.linspace(-10,10,101)
    bincenters = (bins[1:] + bins[:-1])/2

    fig = plt.figure()
    axes = []
    for i, bg in enumerate(['signal','muon','noise','neck','flasher','breakdown']):
        axes.append(plt.subplot(3,2,i+1))
        plt.hist(contamination_pull[bg],bins=bins,histtype='step',normed=True)
        plt.plot(bincenters,norm.pdf(bincenters))
        plt.title(bg.capitalize())
    for ax in axes:
        ax.set_xlim((-10,10))
        despine(ax=ax,left=True,trim=True)
        ax.get_yaxis().set_visible(False)
    plt.tight_layout()

    if args.save:
        fig.savefig("contamination_pull_plot.pdf")
        fig.savefig("contamination_pull_plot.eps")
    else:
        plt.show()
Age	Commit message (Collapse)	Author
2019-06-14	set the maximum kinetic energy in the fit dynamically based on particle ID	tlatorre
	The range and energy loss tables have different maximum values for electrons, muons, and protons so we have to dynamically set the maximum energy of the fit in order to avoid a GSL interpolation error. This commit adds {electron,muon,proton}_get_max_energy() functions to return the maximum energy in the tables and that is then used to set the maximum value in the fit.
2019-03-16	add GPLv3 license	tlatorre

2019-01-27	add photons from delta rays to likelihood calculation	tlatorre
	This commit updates the likelihood function to take into account Cerenkov light produced from delta rays produced by muons. The angular distribution of this light is currently assumed to be constant along the track and parameterized in the same way as the Cerenkov light from an electromagnetic shower. Currently I assume the light is produced uniformly along the track which isn't exactly correct, but should be good enough.
2018-11-11	update likelihood function to fit electrons!	tlatorre
	To characterize the angular distribution of photons from an electromagnetic shower I came up with the following functional form: f(cos_theta) ~ exp(-abs(cos_theta-mu)^alpha/beta) and fit this to data simulated using RAT-PAC at several different energies. I then fit the alpha and beta coefficients as a function of energy to the functional form: alpha = c0 + c1/log(c2T0 + c3) beta = c0 + c1/log(c2T0 + c3). where T0 is the initial energy of the electron in MeV and c0, c1, c2, and c3 are parameters which I fit. The longitudinal distribution of the photons generated from an electromagnetic shower is described by a gamma distribution: f(x) = x*(a-1)exp(-x/b)/(Gamma(a)b*a). This parameterization comes from the PDG "Passage of particles through matter" section 32.5. I also fit the data from my RAT-PAC simulation, but currently I am not using it, and instead using a simpler form to calculate the coefficients from the PDG (although I estimated the b parameter from the RAT-PAC data). I also sped up the calculation of the solid angle by making a lookup table since it was taking a significant fraction of the time to compute the likelihood function.
2018-10-18	update fit to fit for electrons and protons	tlatorre