Key: - To do p Partially done ^ Done ? Not sure if it's done - write cross section section in paper ? explain integral in paper - not sure what integral I was talking about here. I just checked the git history and this was before I had written the fitter, so it must be talking about the integral to compute the expected event rate. p develop signal generator - made signal generator for two particle decays p develop high energy and multi-ring fitter ^ write talk for Monday ^ write a section on atmospheric backgrounds in paper ^ check index of refraction calculation against tables in the paper ^ write more tests for the solid angle calculation - use table from paper ^ make sure normal direction is normalized ^ speed up likelihood calculation - rotate and translate path points in path_init - create fast interp1d for equally spaced points - optimize with -O2 - only calculate average time if mu_direct[i] is not too small and PMT is hit - add likelihood function which calculates total expected charge and only loops over hit PMTs - add fast likelihood which doesn't use a 2D lookup table - add function to compute the Hessian via finite differences - add function to calculate covariance matrix - add function to compute the approximate volume in the likelihood space where the likelihood is greater than some value ^ add output to likelihood ^ add a set of seed points to start the likelihood ^ minimize the likelihood in a do while loop until it converges to a single point ^ once the first position is found, compute the Hough transform to look for other rings p add rayleigh scattering to likelihood function - Done, but it's pretty hacky p add muon shower PDF? delta rays? - Done for delta rays, but need to add shower photons - calculate path length through acrylic? - did some tests on this and it seems to fix the radial energy bias for electrons, so it's definitely an issue. However, currently the small 5% energy bias is not really a big deal, although I would like to fix this eventually. p update estar table with energies above 1 GeV - added values up to 10 GeV ^ speed up normalize() and interp1d() ^ add shower PDF to get_total_charge_approx() x compute mean of starting points ^ speed up time PDF calculation for fast likelihood p calculate psi parameter as a goodness of fit test - Still need to tweak this. It seems to have a strong nhit dependence ^ add a maximum length for the range - now only fit to the end of the PSUP ^ add a time limit for the fit ^ multi-particle fit p optimize CHARGE_FRACTION ? find out why likelihood is sometimes returning nan ^ add pdf for cerenkov light from delta rays ^ tweak find peaks algorithm ^ update zebra to allow use of links p minimum energy for each particle type - I do already have a minimum energy which is the Cerenkov threshold, however I think what I meant here was to have something significantly higher than that since a particle just at the Cerenkov threshold won't produce many PMT hits. I think I was mostly concerned about this issue because many fits were always fitting better by including a low energy electron, however I have solved that problem by simply dropping multi particle fits which have an electron with an energy less than 20 MeV. ^ check all zebra links ^ fix zero logical record size bug in zebra.c p speed up fit - have optimized most of the likelihood function. I think further optimization will require a different technique for evaluating the integrals ^ nhit cut p add flasher cut p default max particles - submit-grid-jobs fits up to 3 particles by default ^ add environment variable to control where to look for pmt.txt and titles files p update charge code to handle highest values for qhs and qlx - don't have this coded into the charge probability code, but I now use QHL if QHS is railed and flag any PMT with a railed QHL ^ use qhs and qlx based on variable in PMT bank - Note: I don't use the best charge variable in the PMT bank, but I do select QHL when QHS is railed ^ fix bug in path_init() ^ load DQXX file based on run number ^ update rayleigh scattering lengths ^ fix delta ray calculation p figure out why electron energy bias is +10% - updated code to use a more accurate approximation for the number of shower photons which seems to bring the bias down to 5% p update find peaks algorithm to do single particle quick fits - I did update the find peaks algorithm to work *much* better, but it still doesn't do single particle quick fits. I think the next improvement would be to add the ability to actually determine the number of rings. ^ figure out how to combine SNO fitter data with my fitter for final analysis. For example, how to apply neutron follower cut? - double check that zdab-reprocess is correct for the D2O and salt phases since it appears to be from the NCD phase ? add code to compute expected deviation from nll_best to normalize psi - tried several different versions of this and nothing seemed to perform as well as psi/nhit. ^ add term to likelihood for probability that a channel is misccalibrated or didn't make it into the event - when calculating the first order statistic for a gaussian is alpha = pi/8 a better choice than 0.375? - speed up charge initialization - determine *real* mean and standard deviation of single PE charge distribution. TELLIE SNO+ data? ^ extend electron range table - extended the electron range table up to 1 TeV ? fix time PDF. Currently take the first order statistic of dark noise + indirect light + direct light all together, but this isn't correct. - thought more about this and it's not actually obvious if what I'm doing is wrong. Need to think more about this. href='#n106'>106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 
#!/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 do final dark matter search analysis. To run it just run:

    $ ./dm-search [list of data fit results] --mc [list of atmospheric MC files] --muon-mc [list of muon MC files] --steps [steps]

After running you will get a plot showing the limits for back to back dark
matter at a range of energies.
"""
from __future__ import print_function, division
import numpy as np
from scipy.stats import iqr, poisson
from matplotlib.lines import Line2D
from scipy.stats import iqr, norm, beta, percentileofscore
from scipy.special import spence
from itertools import izip_longest
from sddm.stats import *
from sddm.dc import estimate_errors, EPSILON, truncnorm_scaled
import emcee
from sddm import printoptions
from sddm.utils import fast_cdf, correct_energy_bias
from scipy.integrate import quad
from sddm.dm import *
from sddm import SNOMAN_MASS, AV_RADIUS
import nlopt

# Likelihood Fit Parameters
# 0 - Atmospheric Neutrino Flux Scale
# 1 - Electron energy bias
# 2 - Electron energy resolution
# 3 - Muon energy bias
# 4 - Muon energy resolution
# 5 - External Muon scale
# 6 - Dark Matter Scale

# Number of events to use in the dark matter Monte Carlo histogram when fitting
# Ideally this would be as big as possible, but the bigger it is, the more time
# the fit takes.
DM_SAMPLES = 10000

DM_MASSES = {2020: np.logspace(np.log10(22),np.log10(10e3 - 500),101),
             2222: np.logspace(np.log10(318),np.log10(10e3 - 500),101)}

DISCOVERY_P_VALUE = 0.05

# Energy resolution as a fraction of energy for dark matter signal
DM_ENERGY_RESOLUTION = 0.1

FIT_PARS = [
    'Atmospheric Neutrino Flux Scale',
    'Electron energy bias',
    'Electron energy resolution',
    'Muon energy bias',
    'Muon energy resolution',
    'External Muon scale',
    'Dark Matter Scale']

# Uncertainty on the energy scale
#
# - the muon energy scale and resolution terms come directly from measurements
#   on stopping muons, so those are known well.
# - for electrons, we only have Michel electrons at the low end of our energy
#   range, and therefore we don't really have any good way of constraining the
#   energy scale or resolution. However, if we assume that the ~7% energy bias
#   in the muons is from the single PE distribution (it seems likely to me that
#   that is a major part of the bias), then the energy scale should be roughly
#   the same. Since the Michel electron distributions are consistent, we leave
#   the mean value at 0, but to be conservative, we set the error to 10%.
# - The energy resolution for muons was pretty much spot on, and so we expect
#   the same from electrons. In addition, the Michel spectrum is consistent so
#   at that energy level we don't see anything which leads us to expect a major
#   difference. To be conservative, and because I don't think it really affects
#   the analysis at all, I'll leave the uncertainty here at 10% anyways.
PRIORS = [
    1.0,   # Atmospheric Neutrino Scale
    0.015, # Electron energy scale
    0.0,   # Electron energy resolution
    0.053, # Muon energy scale
    0.0,   # Muon energy resolution
    0.0,   # Muon scale
    0.0,   # Dark Matter Scale
]

PRIOR_UNCERTAINTIES = [
    0.2,   # Atmospheric Neutrino Scale
    0.03,  # Electron energy scale
    0.05,  # Electron energy resolution
    0.01,  # Muon energy scale
    0.013, # Muon energy resolution
    10.0,  # Muon scale
    np.inf,# Dark Matter Scale
]

# Lower bounds for the fit parameters
PRIORS_LOW = [
    EPSILON,
    -10,
    EPSILON,
    -10,
    EPSILON,
    0,
    0,
]

# Upper bounds for the fit parameters
PRIORS_HIGH = [
    10,
    10,
    10,
    10,
    10,
    1e9,
    1000,
]

particle_id = {20: 'e', 22: r'\mu'}

def plot_hist2(hists, bins, color=None):
    for id in (20,22,2020,2022,2222):
        if id == 20:
            plt.subplot(2,3,1)
        elif id == 22:
            plt.subplot(2,3,2)
        elif id == 2020:
            plt.subplot(2,3,4)
        elif id == 2022:
            plt.subplot(2,3,5)
        elif id == 2222:
            plt.subplot(2,3,6)

        bincenters = (bins[1:] + bins[:-1])/2
        plt.hist(bincenters, bins=bins, histtype='step', weights=hists[id],color=color)
        plt.gca().set_xscale("log")
        plt.xlabel("Energy (MeV)")
        plt.title('$' + ''.join([particle_id[int(''.join(x))] for x in grouper(str(id),2)]) + '$')

    if len(hists):
        plt.tight_layout()

def get_mc_hists(data,x,bins,scale=1.0,reweight=False):
    """
    Returns the expected Monte Carlo histograms for the atmospheric neutrino
    background.

    Args:
        - data: pandas dataframe of the Monte Carlo events
        - x: fit parameters
        - bins: histogram bins
        - scale: multiply histograms by an overall scale factor

    This function does two basic things:

        1. apply the energy bias and resolution corrections
        2. histogram the results

    Returns a dictionary mapping particle id combo -> histogram.
    """
    df_dict = {}
    for id in (20,22,2020,2022,2222):
        df_dict[id] = data[data.id == id]

    return get_mc_hists_fast(df_dict,x,bins,scale,reweight)

def get_mc_hists_fast(df_dict,x,bins,scale=1.0,reweight=False):
    """
    Same as get_mc_hists() but the first argument is a dictionary mapping
    particle id -> dataframe. This is much faster than selecting the events
    from the dataframe every time.
    """
    mc_hists = {}

    for id in (20,22,2020,2022,2222):
        df = df_dict[id]

        if id == 20:
            ke = df.energy1.values*(1+x[1])
            resolution = df.energy1.values*max(EPSILON,x[2])
        elif id == 2020:
            ke = df.energy1.values*(1+x[1]) + df.energy2.values*(1+x[1])
            resolution = np.sqrt((df.energy1.values*max(EPSILON,x[2]))**2 + (df.energy2.values*max(EPSILON,x[2]))**2)
        elif id == 22:
            ke = df.energy1.values*(1+x[3])
            resolution = df.energy1.values*max(EPSILON,x[4])
        elif id == 2222:
            ke = df.energy1.values*(1+x[3]) + df.energy2.values*(1+x[3])
            resolution = np.sqrt((df.energy1.values*max(EPSILON,x[4]))**2 + (df.energy2.values*max(EPSILON,x[4]))**2)
        elif id == 2022:
            ke = df.energy1.values*(1+x[1]) + df.energy2.values*(1+x[3])
            resolution = np.sqrt((df.energy1.values*max(EPSILON,x[2]))**2 + (df.energy2.values*max(EPSILON,x[4]))**2)

        if reweight:
            cdf = fast_cdf(bins[:,np.newaxis],ke,resolution)*df.weight.values
        else:
            cdf = fast_cdf(bins[:,np.newaxis],ke,resolution)

        mc_hists[id] = np.sum(cdf[1:] - cdf[:-1],axis=-1)
        mc_hists[id] *= scale
    return mc_hists

def get_data_hists(data,bins,scale=1.0):
    """
    Returns the data histogrammed into `bins`.
    """
    data_hists = {}
    for id in (20,22,2020,2022,2222):
        data_hists[id] = np.histogram(data[data.id == id].ke.values,bins=bins)[0]*scale
    return data_hists

def make_nll(dm_particle_id, dm_mass, dm_energy, data, muons, mc, atmo_scale_factor, muon_scale_factor, bins, print_nll=False):
    df_dict = {}
    for id in (20,22,2020,2022,2222):
        df_dict[id] = mc[mc.id == id]

    df_dict_muon = {}
    for id in (20,22,2020,2022,2222):
        df_dict_muon[id] = muons[muons.id == id]

    data_hists = get_data_hists(data,bins)

    dm_sample = get_dm_sample(DM_SAMPLES,dm_particle_id,dm_mass,dm_energy)

    df_dict_dm = {}
    for id in (20,22,2020,2022,2222):
        df_dict_dm[id] = dm_sample[dm_sample.id == id]

    def nll(x, grad=None):
        if (x < PRIORS_LOW).any() or (x > PRIORS_HIGH).any():
            return np.inf

        # Get the Monte Carlo histograms. We need to do this within the
        # likelihood function since we apply the energy resolution parameters
        # to the Monte Carlo.
        mc_hists = get_mc_hists_fast(df_dict,x,bins,scale=1/atmo_scale_factor)
        muon_hists = get_mc_hists_fast(df_dict_muon,x,bins,scale=1/muon_scale_factor)
        dm_hists = get_mc_hists_fast(df_dict_dm,x,bins,scale=1/len(dm_sample))

        # Calculate the negative log of the likelihood of observing the data
        # given the fit parameters

        nll = 0
        for id in data_hists:
            oi = data_hists[id]
            ei = mc_hists[id]*x[0] + muon_hists[id]*x[5] + dm_hists[id]*x[6] + EPSILON 
            N = ei.sum()
            nll -= -N - np.sum(gammaln(oi+1)) + np.sum(oi*np.log(ei))

        # Add the priors
        nll -= norm.logpdf(x[:6],PRIORS[:6],PRIOR_UNCERTAINTIES[:6]).sum()

        if print_nll:
            # Print the result
            print("nll = %.2f" % nll)

        return nll
    return nll

def do_fit(dm_particle_id,dm_mass,dm_energy,data,muon,data_mc,atmo_scale_factor,muon_scale_factor,bins,steps,print_nll=False,walkers=100,thin=10):
    """
    Run the fit and return the minimum along with samples from running an MCMC
    starting near the minimum.

    Args:
        - data: pandas dataframe representing the data to fit
        - muon: pandas dataframe representing the expected background from
                external muons
        - data_mc: pandas dataframe representing the expected background from
                   atmospheric neutrino events
        - bins: an array of bins to use for the fit
        - steps: the number of MCMC steps to run

    Returns a tuple (xopt, samples) where samples is an array of shape (steps,
    number of parameters).
    """
    nll = make_nll(dm_particle_id,dm_mass,dm_energy,data,muon,data_mc,atmo_scale_factor,muon_scale_factor,bins,print_nll)

    pos = np.empty((walkers, len(PRIORS)),dtype=np.double)
    for i in range(pos.shape[0]):
        pos[i] = sample_priors()

    nwalkers, ndim = pos.shape

    # We use the KDEMove here because I think it should sample the likelihood
    # better. Because we have energy scale parameters and we are doing a binned
    # likelihood, the likelihood is discontinuous. There can also be several
    # local minima. The author of emcee recommends using the KDEMove with a lot
    # of workers to try and properly sample a multimodal distribution. In
    # addition, I've found that the autocorrelation time for the KDEMove is
    # much better than the other moves.
    sampler = emcee.EnsembleSampler(nwalkers, ndim, lambda x: -nll(x), moves=emcee.moves.KDEMove())
    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.get_chain(flat=True,thin=thin)

    # Now, we use nlopt to find the best set of parameters. We start at the
    # best starting point from the MCMC and then run the SBPLX routine.
    x0 = sampler.get_chain(flat=True)[sampler.get_log_prob(flat=True).argmax()]
    opt = nlopt.opt(nlopt.LN_SBPLX, len(x0))
    opt.set_min_objective(nll)
    low = np.array(PRIORS_LOW)
    high = np.array(PRIORS_HIGH)
    opt.set_lower_bounds(low)
    opt.set_upper_bounds(high)
    opt.set_ftol_abs(1e-10)
    opt.set_initial_step([0.01]*len(x0))
    xopt = opt.optimize(x0)

    return xopt, samples

def sample_priors():
    """
    Returns a random sample of the fit parameters from the priors. For the
    first 6 parameters we use a truncated normal distribution, and for the last
    parameter we use a uniform distribution.
    """
    return np.concatenate((truncnorm_scaled(PRIORS_LOW[:6],PRIORS_HIGH[:6],PRIORS[:6],PRIOR_UNCERTAINTIES[:6]),[np.random.uniform(PRIORS_LOW[6],PRIORS_HIGH[6])]))

def get_dm_sample(n,dm_particle_id,dm_mass,dm_energy):
    """
    Returns a dataframe containing events from a dark matter particle.

    Args:

        - n: int
            number of events
        - dm_particle_id: int
            the particle id of the DM particle (2020 or 2222)
        - dm_energy: float
            The total kinetic energy of the DM particle
        - dm_resolution: float
            The fractional energy resolution of the dark matter particle, i.e.
            the actual energy resolution will be dm_energy*dm_resolution.
    """
    id1 = dm_particle_id//100
    id2 = dm_particle_id % 100
    m1 = SNOMAN_MASS[id1]
    m2 = SNOMAN_MASS[id2]
    energy1 = []
    data = np.empty(n,dtype=[('energy1',np.double),('energy2',np.double),('ke',np.double),('id1',np.int),('id2',np.int),('id',np.int)])
    for i, (v1, v2) in enumerate(islice(gen_decay(dm_mass,dm_energy,m1,m2),n)):
        pos = rand_ball(PSUP_RADIUS)
        E1 = v1[0]
        E2 = v2[0]
        p1 = np.linalg.norm(v1[1:])
        p2 = np.linalg.norm(v2[1:])
        T1 = E1 - m1
        T2 = E2 - m2
        # FIXME: Get electron and muon resolution
        T1 += norm.rvs(scale=T1*0.05)
        T2 += norm.rvs(scale=T2*0.05)
        data[i] = T1, T2, T1 + T2, id1, id2, dm_particle_id
    return pd.DataFrame(data)

def integrate_mc_hist(mc, muons, id, x, a, b, atmo_scale_factor, muon_scale_factor):
    """
    Integrate the Monte Carlo expected histograms from a to b.

    Args:
        - mc: DataFrame
            Pandas dataframe of atmospheric Monte Carlo events.
        - muons: DataFrame
            Pandas dataframe of external muon Monte Carlo events.
        - id: int
            The particle ID histogram to integrate.
        - x: array
            The fit parameters.
        - a, b: float
            Bounds of the integration.
        - atmo_scale_factor, muon_scale_factor: float
            Scale factors for the fit parameters.
    """
    mc_hists = get_mc_hists(mc,x,bins,scale=x[0]/atmo_scale_factor)
    muon_hists = get_mc_hists(muons,x,bins,scale=x[5]/muon_scale_factor)

    def total_hist(x):
        if x < bins[0] or x > bins[-1]:
            return 0
        i = np.digitize(x,bins)
        if i == len(bins):
            i = len(bins) - 1
        return (mc_hists[id][i-1] + muon_hists[id][i-1])/(bins[i]-bins[i-1])

    # Yes, this is a stupid simple integration that I don't need quad for, but
    # I don't want to have to code all the corner cases including when a and b
    # are in the same bin, etc.
    return quad(total_hist,a,b,points=bins[(bins >= a) & (bins <= b)])[0]

def get_limits(dm_masses,data,muon,data_mc,atmo_scale_factor,muon_scale_factor,bins,steps,print_nll,walkers,thin):
    limits = {}
    best_fit = {}
    discovery_array = {}
    for dm_particle_id in (2020,2222):
        limits[dm_particle_id] = []
        best_fit[dm_particle_id] = []
        discovery_array[dm_particle_id] = []
        for dm_mass in dm_masses[dm_particle_id]:
            id1 = dm_particle_id//100
            id2 = dm_particle_id % 100
            m1 = SNOMAN_MASS[id1]
            m2 = SNOMAN_MASS[id2]
            dm_energy = dm_mass
            xopt, samples = do_fit(dm_particle_id,dm_mass,dm_energy,data,muon,data_mc,atmo_scale_factor,muon_scale_factor,bins,steps,print_nll,walkers,thin)

            limit = np.percentile(samples[:,6],90)
            limits[dm_particle_id].append(limit)

            # Here, to determine if there is a discovery we make an approximate
            # calculation of the number of events which would be significant.
            #
            # We expect the likelihood to be approximately that of a Poisson
            # distribution with n background events and we are searching for a
            # signal s. n is constrained by the rest of the histograms, and so
            # we can treat is as being approximately fixed. In this case, the
            # likelihood looks approximately like:
            #
            #     P(s) = e^(-(s+n))(s+n)**i/i!
            #
            # Where i is the actual number of events. Under the null hypothesis
            # (i.e. no dark matter), we expect i to be Poisson distributed with
            # mean n. Therefore s should have the same distribution but offset
            # by n. Therefore, to determine the threshold, we simply look for
            # the threshold we expect in n and then subtract n.
            dm_kinetic_energy = dm_energy - m1 - m2
            a = dm_kinetic_energy - 2*dm_kinetic_energy*DM_ENERGY_RESOLUTION
            b = dm_kinetic_energy + 2*dm_kinetic_energy*DM_ENERGY_RESOLUTION
            n = integrate_mc_hist(data_mc, muon, dm_particle_id, xopt, a, b, atmo_scale_factor, muon_scale_factor)
            # Set our discovery threshold to the p-value we want divided by the
            # number of bins. The idea here is that the number of bins is
            # approximately equal to the number of trials so we need to
            # increase our discovery threshold to account for the look
            # elsewhere effect.
            threshold = DISCOVERY_P_VALUE/(len(bins)-1)
            discovery = poisson.ppf(1-threshold,n) + 1 - n
            discovery_array[dm_particle_id].append(discovery)
            best_fit[dm_particle_id].append(xopt[6])

    return limits, best_fit, discovery_array

if __name__ == '__main__':
    import argparse
    import numpy as np
    import pandas as pd
    import sys
    import h5py
    from sddm.plot_energy import *
    from sddm.plot import *
    from sddm import setup_matplotlib
    import nlopt

    parser = argparse.ArgumentParser("plot fit results")
    parser.add_argument("filenames", nargs='+', help="input files")
    parser.add_argument("--save", action='store_true', default=False, help="save corner plots for backgrounds")
    parser.add_argument("--mc", nargs='+', required=True, help="atmospheric MC files")
    parser.add_argument("--muon-mc", nargs='+', required=True, help="muon 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)")
    parser.add_argument("--steps", type=int, default=1000, help="number of steps in the MCMC chain")
    parser.add_argument("--pull", type=int, default=0, help="plot pull plots")
    parser.add_argument("--weights", nargs='+', required=True, help="GENIE reweight HDF5 files")
    parser.add_argument("--print-nll", action='store_true', default=False, help="print nll values")
    parser.add_argument("--walkers", type=int, default=100, help="number of walkers")
    parser.add_argument("--thin", type=int, default=10, help="number of steps to thin")
    parser.add_argument("--test", type=int, default=0, help="run tests to check discovery threshold")
    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)

    livetime = 0.0
    livetime_pulse_gt = 0.0
    for ev in evs:
        if not np.isnan(ev.attrs['time_10_mhz']):
            livetime += ev.attrs['time_10_mhz']
        else:
            livetime += ev.attrs['time_pulse_gt']
        livetime_pulse_gt += ev.attrs['time_pulse_gt']

    print("livetime            = %.2f" % livetime)
    print("livetime (pulse gt) = %.2f" % livetime_pulse_gt)

    ev = correct_energy_bias(ev)

    # Note: We loop over the MC filenames here instead of just passing the
    # whole list to get_events() because I had to rerun some of the MC events
    # using SNOMAN and so most of the runs actually have two different files
    # and otherwise the GTIDs will clash
    ev_mcs = []
    for filename in args.mc:
        ev_mcs.append(get_events([filename], merge_fits=True, nhit_thresh=args.nhit_thresh, mc=True))
    ev_mc = pd.concat(ev_mcs)
    muon_mc = get_events(args.muon_mc, merge_fits=True, nhit_thresh=args.nhit_thresh, mc=True)
    weights = pd.concat([read_hdf(filename, "weights") for filename in args.weights],ignore_index=True)

    ev_mc = correct_energy_bias(ev_mc)
    muon_mc = correct_energy_bias(muon_mc)

    # Set all prompt events in the MC to be muons
    muon_mc.loc[muon_mc.prompt & muon_mc.filename.str.contains("cosmic"),'muon'] = True

    ev = ev.reset_index()
    ev_mc = ev_mc.reset_index()
    muon_mc = muon_mc.reset_index()

    # 00-orphan cut
    ev = ev[(ev.gtid & 0xff) != 0]
    ev_mc = ev_mc[(ev_mc.gtid & 0xff) != 0]
    muon_mc = muon_mc[(muon_mc.gtid & 0xff) != 0]

    # remove events 200 microseconds after a muon
    ev = ev.groupby('run',group_keys=False).apply(muon_follower_cut)

    # Get rid of events which don't have a successful fit
    ev = ev[~np.isnan(ev.fmin)]
    ev_mc = ev_mc[~np.isnan(ev_mc.fmin)]
    muon_mc = muon_mc[~np.isnan(muon_mc.fmin)]

    # require (r < av radius)
    ev = ev[ev.r < AV_RADIUS]
    ev_mc = ev_mc[ev_mc.r < AV_RADIUS]
    muon_mc = muon_mc[muon_mc.r < AV_RADIUS]

    fiducial_volume = (4/3)*np.pi*(AV_RADIUS)**3

    # require psi < 6
    ev = ev[ev.psi < 6]
    ev_mc = ev_mc[ev_mc.psi < 6]
    muon_mc = muon_mc[muon_mc.psi < 6]

    data = ev[ev.signal & ev.prompt & ~ev.atm]
    data_atm = ev[ev.signal & ev.prompt & ev.atm]

    # Right now we use the muon Monte Carlo in the fit. If you want to use the
    # actual data, you can comment the next two lines and then uncomment the
    # two after that.
    muon = muon_mc[muon_mc.muon & muon_mc.prompt & ~muon_mc.atm]
    muon_atm = muon_mc[muon_mc.muon & muon_mc.prompt & muon_mc.atm]
    #muon = ev[ev.muon & ev.prompt & ~ev.atm]
    #muon_atm = ev[ev.muon & ev.prompt & ev.atm]

    if (~rhdr.run.isin(ev_mc.run)).any():
        print_warning("Error! The following runs have no Monte Carlo: %s" % \
            rhdr.run[~rhdr.run.isin(ev_mc.run)].values)
        sys.exit(1)

    ev_mc = ev_mc[ev_mc.run.isin(rhdr.run)]

    data_mc = ev_mc[ev_mc.signal & ev_mc.prompt & ~ev_mc.atm]
    data_atm_mc = ev_mc[ev_mc.signal & ev_mc.prompt & ev_mc.atm]

    data_mc = ev_mc[ev_mc.signal & ev_mc.prompt & ~ev_mc.atm]

    bins = np.logspace(np.log10(20),np.log10(10e3),21)

    atmo_scale_factor = 100.0
    muon_scale_factor = len(muon) + len(muon_atm)

    if args.pull:
        pull = [[] for i in range(len(FIT_PARS))]

        # Set the random seed so we get reproducible results here
        np.random.seed(0)

        for i in range(args.pull):
            xtrue = sample_priors()

            # Calculate expected number of events
            N = len(data_mc)*xtrue[0]/atmo_scale_factor
            N_atm = len(data_atm_mc)*xtrue[0]/atmo_scale_factor
            N_muon = len(muon)*xtrue[5]/muon_scale_factor
            N_muon_atm = len(muon_atm)*xtrue[5]/muon_scale_factor
            N_dm = xtrue[6]

            # Calculate observed number of events
            n = np.random.poisson(N)
            n_atm = np.random.poisson(N_atm)
            n_muon = np.random.poisson(N_muon)
            n_muon_atm = np.random.poisson(N_muon_atm)
            n_dm = np.random.poisson(N_dm)

            dm_particle_id = np.random.choice([2020,2222])
            dm_mass = np.random.uniform(20,10e3)
            dm_energy = dm_mass

            # Sample data from Monte Carlo
            data = pd.concat((data_mc.sample(n=n,replace=True), muon.sample(n=n_muon,replace=True),get_dm_sample(n_dm,dm_particle_id,dm_mass,dm_energy)))
            data_atm = pd.concat((data_atm_mc.sample(n=n_atm,replace=True), muon_atm.sample(n=n_muon_atm,replace=True)))

            # Smear the energies by the additional energy resolution
            data.loc[data.id1 == 20,'energy1'] *= (1+xtrue[1]+np.random.randn(np.count_nonzero(data.id1 == 20))*xtrue[2])
            data.loc[data.id1 == 22,'energy1'] *= (1+xtrue[3]+np.random.randn(np.count_nonzero(data.id1 == 22))*xtrue[4])
            data.loc[data.id2 == 20,'energy2'] *= (1+xtrue[1]+np.random.randn(np.count_nonzero(data.id2 == 20))*xtrue[2])
            data.loc[data.id2 == 22,'energy2'] *= (1+xtrue[3]+np.random.randn(np.count_nonzero(data.id2 == 22))*xtrue[4])
            data['ke'] = data['energy1'].fillna(0) + data['energy2'].fillna(0) + data['energy3'].fillna(0)

            data_atm.loc[data_atm.id1 == 20,'energy1'] *= (1+xtrue[1]+np.random.randn(np.count_nonzero(data_atm.id1 == 20))*xtrue[2])
            data_atm.loc[data_atm.id1 == 22,'energy1'] *= (1+xtrue[3]+np.random.randn(np.count_nonzero(data_atm.id1 == 22))*xtrue[4])
            data_atm.loc[data_atm.id2 == 20,'energy2'] *= (1+xtrue[1]+np.random.randn(np.count_nonzero(data_atm.id2 == 20))*xtrue[2])
            data_atm.loc[data_atm.id2 == 22,'energy2'] *= (1+xtrue[3]+np.random.randn(np.count_nonzero(data_atm.id2 == 22))*xtrue[4])
            data_atm['ke'] = data_atm['energy1'].fillna(0) + data_atm['energy2'].fillna(0) + data_atm['energy3'].fillna(0)

            xopt, samples = do_fit(dm_particle_id,dm_mass,dm_energy,data,muon,data_mc,atmo_scale_factor,muon_scale_factor,bins,args.steps,args.print_nll,args.walkers,args.thin)

            for i in range(len(FIT_PARS)):
                # The "pull plots" we make here are actually produced via a
                # procedure called "Simulation Based Calibration".
                #
                # See https://arxiv.org/abs/1804.06788.
                pull[i].append(percentileofscore(samples[:,i],xtrue[i]))

        fig = plt.figure()
        axes = []
        for i, name in enumerate(FIT_PARS):
            axes.append(plt.subplot(4,2,i+1))
            n, bins, patches = plt.hist(pull[i],bins=np.linspace(0,100,11),histtype='step')
            expected = len(pull[i])/(len(bins)-1)
            plt.axhline(expected,color='k',ls='--',alpha=0.25)
            plt.axhspan(poisson.ppf(0.005,expected), poisson.ppf(0.995,expected), facecolor='0.5', alpha=0.25)
            plt.title(name)
        for ax in axes:
            despine(ax=ax,left=True,trim=True)
            ax.get_yaxis().set_visible(False)
        plt.tight_layout()

        if args.save:
            fig.savefig("dm_search_pull_plot.pdf")
            fig.savefig("dm_search_pull_plot.eps")
        else:
            plt.show()

        sys.exit(0)

    if args.test:
        # Set the random seed so we get reproducible results here
        np.random.seed(0)

        discoveries = 0

        for i in range(args.test):
            xtrue = sample_priors()

            # Calculate expected number of events
            N = len(data_mc)*xtrue[0]/atmo_scale_factor
            N_atm = len(data_atm_mc)*xtrue[0]/atmo_scale_factor
            N_muon = len(muon)*xtrue[5]/muon_scale_factor
            N_muon_atm = len(muon_atm)*xtrue[5]/muon_scale_factor
            N_dm = xtrue[6]

            # Calculate observed number of events
            n = np.random.poisson(N)
            n_atm = np.random.poisson(N_atm)
            n_muon = np.random.poisson(N_muon)
            n_muon_atm = np.random.poisson(N_muon_atm)
            n_dm = np.random.poisson(N_dm)

            dm_particle_id = np.random.choice([2020,2222])
            dm_mass = np.random.uniform(20,10e3)
            dm_energy = dm_mass

            # Sample data from Monte Carlo
            data = pd.concat((data_mc.sample(n=n,replace=True), muon.sample(n=n_muon,replace=True),get_dm_sample(n_dm,dm_particle_id,dm_mass,dm_energy)))
            data_atm = pd.concat((data_atm_mc.sample(n=n_atm,replace=True), muon_atm.sample(n=n_muon_atm,replace=True)))

            # Smear the energies by the additional energy resolution
            data.loc[data.id1 == 20,'energy1'] *= (1+xtrue[1]+np.random.randn(np.count_nonzero(data.id1 == 20))*xtrue[2])
            data.loc[data.id1 == 22,'energy1'] *= (1+xtrue[3]+np.random.randn(np.count_nonzero(data.id1 == 22))*xtrue[4])
            data.loc[data.id2 == 20,'energy2'] *= (1+xtrue[1]+np.random.randn(np.count_nonzero(data.id2 == 20))*xtrue[2])
            data.loc[data.id2 == 22,'energy2'] *= (1+xtrue[3]+np.random.randn(np.count_nonzero(data.id2 == 22))*xtrue[4])
            data['ke'] = data['energy1'].fillna(0) + data['energy2'].fillna(0) + data['energy3'].fillna(0)

            data_atm.loc[data_atm.id1 == 20,'energy1'] *= (1+xtrue[1]+np.random.randn(np.count_nonzero(data_atm.id1 == 20))*xtrue[2])
            data_atm.loc[data_atm.id1 == 22,'energy1'] *= (1+xtrue[3]+np.random.randn(np.count_nonzero(data_atm.id1 == 22))*xtrue[4])
            data_atm.loc[data_atm.id2 == 20,'energy2'] *= (1+xtrue[1]+np.random.randn(np.count_nonzero(data_atm.id2 == 20))*xtrue[2])
            data_atm.loc[data_atm.id2 == 22,'energy2'] *= (1+xtrue[3]+np.random.randn(np.count_nonzero(data_atm.id2 == 22))*xtrue[4])
            data_atm['ke'] = data_atm['energy1'].fillna(0) + data_atm['energy2'].fillna(0) + data_atm['energy3'].fillna(0)

            limits, best_fit, discovery_array = get_limits(DM_MASSES,data,muon,data_mc,atmo_scale_factor,muon_scale_factor,bins,args.steps,args.print_nll,args.walkers,args.thin)

            for id in (2020,2222):
                if (best_fit[id] > discovery_array[id]).any():
                    discoveries += 1

        print("expected %.2f discoveries" % DISCOVERY_P_VALUE)
        print("actually got %i/%i = %.2f discoveries" % (discoveries,args.test,discoveries/args.test))

        sys.exit(0)

    limits, best_fit, discovery_array = get_limits(DM_MASSES,data,muon,data_mc,atmo_scale_factor,muon_scale_factor,bins,args.steps,args.print_nll,args.walkers,args.thin)

    fig = plt.figure()
    for color, dm_particle_id in zip(('C0','C1'),(2020,2222)):
        plt.plot(DM_MASSES[dm_particle_id],limits[dm_particle_id]/fiducial_volume/livetime,color=color,label='$' + ''.join([particle_id[int(''.join(x))] for x in grouper(str(dm_particle_id),2)]) + '$')
    plt.gca().set_xscale("log")
    despine(fig,trim=True)
    plt.xlabel("Energy (MeV)")
    plt.ylabel("Event Rate Limit (events/cm^3/s)")
    plt.legend()
    plt.tight_layout()

    if args.save:
        plt.savefig("dm_search_limit.pdf")
        plt.savefig("dm_search_limit.eps")
    else:
        plt.suptitle("Dark Matter Limits")

    fig = plt.figure()
    for color, dm_particle_id in zip(('C0','C1'),(2020,2222)):
        plt.plot(DM_MASSES[dm_particle_id],best_fit[dm_particle_id],color=color,label='$' + ''.join([particle_id[int(''.join(x))] for x in grouper(str(dm_particle_id),2)]) + '$')
        plt.plot(DM_MASSES[dm_particle_id],discovery_array[dm_particle_id],color=color,ls='--')
    plt.gca().set_xscale("log")
    despine(fig,trim=True)
    plt.xlabel("Energy (MeV)")
    plt.ylabel("Event Rate Limit (events)")
    plt.legend()
    plt.tight_layout()

    if args.save:
        plt.savefig("dm_best_fit_with_discovery_threshold.pdf")
        plt.savefig("dm_best_fit_with_discovery_threshold.eps")
    else:
        plt.suptitle("Best Fit Dark Matter")
        plt.show()
generated by cgit (git 2.34.1) at 2025-10-13 19:51:09 +0000