add scripts to apply neutrino oscillations to the atmospheric fluxes

This commit adds four scripts:

1. calculate-atmospheric-oscillations

This script uses an independent python package called nucraft to calculate the
neutrino oscillation probabilities for atmospheric neutrinos. These
probabilities are calculated as a function of energy and cosine of the zenith
angle and stored in text files.

2. apply-atmospheric-oscillations

This script combines the high energy 2D atmospheric neutrino flux from Barr and
the low energy 1D flux from Battistoni and then applies neutrino oscillations
to them. The results are then stored in new flux files that can be used with a
modified version of GENIE to simulate the oscillated atmospheric neutrino flux
from 10 MeV to 10 GeV.

3. plot-atmospheric-fluxes

This is a simple script to plot the atmospheric flux files produced by
apply-atmospheric-oscillations.

4. plot-atmospheric-oscillations

This is a simple script to plot the 2D neutrino oscillation probabilities.

5 files changed, 839 insertions, 0 deletions

diff --git a/utils/.gitignore b/utils/.gitignore
new file mode 100644
index 0000000..e307f16
--- /dev/null
+++ b/utils/.gitignore
@@ -0,0 +1,2 @@
+*.eps
+*.pdf
diff --git a/utils/apply-atmospheric-oscillations b/utils/apply-atmospheric-oscillations
new file mode 100755
index 0000000..3d9f32d
--- /dev/null
+++ b/utils/apply-atmospheric-oscillations
@@ -0,0 +1,322 @@
+#!/usr/bin/env python
+"""
+Script to combine the low energy Battistoni atmospheric flux with the high
+energy flux from Giles Barr and apply oscillations.
+
+Note: There are a couple of potential issues with this:
+
+1. The Battistoni fluxes give a total flux integrated over the zenith angle
+whereas we need to account for the zenith dependence. Therefore, we just use
+the zenith dependence of the lowest energy in the Barr flux files.
+
+2. I only have access to the Battistoni fluxes for electron neutrinos.
+Therefore I will assume that the muon neutrino flux is twice as big which seems
+to be roughly correct based on the paper "The Atmospheric Neutrino Flux Below
+100 MeV: The FLUKA Results".
+
+To run it:
+
+    $ ./apply-atmospheric-oscillations --flux-dir ~/atm-production/fluxes/irc01_plus_lowe \
+                                       --osc-dir ~/atm-production/nucraft_osc
+"""
+from __future__ import print_function, division
+import numpy as np
+
+def pdg_code_to_string(pdg):
+    if pdg == 12:
+        return "nue"
+    elif pdg == -12:
+        return "nbe"
+    elif pdg == 14:
+        return "num"
+    elif pdg == -14:
+        return "nbm"
+    elif pdg == 16:
+        return "nut"
+    elif pdg == -16:
+        return "nbt"
+    else:
+        raise ValueError("Unknown pdg code %i" % pdg)
+
+if __name__ == '__main__':
+    import argparse
+    import matplotlib.pyplot as plt
+    from os.path import split, splitext, join
+    from scipy.interpolate import RectBivariateSpline
+    from scipy.integrate import dblquad, nquad
+    import sys
+
+    parser = argparse.ArgumentParser("combine low energy and high energy atmospheric fluxes and apply oscillations")
+    parser.add_argument("--flux-dir",required=True,help="atmospheric production directory")
+    parser.add_argument("--osc-dir",required=True,help="directory with atmospheric oscillations")
+    args = parser.parse_args()
+
+    # Energy and cos(zenith) bins for the fluxes from Barr
+    barr_cos_theta_bins = np.linspace(-1,1,21)
+    barr_energy_bins = np.logspace(-1,1,41)
+
+    # Final energy bins
+    # We go here from 10 MeV -> 10 GeV with 20 points per decade like the Barr
+    # fluxes
+    energy_bins = np.logspace(-2,1,61)
+    cos_theta_bins = barr_cos_theta_bins.copy()
+
+    # Read in Battistoni fluxes
+    nue_battistoni = np.genfromtxt(join(args.flux_dir,"lowe/nue.dat"))
+    nbe_battistoni = np.genfromtxt(join(args.flux_dir,"lowe/nbe.dat"))
+
+    # Convert Battistoni fluxes from MeV -> GeV
+    nue_battistoni[:,0] /= 1000.0
+    nue_battistoni[:,1] *= 1000.0
+    nbe_battistoni[:,0] /= 1000.0
+    nbe_battistoni[:,1] *= 1000.0
+
+    # Convert Battistoni fluxes from cm^-2 -> m^-2
+    nue_battistoni[:,1] *= 100.0**2
+    nbe_battistoni[:,1] *= 100.0**2
+
+    # Assume muon neutrino flux below 100 MeV is twice that of electron
+    # neutrino flux
+    num_battistoni = nue_battistoni.copy()
+    num_battistoni[:,1] *= 2
+    nbm_battistoni = nbe_battistoni.copy()
+    nbm_battistoni[:,1] *= 2
+
+    # Read in Barr fluxes
+    nue_barr = np.genfromtxt(join(args.flux_dir,"irc01/fmax20_i0403z.sno_nue"))
+    nbe_barr = np.genfromtxt(join(args.flux_dir,"irc01/fmax20_i0403z.sno_nbe"))
+    num_barr = np.genfromtxt(join(args.flux_dir,"irc01/fmax20_i0403z.sno_num"))
+    nbm_barr = np.genfromtxt(join(args.flux_dir,"irc01/fmax20_i0403z.sno_nbm"))
+
+    # Read in oscillation probabilities
+    nue_osc_prob = np.genfromtxt(join(args.osc_dir,"nue_osc_prob.txt"))
+    nbe_osc_prob = np.genfromtxt(join(args.osc_dir,"nbe_osc_prob.txt"))
+    num_osc_prob = np.genfromtxt(join(args.osc_dir,"num_osc_prob.txt"))
+    nbm_osc_prob = np.genfromtxt(join(args.osc_dir,"nbm_osc_prob.txt"))
+
+    # Reshape oscillation probability arrays. They should now look like:
+    #
+    #     [[[0.01,  -1,   P(nue), P(num), P(nut)],
+    #       [0.01,  -0.8, P(nue), P(num), P(nut)],
+    #                ...
+    #       [0.01,  1.0,  P(nue), P(num), P(nut)]],
+    #      [[0.02,  -1,   P(nue), P(num), P(nut)],
+    #       [0.02,  -0.8, P(nue), P(num), P(nut)],
+    #                ...
+    #       [0.02,  1.0,  P(nue), P(num), P(nut)]],
+    #                ...
+    #      [[10.0,  -1,   P(nue), P(num), P(nut)],
+    #       [10.0,  -0.8, P(nue), P(num), P(nut)],
+    #                ...
+    #       [10.0,  1.0,  P(nue), P(num), P(nut)]]]
+    shape0 = len(np.unique(nue_osc_prob[:,0]))
+    nue_osc_prob = nue_osc_prob.reshape((shape0,-1,5))
+    nbe_osc_prob = nbe_osc_prob.reshape((shape0,-1,5))
+    num_osc_prob = num_osc_prob.reshape((shape0,-1,5))
+    nbm_osc_prob = nbm_osc_prob.reshape((shape0,-1,5))
+
+    # convert dn/dlnE -> dn/dE
+    nue_barr[:,2] /= nue_barr[:,0]
+    nbe_barr[:,2] /= nbe_barr[:,0]
+    num_barr[:,2] /= num_barr[:,0]
+    nbm_barr[:,2] /= nbm_barr[:,0]
+
+    # Reshape Barr flux arrays. They should now look like:
+    #
+    #     [[[0.1,  -1,   flux,...],
+    #       [0.2,  -1,   flux,...],
+    #               ...
+    #       [10.0, -1,   flux,...]],
+    # 
+    #      [[0.1,  -0.9, flux,...],
+    #       [0.2,  -0.9, flux,...],
+    #              ...
+    #       [10.0, -0.9, flux,...]],
+    #              ...
+    #              ...
+    #      [[0.1,   1.0, flux,...],
+    #       [0.2,   1.0, flux,...],
+    #              ...
+    #       [10.0,  1.0, flux,...]]]
+    shape1 = len(np.unique(nue_barr[:,0]))
+    nue_barr = nue_barr.reshape((-1,shape1,5))
+    nbe_barr = nbe_barr.reshape((-1,shape1,5))
+    num_barr = num_barr.reshape((-1,shape1,5))
+    nbm_barr = nbm_barr.reshape((-1,shape1,5))
+
+    nue_zenith_dist_x = nue_barr[:,0,1].copy()
+    nue_zenith_dist_y = nue_barr[:,0,2].copy()
+    nue_zenith_dist_y /= np.trapz(nue_zenith_dist_y,x=nue_zenith_dist_x)
+    nbe_zenith_dist_x = nbe_barr[:,0,1].copy()
+    nbe_zenith_dist_y = nbe_barr[:,0,2].copy()
+    nbe_zenith_dist_y /= np.trapz(nbe_zenith_dist_y,x=nbe_zenith_dist_x)
+    num_zenith_dist_x = num_barr[:,0,1].copy()
+    num_zenith_dist_y = num_barr[:,0,2].copy()
+    num_zenith_dist_y /= np.trapz(num_zenith_dist_y,x=num_zenith_dist_x)
+    nbm_zenith_dist_x = nbm_barr[:,0,1].copy()
+    nbm_zenith_dist_y = nbm_barr[:,0,2].copy()
+    nbm_zenith_dist_y /= np.trapz(nbm_zenith_dist_y,x=nbm_zenith_dist_x)
+
+    nue_battistoniz = np.empty((nue_barr.shape[0],nue_battistoni.shape[0],4))
+    nue_battistoniz[:,:,0] = nue_battistoni[:,0]
+    nue_battistoniz[:,:,1] = nue_zenith_dist_x[:,np.newaxis]
+    nue_battistoniz[:,:,2] = nue_battistoni[:,1]*nue_zenith_dist_y[:,np.newaxis]/(2*np.pi)
+    nue_battistoniz[:,:,3] = nue_battistoniz[:,:,2]*nue_battistoniz[:,:,0]
+
+    nbe_battistoniz = np.empty((nbe_barr.shape[0],nbe_battistoni.shape[0],4))
+    nbe_battistoniz[:,:,0] = nbe_battistoni[:,0]
+    nbe_battistoniz[:,:,1] = nbe_zenith_dist_x[:,np.newaxis]
+    nbe_battistoniz[:,:,2] = nbe_battistoni[:,1]*nbe_zenith_dist_y[:,np.newaxis]/(2*np.pi)
+    nbe_battistoniz[:,:,3] = nbe_battistoniz[:,:,2]*nbe_battistoniz[:,:,0]
+
+    num_battistoniz = np.empty((num_barr.shape[0],num_battistoni.shape[0],4))
+    num_battistoniz[:,:,0] = num_battistoni[:,0]
+    num_battistoniz[:,:,1] = num_zenith_dist_x[:,np.newaxis]
+    num_battistoniz[:,:,2] = num_battistoni[:,1]*num_zenith_dist_y[:,np.newaxis]/(2*np.pi)
+    num_battistoniz[:,:,3] = num_battistoniz[:,:,2]*num_battistoniz[:,:,0]
+
+    nbm_battistoniz = np.empty((nbm_barr.shape[0],nbm_battistoni.shape[0],4))
+    nbm_battistoniz[:,:,0] = nbm_battistoni[:,0]
+    nbm_battistoniz[:,:,1] = nbm_zenith_dist_x[:,np.newaxis]
+    nbm_battistoniz[:,:,2] = nbm_battistoni[:,1]*nbm_zenith_dist_y[:,np.newaxis]/(2*np.pi)
+    nbm_battistoniz[:,:,3] = nbm_battistoniz[:,:,2]*nbm_battistoniz[:,:,0]
+
+    nue_total = np.empty((nue_barr.shape[0],nue_barr.shape[1]+nue_battistoniz.shape[1],4))
+    nue_total[:,:nue_battistoniz.shape[1],:] = nue_battistoniz
+    nue_total[:,nue_battistoniz.shape[1]:,:] = nue_barr[:,:,:4]
+
+    nbe_total = np.empty((nbe_barr.shape[0],nbe_barr.shape[1]+nbe_battistoniz.shape[1],4))
+    nbe_total[:,:nbe_battistoniz.shape[1],:] = nbe_battistoniz
+    nbe_total[:,nbe_battistoniz.shape[1]:,:] = nbe_barr[:,:,:4]
+
+    num_total = np.empty((num_barr.shape[0],num_barr.shape[1]+num_battistoniz.shape[1],4))
+    num_total[:,:num_battistoniz.shape[1],:] = num_battistoniz
+    num_total[:,num_battistoniz.shape[1]:,:] = num_barr[:,:,:4]
+
+    nbm_total = np.empty((nbm_barr.shape[0],nbm_barr.shape[1]+nbm_battistoniz.shape[1],4))
+    nbm_total[:,:nbm_battistoniz.shape[1],:] = nbm_battistoniz
+    nbm_total[:,nbm_battistoniz.shape[1]:,:] = nbm_barr[:,:,:4]
+
+    flux_arrays = {12: nue_total, -12: nbe_total,
+                   14: num_total, -14: nbm_total}
+
+    # Save unoscillated fluxes
+    for p in [12,-12,14,-14]:
+        np.savetxt("fmax20_i0403z_plus_lowe.sno_%s" % pdg_code_to_string(p),flux_arrays[p].reshape((flux_arrays[p].shape[0]*flux_arrays[p].shape[1],-1)),
+                   fmt='%10.4f %10.3f %20.8g %20.8g',
+                   header="Energy (GeV), Cos(zenith), Flux (m^-2 s^-1 Gev^-1 steradian^-1), Flux (dn/dlnE)")
+
+    osc_prob = {12: nue_osc_prob, -12: nbe_osc_prob,
+                14: num_osc_prob, -14: nbm_osc_prob}
+
+    def get_flux_interp(nu_type):
+        flux_array = flux_arrays[nu_type]
+        flux = flux_array[:,:,2]
+        e = flux_array[0,:,0]
+        cos_theta = flux_array[:,0,1]
+
+        # Use first order splines here since we need to enforce the fact that
+        # the flux is not negative
+        return RectBivariateSpline(e,cos_theta,flux.T,kx=1,ky=1)
+
+    def get_osc_interp(nu_type1,nu_type2):
+        prob = osc_prob[nu_type1]
+        e = prob[:,0,0]
+        cos_theta = prob[0,:,1]
+
+        if np.sign(nu_type1) != np.sign(nu_type2):
+            raise ValueError("asking for oscillation probability from %s -> %s!" % tuple(map(pdg_code_to_string,(nu_type1,nu_type2))))
+
+        # Use second order splines here since oscillation probabilities are
+        # pretty smooth
+        if abs(nu_type2) == 12:
+            return RectBivariateSpline(e,cos_theta,prob[:,:,2],kx=2,ky=2)
+        elif abs(nu_type2) == 14:
+            return RectBivariateSpline(e,cos_theta,prob[:,:,3],kx=2,ky=2)
+        elif abs(nu_type2) == 16:
+            return RectBivariateSpline(e,cos_theta,prob[:,:,4],kx=2,ky=2)
+
+    def get_oscillated_flux(nu_type1, nu_type2, elo, emid, ehi, zlo, zmid, zhi):
+        """
+        Returns the average flux of neutrinos coming from `nu_type1` neutrinos
+        oscillating to `nu_type2` neutrinos for neutrinos in the bin between
+        energies elo and ehi and with a cosine of the zenith angle between zlo
+        and zhi.
+
+        Note: We also pass the midpoint of the bin for both energy and
+        cos(theta) as `emid` and `zmid`. The reason for this is that at least
+        for the Barr fluxes, the midpoint of the bin was chosen as the midpoint
+        of the log of the left and right edge instead of the actual middle of
+        the bin. Therefore to be consistent when interpolating these fluxes we
+        should use the same value.
+
+        The returned flux has units of 1/(m^2 sec steradian GeV).
+        """
+        f_flux1 = get_flux_interp(nu_type1)
+        f_osc1 = get_osc_interp(nu_type1,nu_type2)
+
+        def f_flux(e,z):
+            # Not sure exactly how scipy deals with boundary issues in
+            # RectBivariateSpline so we just make sure everything is within the
+            # range of the values given in the Barr and Battistoni fluxes
+            if e < 0.0106:
+                e = 0.0106
+            if z < -0.95:
+                z = -0.95
+            if z > 0.95:
+                z = 0.95
+            return f_flux1(e,z)
+
+        def f_osc(e,z):
+            # FIXME: Should remove this
+            if e < 0.02:
+                e = 0.02
+            return f_osc1(e,z)
+
+        # Here we have two options for calculating the oscillated flux:
+        #
+        # 1. We interpolate the value of the flux and then multiply by an
+        # average oscillation probability. This is more correct in the sense
+        # that the original flux values are actually a histogram and so it
+        # makes sense to just sample the flux at the middle of the bin.
+        #
+        # 2. We integrate the product of the flux and the oscillation
+        # probability over the whole bin. This is technically more correct
+        # since it will weight the oscillation probability by the flux, but it
+        # may have issues near the edge of the first and last bin since we have
+        # to extrapolate.
+        #
+        # For now, we do 1 since it is much faster. To do the second you can
+        # just comment the next line.
+        return f_flux(emid,zmid)*f_osc1.integral(elo,ehi,zlo, zhi)/(ehi-elo)/(zhi-zlo)
+        return nquad(lambda e, z: f_flux(e,z)*f_osc(e,z), [(elo,ehi), (zlo, zhi)], opts={'limit':1000,'epsrel':1e-3})[0]/(ehi-elo)/(zhi-zlo)
+
+    data = {nu_type: np.zeros((cos_theta_bins.shape[0]-1,energy_bins.shape[0]-1,4)) for nu_type in [12,-12,14,-14,16,-16]}
+    for nu_type1 in [12,-12,14,-14]:
+        if nu_type1 > 0:
+            nu_type2s = [12,14,16]
+        else:
+            nu_type2s = [-12,-14,-16]
+        for nu_type2 in nu_type2s:
+            print("Calculating neutrino flux for %s -> %s" % tuple(map(pdg_code_to_string,(nu_type1,nu_type2))))
+            for i, (elo, ehi) in enumerate(zip(energy_bins[:-1],energy_bins[1:])):
+                for j, (zlo, zhi) in enumerate(zip(cos_theta_bins[:-1],cos_theta_bins[1:])):
+                    print("\r%i/%i" % (i*(len(cos_theta_bins)-1)+j+1,(len(cos_theta_bins)-1)*(len(energy_bins)-1)),end="")
+                    sys.stdout.flush()
+                    # We'll follow the Barr convention here and take the midpoint in log space
+                    emid = np.exp((np.log(elo)+np.log(ehi))/2)
+                    zmid = (zlo + zhi)/2
+                    data[nu_type2][j,i,0] = emid
+                    data[nu_type2][j,i,1] = zmid
+                    data[nu_type2][j,i,2] += get_oscillated_flux(nu_type1,nu_type2,elo,emid,ehi,zlo,zmid,zhi)
+            print()
+
+    for nu_type2 in data:
+        for i, (elo, ehi) in enumerate(zip(energy_bins[:-1],energy_bins[1:])):
+            for j, (zlo, zhi) in enumerate(zip(cos_theta_bins[:-1],cos_theta_bins[1:])):
+                data[nu_type2][j,i,3] = data[nu_type2][j,i,2]*data[nu_type2][j,i,0]
+
+    for p in [12,-12,14,-14,16,-16]:
+        np.savetxt("fmax20_i0403z_plus_lowe.sno_%s.osc" % pdg_code_to_string(p),data[p].reshape((data[p].shape[0]*data[p].shape[1],-1)),
+                    fmt='%10.4f %10.3f %20.8g %20.8g',
+                   header="Energy (GeV), Cos(zenith), Flux (m^-2 s^-1 Gev^-1 steradian^-1), Flux (dn/dlnE), Junk")
diff --git a/utils/calculate-atmospheric-oscillations b/utils/calculate-atmospheric-oscillations
new file mode 100755
index 0000000..356fc1f
--- /dev/null
+++ b/utils/calculate-atmospheric-oscillations
@@ -0,0 +1,116 @@
+#!/usr/bin/env python
+"""
+Script to calculate probabilities for atmospheric neutrino oscillations. To run
+it:
+
+    $ ./calculate-atmospheric-oscillations --atmosphere-mode 3 --num-prec 5e-4
+
+which will then produce the following files:
+
+nue_osc_prob.txt: probability for nues to oscillate
+nbe_osc_prob.txt: probability for anti nues to oscillate
+num_osc_prob.txt: probability for numus to oscillate
+nbm_osc_prob.txt: probability for anti numus to oscillate
+
+The format of each text file is the same. It has the following columns:
+
+    1. Energy of the neutrino in GeV.
+    2. Cosine of the zenith angle.
+    3. Probability to oscillate into nue (or antinue)
+    4. Probability to oscillate into numu (or antinumu)
+    5. Probability to oscillate into nutau (or antinutau)
+"""
+from __future__ import print_function, division
+import numpy as np
+from time import time
+from NuCraft import *
+
+# depth of the SNO detector (km)
+# currently just converted 6800 feet -> km
+SNO_DEPTH = 2.072
+
+# number of energy bins
+eBins = 1000
+# number of zenith angle bins
+zBins = 100
+# zenith angle bins
+zList = np.arccos(np.linspace(-1,1,zBins))
+# energy range in GeV
+eList = np.logspace(np.log10(0.01), np.log10(10), eBins)
+
+# parameters from PDG 2019
+THETA23 = np.arcsin(np.sqrt(0.512))/np.pi*180.
+THETA13 = np.arcsin(np.sqrt(0.0218))/np.pi*180.
+THETA12 = np.arcsin(np.sqrt(0.307))/np.pi*180.
+DM21   = 7.53e-5
+DM31   = 2.444e-3 + DM21
+
+# Akhemdov is implicitely assuming an electron-to-neutron ratio of 0.5; 
+# he is also using the approximation DM31 = DM32;
+# if you want to reproduce his numbers exactly, switch the lines below, and turn
+# atmosphereMode to 0 (no handling of the atmosphere because of )
+# AkhmedovOsci = NuCraft((1., DM21, DM31-DM21), [(1,2,theta12),(1,3,theta13,0),(2,3,theta23)],
+#                        earthModel=EarthModel("prem", y=(0.5,0.5,0.5))
+#                        detectorDepth=0., atmHeight=0.)
+AkhmedovOsci = NuCraft((1., DM21, DM31), [(1,2,THETA12),(1,3,THETA13,0),(2,3,THETA23)],detectorDepth=SNO_DEPTH)
+
+def pdg_code_to_string(pdg):
+    if pdg == 12:
+        return "nue"
+    elif pdg == -12:
+        return "nbe"
+    elif pdg == 14:
+        return "num"
+    elif pdg == -14:
+        return "nbm"
+    elif pdg == 16:
+        return "nut"
+    elif pdg == -16:
+        return "nbt"
+    else:
+        raise ValueError("Unknown pdg code %i" % pdg)
+
+if __name__ == '__main__':
+    import argparse
+
+    atmosphereMode = 3   # default: efficiently calculate eight path lenghts per neutrino and take the average
+
+    # This parameter governs the precision with which nuCraft computes the weights; it is the upper
+    # limit for the deviation of the sum of the resulting probabilities from unitarity.
+    # You can verify this by checking the output plot example-standAlone2.png.
+    numPrec = 5e-4
+
+    parser = argparse.ArgumentParser("script to calculate atmospheric neutrino oscillations")
+    parser.add_argument("--atmosphere-mode", type=int, default=atmosphereMode, help="controls the handling of the atmospheric interaction altitude")
+    parser.add_argument("--num-prec", type=float, default=numPrec, help="parameter which governs the precision with which nuCraft computs the weights")
+    args = parser.parse_args()
+
+
+    # 12, -12:  NuE, NuEBar
+    # 14, -14:  NuMu, NuMuBar
+    # 16, -16:  NuTau, NuTauBar
+    for pType in [12,-12,14,-14]:
+        print("Calculating oscillation probabilities for %s..." % pdg_code_to_string(pType))
+
+        # saving the current time to measure the time needed for the execution of the following code
+        t = time()
+
+        ### using lists (arrays, actually)
+        zz, ee = np.meshgrid(zList, eList)
+        zListLong = zz.flatten()
+        eListLong = ee.flatten()
+        tListLong = np.repeat(pType,len(eListLong))
+
+        # actual call to nuCraft for weight calculations:
+        prob = AkhmedovOsci.CalcWeights((tListLong, eListLong, zListLong), numPrec=args.num_prec, atmMode=args.atmosphere_mode)
+
+        prob = np.array(prob)
+
+        save = np.empty((prob.shape[0],5))
+        save[:,0] = eListLong
+        save[:,1] = np.cos(zListLong)
+        save[:,2:] = prob
+
+        print("Calculating the probabilities took %.0f seconds." % (time()-t))
+
+        np.savetxt("%s_osc_prob.txt" % pdg_code_to_string(pType),save,header="Energy (GeV), Cos(zenith), P(nue), P(num), P(nut)")
diff --git a/utils/plot-atmospheric-fluxes b/utils/plot-atmospheric-fluxes
new file mode 100755
index 0000000..fb4861d
--- /dev/null
+++ b/utils/plot-atmospheric-fluxes
@@ -0,0 +1,285 @@
+#!/usr/bin/env python
+"""
+Script for plotting solar fluxes from
+http://www-pnp.physics.ox.ac.uk/~barr/fluxfiles/0403i/index.html.
+"""
+from __future__ import print_function, division
+import numpy as np
+import os
+
+def splitext(path):
+    """
+    Like os.path.splitext() except it returns the full extension if the
+    filename has multiple extensions, for example:
+
+        splitext('foo.tar.gz') -> 'foo', '.tar.gz'
+    """
+    full_root, full_ext = os.path.splitext(path)
+    while True:
+        root, ext = os.path.splitext(full_root)
+        if ext:
+            full_ext = ext + full_ext
+            full_root = root
+        else:
+            break
+
+    return full_root, full_ext
+
+# Taken from https://raw.githubusercontent.com/mwaskom/seaborn/c73055b2a9d9830c6fbbace07127c370389d04dd/seaborn/utils.py
+def despine(fig=None, ax=None, top=True, right=True, left=False,
+            bottom=False, offset=None, trim=False):
+    """Remove the top and right spines from plot(s).
+
+    fig : matplotlib figure, optional
+        Figure to despine all axes of, default uses current figure.
+    ax : matplotlib axes, optional
+        Specific axes object to despine.
+    top, right, left, bottom : boolean, optional
+        If True, remove that spine.
+    offset : int or dict, optional
+        Absolute distance, in points, spines should be moved away
+        from the axes (negative values move spines inward). A single value
+        applies to all spines; a dict can be used to set offset values per
+        side.
+    trim : bool, optional
+        If True, limit spines to the smallest and largest major tick
+        on each non-despined axis.
+
+    Returns
+    -------
+    None
+
+    """
+    # Get references to the axes we want
+    if fig is None and ax is None:
+        axes = plt.gcf().axes
+    elif fig is not None:
+        axes = fig.axes
+    elif ax is not None:
+        axes = [ax]
+
+    for ax_i in axes:
+        for side in ["top", "right", "left", "bottom"]:
+            # Toggle the spine objects
+            is_visible = not locals()[side]
+            ax_i.spines[side].set_visible(is_visible)
+            if offset is not None and is_visible:
+                try:
+                    val = offset.get(side, 0)
+                except AttributeError:
+                    val = offset
+                _set_spine_position(ax_i.spines[side], ('outward', val))
+
+        # Potentially move the ticks
+        if left and not right:
+            maj_on = any(
+                t.tick1line.get_visible()
+                for t in ax_i.yaxis.majorTicks
+            )
+            min_on = any(
+                t.tick1line.get_visible()
+                for t in ax_i.yaxis.minorTicks
+            )
+            ax_i.yaxis.set_ticks_position("right")
+            for t in ax_i.yaxis.majorTicks:
+                t.tick2line.set_visible(maj_on)
+            for t in ax_i.yaxis.minorTicks:
+                t.tick2line.set_visible(min_on)
+
+        if bottom and not top:
+            maj_on = any(
+                t.tick1line.get_visible()
+                for t in ax_i.xaxis.majorTicks
+            )
+            min_on = any(
+                t.tick1line.get_visible()
+                for t in ax_i.xaxis.minorTicks
+            )
+            ax_i.xaxis.set_ticks_position("top")
+            for t in ax_i.xaxis.majorTicks:
+                t.tick2line.set_visible(maj_on)
+            for t in ax_i.xaxis.minorTicks:
+                t.tick2line.set_visible(min_on)
+
+        if trim:
+            # clip off the parts of the spines that extend past major ticks
+            xticks = ax_i.get_xticks()
+            if xticks.size:
+                firsttick = np.compress(xticks >= min(ax_i.get_xlim()),
+                                        xticks)[0]
+                lasttick = np.compress(xticks <= max(ax_i.get_xlim()),
+                                       xticks)[-1]
+                ax_i.spines['bottom'].set_bounds(firsttick, lasttick)
+                ax_i.spines['top'].set_bounds(firsttick, lasttick)
+                newticks = xticks.compress(xticks <= lasttick)
+                newticks = newticks.compress(newticks >= firsttick)
+                ax_i.set_xticks(newticks)
+
+                xticks_minor = [t for t in ax_i.get_xticks(minor=True) if firsttick < t < lasttick]
+                ax_i.set_xticks(xticks_minor,minor=True)
+
+            yticks = ax_i.get_yticks()
+            if yticks.size:
+                firsttick = np.compress(yticks >= min(ax_i.get_ylim()),
+                                        yticks)[0]
+                lasttick = np.compress(yticks <= max(ax_i.get_ylim()),
+                                       yticks)[-1]
+                ax_i.spines['left'].set_bounds(firsttick, lasttick)
+                ax_i.spines['right'].set_bounds(firsttick, lasttick)
+                newticks = yticks.compress(yticks <= lasttick)
+                newticks = newticks.compress(newticks >= firsttick)
+                ax_i.set_yticks(newticks)
+
+                yticks_minor = [t for t in ax_i.get_yticks(minor=True) if firsttick < t < lasttick]
+                ax_i.set_yticks(yticks_minor,minor=True)
+
+# Data is in the form: Fluxes in bins of neutrino energy (equally spaced bins
+# in logE with 10 bins per decade with the low edge of the first bin at 100
+# MeV) and zenith angle (20 bins equally spaced in cos(zenith) with bin width
+# 0.1), integrated over azimuth. Note logE means log to base e. Fluxes below 10
+# GeV are from the 3D calculation.
+
+# The files all have the same format. After the initial comment lines (starting
+# with a # character), the files contain one line per bin. No smoothoing
+# between bins has been done. The columns are:
+# 
+#     1. Energy at centre of bin in GeV
+#     2. Zenith files: Cos(zenith) at centre of bin
+#        Azimuth files: Azimuth at centre of bin (degrees)
+#     3. Flux in dN/dlogE in /m**2/steradian/sec
+#     4. MC Statistical error on the flux
+#     5. Number of unweighted events entering the bin (not too useful)
+
+if __name__ == '__main__':
+    import argparse
+    import matplotlib
+    import glob
+
+    parser = argparse.ArgumentParser("plot solar fluxes")
+    parser.add_argument("filenames", nargs='+', help="filenames of flux files")
+    parser.add_argument("--save", action="store_true", default=False, help="save plots")
+    args = parser.parse_args()
+
+    if args.save:
+        # default \textwidth for a fullpage article in Latex is 16.50764 cm.
+        # You can figure this out by compiling the following TeX document:
+        #
+        #    \documentclass{article}
+        #    \usepackage{fullpage}
+        #    \usepackage{layouts}
+        #    \begin{document}
+        #    textwidth in cm: \printinunitsof{cm}\prntlen{\textwidth}
+        #    \end{document}
+
+        width = 16.50764
+        width /= 2.54 # cm -> inches
+        # According to this page:
+        # http://www-personal.umich.edu/~jpboyd/eng403_chap2_tuftegospel.pdf,
+        # Tufte suggests an aspect ratio of 1.5 - 1.6.
+        height = width/1.5
+        FIGSIZE = (width,height)
+
+        import matplotlib.pyplot as plt
+
+        font = {'family':'serif', 'serif': ['computer modern roman']}
+        plt.rc('font',**font)
+
+        plt.rc('text', usetex=True)
+    else:
+        # on retina screens, the default plots are way too small
+        # by using Qt5 and setting QT_AUTO_SCREEN_SCALE_FACTOR=1
+        # Qt5 will scale everything using the dpi in ~/.Xresources
+        import matplotlib
+        matplotlib.use("Qt5Agg")
+
+        import matplotlib.pyplot as plt
+
+        # Default figure size. Currently set to my monitor width and height so that
+        # things are properly formatted
+        FIGSIZE = (13.78,7.48)
+
+        font = {'family':'serif', 'serif': ['computer modern roman']}
+        plt.rc('font',**font)
+
+        # Make the defalt font bigger
+        plt.rc('font', size=22)
+
+        plt.rc('text', usetex=True)
+
+    fig = plt.figure(figsize=FIGSIZE)
+
+    colors = plt.rcParams["axes.prop_cycle"].by_key()["color"]
+    linestyles = ['-','--']
+
+    def key(filename):
+        head, tail = os.path.split(filename)
+
+        k = 0
+        if tail.startswith('fmax'):
+            k += 1
+        if 'nue' in tail:
+            k += 10
+        elif 'nbe' in tail:
+            k += 20
+        elif 'num' in tail:
+            k += 30
+        elif 'nbm' in tail:
+            k += 40
+        elif 'nut' in tail:
+            k += 50
+        elif 'nbt' in tail:
+            k += 60
+
+        return k
+
+    for filename in sorted(args.filenames,key=key):
+        head, tail = os.path.split(filename)
+
+        print(filename)
+
+        data = np.genfromtxt(filename)
+
+        shape1 = len(np.unique(data[:,0]))
+
+        x = data[:,0].reshape((-1,shape1))
+        y = data[:,1].reshape((-1,shape1))
+        z = data[:,2].reshape((-1,shape1))
+
+        # Convert to MeV
+        x *= 1000.0
+        z /= 1000.0
+
+        zbins = np.linspace(-1,1,21)
+        dz = zbins[1] - zbins[0]
+
+        x = x[0]
+        # Integrate over cos(theta) and multiply by 2*pi to convert 3D flux to
+        # a total flux
+        y = np.sum(z*dz,axis=0)*2*np.pi
+
+        if 'sno_nue' in tail:
+            plt.plot(x,y,color=colors[0],linestyle=linestyles[0],label=r'$\nu_e$')
+        elif 'sno_nbe' in tail:
+            plt.plot(x,y,color=colors[0],linestyle=linestyles[1],label=r'$\overline{\nu}_e$')
+        elif 'sno_num' in tail:
+            plt.plot(x,y,color=colors[1],linestyle=linestyles[0],label=r'$\nu_\mu$')
+        elif 'sno_nbm' in tail:
+            plt.plot(x,y,color=colors[1],linestyle=linestyles[1],label=r'$\overline{\nu}_\mu$')
+        elif 'sno_nut' in tail:
+            plt.plot(x,y,color=colors[2],linestyle=linestyles[0],label=r'$\nu_\tau$')
+        elif 'sno_nbt' in tail:
+            plt.plot(x,y,color=colors[2],linestyle=linestyles[1],label=r'$\overline{\nu}_\tau$')
+
+    plt.gca().set_xscale("log")
+    plt.gca().set_yscale("log")
+    despine(fig,trim=True)
+    plt.xlabel("$E$ (MeV)")
+    plt.ylabel(r"$\mathrm{d}\Phi/\mathrm{d}E$ (1/$\mathrm{m}^2$/sec/MeV)")
+    plt.legend()
+    plt.tight_layout()
+
+    if args.save:
+        plt.savefig("irc01_atmospheric_flux.pdf")
+        plt.savefig("irc01_atmospheric_flux.eps")
+
+    plt.show()
diff --git a/utils/plot-atmospheric-oscillations b/utils/plot-atmospheric-oscillations
new file mode 100755
index 0000000..c24a776
--- /dev/null
+++ b/utils/plot-atmospheric-oscillations
@@ -0,0 +1,114 @@
+#!/usr/bin/env python
+"""
+Script to plot the probabilities for atmospheric neutrino oscillations. To run
+it:
+
+    $ ./plot-atmospheric-oscillations nue_osc_prob.txt
+"""
+from __future__ import print_function, division
+import numpy as np
+
+if __name__ == '__main__':
+    import argparse
+    from os.path import split, splitext
+
+    parser = argparse.ArgumentParser("script to plot atmospheric oscillations")
+    parser.add_argument("filenames", nargs='+', help="oscillation probability filenames")
+    parser.add_argument("--save", action="store_true", default=False, help="save plots")
+    args = parser.parse_args()
+
+    if args.save:
+        # default \textwidth for a fullpage article in Latex is 16.50764 cm.
+        # You can figure this out by compiling the following TeX document:
+        #
+        #    \documentclass{article}
+        #    \usepackage{fullpage}
+        #    \usepackage{layouts}
+        #    \begin{document}
+        #    textwidth in cm: \printinunitsof{cm}\prntlen{\textwidth}
+        #    \end{document}
+
+        width = 16.50764
+        width /= 2.54 # cm -> inches
+        # According to this page:
+        # http://www-personal.umich.edu/~jpboyd/eng403_chap2_tuftegospel.pdf,
+        # Tufte suggests an aspect ratio of 1.5 - 1.6.
+        height = width/1.5
+        FIGSIZE = (width,height)
+
+        import matplotlib.pyplot as plt
+
+        font = {'family':'serif', 'serif': ['computer modern roman']}
+        plt.rc('font',**font)
+
+        plt.rc('text', usetex=True)
+    else:
+        # on retina screens, the default plots are way too small
+        # by using Qt5 and setting QT_AUTO_SCREEN_SCALE_FACTOR=1
+        # Qt5 will scale everything using the dpi in ~/.Xresources
+        import matplotlib
+        matplotlib.use("Qt5Agg")
+
+        import matplotlib.pyplot as plt
+
+        # Default figure size. Currently set to my monitor width and height so that
+        # things are properly formatted
+        FIGSIZE = (13.78,7.48)
+
+        # Make the defalt font bigger
+        plt.rc('font', size=22)
+
+    for filename in args.filenames:
+        head, tail = split(filename)
+        root, ext = splitext(tail)
+
+        e, z, pnue, pnum, pnut = np.genfromtxt(filename).T
+
+        shape0 = len(np.unique(e))
+
+        ee = e.reshape((shape0,-1))
+        zz = z.reshape((shape0,-1))
+        pnue = pnue.reshape((shape0,-1))
+        pnum = pnum.reshape((shape0,-1))
+        pnut = pnut.reshape((shape0,-1))
+
+        levels = np.linspace(0,1,101)
+
+        plt.figure(figsize=FIGSIZE)
+        plt.contourf(ee,zz,pnue,levels=levels)
+        plt.gca().set_xscale('log')
+        plt.xlabel("Energy (GeV)")
+        plt.ylabel("Cos(Zenith)")
+        plt.colorbar()
+        plt.tight_layout()
+        if args.save:
+            plt.savefig("%s_nue.pdf" % root)
+            plt.savefig("%s_nue.eps" % root)
+        else:
+            plt.title(r"Probability to oscillate to $\nu_e$")
+        plt.figure(figsize=FIGSIZE)
+        plt.contourf(ee,zz,pnum,levels=levels)
+        plt.gca().set_xscale('log')
+        plt.xlabel("Energy (GeV)")
+        plt.ylabel("Cos(Zenith)")
+        plt.colorbar()
+        plt.tight_layout()
+        if args.save:
+            plt.savefig("%s_num.pdf" % root)
+            plt.savefig("%s_num.eps" % root)
+        else:
+            plt.title(r"Probability to oscillate to $\nu_\mu$")
+        plt.figure(figsize=FIGSIZE)
+        plt.contourf(ee,zz,pnut,levels=levels)
+        plt.gca().set_xscale('log')
+        plt.xlabel("Energy (GeV)")
+        plt.ylabel("Cos(Zenith)")
+        plt.colorbar()
+        plt.tight_layout()
+        if args.save:
+            plt.savefig("%s_nut.pdf" % root)
+            plt.savefig("%s_nut.eps" % root)
+        else:
+            plt.title(r"Probability to oscillate to $\nu_\tau$")
+
+    plt.show()