utils.py

from math import sqrt, log10, pi, exp

import os
import numpy as np
from functools import reduce
import sys
import json # config file 
import pickle 
from glob import glob # grabs all the files! 
from numbers import Number
from scipy.integrate import quad

sqtwo = 1/sqrt(2*pi)

"""
Ben Smithers

This defines several utility functions and objects that are frequently used throughout this code base 
"""

flavors = ['E', 'Mu', 'Tau']
neuts = ['nu', 'nuBar']
currents = ['NC', 'CC']

# load in the configuration file
# this defines a lot of... configuration... parameters 
f = open(os.path.join(os.path.dirname(__file__), "config.json"), 'r')
config = json.load(f)
f.close()

import matplotlib
def shift_cmap(cmap, frac):
    """Shifts a colormap by a certain fraction.

    Keyword arguments:
    cmap -- the colormap to be shifted. Can be a colormap name or a Colormap object
    frac -- the fraction of the colorbar by which to shift (must be between 0 and 1)
    """
    N=256
    if isinstance(cmap, str):
        cmap = plt.get_cmap(cmap)
    n = cmap.name
    x = np.linspace(0,1,N)
    out = np.roll(x, int(N*frac))
    new_cmap = matplotlib.colors.LinearSegmentedColormap.from_list(f'{n}_s', cmap(out))
    return new_cmap

import matplotlib.pyplot as plt
def get_color(n, colormax=3.0, cmap="viridis"):
    """
        Discretize a colormap. Great getting nice colors for a series of trends on a single plot! 
    """
    this_cmap = plt.get_cmap(cmap)
    return this_cmap(n/colormax)

def pathmaker(path):
    folder = os.path.split(path)[0]
    if not os.path.exists(path):
        broken = path.split("/")
        working = ""
        for part in broken:
            working = "/".join([working] + [part])
            if not os.path.exists(working):
                os.mkdir(working)

def make_bin_probs(cdf, bin_edges, normalize=False):
    """
    We find the binned likelihoods based on a binned gaussian distribution. 

    As in, if we sample some quantity with a gaussian distribution centered at MEAN with a width SIGMA,
    return the odds it will be measured in each of the bins defined by BIN_EDGES
    """
    

    if not isinstance(bin_edges, (list, tuple, np.ndarray)):
        raise TypeError()
    if len(bin_edges)<2:
        raise ValueError()

    occupation = np.zeros(len(bin_edges)-1)
    
    for i in range(len(occupation)):
        occupation[i] = quad(cdf, a=bin_edges[i], b=bin_edges[i+1])[0]
     
    if normalize:
   #     occupation = np.abs(occupation)
        return occupation/sum(occupation)
    else:
        return occupation

def backup(filename):
    """
    This function checks if a file exists by the given name
    If the file exists, it renames the file by appending "Copy of [...]" to the file's name (considering full path too. This works recursively too! The newest is always the one with the least "Copy of"s

    [File] [Copy of File] 
        becomes
    [File] [Copy of File] [Copy of Copy of File]

    Returns nothing.
    """

    if not os.path.exists(filename):
        return
    else:
        # such a file already exists 
        dirname, file_obj = os.path.split(filename)
    
        # get the new destination for the file
        # then, we call this function to check if something of the same name already exists
        file_obj = "Copy of "+file_obj
        backup(os.path.join(dirname, file_obj)) 

        # Now rename the existing file to the new name 
        os.rename(filename, os.path.join(dirname, file_obj))

def savefile(name, **kwargs):
    """
    This allows me to quickly files. You specify the filename and use keywords to provide the rest of the elements you want to save 

    Then it quickly pickles it
    returns nothing

    Respects the configured "overwrite" settings 
    I really like this script tbh
    """
    if not config["overwrite"]:
        backup(name)

    f = open(name, 'wb')
    pickle.dump( kwargs, f, -1)
    f.close()
    print("Saved {}".format(name))


def sep_by_flavor(nuflux):
    """
    So this takes that nuflux object, a dictionary of 3D arrays, and separates it into two 3D arrays: one for muons and one for non-muons
    """

    if not isinstance(nuflux, dict):
        raise TypeError("nuflux should be a {}, not a {}".format(dict, type(nuflux)))
    if not isinstance(nuflux[list(nuflux.keys())[0]], np.ndarray):
        raise TypeError("Entries in nuflux should all be {}, not {}".format(np.ndarray, type(nuflux[list(nuflux.keys())[0]])))

    entry_shape = np.shape(nuflux[list(nuflux.keys())[0]])
    from_muons = np.zeros(shape=entry_shape)
    from_not = np.zeros(shape=entry_shape)

    for key in nuflux:
        flavor = key.split('_')[0]
        if flavor=="Mu":
            from_muons+=nuflux[key]
        else:
            from_not+=nuflux[key]
    return(from_muons, from_not)

def multimat(*args):
    """
    Slick little function for multiplying an arbitrary number of matrices together! 
    """
    assert(len(args)>=2)
    amt = args[0]
    for arg in range(len(args)):
        if arg==0:
            continue
        amt = np.matmul(amt, args[arg])
    return(amt)

def sci(number, precision=4):
    """
    Returns a string representing the number in scientific notation
    """
    if not isinstance(number, (int, float)):
        raise TypeError("Expected {}, not {}".format(float, type(number)))
    if not isinstance(precision,int):
        raise TypeError("Precision must be {}, not {}".format(int, type(precision)))
    try:
        power = int(log10(abs(number)))
    except ValueError:
        return("0.0")

    return("{0:.{1}f}".format(number/(10**power), precision)+"e{}".format( power))

def check_valid_angle(angle,is_zenith, radians=True):
    """
    Returns True if parameter "angle" is a valid angle.
    "radians" flag used to specify if the value is radians. False means it's degrees
    """
    if not isinstance(angle, (float,int)):
        return False
    if not isinstance(is_zenith, bool):
        raise TypeError("Expected {}, got {} for is_zenith flag".format(bool, type(is_zenith)))
    if not isinstance(radians, bool):
        raise TypeError("Expected {}, got {} for radians specifier".format(bool, type(radians)))

    # convert to radians if necessary 
    scaled = angle if radians else angle*pi/180

    if is_zenith:
        if angle<0 or angle>pi:
            return False
    else: # is azimuth angle
        if angle<0 or angle>(2*pi):
            return False

    return True 

class NewPhysicsParams:
    def __init__(self, **kwargs) -> None:
        pass

    def __eq__(self, other):
        if isinstance(other, NewPhysicsParams):
            return True
        return False

    def __repr__(self):
        return("New Physics Object")

    def __str__(self):
        raise NotImplementedError("")

class SterileParams(NewPhysicsParams):
    """
    This object is used to pass around the new sterile physics parameters around

    TODO:
        - figure out a way to cleanly bring in the phase parameters without making uglier filenames 
    """
    def __init__(self, theta03=0.0, theta13=0.0, theta23=0.0, msq2=0.0, **kwargs):
        if not isinstance(theta03, (int, float)):
            raise TypeError("theta03 should be {}, not {}".format(float, type(theta03)))
        if not isinstance(theta13, (int, float)):
            raise TypeError("theta13 should be {}, not {}".format(float, type(theta13)))
        if not isinstance(theta23, (int, float)):
            raise TypeError("theta23 should be {}, not {}".format(float, type(theta23)))
        if not isinstance(msq2, (int, float)):
            raise TypeError("msq2 should be {}, not {}".format(float, type(msq2)))

        if not check_valid_angle(theta03, True):
            raise ValueError("Invalid theta03: {}".format(theta03))
        if not check_valid_angle(theta13, True):
            raise ValueError("Invalid theta03: {}".format(theta13))       
        if not check_valid_angle(theta23, True):
            raise ValueError("Invalid theta03: {}".format(theta23))
        if msq2<0:
            raise ValueError("Mass-squared difference must be >=0, not {}".format(msq2))

        self.theta03 = theta03
        self.theta13 = theta13
        self.theta23 = theta23

        self.msq2 = msq2

        allowed = ["maj_phase_1","maj_phase_2", "maj_phase_3", "ordering"]

        for kwarg in kwargs:
            if kwarg not in allowed:
                raise ValueError("Unrecognized argument {}".format(kwarg))

        self.majorana = False
        if "maj_phase_1" in kwargs:
            self.maj_phase_1 = kwargs["maj_phase_1"]
            self.majorana = True
        else:
            self.maj_phase_1 = 0.0
        if "maj_phase_2" in kwargs:
            self.maj_phase_2 = kwargs["maj_phase_2"]
            self.majorana = True
        else:
            self.maj_phase_2 = 0.0
        if "maj_phase_3" in kwargs:
            self.maj_phase_3 = kwargs["maj_phase_3"]
            self.majorana = True
        else:
            self.maj_phase_3 = 0.0
        
        if "ordering" in kwargs:
            self.no_ordering = kwargs["ordering"] #NOrmal ordering 
        else:
            self.no_ordering = False
    
    def __eq__(self, other):
        if isinstance(other, SterileParams):
            return ( self.theta03==other.theta03 and self.theta13==other.theta13 and
                     self.theta23==other.theta23 and self.msq2==other.msq2)
        return False

    def __repr__(self):
        return("Sterile-nu Params Object")

    def __str__(self):
        return("_".join((sci(self.theta03), sci(self.theta13), sci(self.theta23), sci(self.msq2))))
    
class NSIParams(NewPhysicsParams):
    def __init__(self, eps_mutau:complex, **kwargs) -> None:
        super().__init__(**kwargs)

        self._epsmutau = eps_mutau

    def __str__(self):
        return "nsiparam_"+"_".join(["{:.6E}".format(entry) for entry in [self._epsmutau.real, self._epsmutau.imag]])
    

def parse_filename(path, as_params=True):
    """
    Takes a filename made by 'gen_filename' and returns the oscillation parameters used to make the filename 
    If as_params is true, the parameters are returned as a SterileParameters object, 
    otherwise they are returned in a tuple 

    returns: three floats in a tuple 
    """
    dirname, filename = os.path.split(path)
    
    name = ".".join(filename.split(".")[:-1])
    entries = name.split("_")
    
    theta03 = float(entries[2])
    theta13 = float(entries[3])
    theta23 = float(entries[4])
    msq2 = float(entries[5])

    params = SterileParams( theta03=theta03, theta13=theta13, theta23=theta23, msq2=msq2)
    
    if as_params:
        return(params)
    else:
        return(theta03, theta13, theta23, msq2)

def gen_filename(dirname, filename, params, subfolder=True):
    """
    Takes a directory, a generic filename (like "datafile.dat"), and some physics parameters

    returns a full path that is unique to that set of physics parameters
    """
    if not isinstance(params, SterileParams):
        raise TypeError("Expected {}, got {}".format(SterileParams, type(params)))

    names = filename.split(".")
    assert(len(names)==2) # name, ext
    prefix = names[0]
    suffix = names[1]
    str_params = str(params)
    filename_partial = prefix+"_"+str_params
    filename = os.path.join( dirname, ".".join((filename_partial,suffix)))
    if not subfolder:
        return(filename)
    # make a subfolder based on theta_24
    th24 = str_params.split("_")[1]
    new_path = os.path.join(dirname, th24, ".".join((filename_partial,suffix)))
    new_dir = os.path.join(dirname, th24)
    if not os.path.exists(new_dir):
        os.mkdir(os.path.join(dirname, th24))
#    pathmaker(new_dir) # default cascade import 
    return new_path


def enumerate_failures(dirname, filename):
    """
    This function provides a list of the parameter points missing, assuming the normal spread of points 
    """
    n_grid=90
    theta24s = np.concatenate(( [0], np.arcsin(np.sqrt(np.logspace(-3, 0, n_grid)))/2.0 ))
    theta34s = np.concatenate(( [0], np.arcsin(np.sqrt(np.logspace(-3, 0, n_grid)))/2.0))
    msqs = np.concatenate( ([0], np.logspace(-2,2,40)) )

    pams = []
    
    count = 0
    found = 0
    for i24 in theta24s:
        for i34 in theta34s:
            for msq in msqs:
                if count%5000==0:
                    print("Done did {} many so far, found {}".format(count, found))
                pam = SterileParams(theta13=i24, theta23=i34, msq2=msq)

                fn = gen_filename(dirname, filename, pam)
                if not os.path.exists(fn):
                    pams.append(pam)
                else:
                    found +=1 
                count+=1
    print("Found {} of {}, that's {:.1f}%".format(found, count, 100*float(found)/count))
    return pams

def get_index( key, n_flavor=3 ):
    '''
    Returns the column in the atmosphere data file for a given key
    '''
    if not isinstance(key, str):
        raise TypeError("Expected {}, got {}".format(str, type(key)))
    split = key.split('_')
    flavor = split[0] # E Mu Tau
    variety = split[1] # nu or nu-bar 

    flav_index = flavors.index(flavor) # 0, 1, or 2
    variety_index = neuts.index(variety) # 0 or 1

    sterile_mod = n_flavor-3 
    return( 2 + int( flav_index + (len(flavors)+sterile_mod)*variety_index) )

def bad_get_loc(value, edges):
    """
    Deprecated, don't use. Just use 'get_loc' 
    """
    if value<edges[0] or value>edges[-1]:
        return None
    else:
        scan = 0
        while not (value>=edges[scan] and value<=edges[scan+1]): # remember, the edges are sorted - so this should happen
            scan += 1
            if scan==len(edges)-1:
                raise Exception("Something bad happened with logic")
        return(scan)


def get_loc(x, domain,closest=False):
    """
    Returns the indices of the entries in domain that border 'x' 
    Raises exception if x is outside the range of domain 

    Assumes 'domain' is sorted!! And this _only_ works if the domain is length 2 or above 

    This is made for finding bin numbers on a list of bin edges 
    """
    if not isinstance(domain, (tuple,list,np.ndarray)):
        raise TypeError("'domain' has unrecognized type {}, try {}".format(type(domain), list))
    if not isinstance(x, (float,int)):
        raise TypeError("'x' should be number-like, not {}".format(type(x)))
    
    if len(domain)<=1:
        raise ValueError("get_loc function only works on domains of length>1. This is length {}".format(len(domain)))

    if x<domain[0] or x>domain[-1]:
        raise ValueError("x={} and is outside the domain: ({}, {})".format(sci(x), sci(domain[0]), sci(domain[-1])))

    # I think this is a binary search
    min_abs = 0
    max_abs = len(domain)-1

    lower_bin = int(abs(max_abs-min_abs)/2)
    upper_bin = lower_bin+1
    

    while not (domain[lower_bin]<=x and domain[upper_bin]>=x):
        if abs(max_abs-min_abs)<=1:
            print("{} in {}".format(x, domain))
            raise Exception("Uh Oh")

        if x<domain[lower_bin]:
            max_abs = lower_bin
        if x>domain[upper_bin]:
            min_abs = upper_bin

        # now choose a new middle point for the upper and lower things
        lower_bin = min_abs + int(abs(max_abs-min_abs)/2)
        upper_bin = lower_bin + 1
    
    assert(x>=domain[lower_bin] and x<=domain[upper_bin])
    if closest:
        return( lower_bin if abs(domain[lower_bin]-x)<abs(domain[upper_bin]-x) else upper_bin )
    else:
        return(lower_bin, upper_bin)


def parse_folder(path, name_tmp = config["recon_flux"]+"*.dat"):
    """
    Takes a folder, and creates lists of all the parameters used there 
    Optionally takes a name template "name_tmp" for the globbing 
    """
    if not os.path.exists(path):
        raise ValueError("Path does not exist: {}".format(path))

    # we want to scan over all these files and build ordered-lists of the paramters 
    all_files = glob( os.path.join( path, name_tmp) )
    def insert( value, list_like ):
        """
        This is a "smart insert" function I wrote

        It adds in the value to the list so long as it's not already there, and it keeps the list ordered. So this really assumes that the list is ordered from the get-go 
        """
        if not isinstance(value, float):
            raise TypeError("Value should be {}, not {}".format(float, type(value)))
        if not isinstance(list_like, list):
            raise TypeError("list_like should be {}, not {}".format(list, type(list_like)))
        
        # these two cases aren't covered by the get_loc function
        if len(list_like)==0:
            return([value])
        
        if value==list_like[0] or value==list_like[-1]:
            return(list_like)

        if value<list_like[0]:
            list_like.insert(0, value)
            return(list_like)
        if value>list_like[-1]:
            list_like.append(value)
            return(list_like)

        bot, top = get_loc(value, list_like) # O(log(N))
        if value==list_like[bot] or value==list_like[top]: #O(1) ZOOM! 
            return(list_like)
        else:
            list_like.insert(top, value) #O(n) complexity >:(
            return(list_like)

    theta03s = []
    theta13s = []
    theta23s = []
    msqs     = []

    for each in all_files:
        theta03, theta13, theta23, msq = parse_filename(each, False)
        theta03s = insert(theta03, theta03s)
        theta13s = insert(theta13, theta13s)
        theta23s = insert(theta23, theta23s)
        msqs = insert(msq, msqs)

    return(theta03s, theta13s, theta23s, msqs)


def get_closest(x, domain, mapped):
    """
    We imagine some function maps from "domain" to "mapped"

    We have several points evaluated for this function
        domain - list-like of floats. 
        mapped - list-like of floats. Entries in domain, evaluated by the function

    The user provides a value "x," and then we interpolate the mapped value on either side of 'x' to approximate the mapped value of 'x' 
    
    This is really just a linear interpolator 
    """
    if not isinstance(domain, (tuple,list,np.ndarray)):
        raise TypeError("'domain' has unrecognized type {}, try {}".format(type(domain), list))
    if not isinstance(mapped, (tuple,list,np.ndarray)):
        print(mapped)
        raise TypeError("'mapped' has unrecognized type {}, try {}".format(type(mapped), list))
    if not isinstance(x, (float,int)):
        raise TypeError("'x' should be number-like, not {}".format(type(x)))

    if len(domain)!=len(mapped):
        raise ValueError("'domain' and 'mapped' should have same length, got len(domain)={}, len(mapped)={}".format(len(domain), len(mapped)))
    
    lower_bin, upper_bin = get_loc(x, domain)
    
    # linear interp time
    x1 = domain[lower_bin]
    x2 = domain[upper_bin]
    y1 = mapped[lower_bin]
    y2 = mapped[upper_bin]

    slope = (y2-y1)/(x2-x1)
    value = (x*slope + y2 -x2*slope)

#    print("({}, {}) to ({}, {}) gave {}".format(x1,y1,x2,y2, value))
    
    return(value)

def bilinear_interp(p0, p1, p2, q11, q12, q21, q22):
    """
    Performs a bilinear interpolation on a 2D surface
    Four values are provided (the qs) relating to the values at the vertices of a square in the (x,y) domain
        p0  - point at which we want a value (len-2 tuple)
        p1  - coordinates bottom-left corner (1,1) of the square in the (x,y) domain (len-2 tuple)
        p2  - upper-right corner (2,2) of the square in the (X,y) domain (len-2 tuple)
        qs  - values at the vertices of the square (See diagram), any value supporting +/-/*
                    right now: floats, ints, np.ndarrays 


        (1,2)----(2,2)
          |        |
          |        |
        (1,1)----(2,1)

    """
    for each in [p0,p1,p2]:
        if not (isinstance(each, tuple) or isinstance(each, list) or isinstance(each, np.ndarray)):
            # I /would/ like to print out the bad value, but it might not be castable to a str?
            try:
                print("Found this: {}".format(each))
            except ValueError:
                pass
            raise TypeError("Expected {} for one of the points, got {}".format(tuple, type(each)))
        if len(each)!=2:
            raise ValueError("Points should be length {}, not {}!".format(2, len(each)))
    for val in [q11, q12, q21, q22]:
        if not isinstance(val, (float, int, np.ndarray)):
            raise TypeError("Expected {} for a value, got {}".format(float, type(val)))
    
    # check this out for the math
    # https://en.wikipedia.org/wiki/Bilinear_interpolation

    x0 = p0[0]
    x1 = p1[0]
    x2 = p2[0]
    y0 = p0[1]
    y1 = p1[1]
    y2 = p2[1]

    if not (x0>=x1 and x0<=x2):
        raise ValueError("You're doing it wrong. x0 should be between {} and {}, got {}".format(x1,x2,x0))
    if not (y0>=y1 and y0<=y2):
        raise ValueError("You're doing it wrong. y0 should be between {} and {}, got {}".format(y1,y2,y0))

    # this is some matrix multiplication. See the above link for details
    # it's not magic, it's math. Mathemagic 
    mat_mult_1 = [q11*(y2-y0) + q12*(y0-y1) , q21*(y2-y0) + q22*(y0-y1)]
    mat_mult_final = (x2-x0)*mat_mult_1[0] + (x0-x1)*mat_mult_1[1]

    rval = mat_mult_final/((x2-x1)*(y2-y1))
    return rval


class Calculable:
    def __init__(self):
        if not os.path.exists(self.filename):
            self._obj = self.generate()
            self._save(self.obj)
        else:
            self._obj = self._load()

    @property
    def obj(self):
        return(self._obj)

    @property
    def filename(self):
        raise NotImplemented("Override default function!")
    
    def _save(self, obj):
        f=open(self.filename,'wb')
        pickle.dump(obj, f, -1)
        f.close()

    def _load(self):
        f = open(self.filename,'rb')
        all_data = pickle.load(f)
        f.close()
        return(all_data)

    def generate(self):
        raise NotImplemented("Override default function!")

    def eval(self, value):
        raise NotImplemented("Override default function!")

class Data:
    """
    This is used as a container for the data loaded in from nuSQuIDS. 
    The main benefit of this is that the objects used by the interpolator are kept in a sterile scope, 
        and we don't have to worry about accidentally renaming an important object!  
    
    It loads it up into a convenient format for access, and provides a function for interpolating what is loaded. 
    """
    def __init__(self, filename=config["nu_flux"], n_flavor = 4):
        """
        Loads in the specified nuSQuIDS datafile. 

        Creates a "flux" dictionary for each type of neutrino and interaction. This is in units of N/s/GeV/cm2/sr
        """

        location = os.path.join(config["datapath"], filename)

        nus_file = os.path.splitext(filename)[1] ==".hdf5"
        
        # store the flavors, neutrinos, and currents
        self.flavors = flavors
        self.neuts = neuts
        self.currents = currents

        self._fluxes = {}


        if nus_file:
            import nuSQuIDS as nsq
            from cascade.nus_utils import get_flavor, get_neut
            data = nsq.nuSQUIDSAtm(location)
            self._energies = data.GetERange()
            self._angles = data.GetCosthRange()

            for key in self.get_keys():
                self._fluxes[ key ] = [[ data.EvalFlavor(get_flavor(key), angle, energy, get_neut(key)) for angle in self._angles] for energy in self._energies]
        else:
            print("Loading Neutrino Flux from {}".format(location))
            data = np.loadtxt(location, dtype=float, comments='#',delimiter=' ')
            n_energies = len(np.unique(data.T[0]))
            n_angles = len(np.unique(data.T[1]))
            GeV=1e9
            if not (len(data)==n_energies*n_angles):
                raise ValueError("Datafile length error? {}!={}".format(len(data), n_energies*n_angles))

    
            # storing the energies and the angles...
            # this was originally supposed to be agnostic to growing/shrinking energies/angles, but the code really assumes increasing.
            self._energies = [10**data[i][0] for i in range(n_energies)]


            self._angles = [data[n_energies*i][1] for i in range(n_angles)]
            


            # let's fill out some flux functions
            # in the data file, these data are written in a big list. But that's not a very handy format
            # so I'm converting these into 2D arrays
            for key in self.get_keys():
                # indexed like [energy_bin][angle_bin]
                # you may notice that NC and CC are treated as having separate fluxes, when really it'sthe same flux 
                #       this is for the most part okay since the interactions are rare enough that the fluxes are unchanged 
                self._fluxes[ key ] = [[ data[energy+angle*n_energies][get_index(key, n_flavor)] for angle in range(n_angles)] for energy in range(n_energies)]

                if np.min(self._fluxes[key])<0:
                    raise ValueError("Tried loading a flux with a negative value {}".format(np.min(self._fluxes[key])))
        
        self.growing = self._energies[1]>self._energies[0]  
        en_width = get_width(self._energies)/GeV
        self._ang_width = get_width(np.arccos(self._angles))
        self.ang_grow = self._angles[1]>self._angles[0]
    
    # define a few access functions to protect the important stuff 
    # the "@property" tag makes it so these are accessed like attributes, not functions! 
    @property
    def energies(self):
        return(self._energies)
    @property
    def angles(self):
        return(self._angles)
    @property
    def ang_width(self):
        return(self._ang_width)
    @property
    def fluxes(self):
        return(self._fluxes) 

    def get_keys(self, just_casc = False, just_tracks=False):
        """
        Returns a list of all the keys in the dictionary of fluxes 
        """
        keys = []
        for flav in self.flavors:
            for neut in self.neuts:
                for curr in self.currents:
                    if just_casc and (flav.lower()=="mu" and curr.lower()=="cc"):
                        continue
                    elif just_tracks and not (flav.lower()=="mu" and curr.lower()=="cc"):
                        continue
                    key = flav+'_'+neut + '_'+curr
                    keys.append(key)
        return(keys)
    def get_flux(self, energy, key, use_overflow = False, angle=None):
        '''
        interpolates between entries in the flux dictionary to return the flux at arbitrary energy and angle
        Energy should be in units of eV
        Angle should be in units of cos(zenith) 
        
        If an angle is provided, 
            Flux is in units of /cm2/GeV/s/sr  (incoming energy, bin width!) 
        If no angle is provided, the zenith angle is integrated over, and the
            Flux is in units of /cm2/GeV/s

        returns DOUBLE  (0.0 if beyond scope of data)
        '''
        if not (key in self._fluxes):
            raise ValueError("Bad key {}".format(key))
        if not (isinstance(energy, float) or isinstance(energy, int)):
            raise TypeError("Expected {}, not {}".format(float, type(energy)))

        if angle is not None:
            integrate = False
            if not (isinstance(angle, float) or isinstance(angle, int)):
                raise TypeError("Expected {}, not {}".format(float, type(angle)))
        else:
            integrate = True
            raise NotImplementedError("This shouldn't be used. It is inaccurate")

        if use_overflow:
            raise NotImplementedError()

        # check if it's outside the extents
        if (energy < self._energies[0] and self.growing) or (energy > self._energies[0] and not self.growing):
            # this overflow thing wasn't implemented right, so I'm disabling it for now .
            if False: # use_overflow:
                return(self._energies[0])
            else:
                return(0)
        if (energy > self._energies[-1] and self.growing) or (energy < self._energies[-1] and not self.growing):
            if False: #use_overflow:
                return(self._energies[n_energies - 1])
            else:
                return(0)

        if not integrate:
            if (angle < self._angles[0] and self.ang_grow) or (angle > self._angles[0] and not self.growing):
                return(0.)
            if (angle > self._angles[-1] and self.ang_grow) or (angle < self._angles[-1] and not self.growing):
                return(0.)
        
        lower_boundary, upper_boundary = get_loc(energy, self._energies)
        if not integrate:
            ang_lower, ang_upper = get_loc(angle, self._angles)
        
        # sanity check... 
        # essentially makes sure that the energies are monotonically increasing 
        if not ((self._energies[lower_boundary] <= energy) and (self._energies[upper_boundary] >= energy)):
            print("energy: {}".format(energy))
            print("lower bound: {}".format(self._energies[lower_boundary]))
            print("upper bound: {}".format(self._energies[upper_boundary]))
            print("indices: {}, {}".format(lower_boundary, upper_boundary))
            raise Exception()

        # if we're integrating, we get the flux at all the angles and scale it by width, otherwise it's bilinear interpolation time! 
        if integrate:
            flux_value = 0.0
            for angle_bin in range(len(self._angles)):
                # linear interpolation 
                y2 = self._fluxes[key][upper_boundary][angle_bin]
                y1 = self._fluxes[key][lower_boundary][angle_bin]
                x2 = self._energies[upper_boundary]
                x1 = self._energies[lower_boundary]
                slope = (y2-y1)/(x2-x1)

                # TODO: this is missing the factor of sin(theta) in the jacobian 
                flux_value += (energy*slope + y2 -x2*slope)*self._ang_width[angle_bin]*2*np.pi
            return(flux_value)
        else:   
        #bilinear_interp(p0, p1, p2, q11, q12, q21, q22):
            p0 = (energy, angle)
            p1 = (self._energies[lower_boundary], self._angles[ang_lower])
            p2 = (self._energies[upper_boundary], self._angles[ang_upper])
            q11 = self._fluxes[key][lower_boundary][ang_lower]
            q21 = self._fluxes[key][upper_boundary][ang_lower]
            q12 = self._fluxes[key][lower_boundary][ang_upper]
            q22 = self._fluxes[key][upper_boundary][ang_upper]
            value =bilinear_interp(p0,p1,p2,q11,q12,q21,q22) 
            #if value<0:
            #    raise ValueError("Somehow have negative flux value {}".format(value))
            return value

    def get_err(self, energy, key, angle):
        """
        This assumes a Poisson distribution defines distributino for the number of observed events in each bin. So, the uncertainty is just the square root of the quantity 
        """
        return(sqrt(self.get_flux(energy=energy, key=key, angle=angle)))

class IllegalArguments(ValueError):
    """
    Just using this to make it clear what the issue is! 
    """
    pass

class bhist:
    """
    It's a 1D or 2D histogram! BHist is for "Ben Hist" or "Binned Hist" depending on who's asking. 

    I made this so I could have a binned histogram that could be used for adding more stuff at arbitrary places according to some "edges" it has. The object would handle figuring out which of its bins would hold the stuff. 

    Also made with the potential to store integers, floats, or whatever can be added together and has both an additive rule and some kind of identity element correlated with the default constructor. 
        If a non-dtype entry is given, it will be explicitly cast to the dtype. 
    """
    def __init__(self,edges, dtype=float):
        """
        Arg 'edges' should be a tuple of length 1 or 2. Length 1 for 1D hist, and length 2 for 2D hist. 
        These edges represent the bin edges. 

        The type-checking could use a bit of work... Right now for 1D histograms you need to give it a length-1 list. 
        """

        if not (isinstance(edges, list) or isinstance(edges, tuple) or isinstance(edges, np.ndarray)):
            raise TypeError("Arg 'edges' must be {}, got {}".format(list, type(edges)))


        for entry in edges:
            if not (isinstance(entry, list) or isinstance(entry, tuple) or isinstance(entry, np.ndarray)):
                raise TypeError("Each entry in 'edges' should be list-like, found {}".format(type(entry)))
            if len(entry)<2:
                raise ValueError("Entries in 'edges' must be at least length 2, got {}".format(len(entry)))
        
        self._edges = np.sort(edges) # each will now be increasing. I think this is Quicksort? 
        self._dtype = dtype

        # Ostensibly you can bin strings... not sure why you would, but you could! 
        try:
            x = dtype() + dtype()
        except Exception:
            raise TypeError("It appears impossible to add {} together.".format(dtype))

        # build the function needed to register additions to the histograms.
        dims = tuple([len(self._edges[i])-1 for i in range(len(self._edges))])
        self._fill = np.zeros( shape=dims, dtype=self._dtype )
        def register( amt, *args, density=True):
            """
            Tries to bin some data passed to the bhist. Arbitrarily dimensioned cause I was moving from 2D-3D and this seemed like a good opportunity 
                amt is the amount to add
                *args specifies the coordinates in our binned space 
                density specifies whether or not we want to divide out bin widths to make amt a density

            As a note, the density thing is implemented as-is since when using this, you won't know how wide the target bin is when you call this register function. You also can't just divide it out afterwards. This needs to happen between getting the bin location and adding it to the bin! 
            """
            if not len(args)==len(self._edges): 
                raise ValueError("Wrong number of args to register! Got {}, not {}".format(len(args), len(self._edges)))
            if not isinstance(amt, self._dtype):
                try:
                    amount = self._dtype(amt)
                except TypeError:
                    raise TypeError("Expected {}, got {}. Tried casting to {}, but failed.".format(self._dtype, type(amt), self._dtype))
            else:
                amount = amt

            bin_loc = tuple([get_loc( args[i], self._edges[i])[0] for i in range(len(args))]) # get the bin for each dimension

            # Verifies that nothing in the list is None-type
            if all([x is not None for x in bin_loc]):
                # itemset works like ( *bins, amount )
                if density: 
                    widths = self.widths 
                    for dim in range(len(self._edges)):
                        amount/=widths[dim][bin_loc[dim]]
                try:
                    self._fill.itemset(bin_loc, self._fill.item(tuple(bin_loc))+amount)
                except TypeError:
                    print("bin_loc: {}".format(bin_loc))
                    print("amount: {}".format(amount))
                    print("previous: {}".format(self._fill.item(tuple(bin_loc))))
                    sys.exit()
                return tuple(bin_loc)
        self.register = register
 
    # some access properties. Note these aren't function calls. They are accessed like "object.centers" 
    @property
    def centers(self):
        complete = [ [0.5*(subedge[i+1]+subedge[i]) for i in range(len(subedge)-1)] for subedge in self._edges]
        return(complete[0] if len(self._edges)==1 else complete)
    @property
    def edges(self):
        complete = [[value for value in subedge] for subedge in self._edges]
        return(complete[0] if len(self._edges)==1 else complete)
    @property
    def widths(self):
        complete = [[abs(subedges[i+1]-subedges[i]) for i in range(len(subedges)-1)] for subedges in self._edges]
        return(complete[0] if len(self._edges)==1 else complete)
    @property
    def fill(self):
        return(self._fill)

def extract_from_edges(edges):
    """
    Takes list-like representing the edges of a bhist, returns the widths and centers 
    """
    if not (isinstance(edges, list) or isinstance(edges,np.ndarray) or isinstance(edges, tuple)):
        raise TypeError("Can't make bhist from {}, need {}".format(type(edges, list)))

    temp = bhist([edges])

    centers = np.array(temp.centers)
    widths = np.array(temp.widths)

    return( centers, widths )

def get_nearest_entry_to( item, array_like):
    """
    This function takes a quantity "item" and a list/array-like item "array_like"
    It returns the index of the entry in "array_like" that is closest to "item"

    Args:
        item - int
        array_like - list (or tuple, np.ndarray)
    Returns:
        index - int. =>0, <len(array_like)

    """
    # verify datatypes
    if not (isinstance(item,int) or isinstance(item, float)):
        raise TypeError("Expected number-like for arg 'item', got {}".format(type(item)))
    if not (isinstance(array_like, list) or isinstance(array_like, tuple) or isinstance(array_like,np.ndarray)):
        raise TypeError("Expected an index-able for arg 'array_like', got {}".format(type(array_like)))

    min_bin = None
    mindist = None

    # we can make no assumptions about the increasing/decreasing nature of 'array_like'
    # so we scan over it 
    for index in range(len(array_like)):
        if min_bin is None:
            min_bin = index
            mindist = abs(array_like[index] - item)
        else:
            new_distance = abs(array_like[index]-item)
            if new_distance < mindist:
                mindist = new_distance
                min_bin = index
  
    return(min_bin)

def get_width( which_list ):
    """
    Takes a list 'which_list' of floats of length N, considered the centers of some bins
    Returns a length N numpy array of floats for the widths of the bins these centers correspond to

    Arg 'which_list' must be monotonically increasing or decreasing
    """
    if not (isinstance(which_list, list) or isinstance(which_list, np.ndarray) or isinstance(which_list, tuple)):
        raise TypeError("Expected list-like, got {}".format(type(which_list)))

    # cast as a list
    if not isinstance(which_list, list):
        use = list(which_list)
    else:
        use = which_list

    n_bins = len(which_list)
    if n_bins<=1:
        raise ValueError("'which_list' should be longer than length {}".format(len(which_list)))

    increasing = which_list[1] > which_list[0]
    for i in range(n_bins-1):
        if not(increasing == (which_list[i+1] > which_list[i])):
            raise TypeError("Arg 'which_list' should be monotonically increasing or decreasing")

    n_bins = len(which_list)
    widths = [ 0. for i in range(n_bins)]
    for i in range(n_bins):
        if i==0:
            widths[i] = abs(use[1]-use[0])
        elif i==(n_bins-1):
            widths[i] = abs(use[-1]-use[-2])
        else:
            widths[i] = abs(0.5*(use[i+1]-use[i-1]))

    if not all(width>0 for width in widths):
        raise Exception("HOW {}".format(widths))

    return(np.array(widths))

def get_exp_std( widths, probs, values ):
    """
    This takes a discretely binned probability density function representing a true continuous one,
    integrates it to get the expectation value and standard deviation of the distribution

    If the probability density isn't normalized, this function will normalize it

    TODO: get asymmetric error bars! 

    RETURNS; means, y+ error, y- error 
    """
    sigma = 0.5+0.341

    if not (len(widths)==len(values) and len(values)==len(probs)):
        raise ValueError("The args should have the same lengths")
   
    if not all(width>=0 for width in widths):
        raise ValueError("Found negative width, this can't be right.")

#    if not all(prob>=0 for prob in probabilities):
#       raise ValueError("Found negative probability. {}".format(min(probabilities)))

    probabilities = np.abs(probs)

    norm = sum([widths[i]*probabilities[i] for i in range(len(widths))  ])
    if norm==0.:
        return(0.,0.,0.)

    prob_density = np.array([ probabilities[i]/norm for i in range(len(probabilities))])
    if abs(1.-sum(prob_density*widths))>(1e-8):
        raise ValueError("Unable to normalize probabilities, got {}".format(sum(prob_density*widths)))
    

    mean=0.
    for item in range(len(widths)):
        # P(x)*X
        mean+= (widths[item]*prob_density[item])*values[item]

    median_bin = 0
    acc_prob = 0.
    while acc_prob<0.5:
        acc_prob+= widths[median_bin]*prob_density[median_bin]
        median_bin+=1
    if median_bin==len(prob_density):
        median_bin-=1
    median = values[median_bin]

    # get upper bound
    upper_bin = median_bin +1
    upper_b = acc_prob
    while upper_b < sigma:
        upper_b += widths[upper_bin]*prob_density[upper_bin]
        upper_bin += 1
        if upper_bin==len(prob_density):
            break

    if upper_bin==len(values):
        upper_bin-=1
    sigma_plus = values[upper_bin] - median

    lower_bin = median_bin -1
    lower_b = acc_prob
    while lower_b > (sigma - 0.5):
        lower_b -= widths[lower_bin]*prob_density[lower_bin]
        lower_bin-=1
        if lower_bin==-1:
            break

    if lower_bin==-1:
        lower_bin+=1
    sigma_minus = median - values[lower_bin]

    var=0.
    for item in range(len(widths)):
        var+= (widths[item]*prob_density[item])*(mean-values[item])**2
    sigma = sqrt(var)

    return( median, sigma_plus, sigma_minus)