import matplotlib
import matplotlib.pyplot as plt
import pylab
import scipy
import numpy as np
from numpy import histogram
from numpy import random
from scipy import misc

# there is a build-in gaussian normpdf, see below.

def gaussian(x, mu, sig):
    return (1.0/(np.sqrt(2.0*np.pi)*sig) * np.exp(-0.5*(x-mu)*(x-mu)/(sig*sig)))

# could plot this too, but caution, wonder carefully what it does when
# you ask for the factorial of a non-integer.
def poisson(x, mu):
    return (np.power(mu,x))/scipy.misc.factorial(x) * np.exp(-mu)

# use one of these two choices
# Your data goes here.
# put your data into an array
# or read it in from a file
data = np.array( [1,2,3,2,1,4,-2,-1,0,-3] )
samplesize = 10

#Alternative, make synthetic random data
#samplesize = 10000
#randommean = 1.1
#randomsigma = 1.3
#data = randomsigma * np.random.randn(samplesize) + randommean

# specify your preferred bin size
lowbound = -6.5
upbound = 6.5
numberofbins = 14
bins = np.linspace(lowbound,upbound,numberofbins)
# often for Poisson data, you want the bins to
# line up on integers (or two or five or ten integers)
# to get the bins to line up on integers,
# need to type in 14 = 13+1 instead of 13.
# for the range -6.5 to +6.5 .   Odd.

# I thought I wanted to use pythons built-in histogram class
# but it doesn't seem I can actually use it for anything.
# myhistogram, bins = np.histogram( data, 9, (-4.5,4.5) )


mymean = np.mean(data)
mystdev = np.std(data)
print("mean {0} stdev {1} " .format(mymean,mystdev))

plt.figure(facecolor="white")
plt.hist(data, bins)
plt.title("illustration a Gaussian on data")
plt.ylabel("occurances in the data set", fontsize=16)  # the fontsize here is gratuitious
plt.xlabel("number of counts", fontsize=16)

# make a finer binning for to overlay the samplesize normalized Gaussian
# caution, what is the meaning of this if you use a poisson expecting integers?
x = np.linspace(lowbound,upbound,100)
plt.plot(x,samplesize*gaussian(x,mymean,mystdev),'-',linewidth = 3.0, color="black")
#plt.plot(x,samplesize*poisson(x,mymean),'-',linewidth = 2.0, color="black")

plt.show()