#Week 4 Examples
import numpy as np
import matplotlib.pyplot as plt 

#Defining a simple 2D array

A = np.array([[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15]])
#If I print A: 
#
# out: array([[ 1, 2, 3, 4, 5]
#             [6, 7, 8, 9, 10]
#             [11,12,13,14,15]]) 

#Using existing arrays and stacking them
a1 = [1,2,3,4,5]
a2 = [2,3,4,5,6]
a3 = [3,4,5,6,7]

two_d = np.vstack((a1,a2,a3))

# If I print two_d:
#
# out: array([[1,2,3,4,5]
#             [2,3,4,5,6]
#             [3,4,5,6,7]])

#Can use hstack if you have columns rather than rows
col1 = np.array([[1],[2],[3]])
col2 = np.array([[5],[7],[1]])
col3 = np.array([[9],[4],[6]])

stacked = np.hstack((col1,col2,col3))
#Output is 
#      array([[1,2,3]
#             [5,7,1]
#             [9,4,6]])
#
#
##########################################################
#Plotting Stuff

#Generate some fake data to play around with
x = np.arange(100)
y = x**2 
y2 = y + 550 * np.random.normal(size=x.shape) #random data in a normal distribution around the original line y=x**2

#simple plot: 
plt.plot(x,y2) #Plot with default settings
plt.title('Most simple plot with default settings')
plt.show() 

#Labeled Plot:
plt.figure() #create a new figure (like a new blank canvas to plot on, so it doesn't mess with the previous plot)
plt.plot(x,y2,'r+',label='Data Points') #using red plus symbols, and creating a label for the legend
plt.legend() #can use arg (loc=1), with integer 1-4 to specify which corner legend is in
plt.title('Plot with Label+legend')
plt.show()

#Error-Bar plot:
y_error = y2/np.random.randint(1,20) 
''' Here I generate an array of "errors" for our fake data from above. 
This is pretty much arbritrary- but generally with measurements of at least
a 1 sigma detection, the error bars' lengths are anywhere up to 1/3 the value at the point.
The exact thing I do is in the yerr array, each value is the value of y2 at that point divided by a random integer 1-20.
'''
plt.figure()
plt.errorbar(x,y2,yerr=y_error,fmt='s',c='r',label='Data')
plt.title('Error bar Plot')
plt.legend(loc=2)
plt.show()
#i.e., we use the yerr argument to specify the array with the error for each point
#There is also an xerr argument if you have an array of uncertainties in x as well
plt.figure()
#Of course, you can plot multiple data sets on the same plot:
y3 = x**2 + 2000
y4 = y3 + 335 * np.random.normal(size=x.shape)
plt.plot(x,y2,'r+',label='Set 1')
plt.plot(x,y4, 'b^', label='Set2')
plt.title('multiple data sets')
plt.legend(loc=2)
plt.show()

#Creating a Histogram 
'''
Histograms are useful because they allow you to see the distribution of a dataset. 
Often times if you look at independently collected data points from sample, 
the means will follow a normal distribution. (our fake data does as well, by construction). 
'''
#Generate some Fake Data
mu = 200
sigma = 25
x = mu + sigma*np.random.randn(10000)
plt.figure()
plt.hist(x, 20, normed=1, histtype='stepfilled', facecolor='g', alpha=0.75)
plt.title('A histogram')
plt.show()

#MISC Plotting

#plt.annotate('text', xy=(1,3)) #put in coords to put text on graph