#Python is an open source programming language.  An easy way to get started 
#with Python is to install a prebuilt distribution of Python, such as Anaconda.
#
#http://continuum.io/downloads#py34
#
#Note that we are using Python 3 rather than Python 2.  Also, make sure to get
#the version that is appropriate for your system (32 bit or 64 bit).
#
#Anaconda includes an IDE (integrated development environment/front end) called
#Spyder.  Spyder is a front end for Python in the same way Rstudio is a front
#end for R.
#
#Like Rstudio, Spyder has a script window and a console window, and we can
#execute commands from the script window using F9 (and a variety of other ways).



###################################################
#SUMMARY OF MAJOR DIFFERENCES BETWEEN PYTHON AND R#
###################################################

#In R, ^ is the exponentiation operation.
#In Python, ** is exponentiation, and ^ is the bitwise XOR operation.

#In R, the first component of a vector x is x[1]
#In Python, the zeroth component of a vector x is x[0]

#In Python, indentation matters in if then statements.



##################
#BASIC ARITHMETIC#
##################

x=5
y=2
x+y
x-y
x*y
x/y
x**y         #Exponentiation, as in SAS
help("**")   #Getting information with the help command


#WARNING:  In Python, ^ is actually the bitwise XOR command, not exponentiation.

#Example:

x=12   #which is 1100 in binary
y=10   #which is 1010 in binary
x^y    #is 6     0110 in binary


#To see a list of variables you have defined, use the variable explorer
#window in the top right corner.

#To delete a variable, use the del command.
a=1
a
del a
a


############################
#MODULES, NUMPY, and ARRAYS#
############################


#Packages in Python are called modules.  The module NumPy will allow us to 
#work with arrays efficiently.

#NumPy tutorial:  http://wiki.scipy.org/Tentative_NumPy_Tutorial


from numpy import *   #Imports all functions from numpy module.

A=array([[1,2],[3,4]])
A
A[0,0]
A[1,0]
A[0,1]
A[1,1]

B=array([[4,0],[-2,5]])
B

#Elementwise operations.

A+B
A-B
A*B
A/B
A+2
A**2


#Matrix operations

dot(A,B)                  #Matrix multiplication
linalg.inv(A)             #Inverse
dot(A,linalg.inv(A))      #Verifying that this is an inverse
transpose(A)              #Transpose
C=linalg.solve(A,B)       #inv(A) times B
dot(A,C)
A.diagonal()              #Diagonal of A


#Stacking Matrices
hstack((A,B))             #Note the double parentheses here.
vstack((A,B))


#Creating arrays
ones([3,5])
zeros([3,5])
identity(3,float) #Here we are specifying data type = float
diag([9,10])      #Diagonal matrix

arange(20,40,5)   #40 not included
arange(20,41,5)   #40 is included

A=arange(12)
A
A=arange(12).reshape(3,4)
A
A.shape   #Returns number of rows and columns.
A.size    #Total number of entries in A.
A.dtype   #Data type (in this case, 32-bit integer)
A.diagonal()
A.diagonal(offset=1)
A.diagonal(offset=-1)

#Rows of A
A[0,:]
A[1,:]
A[2,:]
A[[0,2],:]

#Columns of A
A[:,0]
A[:,1]
A[:,2]
A[:,3]
A[:,[0,2,3]]

#Indexing
x=arange(10)**2
x
x[0]    #0th component
x[2]    #2nd component   
x[2:5]  #2nd through 4th components

x[-1]   #Last component
x[-2]   #Second to last component

x[:5]   #0th through 4th components
x[5:]   #5th through 9th components

index=(x>=40)
index
x[index]


####################
#LOGICAL OPERATIONS#
####################

3==3
3==5
3!=5
3<5
3<=5
3>5
3>=3

(3<5) and (4>7)
(3<5) or (4>7)
not(3<5)



##########################
#SIMPLE PROGRAMMING TOOLS#
##########################

#Example 1
if (3<5):  print("Hooray!")


#Example 2
if (3>5): print("Hooray!")


#Example 3
if (3<5):
    print("Three is less than five")
    print("It really is")
print("Here's a statement that isn't indented")
print("Indentation matters in Python")


#Example 4
if (3>5):
    print("Three is less than five")
    print("It really is")
print("Here's a statement that isn't indented")
print("Indentation matters in Python")


#Example 5
if(3<5):
    print("I like dogs")
else:
    print("I like cats")
print("This line isn't indented")


#Example 6
if(3>5):
    print("I like dogs")
else:
    print("I like cats")
print("This line isn't indented")


#For Loops
x=arange(10)
for i in x:
    print(x[i])


#Functions
def mysum(x,y):
    return x+y
    
mysum(5,9)



##########
#PLOTTING#
##########


from matplotlib import *

x=arange(10)
y=x**2

pyplot.plot(x,y)

#PyPlot documentation:   http://matplotlib.org/api/pyplot_api.html



######################
#STATISTICAL COMMANDS#
######################
x=numpy.random.normal(500,100,1000)
mean(x)
std(x)


from numpy import *
x=random.normal(500,100,1000)

mean(x)
std(x)
min(x)
max(x)
sort(x)


from pylab import *
pylab.hist(x)
hist(x)


x=numpy.random.uniform(low=0,high=1,size=1000)
mean(x)
std(x)
1/sqrt(12)
hist(x)


#Plotting a scatterplot with a regression curve.
x=random.normal(100,15,1000)       
epsilon=random.normal(0,5,1000)    
y=x+epsilon  
plot(x,y)

#Execute this by itself
plot(x,y,'.',color="black")

#Execute this by itself
plot(sort(x),sort(x),'-',color="red")

#Execute these at the same time
plot(x,y,'.',color="black")
plot(sort(x),sort(x),'-',color="red")



################
#IMPORTING DATA#
################

from numpy import *

mydata=genfromtxt(
    "T:\Fall 2014\Math 5364\Python Experimentation\math5305Lab2Data.txt",
    dtype=float,
    delimiter=",")
    
mydata