#Importing all the functions of NumPy
from numpy import *

#Importing NumPy as numpy
import numpy

#Importing NumPy with the alias of np (recommended)
import numpy as np

#Basic functions
print np.exp(10.5), np.log(52.3), np.log10(63.9), np.sqrt(10.0)

#Trigonometric functions
print np.sin(5.0), np.cos(9.6), np.arcsin(0.5), np.arctan(5)

print "The value of PI is %1.6f"%( np.pi )

x.append   x.count    x.extend   x.index    x.insert   x.pop      x.remove   x.reverse  x.sort

x.T             x.clip          x.dot           x.item          x.prod          x.setfield      x.take
x.all           x.compress      x.dtype         x.itemset       x.ptp           x.setflags      x.tofile
x.any           x.conj          x.dump          x.itemsize      x.put           x.shape         x.tolist
x.argmax        x.conjugate     x.dumps         x.max           x.ravel         x.size          x.tostring
x.argmin        x.copy          x.fill          x.mean          x.real          x.sort          x.trace
x.argsort       x.ctypes        x.flags         x.min           x.repeat        x.squeeze       x.transpose
x.astype        x.cumprod       x.flat          x.nbytes        x.reshape       x.std           x.var
x.base          x.cumsum        x.flatten       x.ndim          x.resize        x.strides       x.view
x.byteswap      x.data          x.getfield      x.newbyteorder  x.round         x.sum           
x.choose        x.diagonal      x.imag          x.nonzero       x.searchsorted  x.swapaxes


#Lists and numpy arrays can both store any type of data
x1 = [1.2, 3.5, 1.9]
x2 = np.array([1.6, -2.6, 6.9])
print x1, x2

#For lists, new elements can be added using append method
x1 = [1.2, 3.5, 1.9]
x1.append(5.9)

#For arrays, new elements can be added using append function of NumPy
x2 = np.array([1.6, -2.6, 6.9])
x2 = np.append(x2,3)

print x1,x2

#A list can be converted into a numpy array
x = [1.1,3.4,1.0]
x = np.array(x)
#And a numpy array into a list as well
x = list(x)

#Operator + for lists is overloaded for concatenating 
x1 = [1,2,3]
x2 = [3,2,1]
print x1+x2

#Operator + for numpy arrays is overloaded for adding
x1 = np.array([1,2,3])
x2 = np.array([3,2,1])
print x1+x2

#Lists do not support other operators
x1 = [1.2,4.8,6.9]
x2 = [2.6,2.8,1.1]

#Multiplication
print x1*x2

#Division
print x1/x2

#Subtraction
print x1-x2

#Power
print x1**x2

#Numpy arrays support any mathematical operation (element by element)
x1 = np.array([1.2,4.8,6.9])
x2 = np.array([2.6,2.8,1.1])

print "Adding", x1+x2
print "Multiplication", x1*x2
print "Division", x1/x2
print "Subtraction", x1-x2
print "Power", x1**x2

A = np.array([[1,2],[3,4]])
B = np.array([[4,3],[2,1]])
print A 
print B
print A*B

#It is possible to access elements of a numpy array using booleans
x = np.array([1,2,3,4])
y = np.array([True, False, True, False])
x[y]

#Operators >, <, >=, <= and == are also overloaded for numpy arrays
x = np.array([0,5,8,0])
y = np.array([0,6,5,1])
print x>y
print x<y
print x==y
print x>4

#Combining these features, we can perform searches and comparisons far more efficient
x = np.array([1,4,2,6,8,4,3,0,9,1,3,6,7,])
#A new list with numbers greater than 4
print x[x>4]

#Native methods of numpy arrays allow to calculate basic quantities
x = np.array([1,4,2,6,8,4,3,0,9,1,3,6,7,])
#Maximum element
print "Maximum element", x.max()
#Minimum element
print "Minimum element", x.min()
#Sorted arguments of the array
print "Sorted arguments", x.argsort()
#Sorted array
print "Sorted array", x[x.argsort()]
#Mean value
print "Mean value", x.mean()

#Create an array of 1's with a given size (even 2D sizes)
x = np.ones(5)
print x

#Create an array of zeros with a given size (even 2D sizes)
x = np.zeros( (2,5) )
print x

#Create an array with a given range and a number of intervals
x = np.linspace( -np.pi, np.pi, 10 )
print x

#Create an array with a given range and a given step
x = np.arange( 1, 5, 0.2 )
print x

#Using the function savetxt, it is possible to store data from a numpy array
data = np.array([[3.2, 2.1],[3.1, 4.1]])
np.savetxt( "file.dat", data, fmt="%1.5e  %1.5e" )

#In the same way, using the function loadtxt it is possible to load external data files
data = np.loadtxt("file.dat")
#Data is then a multidimensional array with the loaded data
print data

#Histograms are also useful and NumPy provides functions to do so
x = [1,5,3,7,2,4,6,8,9,5,2,3,5,6,7,8,3,4,5]
np.histogram(x)

#Importing integrate package
import scipy.integrate as integ

integ.Tester        integ.fixed_quad    integ.odepack       integ.quadrature    integ.test          
integ.complex_ode   integ.newton_cotes  integ.quad          integ.romb          integ.tplquad       
integ.cumtrapz      integ.ode           integ.quad_explain  integ.romberg       integ.trapz         
integ.dblquad       integ.odeint        integ.quadpack      integ.simps         integ.vode