1. Understanding Data Types in Python

A Python Integer is more than just an Integer

• C integer is essentially a label for a position in memory whose bytes encode an interger value
• Python integer is a pointer to a position in memory containing all the Python object information, including the bytes that contain the integer value

A Python List is more than just a List

• Because of Python's dynamic typing, we can even create heterogeneous lists.
• To allow these flexible types, each item in the list must contain its own type, reference count, and other information

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• At the implementation level, the array essentially contains a single pointer to one contiguous block of data.
• The Python list contains a pointer to a block of pointers each of which in turn points to a full Python object.

Summary

• The advantage of the list is flexibility : because each list element is a full structure containing both data and type information, the list can be filled with data of any desired type
• Fixed type Numpy-style array lack this flexibility but are much more efficient for storing and manipulating data.

Fixed-Type Arrays in Python

• The built-in array module can be used to create dense arrays of a uniform type

  # In[1]
  import array
  L=list(range(10))
  A=array.array('i',L)
  A

  # Out[1]
  array('i',[0,1,2,3,4,5,6,7,8,9])

Creating Arrays from Python Lists

# we will start with the standard Numpy import
import numpy as np

# In[2]
np.array([1,4,2,5,3])

# Out[2]
array([1,4,2,5,3])

• If types do not match, Numpy will upcast if possible. For example, integers are upcast to floating point like this:

  # In[3]
  np.array([3.14,4,2,3])

  # Out[3]
  array([3.14,4., 2.,3.])

• We can use dtype keyword to set the data type of the resulting array:

  # In[4]
  np.array([1,2,3,4],dtype='float32')

  # Out[4]
  array([1.,2.,3.,4.],dtype=float32)

• Here, float32 means single precision float. Sign bit, 8 bits Exponent, 23 bits Mantissa

Creating Arrays from Scratch

• For larger arrays, it is more efficient to create arrays from scratch using routines built into Numpy.

np.zeros

• Create array filled with 0

  # In[5]
  np.zeros(10,dtype=int)

  # Out[5]
  array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])

np.ones

• Create array filled with 1

  # In[6]
  np.ones((3,5),dtype=float)

  # Out[6]
  array([[1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1.]])

np.full

# In[7]
np.full((3,5),3.14)

# Out[7]
array([[3.14, 3.14, 3.14, 3.14, 3.14],
       [3.14, 3.14, 3.14, 3.14, 3.14],
       [3.14, 3.14, 3.14, 3.14, 3.14]])

np.arange

• Create an array filled with a linear sequence

• Similar to the built-in range function

  # In[8]
  np.arange(0,20,2)

  # Out[8]
  array([ 0,  2,  4,  6,  8, 10, 12, 14, 16, 18])

np.linspace

# In[9]
np.linspace(0,1,5)

# Out[9]
# create an array of five values spaced between 0 and 1
array([0.  , 0.25, 0.5 , 0.75, 1.  ])

np.random

# In[10]
np.random.random((3,3))

# Out[10]
# random values between 0 and 1
array([[0.45216671, 0.39915045, 0.28124739],
       [0.69650235, 0.50474633, 0.7893374 ],
       [0.9051    , 0.74894434, 0.3819369 ]])

---

# In[11]
np.random.normal(0,1,(3,3))

# Out[11]
# create an array with mean 0 and standard deviation 1
array([[ 0.60406596, -0.63038548, -0.09671667],
       [-0.14400673,  0.0967629 , -1.03368308],
       [ 0.24388749,  0.592264  ,  0.09380424]])

• np.random.normal is normal distribution function provided by Numpy.
• Typing parameters (mean, standard deviation, number of data)

---

# In[12]
np.random.randint(0,10,(3,3))

# Out[12]
array([[7, 0, 3],
       [5, 0, 7],
       [8, 5, 1]])

np.eye

• Create identify matrix

  # In[13]
  np.eye(3)

  # Out[13]
  array([[1., 0., 0.],
       [0., 1., 0.],
       [0., 0., 1.]])

np.empty

• Create an uninitialized array

• memory location

  # In[14]
  np.empty(3)

  # Out[14]
  array([1., 1., 1.])