Python Programming

Class 5

NumPy (short for Numerical Python) provides an efficient interface to store and operate on dense data buffers.

• Benefits:
  • Efficient storage
  • Data operations

Arrays from Scratch

Note: unlike Python lists, NumPy is constrained to arrays that all contain the same type. If types do not match, NumPy will upcast if possible (here, integers are upcast to floating point):

#Creating Arrays from Python Lists

array1 = np.array([1, 4, 2, 5, 3])

array2 = np.array([3.14, 4, 2, 3])

array3 = np.array([[1,2,3],[4,5,6]])

array4 = np.array([1, 2, 3, 4], dtype='float32')

Functions to create arrays

#Numpy also provides many functions to create arrays:

a = np.zeros((2,2))   # Array of all zeros

b = np.ones((1,2))    # Array of all ones

c = np.full((2,2), 7)  # Constant array

d = np.eye(2)         # Create a 2x2 identity matrix

e = np.random.random((2,2))  # Array filled with random values

Attributes of arrays

np.random.seed(0) # seed for reproducibility
x1 = np.random.randint(10, size=6) # One-dimensional array
x2 = np.random.randint(10, size=(3, 4)) # Two-dimensional array
x3 = np.random.randint(10, size=(3, 4, 5)) # Three-dimensional array

print("x3 ndim: ", x3.ndim)
print("x3 shape:", x3.shape)
print("x3 size: ", x3.size)

Indexing of arrays

Getting and setting the value of individual array elements

x[start:stop:step]

• If any of these are unspecified, they default to the values start=0, stop=size of dimension, step=1.

• see examples

One-dimensional subarrays

#One dimentional 
x1
x1[0]
x1[4]

x2[0, 0] = 12

#Note
x1[0] = 3.14159 # this will be truncated!x1

x1[:5] # first five elements

x1[5:] # elements after index 5

x1[4:7] # middle subarray

x1[::2]

x1[::]

Multidimensional subarrays

#Multi dimentional 
x2

x2[:2, :3] # two rows, three column

x2[:3, ::2] # all rows, every other column

x2[0, :] # first row of x2

x2[0, :]
x2[0, ::]
x2[0, 0:4:1]

Accessing array rows and columns

x2[:, 0] #first column of x2

One commonly needed routine is accessing single rows or columns of an array. You can do this by combining indexing and slicing, using an empty slice marked by a single colon (:):

Subarrays as no-copy views

x2

x2_sub = x2[:2, :2]

x2_sub[0, 0] = 99

Source: Python Data Science Handbook: Essential Tools for Working with Data

Creating copies of arrays

x2_sub_copy = x2[:2, :2].copy()

x2_sub_copy[0, 0] = 42

x2

Joining arrays

x = np.array([1, 2, 3])
y = np.array([3, 2, 1])

z = np.concatenate([x, y]) #concatenate
z = np.hstack([x, y])  #hstack 
z = np.vstack([x, y])  #vstack

Vectorized operations

• see examples

Source: Python Data Science Handbook: Essential Tools for Working with Data

Challenge 1

Average is 4.413

Variance is 8.216431

Standard deviation is 2.86643175394

Write a Python script to create a random array with 1000 elements (each element in range [0,10) ) and

compute the average, variance, standard deviation of the array elements.

Note: use 1 as random seed.

Documentation: https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.random.randint.html

Answer 1

import numpy as np

np.random.seed(1) 

random_array = np.random.randint(10, size=(1000,1)) 

print('Average is ' + str(np.average(random_array)))
print('Variance is ' + str(np.var(random_array)))
print('Standard deviation is '+ str(np.std(random_array)))

Challenge 2

Maximum value is: 97

Index of Maximum value is: 3

Write a Python script that:

1. Create two random matrices of integers (each element in range [0,10), size =(3,4))
2. Multiply matrices element wise and save result in new variable
3. Sum each column and save array in new variable.
4. Find maximum value of array
5. Find maximum value index

Note: use 1 as random seed.

Answer 2

import numpy as np

#Create two random matrices of integers (max posible value 10, size = (3,4))
np.random.seed(1) # seed for reproducibility
a = np.random.randint(10, size=(3, 4)) # Two-dimensional array
c = np.random.randint(10, size=(3, 4))

#Multiply matrices element wise
d = np.multiply(a, c)

#Sum Columns
e = np.sum(d,axis=0)

#Fin maximum value
print('Maximum value is: '+str(np.max(e)))

#Find Maximun value index
print('Index of Maximum value is: '+str(np.argmax(e)))

Resources

• http://cs231n.github.io/python-numpy-tutorial/#numpy​
• Python Data Science Handbook: Essential Tools for Working with Data