09 NumPy Udemy

Question 1

NumPy is a Linear Algebra Library for Python, the Reasos it is so important for Data Science with Python is that almost all of the libraries in the PyData Ecosystem rely on NumPy as one of their main building blocks

Answer 1

NumPy is also incredibly fast, as it has bindings to C libraries

Question 2

Vectors are strictly 1-d arrays

Answer 2

Matrices are 2-d

but can still have only one row or one columns

Question 3

NumPy Arrays

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

Answer 3

my_matrix = [[1,2,3],[4,5,6],[7,8,9]]
my_matrix
np.array(my_matrix)
==
[[1, 2, 3], [4, 5, 6], [7, 8, 9]]
array([[1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]])

Question 4

np.arange(0,10,2)

==

Answer 4

array([ 0, 2, 4, 6, 8])

Question 5

np.zeros((4,5))

==

Answer 5

array([[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.]])

Question 6

np.ones((2,3))

==

Answer 6

array([[ 1., 1., 1.],

[ 1., 1., 1.]])

Question 7

np.linspace(0,10,3)

array([ 0., 5., 10.])

Answer 7

np.linspace(0,10,6)

array([ 0., 2., 4., 6., 8., 10.])

Question 8

np.eye(4)

==

Answer 8

array([[1., 0., 0., 0.],
[0., 1., 0., 0.],
[0., 0., 1., 0.],
[0., 0., 0., 1.]])

Question 9

np.random.rand(4,3)

==

Answer 9

rray([[0.88277868, 0.64350899, 0.34540502],
[0.48679882, 0.27605306, 0.78273307],
[0.62853873, 0.68858502, 0.81299911],
[0.80075412, 0.49107607, 0.90190195]])

Create an array of the given shape and populate it with random samples from a uniform distribution over [0, 1)

Question 10

np.random.randn(5,4)

==

Answer 10

array([[-0.6898178 , -2.19758573, 0.0801776 , -0.04129733],
[-2.7230242 , 0.43690199, -0.23268161, 0.88727527],
[ 0.38131687, -0.15555836, 1.11193221, -2.1126014 ],
[-0.70322463, -0.16923125, -1.80195906, 2.00983817],
[-0.97640657, 1.14549034, -1.05173513, -0.80275212]])

Return a sample (or samples) from the “standard normal” distribution. Unlike rand which is uniform:

Question 11

np.random.randint(1,11,100)

==

Answer 11

Return random integers from low (inclusive) to high (exclusive).

array([ 5, 8, 10, 5, 7, 10, 5, 3, 3, 3, 9, 8, 3, 1, 9, 10, 1,
5, 10, 2, 3, 9, 8, 2, 2, 7, 3, 4, 6, 10, 8, 7, 6, 5,
8, 2, 1, 8, 9, 4, 3, 5, 2, 9, 8, 6, 10, 8, 7, 9, 9,
7, 9, 5, 3, 4, 10, 10, 3, 3, 2, 1, 8, 5, 8, 4, 7, 10,
8, 1, 10, 10, 9, 10, 8, 3, 4, 4, 5, 6, 2, 5, 1, 3, 5,
8, 10, 10, 10, 6, 4, 4, 8, 5, 6, 8, 8, 7, 1, 8])

Question 12

arr = np.arange(25)
arr
==
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24])

Answer 12

arr.reshape(5,5)
==
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24]])

Question 13

ranarr = np.random.randint(0,50,10)
ranarr
==
array([38, 12, 4, 45, 4, 23, 14, 49, 41, 21])

ranarr. max() == ???
ranarr. argmax() == ???

Answer 13

49
7

(pra mínimo (min) o raciocínio é o mesmo)
argmax é o índice / posição

Question 14

x.shape

mostra o formato

Answer 14

x.dtype

mostro o tipo de arquivo

Question 15

arr = np.arange(0,11)
arr[1:5]
==

Answer 15

array([1, 2, 3, 4])

Bracket Indexing and Selection
The simplest way to pick one or some elements of an array looks very similar to python lists:

Question 16

Broadcasting
Numpy arrays differ from a normal Python list because of their ability to broadcast

arr
== >
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

arr[0:5]=100
== >
array([100, 100, 100, 100, 100, 5, 6, 7, 8, 9, 10])

Answer 16

slice_of_arr = arr[0:6]
slice_of_arr[:]=99
slice_of_arr
arr
== >
array([99, 99, 99, 99, 99, 99])
array([99, 99, 99, 99, 99, 99,  6,  7,  8,  9, 10])

Now note the changes also occur in our original array!
Data is not copied, it’s a view of the original array! This avoids memory problems!

### To get a copy, need to be explicit
arr_copy = arr.copy()

Question 17

Indexing a 2D array (matrices)

The general format is arr_2d[row][col] or arr_2d[row,col].

I recommend usually using the comma notation for clarity.

Answer 17

array([[ 5, 10, 15],
[20, 25, 30],
[35, 40, 45]])

arr_2d[:2,1:]
==>
array([[10, 15],
[25, 30]])

Question 18

Fancy Indexing
Fancy indexing allows you to select entire rows or columns out of order,to show this, let’s quickly build out a numpy array:

#Set up matrix
arr2d = np.zeros((10,10))

#Length of array
arr_length = arr2d.shape[1]

for i in range(arr_length):
arr2d[i] = i
arr2d
==>
array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
[2., 2., 2., 2., 2., 2., 2., 2., 2., 2.],
[3., 3., 3., 3., 3., 3., 3., 3., 3., 3.],
[4., 4., 4., 4., 4., 4., 4., 4., 4., 4.],
[5., 5., 5., 5., 5., 5., 5., 5., 5., 5.],
[6., 6., 6., 6., 6., 6., 6., 6., 6., 6.],
[7., 7., 7., 7., 7., 7., 7., 7., 7., 7.],
[8., 8., 8., 8., 8., 8., 8., 8., 8., 8.],
[9., 9., 9., 9., 9., 9., 9., 9., 9., 9.]])

Answer 18

Allows in any order

Fancy indexing allows the following

arr2d[[2,4,6,8]]
==>
array([[ 2., 2., 2., 2., 2., 2., 2., 2., 2., 2.],
[ 4., 4., 4., 4., 4., 4., 4., 4., 4., 4.],
[ 6., 6., 6., 6., 6., 6., 6., 6., 6., 6.],
[ 8., 8., 8., 8., 8., 8., 8., 8., 8., 8.]])

arr2d[[6,4,2,7]]
==>
array([[ 6., 6., 6., 6., 6., 6., 6., 6., 6., 6.],
[ 4., 4., 4., 4., 4., 4., 4., 4., 4., 4.],
[ 2., 2., 2., 2., 2., 2., 2., 2., 2., 2.],
[ 7., 7., 7., 7., 7., 7., 7., 7., 7., 7.]])

Question 19

arr1 = np.arange(1,11)
arr1
==>
array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

arr1 > 4
==>
array([False, False, False, False, True, True, True, True, True, True], dtype=bool)

bool_arr = arr1 >4
bool_arr
==>
array([False, False, False, False, True, True, True, True, True, True], dtype=bool)

Answer 19

arr1[bool_arr]
==>
array([ 5, 6, 7, 8, 9, 10])

arr1[arr1>2]
==>
array([ 3, 4, 5, 6, 7, 8, 9, 10])

Question 20

arr = np.arange(0,10)
arr
arr + 100
arr * arr
==>
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
array([100, 101, 102, 103, 104, 105, 106, 107, 108, 109])
array([ 0,  1,  4,  9, 16, 25, 36, 49, 64, 81])

Answer 20

arr/arr
==>
array([nan, 1., 1., 1., 1., 1., 1., 1., 1., 1.])
# 0/0 == null (nan no np)

1/arr
==>
array([ inf, 1. , 0.5 , 0.33333333, 0.25 ,
0.2 , 0.16666667, 0.14285714, 0.125 , 0.11111111])
## resultado é infinito + warning