Numpy

Question 1

What is common acronym for numpy when importing?

Answer 1

import numpy as np

Question 2

What is numpy short for?

Answer 2

Numerical Python

Question 3

What does numpy provide?

Answer 3

An efficient interface to store and operate on dense data buffers.

Question 4

How are numpy arrays better than Python lists - 1?

Answer 4

NumPy arrays are like Python’s built-in list type, but NumPy arrays provide much more efficient storage and data operations as the arrays grow larger in size.

Question 5

What is the difference between a dynamic-type list and a fixed-type (numpy style) array?

Answer 5

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

Question 6

Can numpy arrays contain elements of mixed type?

Answer 6

No. All elements must be the same.

Question 7

How do you create a fixed-type array in Python?

Answer 7

import array
L = list(range(10))
A = array.array(‘i’, L)

returns: array(‘i’, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

where ‘i’ is type code indicating integers

Question 8

How do you create an numpy array from Python list?

Answer 8

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

Question 9

What happens when creating numpy arrays which are not of the same type?

Answer 9

Numpy will attempt to upcast if possible. ints upcast to floats

Question 10

How do we explicitly set the data type of an numpy array?

Answer 10

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

Question 11

Is it more efficient to create a numpy array from scratch or from existing list?

Answer 11

From scratch - especially for larger arrays

Question 12

Create numpy array all zeros

Answer 12

np.zeros(10, dtype=int) # 10 indicates 10 values

Question 13

Create numpy array all ones

Answer 13

np.ones(10, dtype=int) # 10 indicates 10 values

Question 14

Create numpy array with 1 specific value

Answer 14

np.full(10, 3.14, dtype=int) # 10 indicates 10 values, 3.14 is the value to include

Question 15

Create multi-dimensional numpy array

Answer 15

np.zeros((3,5), dtype=float) # create a 3x5 array poulated with zeros in float type

Question 16

What is syntax for numpy array filled with a linear sequence?

Answer 16

np.arange(0, 20, 2) # values from 0 up to, not including 20, step by 2

Question 17

What is syntax for numpy array of x values equally spaced btw two values?

Answer 17

np.linspace(0, 1, 5)

where 0 and 1 are bounding values, and 5 = x

Question 18

How do you create a numpy array of 3x3 random ints between 0 and 10?

Answer 18

np.random.randint(0, 10, (3, 3))

Question 19

What are the attributes of an numpy array, where array = x3.

Answer 19

x3. ndim = number of dimensions
x3. shape = shape of the array
x3. size = number of elements in array
x3. dtype = datatype

Question 20

How do you access the i-th element in a 1 dimensional numpy array x?

Answer 20

x[i] - same as for Python lists

Question 21

How do you access the elements in a multi-dimensional numpy array x?

Answer 21

x[2,0] # will return 1 for below array

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

Question 22

How do you modify the elements in a multi-dimensional numpy array x?

Answer 22

x[2,0] = 12 # will set the below value 1 to 12

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

NB. Numpy arrays are fixed type. If you attempt to set value to a float in above array then it will be silently truncated.

Question 23

What is numpy array slicing for 1-D arrays?

Answer 23

Similar to List slicing, same syntax used.

x[:5] # first five elements

Question 24

How does numpy slicing work for multi-dimensional arrays?

Answer 24

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

array([[12, 5, 2, 4],
[ 7, 6, 8, 8],
[ 1, 6, 7, 7]])

returns for the above array
array([[12, 5, 2],
[ 7, 6, 8]])

Question 25

How can you reverse a multi-dimensional array?

Answer 25

x2[::-1, ::-1]

Question 26

How can you access single rows/columns in multi-dimensional arrays?

Answer 26

print(x2[:, 0]) # first column of x2

print(x2[0, :]) # first row of x2

In the case of row access, the empty slice can be omitted for a more compact syntax: print(x2[0])

Question 27

Does numpy array slicing return a view or a copy of the array data?

Answer 27

A view. This differs from Python slicing, where slices are copies.

This means if a sliced array is altered, then the original array is also altered. This is useful when working with large arrays as it means we can access and process specific parts of the dataset.

Question 28

How can a copy of array data be made with array slicing?

Answer 28

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

This means if the sub array is modified, the original array will not be updated.

Question 29

How can numpy arrays be reshaped - 1?

Answer 29

If you want to put the numbers 1 through 9 in a 3×3 grid, you can do the following:

grid = np.arange(1, 10).reshape((3, 3))
print(grid)

NB. Note that for this to work, the size of the initial array must match the size of the reshaped array

Question 30

How can numpy arrays be reshaped - 2?

Answer 30

Use the newaxis keyword within slice operation. *** Not so sure about this one

# row vector via newaxis
x[np.newaxis, :]

# column vector via newaxis
x[:, np.newaxis]

Question 31

How can you concatenate numpy arrays?

Answer 31

Use the concatenate method…

x = np.array([1, 2, 3])
y = np.array([3, 2, 1])
np.concatenate([x, y]) # a list of arrays must be passed

Can also be used on multi-dimensional arrays

Question 32

How can you concatenate numpy arrays of different dimensions?

Answer 32

Can use np.concatenate if possible but clearer to use np.vstack and np.hstack

Question 33

How can a numpy array be split?

Answer 33

Use np.split …

x = [1, 2, 3, 99, 99, 3, 2, 1]
x1, x2, x3 = np.split(x, [3, 5])
print(x1, x2, x3)

Question 34

Why is numpy important in the Data Science world?

Answer 34

It provides an easy and flexible interface to optimized computation with arrays of data

Question 35

What is the key to making numpy computation fast?

Answer 35

Use vectorized operations - generally implemented through universal functions (ufuncs)

Question 36

What are numpy universal functions (ufuncs)?

Answer 36

They can be used to make repeated calculations on array element more efficient by using vectorized operations. They perform an operation on an array, which is then applied to each element … designed to push the loop in the compiled layer than underlies numpy.

Question 37

Give an example of some numpy ufuncs?

Answer 37

np. add or +
np. subtract or -
np. multiply or *
np. power or **

e.g.
x = np.arange(4)
x+5

x = [0 1 2 3]
x + 5 = [5 6 7 8]

Question 38

How can you sum all elements of an numpy array?

Answer 38

np.sum(x)

Use np.sum over python’s sum function, since np version much quicker

Question 39

What are multi-dimensional aggegrates in numpy?

Answer 39

One common type of aggregation operation is an aggregate along a row or column. For a multi-dimensional array such as

M = np.random.random((3, 4))

running M.sum() will return sum of all elements
However, running M.min(axis=0) will return the min value for each column … axis=1, will return values for rows

Question 40

In multi dimensional aggregate functions, how does the axis keyword work?

Answer 40

The axis keyword specifies the dimension of the array that will be collapsed, rather than the dimension that will be returned. So specifying axis=0 means that the first axis will be collapsed: for two-dimensional arrays, this means that values within each column will be aggregated.

Question 41

What is Broadcasting?

Answer 41

Broadcasting is simply a set of rules for applying binary ufuncs (e.g., addition, subtraction, multiplication, etc.) on arrays of different sizes.

Question 42

Give an example of Broadcasting that adds a scalar to an array

Answer 42

a = np.array([0, 1, 2])
a + 5

We can think of this as an operation that stretches or duplicates the value 5 into the array [5, 5, 5], and adds the results. The advantage of NumPy’s broadcasting is that this duplication of values does not actually take place, but it is a useful mental model as we think about broadcasting

Question 43

Give an example of Broadcasting that adds a 1-D array to a 2-D array

Answer 43

a = np.array([0, 1, 2])
M = np.ones((3, 3))
M + a

Here the one-dimensional array a is stretched, or broadcast across the second dimension in order to match the shape of M.

Question 44

Give an example of Broadcasting that involves Broadcasting of both arrays

Answer 44

a = np.arange(3)
b = np.arange(3)[:, np.newaxis]
a + b

a = [0 1 2]
b = [[0]
[1]
[2]]

becomes …

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

Question 45

Give an example of comparison operators used with ufuncs

Answer 45

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

x < 3 # this is the example

returns … array([ True, True, False, False, False], dtype=bool)

Could also use:

x <= 3
x >= 3
x == 3
(2 * x) == (x ** 2) # compound expression

Question 46

How can you count entries in a Boolean numpy array?

Answer 46

Given x =
[[5 0 3 3]
[7 9 3 5]
[2 4 7 6]]

# how many values less than 6?
np.count_nonzero(x < 6)

answer = 8

Question 47

How can you count entries in a Boolean numpy array - different to np.count_nonzero?

Answer 47

Given x =
[[5 0 3 3]
[7 9 3 5]
[2 4 7 6]]

np.sum(x < 6)
answer = 8 # False is interpreted as 0, and True is interpreted as 1

The benefit of using sum() is that summation can be done across rows or columns ….

# how many values less than 6 in each row?
np.sum(x < 6, axis=1)

Question 48

How can you check that any or all Boolean values in an array are true?

Answer 48

np. any(x > 8) # returns True or False
np. all(x > 8) # returns True or False

Can also use with axis keyword

Question 49

How can you use Boolean arrays as masks in numpy?

Answer 49

with x =
array([[5, 0, 3, 3],
[7, 9, 3, 5],
[2, 4, 7, 6]])

To select values where x < 5, do:

x[x < 5] # returns

array([0, 3, 3, 3, 2, 4])

Fuller example …

# construct a mask of all rainy days
rainy = (inches > 0)

# construct a mask of all summer days (June 21st is the 172nd day)
days = np.arange(365)
summer = (days > 172) &amp; (days < 262)

print(“Median precip on rainy days in 2014 (inches): “,
np.median(inches[rainy]))
print(“Median precip on summer days in 2014 (inches): “,
np.median(inches[summer]))
print(“Maximum precip on summer days in 2014 (inches): “,
np.max(inches[summer]))
print(“Median precip on non-summer rainy days (inches):”,
np.median(inches[rainy & ~summer]))

Question 50

What is fancy indexing?

Answer 50

It means passing an array of indices to access multiple array elements at once

Question 51

Give an example of fancy indexing

Answer 51

import numpy as np
rand = np.random.RandomState(42)

x = rand.randint(100, size=10)
ind = [3, 7, 4]
x[ind]

returns … array([71, 86, 60])

Question 52

What is the shape of the result of fancy indexing?

Answer 52

The shape of the result reflects the shape of the index arrays rather than the shape of the array being indexed:

e.g. if a 2-D array of indices is used to access a 1-D array. The results will be presented in 2-D

Question 53

Does fancy indexing work in multiple dimensions?

Answer 53

Yes.

X = np.arange(12).reshape((3, 4))
row = np.array([0, 1, 2])
col = np.array([2, 1, 3])
X[row, col]

returns … array([ 2, 5, 11])

Notice that the first value in the result is X[0, 2], the second is X[1, 1], and the third is X[2, 3]