Category: Programming

For some applications, it’s quite useful to convert a list of lists into a dictionary.

• Databases: List of list is table where the inner lists are the database rows and you want to assign each row to a primary key in a new dictionary.
• Spreadsheet: List of list is two-dimensional spreadsheet data and you want to assign each row to a key (=row name).
• Data Analytics: You’ve got a two-dimensional matrix (=NumPy array) that’s initially represented as a list of list and you want to obtain a dictionary to ease data access.

There are three main ways to convert a list of lists into a dictionary in Python (source):

1. Dictionary Comprehension
2. Generator Expression
3. For Loop

Let’s dive into each of those.

1. Dictionary Comprehension

Problem: Say, you’ve got a list of lists where each list represents a person and consists of three values for the person’s name, age, and hair color. For convenience, you want to create a dictionary where you use a person’s name as a dictionary key and the sublist consisting of the age and the hair color as the dictionary value.

Solution: You can achieve this by using the beautiful (but, surprisingly, little-known) feature of dictionary comprehension in Python.

persons = [['Alice', 25, 'blonde'], ['Bob', 33, 'black'], ['Ann', 18, 'purple']] persons_dict = {x[0]: x[1:] for x in persons}
print(persons_dict)
# {'Alice': [25, 'blonde'],
# 'Bob': [33, 'black'],
# 'Ann': [18, 'purple']}

Explanation: The dictionary comprehension statement consists of the expression x[0]: x[1:] that assigns a person’s name x[0] to the list x[1:] of the person’s age and hair color. Further, it consists of the context for x in persons that iterates over all “data rows”.

Exercise: Can you modify the code in our interactive code shell so that each hair color is used as a key and the name and age are used as the values?

Modify the code and click the “run” button to see if you were right!

2. Generator Expression

A similar way of achieving the same thing is to use a generator expression in combination with the dict() constructor to create the dictionary.

persons = [['Alice', 25, 'blonde'], ['Bob', 33, 'black'], ['Ann', 18, 'purple']] persons_dict = dict((x[0], x[1:]) for x in persons)
print(persons_dict)
# {'Alice': [25, 'blonde'],
# 'Bob': [33, 'black'],
# 'Ann': [18, 'purple']}

This code snippet is almost identical to the one used in the “list comprehension” part. The only difference is that you use tuples rather than direct mappings to fill the dictionary.

3. For Loop

Of course, there’s no need to get fancy here. You can also use a regular for loop and define the dictionary elements one by one within a simple for loop. Here’s the alternative code:

persons = [['Alice', 25, 'blonde'], ['Bob', 33, 'black'], ['Ann', 18, 'purple']] persons_dict = {}
for x in persons: persons_dict[x[0]] = x[1:] print(persons_dict)
# {'Alice': [25, 'blonde'],
# 'Bob': [33, 'black'],
# 'Ann': [18, 'purple']}

Again, you map each person’s name to the list consisting of its age and hair color.

Where to Go From Here?

Enough theory, let’s get some practice!

To become successful in coding, you need to get out there and solve real problems for real people. That’s how you can become a six-figure earner easily. And that’s how you polish the skills you really need in practice. After all, what’s the use of learning theory that nobody ever needs?

Practice projects is how you sharpen your saw in coding!

Do you want to become a code master by focusing on practical code projects that actually earn you money and solve problems for people?

Then become a Python freelance developer! It’s the best way of approaching the task of improving your Python skills—even if you are a complete beginner.

Join my free webinar “How to Build Your High-Income Skill Python” and watch how I grew my coding business online and how you can, too—from the comfort of your own home.

Join the free webinar now!

Problem: Given a Python tuple with n elements. How to convert it into a list with the same n elements?

Examples:

• Convert tuple (1, 2, 3, 4, 5) into list [1, 2, 3, 4, 5].
• Convert tuple ('Alice', 'Bob', 'Ann') into list ['Alice', 'Bob', 'Ann'].
• Convert tuple (1,) into list [1].

Note Tuple: Tuples are similar to lists—with the difference that you cannot change the tuple values (tuples are immutable) and you use parentheses rather than square brackets.

Solution: Use the built-in Python list() function to convert a list into a tuple. You don’t need to import any external library.

Code: The following code converts the three given tuples into lists.

tuple_1 = (1, 2, 3, 4, 5)
print(list(tuple_1))
# [1, 2, 3, 4, 5] tuple_2 = ('Alice', 'Bob', 'Ann')
print(list(tuple_2))
# ['Alice', 'Bob', 'Ann'] tuple_3 = (1,)
print(list(tuple_3))
# [1]

Try It Yourself: With our interactive code shell, you can try it yourself. As a small exercise, try to convert the empty tuple () into a list and see what happens.

Explanation: You can see that converting a tuple with one element leads to a list with one element. The list() function is the easiest way to convert a tuple into a list. Note that the values in the tuple are not copied—only a new reference to the same element is created:

The graphic also shows how to convert a tuple back to a list by using the tuple() function (that’s also a Python built-in function). Thus, calling list(tuple(lst)) on a list lst will result in a new list with the same elements.

Related articles:

• List copy
• List complete guide
• Convert list to tuple
• Convert list to dict

Try to execute this code with the interactive Python tutor:

Summing up a list of numbers appears everywhere in coding. Fortunately, Python provides the built-in sum() function to sum over all elements in a Python list—or any other iterable for that matter. (Official Docs)

The syntax is sum(iterable, start=0):

Argument	Description
iterable	Sum over all elements in the iterable. This can be a list, a tuple, a set, or any other data structure that allows you to iterate over the elements. Example: sum([1, 2, 3]) returns 1+2+3=6.
start	(Optional.) The default start value is 0. If you define another start value, the sum of all values in the iterable will be added to this start value. Example: sum([1, 2, 3], 9) returns 9+1+2+3=15.

Check out the Python Freelancer Webinar and KICKSTART your coding career!

Code: Let’s check out a practical example!

lst = [1, 2, 3, 4, 5, 6] print(sum(lst))
# 21 print(sum(lst, 10))
# 31

Exercise: Try to modify the sequence so that the sum is 30 in our interactive Python shell:

Let’s explore some important details regarding the sum() function in Python.

Errors

A number of errors can happen if you use the sum() function in Python.

TypeError: Python will throw a TypeError if you try to sum over elements that are not numerical. Here’s an example:

# Demonstrate possible execeptions
lst = ['Bob', 'Alice', 'Ann'] # WRONG:
s = sum(lst)

If you run this code, you’ll get the following error message:

Traceback (most recent call last): File "C:\Users\xcent\Desktop\code.py", line 3, in <module> s = sum(lst)
TypeError: unsupported operand type(s) for +: 'int' and 'str'

Python tries to perform string concatenation using the default start value of 0 (an integer). Of course, this fails. The solution is simple: sum only over numerical values in the list.

If you try to “hack” Python by using an empty string as start value, you’ll get the following exception:

# Demonstrate possible execeptions
lst = ['Bob', 'Alice', 'Ann'] # WRONG:
s = sum(lst, '')

Output:

Traceback (most recent call last): File "C:\Users\xcent\Desktop\code.py", line 5, in <module> s = sum(lst, '')
TypeError: sum() can't sum strings [use ''.join(seq) instead]

You can get rid of all those errors by summing only over numerical elements in the list.

(For more information about the join() method, check out this blog article.)

Python Sum List Time Complexity

The time complexity of the sum() function is linear in the number of elements in the iterable (list, tuple, set, etc.). The reason is that you need to go over all elements in the iterable and add them to a sum variable. Thus, you need to “touch” every iterable element once.

Python Sum List of Strings

Problem: How can you sum a list of strings such as ['python', 'is', 'great']? This is called string concatenation.

Solution: Use the join() method of Python strings to concatenate all strings in a list. The sum() function works only on numerical input data.

Code: The following example shows how to “sum” up (i.e., concatenate) all elements in a given list of strings.

# List of strings
lst = ['Bob', 'Alice', 'Ann'] print(''.join(lst))
# BobAliceAnn print(' '.join(lst))
# Bob Alice Ann

Python Sum List of Lists

Problem: How can you sum a list of lists such as [[1, 2], [3, 4], [5, 6]] in Python?

Solution: Use a simple for loop with a helper variable to concatenate all lists.

Code: The following code concatenates all lists into a single list.

# List of lists
lst = [[1, 2], [3, 4], [5, 6]] s = []
for x in lst: s.extend(x)
print(s)
# [1, 2, 3, 4, 5, 6]

The extend() method is little-known in Python—but it’s very effective to add a number of elements to a Python list at once. Check out my detailed tutorial on this Finxter blog.

Python Sum List While Loop

Problem: How can you sum over all list elements using a while loop (without sum())?

Solution: Create an aggregation variable and iteratively add another element from the list.

Code: The following code shows how to sum up all numerical values in a Python list without using the sum() function.

# list of integers
lst = [1, 2, 3, 4, 5] # aggregation variable
s = 0 # index variable
i = 0 # sum everything up
while i<len(lst): s += lst[i] i += 1 # print the result
print(s)
# 15

This is not the prettiest way but it’s readable and it works (and, you didn’t want to use the sum() function, right?).

Python Sum List For Loop

Problem: How can you sum over all list elements using a for loop (without sum())?

Solution: Create an aggregation variable and iteratively add another element from the list.

Code: The following code shows how to sum up all numerical values in a Python list without using the sum() function.

# list of integers
lst = [1, 2, 3, 4, 5] # aggregation variable
s = 0 # sum everything up
for x in lst: s += x # print the result
print(s)
# 15

This is a bit more readable than the previous version with the while loop because you don’t have to keep track about the current index.

Python Sum List with List Comprehension

List comprehension is a powerful Python features that allows you to create a new list based on an existing iterable. Can you sum up all values in a list using only list comprehension?

The answer is no. Why? Because list comprehension exists to create a new list. Summing up values is not about creating a new list. You want to get rid of the list and aggregate all values in the list into a single numerical “sum”.

Python Sum List of Tuples Element Wise

Problem: How to sum up a list of tuples, element-wise?

Example: Say, you’ve got list [(1, 1), (2, 0), (0, 3)] and you want to sum up the first and the second tuple values to obtain the “summed tuple” (1+2+0, 1+0+3)=(3, 4).

Solution: Unpack the tuples into the zip function to combine the first and second tuple values. Then, sum up those values separately. Here’s the code:

# list of tuples
lst = [(1, 1), (2, 0), (0, 3)] # aggregate first and second tuple values
zipped = list(zip(*lst))
# result: [(1, 2, 0), (1, 0, 3)] # calculate sum of first and second tuple values
res = (sum(zipped[0]), sum(zipped[1])) # print result to the shell
print(res)
# result: (3, 4)

Need a refresher of the zip() function and unpacking? Check out these articles on the Finxter blog:

• Zip refresher
• Unpacking refresher

Python Sum List Slice

Problem: Given a list. Sum up a slice of the original list between the start and the step indices (and assuming the given step size as well).

Example: Given is list [3, 4, 5, 6, 7, 8, 9, 10]. Sum up the slice lst[2:5:2] with start=2, stop=5, and step=2.

Solution: Use slicing to access the list. Then, apply the sum() function on the result.

Code: The following code computes the sum of a given slice.

# create the list
lst = [3, 4, 5, 6, 7, 8, 9, 10] # create the slice
slc = lst[2:5:2] # calculate the sum
s = sum(slc) # print the result
print(s)
# 12 (=5+7)

Let’s examine an interesting problem: to sum up conditionally!

Python Sum List Condition

Problem: Given is a list. How to sum over all values that meet a certain condition?

Example: Say, you’ve got the list lst = [5, 8, 12, 2, 1, 3] and you want to sum over all values that are larger than 4.

Solution: Use list comprehension to filter the list so that only the elements that satisfy the condition remain. Then, use the sum() function to sum over the remaining values.

Code: The following code sums over all values that satisfy a certain condition (e.g., x>4).

# create the list
lst = [5, 8, 12, 2, 1, 3] # filter the list
filtered = [x for x in lst if x>4]
# remaining list: [5, 8, 12] # sum over the filtered list
s = sum(filtered) # print everything
print(s)
# 25

Need a refresher on list comprehension? Check out my in-depth tutorial on the Finxter blog.

Python Sum List Ignore None

Problem: Given is a list of numerical values that may contain some values None. How to sum over all values that are not the value None?

Example: Say, you’ve got the list lst = [5, None, None, 8, 12, None, 2, 1, None, 3] and you want to sum over all values that are not None.

Solution: Use list comprehension to filter the list so that only the elements that satisfy the condition remain (that are different from None). You see, that’s a special case of the previous paragraph that checks for a general condition. Then, use the sum() function to sum over the remaining values.

Code: The following code sums over all values that are not None.

# create the list
lst = [5, None, None, 8, 12, None, 2, 1, None, 3] # filter the list
filtered = [x for x in lst if x!=None]
# remaining list: [5, 8, 12, 2, 1, 3] # sum over the filtered list
s = sum(filtered) # print everything
print(s)
# 31

A similar thing can be done with the value Nan that can disturb your result if you aren’t careful.

Python Sum List Ignore Nan

Problem: Given is a list of numerical values that may contain some values nan (=”not a number”). How to sum over all values that are not the value nan?

Example: Say, you’ve got the list lst = [1, 2, 3, float("nan"), float("nan"), 4] and you want to sum over all values that are not nan.

Solution: Use list comprehension to filter the list so that only the elements that satisfy the condition remain (that are different from nan). You see, that’s a special case of the previous paragraph that checks for a general condition. Then, use the sum() function to sum over the remaining values.

Code: The following code sums over all values that are not nan.

# for checking isnan(x)
import math # create the list
lst = [1, 2, 3, float("nan"), float("nan"), 4] # forget to ignore 'nan'
print(sum(lst))
# nan # ignore 'nan'
print(sum([x for x in lst if not math.isnan(x)]))
# 10

Phew! Quite some stuff. Thanks for reading through this whole article! I hope you’ve learned something out of this tutorial and remain with the following recommendation:

Where to Go From Here?

Enough theory, let’s get some practice!

To become successful in coding, you need to get out there and solve real problems for real people. That’s how you can become a six-figure earner easily. And that’s how you polish the skills you really need in practice. After all, what’s the use of learning theory that nobody ever needs?

Practice projects is how you sharpen your saw in coding!

Do you want to become a code master by focusing on practical code projects that actually earn you money and solve problems for people?

Then become a Python freelance developer! It’s the best way of approaching the task of improving your Python skills—even if you are a complete beginner.

Join my free webinar “How to Build Your High-Income Skill Python” and watch how I grew my coding business online and how you can, too—from the comfort of your own home.

Join the free webinar now!

How to print a Python list in a beautiful and fully customizable way?

This article shows you six effective ways of doing it. By studying these alternatives, you’ll not only learn how to print lists in Python, you’ll become a better coder overall.

If you just want to know the best way to print a list in Python, here’s the short answer:

• Pass a list as an input to the print() function in Python.
• Use the asterisk operator * in front of the list to “unpack” the list into the print function.
• Use the sep argument to define how to separate two list elements visually.

Here’s the code:

# Create the Python List
lst = [1, 2, 3, 4, 5] # Use three underscores as separator
print(*lst, sep='___')
# 1___2___3___4___5 # Use an arrow as separator
print(*lst, sep='-->')
# 1-->2-->3-->4-->5

Try It Yourself in Our Interactive Code Shell:

This is the best and most Pythonic way to print a Python list. If you still want to learn about alternatives—and improve your Python skills in the process of doing so—keep reading!

Method: Use Default print() Statement

The default print() statement converts the list into a string representation that encloses the list elements in the square brackets [ and ], and separates two subsequent elements with the comma and an empty space a, b. This is the standard list representation.

lst = [1, 2, 3, 4, 5]
print(lst)

The output is the following:

[1, 2, 3, 4, 5]

Advantages	Disadvantages
Easy to read and write	Non-customizable
Fast
Concise

Try It Yourself in Our Interactive Code Shell:

The next method overcomes the main disadvantage of being not very customizable.

Method: Iterate In a For Loop

If you want full control about the output of each list element, you can use the straightforward approach of using a for loop to iterate over each element x in the list. You can then decide for yourself how to print each element.

# Create the Python List
lst = [1, 2, 3, 4, 5] # Iterate over each element x
# in the list and customize printing
for x in lst: print('Element: ' + x)

The output is the following:

Element: 1
Element: 2
Element: 3
Element: 4
Element: 5

Advantages	Disadvantages
Fully customizable	Relatively slow
Simple	Less concise
	Newline after each element

Try It Yourself in Our Interactive Python Shell:

Method: Iterate in For Loop with End Argument

If you’d rather print all elements in a single line, separated by three whitespace characters, you can do so by defining the end argument of the print() function that defines which character is added after each element that was printed to the shell (default: new-line character \n):

# Create the Python List
lst = [1, 2, 3, 4, 5] # Iterate over each element x
# in the list and customize printing
for x in lst: # Use the end argument to define # what to print after each element print(str(x), end=' ')

The output is:

1 2 3 4 5 

You see that the end argument overwrites the default behavior of printing a new-line character at the end of each element. Instead, each two elements are separated by three empty spaces.

Advantages	Disadvantages
Fully customizable	Relatively slow
Simple	Less concise

Try It Yourself in Our Interactive Code Shell:

Let’s overcome the disadvantage of the for loop of being less concise!

Method: Unpacking With Separator Argument

The print() function works with an iterable as input. You can use the asterisk operator * in front of the list to “unpack” the list into the print function. Now, you can use the sep argument of the print() function to define how to separate two elements of the iterable.

# Create the Python List
lst = [1, 2, 3, 4, 5] # Use three underscores as separator
print(*lst, sep='___')
# 1___2___3___4___5 # Use an arrow as separator
print(*lst, sep='-->')
# 1-->2-->3-->4-->5

The sep argument allows you to define precisely what to put between each pair of elements in an iterable. This allows you full customization and keeps the code lean and concise.

Advantages	Disadvantages
Fully customizable	Harder to read for beginners
Fast
Concise

Try It Yourself in Our Interactive Code Shell:

This is the best and most Pythonic way to print a Python list. If you still want to learn about alternatives, keep reading.

Method: Use the string.join() Method

The string.join(iterable) method joins together all elements in the iterable, using the string as a separator between two elements. Thus, it works exactly like the sep argument of the print() function.

# Create the Python List
lst = ['1', '2', '3', '4', '5'] # Use three underscores as separator
print('___'.join(lst))
# 1___2___3___4___5 # Use arrow as separator
print('-->'.join(lst))
# 1-->2-->3-->4-->5

Note that you can only use this methods if the list elements are already strings. If they are integers, joining them together doesn’t work and Python throws an error:

TypeError: sequence item 0: expected str instance, int found

Advantages	Disadvantages
Fully customizable	Harder to read for beginners
Concise	Slow
	Works only for string elements

Try It Yourself in Our Interactive Code Shell:

So how do you apply this method to integer lists?

Method: Use the string.join() Method with Map()

The string.join(iterable) method joins together all elements in the iterable, using the string as a separator between two elements. But it expects that all elements in the iterable are already strings. If they aren’t, you need to convert them first. To achieve this, you can use the built-in map() method in Python 3.x.

# Create the Python List
lst = [1, 2, 3, 4, 5] # Use three underscores as separator
print('___'.join(map(str, lst)))
# 1___2___3___4___5 # Use arrow as separator
print('-->'.join(map(str, lst)))
# 1-->2-->3-->4-->5

The map(str, lst) method applies the function str(x) to each element x in the list. In other words, it converts each integer element to a string. An alternative way without the map(str, lst) function would be list comprehension [str(x) for x in lst] that results in the same output.

Advantages	Disadvantages
Fully customizable	Harder to read for beginners
Concise	Slow
Works for all data types

Try It Yourself in Our Interactive Code Shell:

So, let’s finish this up!

Where to Go From Here?

Enough theory, let’s get some practice!

To become successful in coding, you need to get out there and solve real problems for real people. That’s how you can become a six-figure earner easily. And that’s how you polish the skills you really need in practice. After all, what’s the use of learning theory that nobody ever needs?

Practice projects is how you sharpen your saw in coding!

Do you want to become a code master by focusing on practical code projects that actually earn you money and solve problems for people?

Then become a Python freelance developer! It’s the best way of approaching the task of improving your Python skills—even if you are a complete beginner.

Join my free webinar “How to Build Your High-Income Skill Python” and watch how I grew my coding business online and how you can, too—from the comfort of your own home.

Join the free webinar now!

Given is the following regular expression:

regex = '[a-z.]+'

Note the dot character inside the character set. As you may know, the dot metacharacter matches an arbitrary character if it is used outside a character set.

But what does it match if you place the dot character inside a regex character set?

The answer is that the dot inside the character set matches the dot symbol—and not an arbitrary character. The reason is that the character set removes the special meaning of the dot symbol.

Here’s a simple example:

import re regex = '[a-z.]+' text_1 = 'hello.world'
text_2 = 'HELLO.WORLD' print(re.match(regex, text_1))
# <re.Match object; span=(0, 11), match='hello.world'> print(re.match(regex, text_2))
# None

The first text will be matched in both cases (the dot character matches an arbitrary character or the dot symbol).

But the second text will only match if the dot has the meaning: “match an arbitrary character”. Otherwise, the character set cannot match the text.

As the result is None, the text could not have been matched. This proves that the dot metacharacter loses its special meaning inside a character set.

If you’ve already learned how to make basic 3d plots in maptlotlib and want to take them to the next level, then look no further. In this article, I’ll teach you how to create the two most common 3D plots (surface and wireframe plots) and a step-by-step method you can use to create any shape you can imagine.

In addition to import matplotlib.pyplot as plt and calling plt.show(), to create a 3D plot in matplotlib, you need to:

1. Import the Axes3D object
2. Initialize your Figure and Axes3D object
3. Get some 3D data
4. Plot it using Axes notation

Here’s a wireframe plot:

# Standard import
import matplotlib.pyplot as plt # Import 3D Axes
from mpl_toolkits.mplot3d import axes3d # Set up Figure and 3D Axes
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d') # Get some data
X, Y, Z = axes3d.get_test_data(0.1) # Plot using Axes notation
ax.plot_wireframe(X, Y, Z)
plt.show()

Try It Yourself on our interactive Python shell (and check out the file 'plot.png'):

Changing the plot call to ax.plot_surface(X, Y, Z) gives

Great! You’ve just created your first 3D wireframe and surface plots. Don’t worry if that was a bit fast; let’s dive into a more detailed example.

But first, note that your plots may look different to mine because I use the seaborn style throughout. You can set this by installing the seaborn library and calling the set function at the top of your code.

import seaborn as sns; sns.set()

Matplotlib 3D Plot Example

The four steps needed to create advanced 3D plots are the same as those needed to create basic ones. If you don’t understand those steps, check out my article on how to make basic 3D plots first.

The most difficult part of creating surface and wireframe plots is step 3: getting 3D data. Matplotlib actually includes a helper function axes3d.get_test_data() to generate some data for you. It accepts a float and, for best results, choose a value between 0 and 1. It always produces the same plot, but different floats give you different sized data and thus impact how detailed the plot is.

However, the best way to learn 3D plotting is to create custom plots.

At the end of step 3, you want to have three numpy arrays X, Y and Z, which you will pass to ax.plot_wireframe() or ax.plot_surface(). You can break step 3 down into four steps:

1. Define the x-axis and y-axis limits
2. Create a grid of XY-points (to get X and Y)
3. Define a z-function
4. Apply the z-function to X and Y (to get Z)

In matplotlib, the z-axis is vertical by default. So, the ‘bottom’ of the Axes3D object is a grid of XY points. For surface or wireframe plots, each pair of XY points has a corresponding Z value. So, we can think of surface/wireframe plots as the result of applying some z-function to every XY-pair on the ‘bottom’ of the Axes3D object.

Since there are infinitely many numbers on the XY-plane, it is not possible to map every one to a Z-value. You just need an amount large enough to deceive humans – anything above 50 pairs usually works well.

To create your XY-points, you first need to define the x-axis and y-axis limits. Let’s say you want X-values ranging from -5 to +5 and Y-values from -2 to +2. You can create an array of numbers for each of these using the np.linspace() function. For reasons that will become clear later, I will make x have 100 points, and y have 70.

x = np.linspace(-5, 5, num=100)
y = np.linspace(-2, 2, num=70)

Both x and y are 1D arrays containing num equally spaced floats in the ranges [-5, 5] and [-2, 2] respectively.

Since the XY-plane is a 2D object, you now need to create a rectangular grid of all xy-pairs. To do this, use the numpy function np.meshgrid(). It takes n 1D arrays and turns them into an N-dimensional grid. In this case, it takes two 1D arrays and turns them into a 2D grid.

X, Y = np.meshgrid(x, y)

Now you’ve created X and Y, so let’s inspect them.

print(f'Type of X: {type(X)}')
print(f'Shape of X: {X.shape}\n')
print(f'Type of Y: {type(Y)}')
print(f'Shape of Y: {Y.shape}')

Type of X: <class 'numpy.ndarray'>
Shape of X: (70, 100) Type of Y: <class 'numpy.ndarray'>
Shape of Y: (70, 100)

Both X and Y are numpy arrays of the same shape: (70, 100). This corresponds to the size of y and x respectively. As you would expect, the size of y dictates the height of the array, i.e., the number of rows and the size of x dictates the width, i.e., the number of columns.

Note that I used lowercase x and y for the 1D arrays and uppercase X and Y for the 2D arrays. This is standard practice when making 3D plots, and I use it throughout the article.

Now you’ve created your grid of points; it’s time to define a function to apply to them all. Since this function outputs z-values, I call it a z-function. Common z-functions contain np.sin() and np.cos() because they create repeating, cyclical patterns that look interesting when plotted in 3D. Additionally, z-functions usually combine both X and Y variables as 3D plots look at how all the variables interact.

# Define z-function with 2 arguments: x and y
def z_func(x, y): return np.sin(np.cos(x) + y) # Apply to X and Y
Z = z_func(X, Y)

Here I defined a z-function that accepts 2 variables – x and y – and is a combination of np.sin() and np.cos() functions. Then I applied it to X and Y to get the Z array. Thanks to numpy broadcasting, python applies the z-function to every XY pair almost instantly and saves you from having to write a wildly inefficient for loop.

Note that Z is the same shape and type as both X and Y.

print(f'Type of Z: {type(Z)}')
print(f'Shape of Z: {Z.shape}')

Type of Z: <class 'numpy.ndarray'>
Shape of Z: (70, 100)

Now that you have got your data, all that is left to do is make the plots. Let’s put all the above code together:

# Set up Figure and 3D Axes
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d') # Create x and y 1D arrays
x = np.linspace(-5, 5, num=100)
y = np.linspace(-2, 2, num=70) # Create X and Y 2D arrays
X, Y = np.meshgrid(x, y) # Define Z-function
def z_func(x, y): return np.sin(np.cos(x) + y) # Create Z 2D array
Z = z_func(X, Y) # Plot using Axes notation
ax.plot_wireframe(X, Y, Z)
# Set axes lables
ax.set(xlabel='x', ylabel='y', zlabel='z')
plt.show()

Great, I found the above plot by playing around with different z-functions and think it looks pretty cool! Z-functions containing np.log(), np.exp(), np.sin(), np.cos() and combinations of x and y usually lead to interesting plots – I encourage you to experiment yourself.

Now I’ll create 3 different z-functions with the same X and Y as before and create a subplot of them so you can see the differences.

# Set up Figure and Axes
fig, axes = plt.subplots(1, 3, subplot_kw=dict(projection='3d'), figsize=plt.figaspect(1/3)) # Create 3 z-functions
def z_1(x, y): return np.exp(np.cos(x)*y)
def z_2(x, y): return np.log(x**2 + y**4)
def z_3(x, y): return np.sin(x * y) # Create 3 Z arrays Z_arrays = [z_1(X, Y), z_2(X, Y), z_3(X, Y)]
# Titles for the plots
z_func_names = ['np.exp(np.cos(x)*y)', 'np.log(x**2 + y**4)', 'np.sin(x * y)'] # Plot all 3 wireframes
for Z_array, z_name, ax in zip(Z_arrays, z_func_names, axes): ax.plot_wireframe(X, Y, Z_array) ax.set(title=z_name)
plt.show()

I think all of these images demonstrate the power of 3D plotting, and I hope they have encouraged you to create your own.

Now you know how to create any surface or wireframe plot with your data. But so far, you have only used the default settings. Let’s modify them using the available keyword arguments.

Matplotlib 3D Plot Wireframe

To make a wireframe plot, call ax.plot_wireframe(X, Y, Z). These plots give you an overview of the surface. Plus, you can see through them to more easily identify peaks and troughs that may otherwise be hidden.

A wireframe plot works by only plotting a sample of the data passed to it. You can modify how large the samples are with 4 keyword arguments:

1. rstride and cstride, or
2. rcount and ccount

The r and c stand for row and column respectively. The difference between them is similar to the difference between np.arange() and np.linspace().

The stride arguments default to 1 and set the step sizes between each sampled point. A stride of 1 means that every value is chosen, and a stride of 10 means that every 10th value is chosen. In this way, it is similar to np.arange() where you select the step size. A larger stride means fewer values are chosen, so your plot renders faster and is less detailed.

The count arguments default to 50 and set the number of (equally spaced) rows/columns sampled. A count of 1 means you use 1 row/column, and a count of 100 means you use 100. In this way, it is similar to np.linspace() where you select the total number of values with the num keyword argument. A larger count means more values are chosen, so your plot renders slower and is more detailed.

The matplotlib docs say that you should use the count arguments. However, both are still available, and it doesn’t look like the stride arguments will be depreciated any time soon. Note, though, that you cannot use both count and stride, and if you try to do so, it’s a ValueError.

By setting any of the keyword arguments to 0, you do not sample data along that axis. The result is then a 3D line plot rather than a wireframe.

To demonstrate the differences between different counts or strides, I’ll create a subplot with the same X, Y and Z arrays as the first example but with different stride and count values.

fig, axes = plt.subplots(nrows=1, ncols=3, subplot_kw=dict(projection='3d'), figsize=plt.figaspect(1/3))
# Same as first example
x = np.linspace(-5, 5, num=100)
y = np.linspace(-2, 2, num=70)
X, Y = np.meshgrid(x, y) def z_func(x, y): return np.sin(np.cos(x) + y)
Z = z_func(X, Y) # Define different strides
strides = [1, 5, 10] for stride, ax in zip(strides, axes.flat): ax.plot_wireframe(X, Y, Z, rstride=stride, cstride=stride) ax.set(title=f'stride={stride}') plt.show() 

Here you can see that a larger stride produces a less detailed wireframe plot. Note that stride=1 is the default and is incredibly detailed for a plot that is supposed to give a general overview of the data.

fig, axes = plt.subplots(nrows=1, ncols=3, subplot_kw=dict(projection='3d'), figsize=plt.figaspect(1/3)) counts = [5, 20, 50] for count, ax in zip(counts, axes.flat): # Use same data as the above plots ax.plot_wireframe(X, Y, Z, rcount=count, ccount=count) ax.set(title=f'count={count}') plt.show()

Here you can see that a larger count produces a more detailed wireframe plot. Again note that the default count=50 produces a very detailed plot.

Other keyword arguments are passed to LineCollection. So you can also change the color (c) and linestyle (ls) amongst other things.

Matplotlib 3D Plot Surface

To make a surface plot call ax.plot_surface(X, Y, Z). Surface plots are the same as wireframe plots, except that spaces in between the lines are colored. Plus, there are some additional keyword arguments you can use, which can add a ton of value to the plot.

First, let’s make the same plots as above with the default surface plot settings and different rcount and ccount values.

fig, axes = plt.subplots(nrows=1, ncols=3, subplot_kw=dict(projection='3d'), figsize=plt.figaspect(1/3)) counts = [5, 20, 50] for count, ax in zip(counts, axes.flat): # Use same data as the above plots surf = ax.plot_surface(X, Y, Z, rcount=count, ccount=count) ax.set(title=f'count={count}') plt.show()

In contrast to wireframe plots, the space in between each line is filled with the color blue. Note that the plots get whiter as the count gets larger. This is because the lines are white, and, as the count increases, there are more lines on each plot. You can modify this by setting the linewidth or lw argument to a smaller number such, as 0.1 or even 0.

fig = plt.figure()
ax = plt.axes(projection='3d')
ax.plot_surface(X, Y, Z, linewidth=0) ax.set(title="linewidth=0")
plt.show()

Much nicer! Now you can see the color of the plot rather than the color of the lines. It is possible to almost completely remove the lines by setting antialiased=False.

Antialiasing removes noise from data and smooths out images. By turning it off, the surface is less smooth, and so you can’t see the lines as easily.

fig = plt.figure()
ax = plt.axes(projection='3d')
ax.plot_surface(X, Y, Z, linewidth=0, antialiased=False) ax.set(title="linewidth=0, antialiased=False")
plt.show()

Now the surface is slightly less smooth, and so you can’t see the lines.

Maptlotlib 3D Surface Plot Cmap

Arguably the most crucial keyword argument for surface plots is cmap which sets the colormap. When you look at a surface plot from different angles, having a colormap helps you understand which parts of the surface are where. Usually, you want high points to be one color (e.g., orange) and low points to be another (e.g., black). Having two distinct colors is especially helpful if you look at a plot from different angles (which I will show you how to do in a moment).

There are loads of colormaps in matplotlib, and you can see several used in my article on the matplotlib imshow function.

Now I’ll plot the same data as above but set the colormap to copper.

fig = plt.figure()
ax = plt.axes(projection='3d') ax.plot_surface(X, Y, Z, lw=0, cmap='copper')
plt.show()

The colormap copper maps large z-values to orange and smaller ones to black.

Now I’ll use 3 different and commonly used colormaps for the same plot to give you an idea of how color can help and (massively) hinder your plots.

fig, axes = plt.subplots(nrows=1, ncols=3, subplot_kw=dict(projection='3d'), figsize=plt.figaspect(1/3)) cmaps = ['copper', 'coolwarm', 'jet'] for cmap, ax in zip(cmaps, axes): ax.plot_surface(X, Y, Z, lw=0, cmap=cmap) ax.set(title=f'{cmap}')
plt.show()

The coolwarm colormap works well if you want to highlight extremely high and extremely low points. This non-technical paper defines a colormap similar to coolwarm and argues it should be the default cmap for all data science work.

The jet colormap is well known and is a terrible choice for all of your plotting needs. It contains so many colors that it is hard for a human to know which corresponds to high, low, or middle points. I included it as an example here but urge you to never use it in any of your plots.

Now let’s look at how the count and stride arguments can affect the color of your surface plots. For brevity, I will just make one subplot demonstrating different rccount and ccount sizes and leave the reader to experiment with rstride and cstride.

fig, axes = plt.subplots(nrows=1, ncols=3, subplot_kw=dict(projection='3d'), figsize=plt.figaspect(1/3)) counts = [5, 20, 50] for count, ax in zip(counts, axes.flat): # Use same data as the above plots ax.plot_surface(X, Y, Z, rcount=count, ccount=count, cmap='copper', lw=0) ax.set(title=f'count={count}')
plt.show()

If you pass a lower value to the count keyword arguments, there are fewer areas that can be colored. As such, the colors have much more distinct bands when you set the count keyword arguments to smaller values. The change in color is much smoother in the plots that have large count arguments.

Matplotlib 3D Plot Colorbar

Adding a colorbar to a 3D surface plot is the same as adding them to other plots.

The simplest method is to save the output of ax.plot_surface() in a variable such as surf and pass that variable to plt.colorbar().

Here’s an example using the three different colormaps from before.

fig, axes = plt.subplots(nrows=1, ncols=3, subplot_kw=dict(projection='3d'), figsize=plt.figaspect(1/3)) cmaps = ['copper', 'coolwarm', 'jet'] for cmap, ax in zip(cmaps, axes): # Save surface in a variable: surf surf = ax.plot_surface(X, Y, Z, lw=0, cmap=cmap) # Plot colorbar on the correct Axes: ax fig.colorbar(surf, ax=ax) ax.set(title=f'{cmap}')
plt.show()

It’s essential to provide a colorbar for any colored plots you create, especially if you use different colormaps. Remember that colorbar() is a Figure (not Axes) method, and you must use the ax keyword argument to place it on the correct Axes.

Now, let’s see why colormaps are so crucial by rotating the surface plots and viewing them from different angles.

Matplotlib 3D Plot View_Init

One way to rotate your plots is by using the magic command %matplotlib notebook at the top of your Jupyter notebooks. If you do this, all your plots appear in interactive windows. If instead, you use %matplotlib inline (the default settings), you have to rotate your plots using code.

Two attributes that control the rotation of a 3D plot: ax.elev and ax.azim, which represent the elevation and azimuthal angles of the plot, respectively.

The elevation is the angle above the XY-plane and the azimuth (don’t worry, I hadn’t heard of it before either) is the counter-clockwise rotation about the z-axis. Note that they are properties of the Axes3D object and so you can happily create subplots where each has a different angle.

Let’s find the default values.

fig = plt.figure()
ax = plt.axes(projection='3d') print(f'The default elevation angle is: {ax.elev}')
print(f'The default azimuth angle is: {ax.azim}')

The default elevation angle is: 30
The default azimuth angle is: -60

You can see that the defaults are 30 and -60 degrees for the elevation and azimuth, respectively.

You can set them to any float you want, and there are two ways to do it:

1. Reassign the ax.azim and ax.elev attributes, or
2. Use the ax.view_init(elev, azim) method

Here’s an example with method 1.

# Same as usual
fig = plt.figure()
ax = plt.axes(projection='3d')
ax.plot_surface(X, Y, Z, lw=0, cmap='copper')
# Set axis labels so you know what you are looking at
ax.set(xlabel='x', ylabel='y', zlabel='z') # Reassign rotation angles to 0
ax.azim, ax.elev = 0, 0
plt.show()

Here I set both angles to 0, and you can see the y-axis at the front, the x-axis at the side, and the z-axis as vertical.

I’ll now create the same plot using the ax.view_init() method, which accepts two floats: the elevation and azimuth.

# Same as usual
fig = plt.figure()
ax = plt.axes(projection='3d')
ax.plot_surface(X, Y, Z, lw=0, cmap='copper')
# Set axis labels so you know what you are looking at
ax.set(xlabel='x', ylabel='y', zlabel='z') # Reassign rotation angles to 0
ax.view_init(elev=0, azim=0)
plt.show()

Excellent! This plot looks identical to the one above, but I used the ax.view_init() method instead. If you just want to change one of the angles, only pass one of the keyword arguments.

# Same as usual
fig = plt.figure()
ax = plt.axes(projection='3d')
ax.plot_surface(X, Y, Z, lw=0, cmap='copper')
# Set axis labels so you know what you are looking at
ax.set(xlabel='x', ylabel='y', zlabel='z') # Set elevation to 90 degrees
ax.view_init(elev=90)
plt.show()

Here I set the elevation to 90 degrees but left the azimuth with its default value. This demonstrates one more reason why colormaps are important: you can infer the shape of the surface from the color (black is low, light is high).

Conclusion

Now you know how to create the most critical 3D plots: wireframe and surface plots.

You’ve learned how to create custom 3D plot datasets using np.linspace(), np.meshgrid() and z-functions. Plus, you can create them with varying degrees of accuracy by modifying the count and stride keyword arguments.

You can make surface plots of any color and colormap and modify them so that the color of the lines doesn’t take over the plot. Finally, you can rotate them by setting the ax.azim or ax.elev attributes to a float of your choice and even use the ax.view_init() method to do the same thing.

Congratulations on mastering these plots! Creating other advanced ones such as contour, tri-surface, and quiver plots for you will be easy. You know all the high-level skills; you just need to go out there and practice.

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When does the IndexError: list assignment index out of range appear?

Python throws an IndexError if you try to assign a value to a list index that doesn’t exist, yet. For example, if you execute the expression list[1] = 10 on an empty list, Python throws the IndexError. Simply resolve it by adding elements to your list until the index actually exists.

Here’s the minimal example that throws the IndexError:

lst = []
lst[1] = 10

If you run this code, you’ll see that Python throws an IndexError:

Traceback (most recent call last): File "C:\Users\xcent\Desktop\code.py", line 2, in <module> lst[1] = 10
IndexError: list assignment index out of range

You can resolve it by adding two “dummy” elements to the list so that the index 1 actually exists in the list:

lst = [None, None]
lst[1] = 10
print(lst)

Now, Python will print the expected output:

[None, 10]

Try to fix the IndexError in the following interactive code shell:

Exercise: Can you fix this code?

So what are some other occurrences of the IndexError?

IndexError in For Loop

Frequently, the IndexError happens if you use a for loop to modify some list elements like here:

# WRONG CODE:
lst = []
for i in range(10): lst[i] = i
print(lst)

Again, the result is an IndexError:

Traceback (most recent call last): File "C:\Users\xcent\Desktop\code.py", line 4, in <module> lst[i] = i
IndexError: list assignment index out of range

You modify a list element at index i that doesn’t exist in the list. Instead, create the list using the list(range(10)) list constructor.

# CORRECT CODE:
lst = list(range(10))
print(lst)
# [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

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