Python's sum(): The Pythonic Way to Sum Values

The Required Argument: iterable

Accepting any Python iterable as its first argument makes sum() generic, reusable, and polymorphic. Because of this feature, you can use sum() with lists, tuples, sets, range objects, and dictionaries:

>>> # Use a list
>>> sum([1, 2, 3, 4, 5])
15

>>> # Use a tuple
>>> sum((1, 2, 3, 4, 5))
15

>>> # Use a set
>>> sum({1, 2, 3, 4, 5})
15

>>> # Use a range
>>> sum(range(1, 6))
15

>>> # Use a dictionary
>>> sum({1: "one", 2: "two", 3: "three"})
6
>>> sum({1: "one", 2: "two", 3: "three"}.keys())
6

In all these examples, sum() computes the arithmetic sum of all the values in the input iterable regardless of their types. In the two dictionary examples, both calls to sum() return the sum of the keys of the input dictionary. The first example sums the keys by default and the second example sums the keys because of the .keys() call on the input dictionary.

If your dictionary stores numbers in its values and you would like to sum these values instead of the keys, then you can do this by using .values() just like in the .keys() example.

You can also use sum() with a list comprehension as an argument. Here’s an example that computes the sum of the squares of a range of values:

>>> sum([x ** 2 for x in range(1, 6)])
55

Python 2.4 added generator expressions to the language. Again, sum() works as expected when you use a generator expression as an argument:

>>> sum(x ** 2 for x in range(1, 6))
55

This example shows one of the most Pythonic techniques to approach the summation problem. It provides an elegant, readable, and efficient solution in a single line of code.

The Optional Argument: start

The second and optional argument, start, allows you to provide a value to initialize the summation process. This argument is handy when you need to process cumulative values sequentially:

>>> sum([1, 2, 3, 4, 5], 100)  # Positional argument
115

>>> sum([1, 2, 3, 4, 5], start=100)  # Keyword argument
115

Here, you provide an initial value of 100 to start. The net effect is that sum() adds this value to the cumulative sum of the values in the input iterable. Note that you can provide start as a positional argument or as a keyword argument. The latter option is way more explicit and readable.

If you don’t provide a value to start, then it defaults to 0. A default value of 0 ensures the expected behavior of returning the total sum of the input values.

Computing Cumulative Sums

The first example you’ll code has to do with how to take advantage of the start argument for summing cumulative lists of numeric values.

Say you’re developing a system to manage the sales of a given product at several different points of sale. Every day, you get a sold units report from each point of sale. You need to systematically compute the cumulative sum to know how many units the whole company sold over the week. To solve this problem, you can use sum():

>>> cumulative_sales = 0

>>> monday = [50, 27, 42]
>>> cumulative_sales = sum(monday, start=cumulative_sales)
>>> cumulative_sales
119

>>> tuesday = [12, 32, 15]
>>> cumulative_sales = sum(tuesday, start=cumulative_sales)
>>> cumulative_sales
178

>>> wednesday = [20, 24, 42]
>>> cumulative_sales = sum(wednesday, start=cumulative_sales)
>>> cumulative_sales
264
    ...

By using start, you set an initial value to initialize the sum, which allows you to add successive units to the previously computed subtotal. At the end of the week, you’ll have the company’s total count of sold units.

Calculating the Mean of a Sample

Another practical use case of sum() is to use it as an intermediate calculation before doing further calculations. For example, say you need to calculate the arithmetic mean of a sample of numeric values. The arithmetic mean, also known as the average, is the total sum of the values divided by the number of values, or data points, in the sample.

If you have the sample [2, 3, 4, 2, 3, 6, 4, 2] and you want to calculate the arithmetic mean by hand, then you can solve this operation:

(2 + 3 + 4 + 2 + 3 + 6 + 4 + 2) / 8 = 3.25

If you want to speed this up by using Python, you can break it up into two parts. The first part of this computation, where you are adding together the numbers, is a task for sum(). The next part of the operation, where you are dividing by 8, uses the count of numbers in your sample. To calculate your divisor, you can use len():

>>> data_points = [2, 3, 4, 2, 3, 6, 4, 2]

>>> sum(data_points) / len(data_points)
3.25

Here, the call to sum() computes the total sum of the data points in your sample. Next, you use len() to get the number of data points. Finally, you perform the required division to calculate the sample’s arithmetic mean.

In practice, you may want to turn this code into a function with some additional features, such as a descriptive name and a check for empty samples:

>>> # Python >= 3.8

>>> def average(data_points):
...     if (num_points := len(data_points)) == 0:
...         raise ValueError("average requires at least one data point")
...     return sum(data_points) / num_points
...

>>> average([2, 3, 4, 2, 3, 6, 4, 2])
3.25

>>> average([])
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "<stdin>", line 3, in average
ValueError: average requires at least one data point

Inside average(), you first check if the input sample has any data points. If not, then you raise a ValueError with a descriptive message. In this example, you use the walrus operator to store the number of data points in the variable num_points so that you won’t need to call len() again. The return statement computes the sample’s arithmetic mean and sends it back to the calling code.

>>> from statistics import mean

>>> mean([2, 3, 4, 2, 3, 6, 4, 2])
3.25

>>> mean([])
Traceback (most recent call last):
    ...
statistics.StatisticsError: mean requires at least one data point

Note that when you call average() with a proper sample, you’ll get the desired mean. If you call average() with an empty sample, then you get a ValueError as expected.

Finding the Dot Product of Two Sequences

Another problem you can solve using sum() is finding the dot product of two equal-length sequences of numeric values. The dot product is the algebraic sum of products of every pair of values in the input sequences. For example, if you have the sequences (1, 2, 3) and (4, 5, 6), then you can calculate their dot product by hand using addition and multiplication:

1 × 4 + 2 × 5 + 3 × 6 = 32

To extract successive pairs of values from the input sequences, you can use zip(). Then you can use a generator expression to multiply each pair of values. Finally, sum() can sum the products:

>>> x_vector = (1, 2, 3)
>>> y_vector = (4, 5, 6)

>>> sum(x * y for x, y in zip(x_vector, y_vector))
32

With zip(), you generate a list of tuples with the values from each of the input sequences. The generator expression loops over each tuple while multiplying the successive pairs of values previously arranged by zip(). The final step is to add the products together using sum().

The code in the above example works. However, the dot product is defined for sequences of equal length, so what happens if you provide sequences with different lengths? In that case, zip() ignores the extra values from the longest sequence, which leads to an incorrect result.

To deal with this possibility, you can wrap the call to sum() in a custom function and provide a proper check for the length of the input sequences:

>>> def dot_product(x_vector, y_vector):
...     if len(x_vector) != len(y_vector):
...         raise ValueError("Vectors must have equal sizes")
...     return sum(x * y for x, y in zip(x_vector, y_vector))
...

>>> dot_product((1, 2, 3), (4, 5, 6))
32

>>> dot_product((1, 2, 3, 4), (5, 6, 3))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "<stdin>", line 3, in dot_product
ValueError: Vectors must have equal sizes

Here, dot_product() takes two sequences as arguments and returns their corresponding dot product. If the input sequences have different lengths, then the function raises a ValueError.

Embedding the functionality in a custom function allows you to reuse the code. It also gives you the opportunity to name the function descriptively so that the user knows what the function does just by reading its name.

Flattening a List of Lists

Flattening a list of lists is a common task in Python. Say you have a list of lists and need to flatten it into a single list containing all the items from the original nested lists. You have options when deciding how to flatten lists in Python. For example, you can use a for loop, as in the following code:

>>> def flatten_list(a_list):
...     flat = []
...     for sublist in a_list:
...         flat += sublist
...     return flat
...

>>> matrix = [
...     [1, 2, 3],
...     [4, 5, 6],
...     [7, 8, 9],
... ]

>>> flatten_list(matrix)
[1, 2, 3, 4, 5, 6, 7, 8, 9]

Inside flatten_list(), the loop iterates over all the nested lists contained in a_list. Then it concatenates them in flat using an augmented assignment operation (+=). As the result, you get a flat list with all the items from the original nested lists.

But hold on! You’ve already learned how to use sum() to concatenate sequences in this tutorial. Can you use that feature to flatten a list of lists like you did in the example above? Yes! Here’s how:

>>> matrix = [
...     [1, 2, 3],
...     [4, 5, 6],
...     [7, 8, 9],
... ]

>>> sum(matrix, [])
[1, 2, 3, 4, 5, 6, 7, 8, 9]

That was quick! A single line of code and matrix is now a flat list. However, using sum() doesn’t seem to be the fastest solution.

Using a list comprehension is another common way to flatten a list of list in Python:

>>> def flatten_list(a_list):
...     return [item for sublist in a_list for item in sublist]
...

>>> matrix = [
...     [1, 2, 3],
...     [4, 5, 6],
...     [7, 8, 9],
... ]

>>> flatten_list(matrix)
[1, 2, 3, 4, 5, 6, 7, 8, 9]

This new version of flatten_list() uses a comprehension instead of a regular for loop. However, the nested comprehensions can be challenging to read and understand.

Using .append() is another way to flatten a list of lists:

>>> def flatten_list(a_list):
...     flat = []
...     for sublist in a_list:
...         for item in sublist:
...             flat.append(item)
...     return flat
...

>>> matrix = [
...     [1, 2, 3],
...     [4, 5, 6],
...     [7, 8, 9],
... ]

>>> flatten_list(matrix)
[1, 2, 3, 4, 5, 6, 7, 8, 9]

In this version of flatten_list(), someone reading your code can see that the function iterates over every sublist in a_list. In the second for loop, the function iterates over each item in sublist to finally populate the new flat list with .append(). Arguably, readability can be an advantage of this solution.

Summing Floating-Point Numbers: math.fsum()

If your code is constantly summing floating-point numbers with sum(), then you should consider using math.fsum() instead. This function performs floating-point computations more carefully than sum(), which improves the precision of your computation.

According to its documentation, fsum() “avoids loss of precision by tracking multiple intermediate partial sums.” The documentation provides the following example:

>>> from math import fsum

>>> sum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
0.9999999999999999

>>> fsum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
1.0

With fsum(), you get a more precise result. However, you should note that fsum() doesn’t solve the representation error in floating-point arithmetic. The following example uncovers this limitation:

>>> from math import fsum

>>> sum([0.1, 0.2])
0.30000000000000004

>>> fsum([0.1, 0.2])
0.30000000000000004

In these examples, both functions return the same result. This is due to the impossibility of accurately representing both values 0.1 and 0.2 in binary floating-point:

>>> f"{0.1:.28f}"
'0.1000000000000000055511151231'

>>> f"{0.2:.28f}"
'0.2000000000000000111022302463'

Unlike sum(), however, fsum() can help you reduce floating-point error propagation when you add very large and very small numbers together:

>>> from math import fsum

>>> sum([1e-16, 1, 1e16])
1e+16
>>> fsum([1e-16, 1, 1e16])
1.0000000000000002e+16

>>> sum([1, 1, 1e100, -1e100] * 10_000)
0.0
>>> fsum([1, 1, 1e100, -1e100] * 10_000)
20000.0

Wow! The second example is pretty surprising and totally defeats sum(). With sum(), you get 0.0 as a result. This is quite far away from the correct result of 20000.0, as you get with fsum().

Concatenating Iterables With itertools.chain()

If you’re looking for a handy tool for concatenating or chaining a series of iterables, then consider using chain() from itertools. This function can take multiple iterables and build an iterator that yields items from the first one, from the second one, and so on until it exhausts all the input iterables:

>>> from itertools import chain

>>> numbers = chain([1, 2, 3], [4, 5, 6], [7, 8, 9])
>>> numbers
<itertools.chain object at 0x7f0d0f160a30>
>>> next(numbers)
1
>>> next(numbers)
2

>>> list(chain([1, 2, 3], [4, 5, 6], [7, 8, 9]))
[1, 2, 3, 4, 5, 6, 7, 8, 9]

When you call chain(), you get an iterator of the items from the input iterables. In this example, you access successive items from numbers using next(). If you want to work with a list instead, then you can use list() to consume the iterator and return a regular Python list.

chain() is also a good option for flattening a list of lists in Python:

>>> from itertools import chain

>>> matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

>>> list(chain(*matrix))
[1, 2, 3, 4, 5, 6, 7, 8, 9]

To flatten a list of lists with chain(), you need to use the iterable unpacking operator (*). This operator unpacks all the input iterables so that chain() can work with them and generate the corresponding iterator. The final step is to call list() to build the desired flat list.

Concatenating Strings With str.join()

As you’ve already seen, sum() doesn’t concatenate or join strings. If you need to do so, then the preferred and fastest tool available in Python is str.join(). This method takes a sequence of strings as an argument and returns a new, concatenated string:

>>> greeting = ["Hello,", "welcome to", "Real Python!"]

>>> " ".join(greeting)
'Hello, welcome to Real Python!'

Using .join() is the most efficient and Pythonic way to concatenate strings. Here, you use a list of strings as an argument and build a single string from the input. Note that .join() uses the string on which you call the method as a separator during the concatenation. In this example, you call .join() on a string that consists of a single space character (" "), so the original strings from greeting are separated by spaces in your final string.