Numerical Data in Python with NumPy

16. Numerical Data in Python with NumPy#

NumPy is arguably the most important Python library for working with (numerical) data. The name itself comes from Numerical Python. NumPy introduces not only a central new data type, the NumPy array, but also a wide range of functions and methods for working with vectors, matrices, and tensors.

NumPy often simplifies coding tasks and is optimized for computational speed, as its core methods are implemented using compiled C libraries.

Let’s start with an example.

Imagine we’ve collected survey data. Participants rated how much they agreed with various statements on a scale from 1 (not at all) to 5 (completely). The data is imported into Python as lists, and we want to compare the answers of two participants. Specifically, we calculate the difference in values at corresponding positions. Using Python lists, we might code it as follows:

survey_person1 = [2, 3, 5, 4, 5, 2, 1, 3, 4, 4, 3]
survey_person2 = [4, 4, 2, 2, 4, 4, 3, 1, 5, 4, 2]

survey_diffs = []
for i in range(len(survey_person1)):
    survey_diffs.append(survey_person1[i] - survey_person2[i])
    
print(survey_diffs)

# Now calculate the absolute differences --> abs()
print([abs(x) for x in survey_diffs])
~~~

With NumPy, this task is much simpler:

```python
import numpy as np

survey_person1 = np.array([2, 3, 5, 4, 5, 2, 1, 3, 4, 4, 3])
survey_person2 = np.array([4, 4, 2, 2, 4, 4, 3, 1, 5, 4, 2])

print(survey_person1 - survey_person2)
print(abs(survey_person1 - survey_person2))

Here, we immediately used NumPy’s central data type: NumPy arrays!

print(type(survey_person1))  # => <class 'numpy.ndarray'>

16.1. Creating NumPy Arrays#

NumPy arrays can be easily created from Python lists:

import numpy as np

a = np.array([2, 5.9, 7.7, 100.0])
b = np.array([[2, 4, 7],
              [3, 5, 11]])

print(a)
print(b)

NumPy arrays differ from lists in several key ways:

  • All elements must have the same data type (e.g., all floats or integers). NumPy supports a wide range of numerical data types (NumPy data types).

  • For tables/matrices/tensors, all rows must have the same number of elements (unlike nested lists in Python).

  • Python dynamically adjusts the memory allocation for numbers, while NumPy arrays allocate fixed memory for each number (e.g., all entries as int64 or float64).

16.2. Getting Information About NumPy Arrays#

You can query the following properties of a NumPy array:

  • Data type: .dtype

  • Shape (rows, columns): .shape

  • Total number of elements: .size

  • Number of dimensions: .ndim

import numpy as np

b = np.array([[2, 4, 7],
              [3, 5, 11]])

print("Matrix shape:", b.shape)
print("Total number of elements:", b.size)
print("Matrix dimensions:", b.ndim)
print("Data type:", b.dtype)

16.3. Slicing and Indexing#

NumPy arrays support slicing and indexing, similar to Python lists, but with additional features:

import numpy as np

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

print(matrix_list[1])
print(matrix_list[1][2])

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

print(matrix[1])
print(matrix[1][2])

Mini-Quiz: What is the value of matrix[1][2]?

NumPy also supports multi-indexing for simpler syntax:

print(matrix[1, 2])

# Other slicing options:
print("First row:", matrix[0, :])
print("Last column:", matrix[:, -1])
print("Lower-right corner:", matrix[1:, 1:])

NumPy arrays allow advanced indexing using lists, arrays, or Boolean masks:

indices = [2, 0, 2, 0]
print(matrix[indices])

# Boolean mask
mask = [True, False, True]
print(matrix[mask])

16.4. Mathematical Operations on Arrays#

NumPy arrays support element-wise operations:

import numpy as np

numbers = np.array([4, 5, 2, 3, 1, 5, 5, 2])
print(numbers - 5)

other_numbers = np.array([2, 5, 1, 1, 4, 3, 4, 3])
print(numbers - other_numbers)

The same applies to other operations:

numbers = np.array([4, 5, 2, 3, 1, 5, 5, 2])
print(numbers * 5)

other_numbers = np.array([2, 5, 1, 1, 4, 3, 4, 3])
print(numbers * other_numbers)

16.5. Useful NumPy Methods#

NumPy provides many methods for numerical and statistical operations. For example, .sum() calculates the sum of all elements:

import numpy as np

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

print(matrix.sum())
print(np.sum(matrix))

You can calculate sums along specific axes:

print(matrix.sum(axis=0))  # Sum of each column
print(matrix.sum(axis=1))  # Sum of each row

16.6. Creating Arrays#

Other ways to create arrays include:

  • Zeros and ones:

    data = np.zeros((3, 4))
print(data)

data = np.ones((3, 4))
print(data)

  • Random values:

    data = np.random.random((3, 4))
print(data)

  • Range of values (np.arange):

    data = np.arange(-10, 10, 1)
print(data)

  • Linearly spaced values (np.linspace):

    data = np.linspace(-10, 10, num=10)
print(data)

16.7. Modifying Arrays#

NumPy arrays can be modified like lists:

data = np.array([1, 2, 3, 4, 5, 6, 7, 8])
data[-1] = 12
data[:3] = -1
print(data)

Arrays can also be concatenated using np.concatenate:

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

arr = np.concatenate((a, b))
print(arr)

For multidimensional arrays, specify the axis:

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

arr = np.concatenate((a, b), axis=0)
print(arr)

arr = np.concatenate((a, b), axis=1)
print(arr)

Arrays can also be reshaped or flattened:

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

data_reshaped = data.reshape(3, 2)
print(data_reshaped)

data_flattened = data_reshaped.flatten()
print(data_flattened)
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