Lecture VII - NumPy for Scientific Computing

Programming with Python

Author
Affiliation

Dr. Tobias Vlćek

Kühne Logistics University Hamburg - Fall 2024

Quick Recap of the last Lecture

Modules

  • Modules are .py files containing Python code
  • They are used to organize and reuse code
  • They can define functions, classes, and variables
  • Can be imported into other scripts

. . .

Tip

We can import entire modules or individual functions, classes or variables.

Standard Libraries

  • Python includes many built-in modules like:
    • random provides functions for random numbers
    • os allows interaction with the operating system
    • csv is used for reading and writing CSV files
    • re is used for working with regular expressions

Packages

  • Packages are collections of modules
  • Often available from the Python Package Index (PyPI)
  • Install using pip install <package_name>
  • Virtual environments help manage dependencies

. . .

Tip

Virtual environments are not that important for you right now, as they are mostly used if you work on several projects with different dependecies at once.

NumPy Module

What is NumPy?

  • NumPy is a package for scientific computing in Python
  • Provides large, multi-dimensional arrays and matrices
  • Wide range of functions to operate on these
  • Python lists can be slow - Numpy arrays are much faster

. . .

Note

The name of the package comes from Numerical Python.

Why is NumPy so fast?

  • Arrays are stored in a contiguous block of memory
  • This allows for efficient memory access patterns
  • Operations are implemented in the languages C and C++

. . .

Question: Have you heard of C and C++?

How to get started

  1. Install NumPy using pip install numpy
  2. In Thonny, Tools -> Manage Packages...
  3. Import NumPy in a script using import numpy as np

. . .

import numpy as np
x = np.array([1, 2, 3, 4, 5]); type(x)
numpy.ndarray

. . .

Note

You don’t have to use as np. But it is a common practice to do so.

Creating Arrays

  • The backbone of Numpy is the so called ndarray
  • Can be initialized from different data structures:
import numpy as np

array_from_list = np.array([1, 1, 1, 1])
print(array_from_list)
[1 1 1 1]
import numpy as np

array_from_tuple = np.array((2, 2, 2, 2))
print(array_from_tuple)
[2 2 2 2]

Hetergenous Data Types

  • It is possible to store different data types in a ndarray
import numpy as np

array_different_types = np.array(["s", 2, 2.0, "i"])
print(array_different_types)
['s' '2' '2.0' 'i']

. . .

Note

But it is mostly not recommended, as it can lead to performance issues. If possible, try to keep the types homogenous.

Prefilled Arrays

Improve performance by allocating memory upfront

  • np.zeros(shape): to create an array of zeros
  • np.random.rand(shape): array of random values
  • np.arange(start, stop, step): evenly spaced
  • np.linspace(start, stop, num): evenly spaced

. . .

Note

The shape refers to the size of the array. It can have one or multiple dimensions.

Dimensions

  • The shape is specified as tuple in these arrays
  • (2) or 2 creates a 1-dimensional array (vetor)
  • (2,2) creates a 2-dimensional array (matrix)
  • (2,2,2) 3-dimensional array (3rd order tensor)
  • (2,2,2,2) 4-dimensional array (4th order tensor)
  • …

Computations

  • We can apply operations to the entire array at once
  • This is much faster than applying them element-wise

. . .

import numpy as np
x = np.array([1, 2, 3, 4, 5])
x + 1
array([2, 3, 4, 5, 6])

Arrays in Action

Task: Practice working with Numpy:

# TODO: Create a 3-dimensional tensor with filled with zeros
# Choose the shape of the tensor, but it should have 200 elements
# Add the number 5 to all values of the tensor

# Your code here
assert sum(tensor) == 1000

# TODO: Print the shape of the tensor using the method shape()
# TODO: Print the dtype of the tensor using the method dtype()
# TODO: Print the size of the tensor using the method size()

Indexing and Slicing

  • Accessing and slicing ndarray works as before
  • Higher dimension element access with multiple indices

. . .

Question: What do you expect will be printed?

import numpy as np
x = np.random.randint(0, 10, size=(3, 3))
print(x); print("---")
print(x[0:2,0:2])
[[3 9 0]
 [1 9 9]
 [4 0 6]]
---
[[3 9]
 [1 9]]

Data Types

  • Numpy provides data types as characters
  • i: integer
  • b: boolean
  • f: float
  • S: string
  • U: unicode

. . .

string_array = np.array(["Hello", "World"]); string_array.dtype
dtype('<U5')

Enforcing Data Types

  • We can also provide the type when creating arrays

. . .

x = np.array([1, 2, 3, 4, 5],  dtype = 'f'); print(x.dtype)
float32

. . .

  • Or we can change them for existing arrays
x = np.array([1, 2, 3, 4, 5],  dtype = 'f'); print(x.astype('i').dtype)
int32

. . .

Note

Note, how the types are specified as int32 and float32.

Sidenote: Bits

Question: Do you have an idea what 32 stands for?

. . .

  • It’s the number of bits used to represent a number
    • int16 is a 16-bit integer
    • float32 is a 32-bit floating point number
    • int64 is a 64-bit integer
    • float128 is a 128-bit floating point number

Why do Bits Matter?

  • They matter, because they can affect:
    • the performance of your code
    • the precision of your results

. . .

  • That’s why numbers can have a limited precision!
    • An int8 has to be in the range of -128 to 127
    • An int16 has to be in the range of -32768 to 32767

. . .

Question: Size difference between int16 and int64?

Joining Arrays

  • You can use concatenate two join arrays
  • With axis you can specify the dimension
  • In 2-dimensions hstack() and vstack() are easier

. . .

Question: What do you expect will be printed?

import numpy as np
ones = np.array((1,1,1,1))
twos = np.array((1,1,1,1)) *2
print(np.vstack((ones,twos))); print(np.hstack((ones,twos)))
[[1 1 1 1]
 [2 2 2 2]]
[1 1 1 1 2 2 2 2]

Common Methods

  • sort(): sort the array from low to high
  • reshape(): reshape the array into a new shape
  • flatten(): flatten the array into a 1D array
  • squeeze(): squeeze the array to remove 1D entries
  • transpose(): transpose the array

. . .

Tip

Try experiment with these methods, they can make your work much easier.

Speed Differences in Action

Task: Complete the following task to practice with Numpy:

# TODO: Create a 2-dimensional matrix with filled with ones of size 1000 x 1000.
# Afterward, flatten the matrix to a vector and loop over the vector.
# In each loop iteration, add a random number between 1 and 10000.
# TODO: Now, do the same with a list of the same size and fill it with random numbers. 
# Then, sort the list as you have done with the Numpy vector before.
# You can use the `time` module to compare the runtime of both approaches.
import time
start = time.time()
# Your code here
end = time.time()
print(end - start) # time in seconds
1.0967254638671875e-05

That’s it for today!

Note

And that’s it for todays lecture!
You now have the basic knowledge to start working with scientific computing.

Literature

Interesting Books

  • Downey, A. B. (2024). Think Python: How to think like a computer scientist (Third edition). O’Reilly. Link to free online version
  • Elter, S. (2021). Schrödinger programmiert Python: Das etwas andere Fachbuch (1. Auflage). Rheinwerk Verlag.

. . .

For more interesting literature to learn more about Python, take a look at the literature list of this course.