Book Image

Mastering Numerical Computing with NumPy

By : Umit Mert Cakmak, Tiago Antao, Mert Cuhadaroglu
Book Image

Mastering Numerical Computing with NumPy

By: Umit Mert Cakmak, Tiago Antao, Mert Cuhadaroglu

Overview of this book

NumPy is one of the most important scientific computing libraries available for Python. Mastering Numerical Computing with NumPy teaches you how to achieve expert level competency to perform complex operations, with in-depth coverage of advanced concepts. Beginning with NumPy's arrays and functions, you will familiarize yourself with linear algebra concepts to perform vector and matrix math operations. You will thoroughly understand and practice data processing, exploratory data analysis (EDA), and predictive modeling. You will then move on to working on practical examples which will teach you how to use NumPy statistics in order to explore US housing data and develop a predictive model using simple and multiple linear regression techniques. Once you have got to grips with the basics, you will explore unsupervised learning and clustering algorithms, followed by understanding how to write better NumPy code while keeping advanced considerations in mind. The book also demonstrates the use of different high-performance numerical computing libraries and their relationship with NumPy. You will study how to benchmark the performance of different configurations and choose the best for your system. By the end of this book, you will have become an expert in handling and performing complex data manipulations.
Table of Contents (11 chapters)

Computing the norm and determinant

This subsection will introduce two important values in linear algebra, namely the norm and determinant. Briefly, the norm gives length of a vector. The most commonly used norm is the L2-norm, which is also known as the Euclidean norm. Formally, the Lp-norm of x is calculated as follows:

The L0-norm is actually the cardinality of a vector. You can calculate it by just counting the total number of non-zero elements. For example, the vector A =[2,5,9,0] contains three non-zero elements, therefore ||A||0 = 3. The following code block shows the same norm calculation with numpy:

In [24]: import numpy as np 
x = np.array([2,5,9,0])
Out[24]: 3.0

In NumPy, you can calculate the norm of the vector with the use of the linalg.norm() method. The first parameter is the input array and the ord parameter is for order...