Search icon CANCEL
Subscription
0
Cart icon
Your Cart (0 item)
Close icon
You have no products in your basket yet
Save more on your purchases now! discount-offer-chevron-icon
Savings automatically calculated. No voucher code required.
Arrow left icon
Explore Products
Best Sellers
New Releases
Books
Videos
Audiobooks
Learning Hub
Conferences
Free Learning
Arrow right icon
Arrow up icon
GO TO TOP
Scientific Computing with Python

You're reading from   Scientific Computing with Python High-performance scientific computing with NumPy, SciPy, and pandas

Arrow left icon
Product type Paperback
Published in Jul 2021
Publisher Packt
ISBN-13 9781838822323
Length 392 pages
Edition 2nd Edition
Languages
Tools
Arrow right icon
Authors (4):
Arrow left icon
Olivier Verdier Olivier Verdier
Author Profile Icon Olivier Verdier
Olivier Verdier
Jan Erik Solem Jan Erik Solem
Author Profile Icon Jan Erik Solem
Jan Erik Solem
Claus Führer Claus Führer
Author Profile Icon Claus Führer
Claus Führer
Claus Fuhrer Claus Fuhrer
Author Profile Icon Claus Fuhrer
Claus Fuhrer
Arrow right icon
View More author details
Toc

Table of Contents (23) Chapters Close

Preface 1. Getting Started 2. Variables and Basic Types FREE CHAPTER 3. Container Types 4. Linear Algebra - Arrays 5. Advanced Array Concepts 6. Plotting 7. Functions 8. Classes 9. Iterating 10. Series and Dataframes - Working with Pandas 11. Communication by a Graphical User Interface 12. Error and Exception Handling 13. Namespaces, Scopes, and Modules 14. Input and Output 15. Testing 16. Symbolic Computations - SymPy 17. Interacting with the Operating System 18. Python for Parallel Computing 19. Comprehensive Examples 20. About Packt 21. Other Books You May Enjoy 22. References

Functions of two variables

Suppose  and  are vectors and we want to form the matrix  with elements . This would correspond to the function . The matrix  is merely defined by:

W=u.reshape(-1,1) + v

If the vectors  and  are and  respectively, the result is:

array([[2, 3, 4],
[3, 4, 5]])

More generally, suppose that we want to sample the function . Supposing that the vectors  and  are defined, the matrix  of sampled values is obtained with:

W = cos(x).reshape(-1,1) + sin(2*y)

Note that this is very frequently used in combination with ogrid. The vectors obtained from ogrid are already conveniently shaped for broadcasting. This allows for the following elegant sampling of the function :

x,y = ogrid[0:1:3j,0:1:3j] 
# x,y are vectors with the contents of linspace(0,1,3)
w = cos(x) + sin(2*y)

The syntax of ogrid needs some explanation: First, ogrid is not a function. It is an instance...

lock icon The rest of the chapter is locked
Register for a free Packt account to unlock a world of extra content!
A free Packt account unlocks extra newsletters, articles, discounted offers, and much more. Start advancing your knowledge today.
Unlock this book and the full library FREE for 7 days
Get unlimited access to 7000+ expert-authored eBooks and videos courses covering every tech area you can think of
Renews at $19.99/month. Cancel anytime