![2020-04-30: First release
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responsibility for errors or omissions, including without
limitation responsibility for damages resulting from the use of or
reliance on this work. Use of the information and instructions
contained in this work is at your own risk. If any code samples
or other technology this work contains or describes is subject
to open source licenses or the intellectual property rights of
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[LSI]](https://image.slidesharecdn.com/21185358-250519104953-0a00c180/85/High-Performance-Python-2nd-Edition-Micha-Gorelick-Ian-Ozsvald-21-320.jpg)
!["The quæstors led the man [Spurius Cassius] to the top of the
precipice that commands the Forum, and in the presence of all the
citizens threw him down from the rock. For this was the established
punishment at that time among the Romans for those who were
condemned to die"—A.U.C. 269—(Dionysius, viii. 78).
If we look back up the street we came down, the height will be seen
in the garden above us. It must be remembered that the top of the
hill has been levelled, and the valley below filled in thirty feet;
allowing for this there would have been a fall of upwards of 160 feet.
The steps on our left formed the third ancient approach to the arx,
the Centum Gradus, up which the Vitellians climbed when they took
the citadel. On the site of the garden above stood
CAMILLUS'S TEMPLES TO CONCORD AND JUNO.
The first Temple of Concord of which we have any notice was that
dedicated by Camillus, A.U.C. 388.
"When the dictator was one day sitting on the tribunal in the Forum,
the people called out to drag him from his seat; but he led off the
patricians to the senate house. Previous to his entering it he turned
towards the Capitol [this shows that the senate house was not on
the Capitol, as some would have us believe; for if so, he would not
have turned towards the Capitol before entering the senate house—
he would have already faced it], and besought the gods to put a
happy end to the present disturbances, vowing to build a temple to
Concord when the tumult should be appeased.... Next day they
assembled and voted that the temple which Camillus had vowed to
Concord should, on account of this great event, be built upon a spot
viewing from a height the Forum and place of assembly" (Plutarch,
in "Camillus"). Ovid, speaking of the same temple ("Fasti," i. 640),
says: "Fair Concord, the succeeding day places thee in a snow-white
shrine, near where elevated Moneta raises her steps on high: now
with ease wilt thou look down upon the Latin crowd. Now have the
august hands of Cæsar restored thee,"—referring to its rebuilding by](https://image.slidesharecdn.com/21185358-250519104953-0a00c180/85/High-Performance-Python-2nd-Edition-Micha-Gorelick-Ian-Ozsvald-64-320.jpg)
![1, 2. Cases of small bronze articles found at various times. 3. A
bronze biga, or two-horse chariot, with reliefs depicting scenes from
the circus; restored upon a wooden frame, and given by Signor A.
Castellani. 4. A bisellium, or chair of state. 8. Lectica, or sedan chair.
"These infirmities caused him [Claudius] to be carried in a close
chair, which no Roman had ever used before; and from thence have
the emperors and the rest of us consular men taken the custom of
using chairs of that sort, for neither Augustus nor Tiberius used
anything but small litters, which are still in fashion for the women"
(Dion Cassius). 9, 10. Shelves containing household utensils, &c. 11.
Fragments of columns of Bigio marble.
ROOM OF COINS.
The beautiful alabaster pavement of this room was found, as now
fixed, upon the Esquiline Hill, on Christmas eve, 1874. It formed part
of the House of the Larmæ, where the statues were found. The
coins formed part of the Campana Collection, and are of great value.
The small case of gems is worth looking into; it contains some
fragments not unlike the Portland vase, white reliefs on a blue
ground.
We now enter the new
OCTAGONAL HALL.
(The order is liable to alteration, as objects are constantly being
added.)
This museum is formed of the remains found in the excavations of
the municipality since Rome was made the capital of united Italy.
The new circular hall, designed by Signor Vespignani, presents a
light and elegant effect. Amongst the most important subjects
placed in the new hall, we may mention No. 2, the monument of
Quintus Sulpicius Maximus, found in 1870 in the Old Porta Salaria.
The inscription states that he died at the early age of thirteen years,](https://image.slidesharecdn.com/21185358-250519104953-0a00c180/85/High-Performance-Python-2nd-Edition-Micha-Gorelick-Ian-Ozsvald-76-320.jpg)
High Performance Python 2nd Edition Micha Gorelick Ian Ozsvald
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- 6. 1. Foreword 2. Preface a. Who This Book Is For b. Who This Book Is Not For c. What You’ll Learn d. Python 3 e. Changes from Python 2.7 f. License g. How to Make an Attribution h. Errata and Feedback i. Conventions Used in This Book j. Using Code Examples k. O’Reilly Online Learning l. How to Contact Us m. Acknowledgments 3. 1. Understanding Performant Python a. The Fundamental Computer System i. Computing Units ii. Memory Units iii. Communications Layers b. Putting the Fundamental Elements Together
- 7. i. Idealized Computing Versus the Python Virtual Machine c. So Why Use Python? d. How to Be a Highly Performant Programmer i. Good Working Practices ii. Some Thoughts on Good Notebook Practice iii. Getting the Joy Back into Your Work 4. 2. Profiling to Find Bottlenecks a. Profiling Efficiently b. Introducing the Julia Set c. Calculating the Full Julia Set d. Simple Approaches to Timing—print and a Decorator e. Simple Timing Using the Unix time Command f. Using the cProfile Module g. Visualizing cProfile Output with SnakeViz h. Using line_profiler for Line-by-Line Measurements i. Using memory_profiler to Diagnose Memory Usage j. Introspecting an Existing Process with PySpy k. Bytecode: Under the Hood
- 8. i. Using the dis Module to Examine CPython Bytecode ii. Different Approaches, Different Complexity l. Unit Testing During Optimization to Maintain Correctness i. No-op @profile Decorator m. Strategies to Profile Your Code Successfully n. Wrap-Up 5. 3. Lists and Tuples a. A More Efficient Search b. Lists Versus Tuples i. Lists as Dynamic Arrays ii. Tuples as Static Arrays c. Wrap-Up 6. 4. Dictionaries and Sets a. How Do Dictionaries and Sets Work? i. Inserting and Retrieving ii. Deletion iii. Resizing iv. Hash Functions and Entropy b. Dictionaries and Namespaces c. Wrap-Up
- 9. 7. 5. Iterators and Generators a. Iterators for Infinite Series b. Lazy Generator Evaluation c. Wrap-Up 8. 6. Matrix and Vector Computation a. Introduction to the Problem b. Aren’t Python Lists Good Enough? i. Problems with Allocating Too Much c. Memory Fragmentation i. Understanding perf ii. Making Decisions with perf’s Output iii. Enter numpy d. Applying numpy to the Diffusion Problem i. Memory Allocations and In-Place Operations ii. Selective Optimizations: Finding What Needs to Be Fixed e. numexpr: Making In-Place Operations Faster and Easier f. A Cautionary Tale: Verify “Optimizations” (scipy) g. Lessons from Matrix Optimizations h. Pandas
- 10. i. Pandas’s Internal Model ii. Applying a Function to Many Rows of Data iii. Building DataFrames and Series from Partial Results Rather than Concatenating iv. There’s More Than One (and Possibly a Faster) Way to Do a Job v. Advice for Effective Pandas Development i. Wrap-Up 9. 7. Compiling to C a. What Sort of Speed Gains Are Possible? b. JIT Versus AOT Compilers c. Why Does Type Information Help the Code Run Faster? d. Using a C Compiler e. Reviewing the Julia Set Example f. Cython i. Compiling a Pure Python Version Using Cython g. pyximport i. Cython Annotations to Analyze a Block of Code ii. Adding Some Type Annotations
- 11. h. Cython and numpy i. Parallelizing the Solution with OpenMP on One Machine i. Numba i. Numba to Compile NumPy for Pandas j. PyPy i. Garbage Collection Differences ii. Running PyPy and Installing Modules k. A Summary of Speed Improvements l. When to Use Each Technology i. Other Upcoming Projects m. Graphics Processing Units (GPUs) i. Dynamic Graphs: PyTorch ii. Basic GPU Profiling iii. Performance Considerations of GPUs iv. When to Use GPUs n. Foreign Function Interfaces i. ctypes ii. cffi iii. f2py iv. CPython Module o. Wrap-Up
- 12. 10. 8. Asynchronous I/O a. Introduction to Asynchronous Programming b. How Does async/await Work? i. Serial Crawler ii. Gevent iii. tornado iv. aiohttp c. Shared CPU–I/O Workload i. Serial ii. Batched Results iii. Full Async d. Wrap-Up 11. 9. The multiprocessing Module a. An Overview of the multiprocessing Module b. Estimating Pi Using the Monte Carlo Method c. Estimating Pi Using Processes and Threads i. Using Python Objects ii. Replacing multiprocessing with Joblib iii. Random Numbers in Parallel Systems iv. Using numpy d. Finding Prime Numbers i. Queues of Work
- 13. e. Verifying Primes Using Interprocess Communication i. Serial Solution ii. Naive Pool Solution iii. A Less Naive Pool Solution iv. Using Manager.Value as a Flag v. Using Redis as a Flag vi. Using RawValue as a Flag vii. Using mmap as a Flag viii. Using mmap as a Flag Redux f. Sharing numpy Data with multiprocessing g. Synchronizing File and Variable Access i. File Locking ii. Locking a Value h. Wrap-Up 12. 10. Clusters and Job Queues a. Benefits of Clustering b. Drawbacks of Clustering i. $462 Million Wall Street Loss Through Poor Cluster Upgrade Strategy ii. Skype’s 24-Hour Global Outage c. Common Cluster Designs d. How to Start a Clustered Solution
- 14. e. Ways to Avoid Pain When Using Clusters f. Two Clustering Solutions i. Using IPython Parallel to Support Research ii. Parallel Pandas with Dask g. NSQ for Robust Production Clustering i. Queues ii. Pub/sub iii. Distributed Prime Calculation h. Other Clustering Tools to Look At i. Docker i. Docker’s Performance ii. Advantages of Docker j. Wrap-Up 13. 11. Using Less RAM a. Objects for Primitives Are Expensive i. The array Module Stores Many Primitive Objects Cheaply ii. Using Less RAM in NumPy with NumExpr b. Understanding the RAM Used in a Collection c. Bytes Versus Unicode d. Efficiently Storing Lots of Text in RAM
- 15. i. Trying These Approaches on 11 Million Tokens e. Modeling More Text with Scikit-Learn’s FeatureHasher f. Introducing DictVectorizer and FeatureHasher i. Comparing DictVectorizer and FeatureHasher on a Real Problem g. SciPy’s Sparse Matrices h. Tips for Using Less RAM i. Probabilistic Data Structures i. Very Approximate Counting with a 1- Byte Morris Counter ii. K-Minimum Values iii. Bloom Filters iv. LogLog Counter v. Real-World Example 14. 12. Lessons from the Field a. Streamlining Feature Engineering Pipelines with Feature-engine i. Feature Engineering for Machine Learning ii. The Hard Task of Deploying Feature Engineering Pipelines iii. Leveraging the Power of Open Source Python Libraries
- 16. iv. Feature-engine Smooths Building and Deployment of Feature Engineering Pipelines v. Helping with the Adoption of a New Open Source Package vi. Developing, Maintaining, and Encouraging Contribution to Open Source Libraries b. Highly Performant Data Science Teams i. How Long Will It Take? ii. Discovery and Planning iii. Managing Expectations and Delivery c. Numba i. A Simple Example ii. Best Practices and Recommendations iii. Getting Help d. Optimizing Versus Thinking e. Adaptive Lab’s Social Media Analytics (2014) i. Python at Adaptive Lab ii. SoMA’s Design iii. Our Development Methodology iv. Maintaining SoMA v. Advice for Fellow Engineers
- 17. f. Making Deep Learning Fly with RadimRehurek.com (2014) i. The Sweet Spot ii. Lessons in Optimizing iii. Conclusion g. Large-Scale Productionized Machine Learning at Lyst.com (2014) i. Cluster Design ii. Code Evolution in a Fast-Moving Start- Up iii. Building the Recommendation Engine iv. Reporting and Monitoring v. Some Advice h. Large-Scale Social Media Analysis at Smesh (2014) i. Python’s Role at Smesh ii. The Platform iii. High Performance Real-Time String Matching iv. Reporting, Monitoring, Debugging, and Deployment i. PyPy for Successful Web and Data Processing Systems (2014) i. Prerequisites ii. The Database
- 18. iii. The Web Application iv. OCR and Translation v. Task Distribution and Workers vi. Conclusion j. Task Queues at Lanyrd.com (2014) i. Python’s Role at Lanyrd ii. Making the Task Queue Performant iii. Reporting, Monitoring, Debugging, and Deployment iv. Advice to a Fellow Developer 15. Index
- 19. High Performance Python SECOND EDITION Practical Performant Programming for Humans Micha Gorelick and Ian Ozsvald
- 20. High Performance Python by Micha Gorelick and Ian Ozsvald Copyright © 2020 Micha Gorelick and Ian Ozsvald. All rights reserved. Printed in the United States of America. Published by O’Reilly Media, Inc., 1005 Gravenstein Highway North, Sebastopol, CA 95472. O’Reilly books may be purchased for educational, business, or sales promotional use. Online editions are also available for most titles (http://oreilly.com). For more information, contact our corporate/institutional sales department: 800-998-9938 or [email protected]. Acquisitions Editor: Tyler Ortman Indexer: Potomac Indexing, LLC Development Editor: Sarah Grey Interior Designer: David Futato Production Editor: Christopher Faucher Cover Designer: Karen Montgomery Copyeditor: Arthur Johnson Illustrator: Rebecca Demarest Proofreader: Sharon Wilkey September 2014: First Edition May 2020: Second Edition Revision History for the Second Edition
- 21. 2020-04-30: First release See http://oreilly.com/catalog/errata.csp?isbn=9781492055020 for release details. The O’Reilly logo is a registered trademark of O’Reilly Media, Inc. High Performance Python, the cover image, and related trade dress are trademarks of O’Reilly Media, Inc. The views expressed in this work are those of the authors, and do not represent the publisher’s views. While the publisher and the authors have used good faith efforts to ensure that the information and instructions contained in this work are accurate, the publisher and the authors disclaim all responsibility for errors or omissions, including without limitation responsibility for damages resulting from the use of or reliance on this work. Use of the information and instructions contained in this work is at your own risk. If any code samples or other technology this work contains or describes is subject to open source licenses or the intellectual property rights of others, it is your responsibility to ensure that your use thereof complies with such licenses and/or rights. High Performance Python is available under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 International License. 978-1-492-05502-0 [LSI]
- 23. Foreword When you think about high performance computing, you might imagine giant clusters of machines modeling complex weather phenomena or trying to understand signals in data collected about far-off stars. It’s easy to assume that only people building specialized systems should worry about the performance characteristics of their code. By picking up this book, you’ve taken a step toward learning the theory and practices you’ll need to write highly performant code. Every programmer can benefit from understanding how to build performant systems. There are an obvious set of applications that are just on the edge of possible, and you won’t be able to approach them without writing optimally performant code. If that’s your practice, you’re in the right place. But there is a much broader set of applications that can benefit from performant code. We often think that new technical capabilities are what drives innovation, but I’m equally fond of capabilities that increase the accessibility of technology by orders of magnitude. When something becomes ten times cheaper in time or compute costs, suddenly the set of applications you can address is wider than you imagined. The first time this principle manifested in my own work was over a decade ago, when I was working at a social media company, and we ran an analysis over multiple terabytes of
- 24. data to determine whether people clicked on more photos of cats or dogs on social media. It was dogs, of course. Cats just have better branding. This was an outstandingly frivolous use of compute time and infrastructure at the time! Gaining the ability to apply techniques that had previously been restricted to sufficiently high-value applications, such as fraud detection, to a seemingly trivial question opened up a new world of now- accessible possibilities. We were able to take what we learned from these experiments and build a whole new set of products in search and content discovery. For an example that you might encounter today, consider a machine-learning system that recognizes unexpected animals or people in security video footage. A sufficiently performant system could allow you to embed that model into the camera itself, improving privacy or, even if running in the cloud, using significantly less compute and power—benefiting the environment and reducing your operating costs. This can free up resources for you to look at adjacent problems, potentially building a more valuable system. We all desire to create systems that are effective, easy to understand, and performant. Unfortunately, it often feels like we have to pick two (or one) out of the three! High Performance Python is a handbook for people who want to make things that are capable of all three.
- 25. This book stands apart from other texts on the subject in three ways. First, it’s written for us—humans who write code. You’ll find all of the context you need to understand why you might make certain choices. Second, Gorelick and Ozsvald do a wonderful job of curating and explaining the necessary theory to support that context. Finally, in this updated edition, you’ll learn the specific quirks of the most useful libraries for implementing these approaches today. This is one of a rare class of programming books that will change the way you think about the practice of programming. I’ve given this book to many people who could benefit from the additional tools it provides. The ideas that you’ll explore in its pages will make you a better programmer, no matter what language or environment you choose to work in. Enjoy the adventure. Hilary Mason, Data Scientist in Residence at Accel
- 26. Preface Python is easy to learn. You’re probably here because now that your code runs correctly, you need it to run faster. You like the fact that your code is easy to modify and you can iterate with ideas quickly. The trade-off between easy to develop and runs as quickly as I need is a well-understood and often-bemoaned phenomenon. There are solutions. Some people have serial processes that have to run faster. Others have problems that could take advantage of multicore architectures, clusters, or graphics processing units. Some need scalable systems that can process more or less as expediency and funds allow, without losing reliability. Others will realize that their coding techniques, often borrowed from other languages, perhaps aren’t as natural as examples they see from others. In this book we will cover all of these topics, giving practical guidance for understanding bottlenecks and producing faster and more scalable solutions. We also include some war stories from those who went ahead of you, who took the knocks so you don’t have to. Python is well suited for rapid development, production deployments, and scalable systems. The ecosystem is full of
- 27. people who are working to make it scale on your behalf, leaving you more time to focus on the more challenging tasks around you.
- 28. Who This Book Is For You’ve used Python for long enough to have an idea about why certain things are slow and to have seen technologies like Cython, numpy, and PyPy being discussed as possible solutions. You might also have programmed with other languages and so know that there’s more than one way to solve a performance problem. While this book is primarily aimed at people with CPU-bound problems, we also look at data transfer and memory-bound solutions. Typically, these problems are faced by scientists, engineers, quants, and academics. We also look at problems that a web developer might face, including the movement of data and the use of just-in-time (JIT) compilers like PyPy and asynchronous I/O for easy-win performance gains. It might help if you have a background in C (or C++, or maybe Java), but it isn’t a prerequisite. Python’s most common interpreter (CPython—the standard you normally get if you type python at the command line) is written in C, and so the hooks and libraries all expose the gory inner C machinery. There are lots of other techniques that we cover that don’t assume any knowledge of C. You might also have a lower-level knowledge of the CPU, memory architecture, and data buses, but again, that’s not
- 30. Who This Book Is Not For This book is meant for intermediate to advanced Python programmers. Motivated novice Python programmers may be able to follow along as well, but we recommend having a solid Python foundation. We don’t cover storage-system optimization. If you have a SQL or NoSQL bottleneck, then this book probably won’t help you. What You’ll Learn Your authors have been working with large volumes of data, a requirement for I want the answers faster! and a need for scalable architectures, for many years in both industry and academia. We’ll try to impart our hard-won experience to save you from making the mistakes that we’ve made. At the start of each chapter, we’ll list questions that the following text should answer. (If it doesn’t, tell us and we’ll fix it in the next revision!) We cover the following topics: Background on the machinery of a computer so you know what’s happening behind the scenes Lists and tuples—the subtle semantic and speed differences in these fundamental data structures Dictionaries and sets—memory allocation strategies and access algorithms in these important data
- 31. structures Iterators—how to write in a more Pythonic way and open the door to infinite data streams using iteration Pure Python approaches—how to use Python and its modules effectively Matrices with numpy—how to use the beloved numpy library like a beast Compilation and just-in-time computing—processing faster by compiling down to machine code, making sure you’re guided by the results of profiling Concurrency—ways to move data efficiently multiprocessing—various ways to use the built-in multiprocessing library for parallel computing and to efficiently share numpy matrices, and some costs and benefits of interprocess communication (IPC) Cluster computing—convert your multiprocessing code to run on a local or remote cluster for both research and production systems Using less RAM—approaches to solving large problems without buying a humungous computer Lessons from the field—lessons encoded in war stories from those who took the blows so you don’t have to Python 3 Python 3 is the standard version of Python as of 2020, with Python 2.7 deprecated after a 10-year migration process. If you’re still on Python 2.7, you’re doing it wrong—many libraries
- 32. are no longer supported for your line of Python, and support will become more expensive over time. Please do the community a favor and migrate to Python 3, and make sure that all new projects use Python 3. In this book, we use 64-bit Python. Whilst 32-bit Python is supported, it is far less common for scientific work. We’d expect all the libraries to work as usual, but numeric precision, which depends on the number of bits available for counting, is likely to change. 64-bit is dominant in this field, along with *nix environments (often Linux or Mac). 64-bit lets you address larger amounts of RAM. *nix lets you build applications that can be deployed and configured in well-understood ways with well- understood behaviors. If you’re a Windows user, you’ll have to buckle up. Most of what we show will work just fine, but some things are OS- specific, and you’ll have to research a Windows solution. The biggest difficulty a Windows user might face is the installation of modules: research in sites like Stack Overflow should give you the solutions you need. If you’re on Windows, having a virtual machine (e.g., using VirtualBox) with a running Linux installation might help you to experiment more freely. Windows users should definitely look at a packaged solution like those available through Anaconda, Canopy, Python(x,y), or Sage. These same distributions will make the lives of Linux and Mac users far simpler too.
- 33. Changes from Python 2.7 If you’ve upgraded from Python 2.7, you might not be aware of a few relevant changes: / meant integer division in Python 2.7, whereas it performs float division in Python 3. str and unicode were used to represent text data in Python 2.7; in Python 3, everything is a str, and these are always Unicode. For clarity, a bytes type is used if we’re using unencoded byte sequences. If you’re in the process of upgrading your code, two good guides are “Porting Python 2 Code to Python 3” and “Supporting Python 3: An in-depth guide”. With a distribution like Anaconda or Canopy, you can run both Python 2 and Python 3 simultaneously—this will simplify your porting. License This book is licensed under Creative Commons Attribution- NonCommercial-NoDerivs 3.0. You’re welcome to use this book for noncommercial purposes, including for noncommercial teaching. The license allows only for complete reproductions; for partial reproductions, please contact O’Reilly (see “How to Contact Us”). Please attribute the book as noted in the following section.
- 34. We negotiated that the book should have a Creative Commons license so the contents could spread further around the world. We’d be quite happy to receive a beer if this decision has helped you. We suspect that the O’Reilly staff would feel similarly about the beer. How to Make an Attribution The Creative Commons license requires that you attribute your use of a part of this book. Attribution just means that you should write something that someone else can follow to find this book. The following would be sensible: “High Performance Python, 2nd ed., by Micha Gorelick and Ian Ozsvald (O’Reilly). Copyright 2020 Micha Gorelick and Ian Ozsvald, 978-1-492- 05502-0.” Errata and Feedback We encourage you to review this book on public sites like Amazon—please help others understand if they would benefit from this book! You can also email us at [email protected]. We’re particularly keen to hear about errors in the book, successful use cases where the book has helped you, and high performance techniques that we should cover in the next edition. You can access the web page for this book at https://oreil.ly/high-performance-python-2e.
- 35. Complaints are welcomed through the instant-complaint- transmission-service > /dev/null. Conventions Used in This Book The following typographical conventions are used in this book: Italic Indicates new terms, URLs, email addresses, filenames, and file extensions. Constant width Used for program listings, as well as within paragraphs to refer to program elements such as variable or function names, databases, datatypes, environment variables, statements, and keywords. Constant width bold Shows commands or other text that should be typed literally by the user. Constant width italic Shows text that should be replaced with user-supplied values or by values determined by context. TIP This element signifies a tip, suggestion, or critical thinking question.
- 36. NOTE This element signifies a general note. WARNING This element indicates a warning or caution. Using Code Examples Supplemental material (code examples, exercises, etc.) is available for download at https://github.com/mynameisfiber/high_performance_python_2 e. If you have a technical question or a problem using the code examples, please send email to [email protected]. This book is here to help you get your job done. In general, if example code is offered with this book, you may use it in your programs and documentation. You do not need to contact us for permission unless you’re reproducing a significant portion of the code. For example, writing a program that uses several chunks of code from this book does not require permission. Selling or distributing examples from O’Reilly books does require permission. Answering a question by citing this book and quoting example code does not require permission. Incorporating a significant amount of example code from this
- 37. book into your product’s documentation does require permission. If you feel your use of code examples falls outside fair use or the permission given above, feel free to contact us at [email protected]. O’Reilly Online Learning NOTE For more than 40 years, O’Reilly Media has provided technology and business training, knowledge, and insight to help companies succeed. Our unique network of experts and innovators share their knowledge and expertise through books, articles, and our online learning platform. O’Reilly’s online learning platform gives you on-demand access to live training courses, in-depth learning paths, interactive coding environments, and a vast collection of text and video from O’Reilly and 200+ other publishers. For more information, visit http://oreilly.com. How to Contact Us Please address comments and questions concerning this book to the publisher: O’Reilly Media, Inc.
- 38. 1005 Gravenstein Highway North Sebastopol, CA 95472 800-998-9938 (in the United States or Canada) 707-829-0515 (international or local) 707-829-0104 (fax) Email [email protected] to comment or ask technical questions about this book. For news and more information about our books and courses, see our website at http://oreilly.com. Find us on Facebook: http://facebook.com/oreilly Follow us on Twitter: http://twitter.com/oreillymedia Watch us on YouTube: http://youtube.com/oreillymedia Acknowledgments Hilary Mason wrote our foreword—thanks for composing such a wonderful opening narrative for our book. Giles Weaver and Dimitri Denisjonok provided invaluable technical feedback on this edition; great work, chaps. Thanks to Patrick Cooper, Kyran Dale, Dan Foreman-Mackey, Calvin Giles, Brian Granger, Jamie Matthews, John
- 39. Montgomery, Christian Schou Oxvig, Matt “snakes” Reiferson, Balthazar Rouberol, Michael Skirpan, Luke Underwood, Jake Vanderplas, and William Winter for invaluable feedback and contributions. Ian thanks his wife, Emily, for letting him disappear for another eight months to write this second edition (thankfully, she’s terribly understanding). Ian apologizes to his dog for sitting and writing rather than walking in the woods quite as much as she’d have liked. Micha thanks Marion and the rest of his friends and family for being so patient while he learned to write. O’Reilly editors are rather lovely to work with; do strongly consider talking to them if you want to write your own book. Our contributors to the “Lessons from the Field” chapter very kindly shared their time and hard-won lessons. We give thanks to Soledad Galli, Linda Uruchurtu, Vanentin Haenel, and Vincent D. Warmerdam for this edition and to Ben Jackson, Radim Řehůřek, Sebastjan Trepca, Alex Kelly, Marko Tasic, and Andrew Godwin for their time and effort during the previous edition.
- 40. Chapter 1. Understanding Performant Python QUESTIONS YOU’LL BE ABLE TO ANSWER AFTER THIS CHAPTER What are the elements of a computer’s architecture? What are some common alternate computer architectures? How does Python abstract the underlying computer architecture? What are some of the hurdles to making performant Python code? What strategies can help you become a highly performant programmer? Programming computers can be thought of as moving bits of data and transforming them in special ways to achieve a particular result. However, these actions have a time cost. Consequently, high performance programming can be thought of as the act of minimizing these operations either by reducing the overhead (i.e., writing more efficient code) or by changing the way that we do these operations to make each one more meaningful (i.e., finding a more suitable algorithm). Let’s focus on reducing the overhead in code in order to gain more insight into the actual hardware on which we are moving these bits. This may seem like a futile exercise, since Python works quite hard to abstract away direct interactions with the hardware. However, by understanding both the best way that
- 41. bits can be moved in the real hardware and the ways that Python’s abstractions force your bits to move, you can make progress toward writing high performance programs in Python. The Fundamental Computer System The underlying components that make up a computer can be simplified into three basic parts: the computing units, the memory units, and the connections between them. In addition, each of these units has different properties that we can use to understand them. The computational unit has the property of how many computations it can do per second, the memory unit has the properties of how much data it can hold and how fast we can read from and write to it, and finally, the connections have the property of how fast they can move data from one place to another. Using these building blocks, we can talk about a standard workstation at multiple levels of sophistication. For example, the standard workstation can be thought of as having a central processing unit (CPU) as the computational unit, connected to both the random access memory (RAM) and the hard drive as two separate memory units (each having different capacities and read/write speeds), and finally a bus that provides the connections between all of these parts. However, we can also go into more detail and see that the CPU itself has several memory units in it: the L1, L2, and sometimes even the L3 and L4 cache, which have small capacities but very fast speeds (from several kilobytes to a dozen megabytes). Furthermore,
- 42. new computer architectures generally come with new configurations (for example, Intel’s SkyLake CPUs replaced the frontside bus with the Intel Ultra Path Interconnect and restructured many connections). Finally, in both of these approximations of a workstation we have neglected the network connection, which is effectively a very slow connection to potentially many other computing and memory units! To help untangle these various intricacies, let’s go over a brief description of these fundamental blocks. Computing Units The computing unit of a computer is the centerpiece of its usefulness—it provides the ability to transform any bits it receives into other bits or to change the state of the current process. CPUs are the most commonly used computing unit; however, graphics processing units (GPUs) are gaining popularity as auxiliary computing units. They were originally used to speed up computer graphics but are becoming more applicable for numerical applications and are useful thanks to their intrinsically parallel nature, which allows many calculations to happen simultaneously. Regardless of its type, a computing unit takes in a series of bits (for example, bits representing numbers) and outputs another set of bits (for example, bits representing the sum of those numbers). In addition to the basic arithmetic operations on integers and real numbers and bitwise operations on binary numbers, some computing units also provide very specialized operations, such
- 43. as the “fused multiply add” operation, which takes in three numbers, A, B, and C, and returns the value A * B + C. The main properties of interest in a computing unit are the number of operations it can do in one cycle and the number of cycles it can do in one second. The first value is measured by its instructions per cycle (IPC), while the latter value is measured by its clock speed. These two measures are always competing with each other when new computing units are being made. For example, the Intel Core series has a very high IPC but a lower clock speed, while the Pentium 4 chip has the reverse. GPUs, on the other hand, have a very high IPC and clock speed, but they suffer from other problems like the slow communications that we discuss in “Communications Layers”. Furthermore, although increasing clock speed almost immediately speeds up all programs running on that computational unit (because they are able to do more calculations per second), having a higher IPC can also drastically affect computing by changing the level of vectorization that is possible. Vectorization occurs when a CPU is provided with multiple pieces of data at a time and is able to operate on all of them at once. This sort of CPU instruction is known as single instruction, multiple data (SIMD). In general, computing units have advanced quite slowly over the past decade (see Figure 1-1). Clock speeds and IPC have both been stagnant because of the physical limitations of making transistors smaller and smaller. As a result, chip 1
- 44. manufacturers have been relying on other methods to gain more speed, including simultaneous multithreading (where multiple threads can run at once), more clever out-of-order execution, and multicore architectures. Hyperthreading presents a virtual second CPU to the host operating system (OS), and clever hardware logic tries to interleave two threads of instructions into the execution units on a single CPU. When successful, gains of up to 30% over a single thread can be achieved. Typically, this works well when the units of work across both threads use different types of execution units—for example, one performs floating-point operations and the other performs integer operations. Out-of-order execution enables a compiler to spot that some parts of a linear program sequence do not depend on the results of a previous piece of work, and therefore that both pieces of work could occur in any order or at the same time. As long as sequential results are presented at the right time, the program continues to execute correctly, even though pieces of work are computed out of their programmed order. This enables some instructions to execute when others might be blocked (e.g., waiting for a memory access), allowing greater overall utilization of the available resources. Finally, and most important for the higher-level programmer, there is the prevalence of multicore architectures. These architectures include multiple CPUs within the same unit, which increases the total capability without running into barriers to
- 45. making each individual unit faster. This is why it is currently hard to find any machine with fewer than two cores—in this case, the computer has two physical computing units that are connected to each other. While this increases the total number of operations that can be done per second, it can make writing code more difficult! Figure 1-1. Clock speed of CPUs over time (from CPU DB) Simply adding more cores to a CPU does not always speed up a program’s execution time. This is because of something known as Amdahl’s law. Simply stated, Amdahl’s law is this: if a program designed to run on multiple cores has some subroutines that must run on one core, this will be the limitation for the maximum speedup that can be achieved by allocating more cores. For example, if we had a survey we wanted one hundred people to fill out, and that survey took 1 minute to complete, we could complete this task in 100 minutes if we had one person asking the questions (i.e., this person goes to participant 1, asks the questions, waits for the responses, and then moves to participant 2). This method of having one person asking the questions and waiting for responses is similar to a serial process. In serial processes, we have operations being satisfied one at a time, each one waiting for the previous operation to complete. However, we could perform the survey in parallel if we had two people asking the questions, which would let us finish the
- 46. process in only 50 minutes. This can be done because each individual person asking the questions does not need to know anything about the other person asking questions. As a result, the task can easily be split up without having any dependency between the question askers. Adding more people asking the questions will give us more speedups, until we have one hundred people asking questions. At this point, the process would take 1 minute and would be limited simply by the time it takes a participant to answer questions. Adding more people asking questions will not result in any further speedups, because these extra people will have no tasks to perform—all the participants are already being asked questions! At this point, the only way to reduce the overall time to run the survey is to reduce the amount of time it takes for an individual survey, the serial portion of the problem, to complete. Similarly, with CPUs, we can add more cores that can perform various chunks of the computation as necessary until we reach a point where the bottleneck is the time it takes for a specific core to finish its task. In other words, the bottleneck in any parallel calculation is always the smaller serial tasks that are being spread out. Furthermore, a major hurdle with utilizing multiple cores in Python is Python’s use of a global interpreter lock (GIL). The GIL makes sure that a Python process can run only one instruction at a time, regardless of the number of cores it is currently using. This means that even though some Python code has access to multiple cores at a time, only one core is
- 47. running a Python instruction at any given time. Using the previous example of a survey, this would mean that even if we had 100 question askers, only one person could ask a question and listen to a response at a time. This effectively removes any sort of benefit from having multiple question askers! While this may seem like quite a hurdle, especially if the current trend in computing is to have multiple computing units rather than having faster ones, this problem can be avoided by using other standard library tools, like multiprocessing (Chapter 9), technologies like numpy or numexpr (Chapter 6), Cython (Chapter 7), or distributed models of computing (Chapter 10). NOTE Python 3.2 also saw a major rewrite of the GIL, which made the system much more nimble, alleviating many of the concerns around the system for single-thread performance. Although it still locks Python into running only one instruction at a time, the GIL now does better at switching between those instructions and doing so with less overhead. Memory Units Memory units in computers are used to store bits. These could be bits representing variables in your program or bits representing the pixels of an image. Thus, the abstraction of a memory unit applies to the registers in your motherboard as well as your RAM and hard drive. The one major difference between all of these types of memory units is the speed at which they can read/write data. To make things more
- 48. complicated, the read/write speed is heavily dependent on the way that data is being read. For example, most memory units perform much better when they read one large chunk of data as opposed to many small chunks (this is referred to as sequential read versus random data). If the data in these memory units is thought of as pages in a large book, this means that most memory units have better read/write speeds when going through the book page by page rather than constantly flipping from one random page to another. While this fact is generally true across all memory units, the amount that this affects each type is drastically different. In addition to the read/write speeds, memory units also have latency, which can be characterized as the time it takes the device to find the data that is being used. For a spinning hard drive, this latency can be high because the disk needs to physically spin up to speed and the read head must move to the right position. On the other hand, for RAM, this latency can be quite small because everything is solid state. Here is a short description of the various memory units that are commonly found inside a standard workstation, in order of read/write speeds: Spinning hard drive Long-term storage that persists even when the computer is shut down. Generally has slow read/write speeds because the disk must be physically spun and moved. Degraded 2
- 49. performance with random access patterns but very large capacity (10 terabyte range). Solid-state hard drive Similar to a spinning hard drive, with faster read/write speeds but smaller capacity (1 terabyte range). RAM Used to store application code and data (such as any variables being used). Has fast read/write characteristics and performs well with random access patterns, but is generally limited in capacity (64 gigabyte range). L1/L2 cache Extremely fast read/write speeds. Data going to the CPU must go through here. Very small capacity (megabytes range). Figure 1-2 gives a graphic representation of the differences between these types of memory units by looking at the characteristics of currently available consumer hardware. A clearly visible trend is that read/write speeds and capacity are inversely proportional—as we try to increase speed, capacity gets reduced. Because of this, many systems implement a tiered approach to memory: data starts in its full state in the hard drive, part of it moves to RAM, and then a much smaller subset moves to the L1/L2 cache. This method of tiering enables programs to keep memory in different places depending on access speed requirements. When trying to optimize the memory patterns of a program, we are simply
- 50. optimizing which data is placed where, how it is laid out (in order to increase the number of sequential reads), and how many times it is moved among the various locations. In addition, methods such as asynchronous I/O and preemptive caching provide ways to make sure that data is always where it needs to be without having to waste computing time—most of these processes can happen independently, while other calculations are being performed!
- 51. Figure 1-2. Characteristic values for different types of memory units (values from February 2014) Communications Layers
- 52. Finally, let’s look at how all of these fundamental blocks communicate with each other. Many modes of communication exist, but all are variants on a thing called a bus. The frontside bus, for example, is the connection between the RAM and the L1/L2 cache. It moves data that is ready to be transformed by the processor into the staging ground to get ready for calculation, and it moves finished calculations out. There are other buses, too, such as the external bus that acts as the main route from hardware devices (such as hard drives and networking cards) to the CPU and system memory. This external bus is generally slower than the frontside bus. In fact, many of the benefits of the L1/L2 cache are attributable to the faster bus. Being able to queue up data necessary for computation in large chunks on a slow bus (from RAM to cache) and then having it available at very fast speeds from the cache lines (from cache to CPU) enables the CPU to do more calculations without waiting such a long time. Similarly, many of the drawbacks of using a GPU come from the bus it is connected on: since the GPU is generally a peripheral device, it communicates through the PCI bus, which is much slower than the frontside bus. As a result, getting data into and out of the GPU can be quite a taxing operation. The advent of heterogeneous computing, or computing blocks that have both a CPU and a GPU on the frontside bus, aims at reducing the data transfer cost and making GPU computing
- 53. more of an available option, even when a lot of data must be transferred. In addition to the communication blocks within the computer, the network can be thought of as yet another communication block. This block, though, is much more pliable than the ones discussed previously; a network device can be connected to a memory device, such as a network attached storage (NAS) device or another computing block, as in a computing node in a cluster. However, network communications are generally much slower than the other types of communications mentioned previously. While the frontside bus can transfer dozens of gigabits per second, the network is limited to the order of several dozen megabits. It is clear, then, that the main property of a bus is its speed: how much data it can move in a given amount of time. This property is given by combining two quantities: how much data can be moved in one transfer (bus width) and how many transfers the bus can do per second (bus frequency). It is important to note that the data moved in one transfer is always sequential: a chunk of data is read off of the memory and moved to a different place. Thus, the speed of a bus is broken into these two quantities because individually they can affect different aspects of computation: a large bus width can help vectorized code (or any code that sequentially reads through memory) by making it possible to move all the relevant data in one transfer, while, on the other hand, having a small bus width but a very high frequency of transfers can help code that must
- 54. do many reads from random parts of memory. Interestingly, one of the ways that these properties are changed by computer designers is by the physical layout of the motherboard: when chips are placed close to one another, the length of the physical wires joining them is smaller, which can allow for faster transfer speeds. In addition, the number of wires itself dictates the width of the bus (giving real physical meaning to the term!). Since interfaces can be tuned to give the right performance for a specific application, it is no surprise that there are hundreds of types. Figure 1-3 shows the bitrates for a sampling of common interfaces. Note that this doesn’t speak at all about the latency of the connections, which dictates how long it takes for a data request to be responded to (although latency is very computer-dependent, some basic limitations are inherent to the interfaces being used).
- 55. Another Random Document on Scribd Without Any Related Topics
- 56. Thence passing into the Piazza del Gesù, we can visit the CHURCH OF THE JESUITS (Il Gesu), one of the finest in Rome. Its interior is rich in stuccoes, paintings, and sculptures. The frescoes of the tribune, the dome, and the roof are by Baciccio. The Chapel of S. Ignatius is very fine; the columns and ball over the altar are composed of lapis-lazuli. Beneath the altar, in an urn of gilt bronze, is the body of the saint. The small circular chapel close by is rich in paintings and stained-glass windows. It is well worth a visit there to hear mass, vespers, or one of the fathers preaching. The wind generally blows in the piazza, which is thus accounted for. One day the wind and the devil were out for a ramble; and, on arriving at this square, the old gentleman asked the wind to stop a moment while he went into the church. The wind is still stopping for the devil, who has not yet come out. The Via Cesarini, down the new Corso Vittorio Emanuele, leads to the Piazza of S. Nicola a Cesarini. In the court of No. 56 is THE TEMPLE OF CASTOR. The remains show that it was a circular building. It stood near the Flaminian Circus. (Vitruvius, iv. 7.) Four fluted tufa columns exist. From Piazza del Gesù we proceed up Via Ara Cœli. Before us is THE CAPITOLINE HILL. It was originally called the Hill of Saturn (Dionysius, ii. 1), being occupied by Romulus as a defence for the Palatine Hill (Plutarch, in "Rom."), and was betrayed to the Sabines by Tarpeia, the daughter
- 57. of the commandant of the fortress (Livy, i. 11). When the Palatine and Capitoline Hills were united into one city, and the two kings reigned together, the name of the hill was changed and called the Tarpeian Hill. In the 138th year after the foundation of Rome, when Tarquin the Great was making the foundations for the great Temple of Jupiter, they found a human head; and the oracle told them that the spot where the head was found should become the head of the world; and so they changed the name of the hill again, and called it the Capitoline Hill,—from caput, a head (Livy, i. 55; Pliny, xxviii. 4). The whole hill was the Arx or Citadel of Rome, just the same as at Athens, Veii, Tusculum, &c. Several ancient authors agree in this. The shape of the hill is a saddle-back,—the centre being depressed, with an eminence at each end. The one on our left is known as the Ara Cœli height, and the one on our right as the Caffarella height. On the Ara Cœli height stood the great Temple of Jupiter, facing south, and approached from the Area Capitolina (Piazza del Campidoglio) by a flight of steps. On the opposite or Caffarella height stood the Temple of Juno Moneta or the Mint, and the Temple of Concord, both built by Camillus; and the Temple of Jupiter Feretrius, founded by Romulus. Many other temples, altars, and shrines occupied the space inside the citadel, which was approached by three ascents upon its eastern side,—the Clivus Capitolinus, the Pass of the Two Groves, and the Hundred Steps. The ascents upon its western side date from 1348, when the marble stairs on our left, leading up to the Ara Cœli, were erected out of the stairs that led up to the Temple of Quirinus (Romulus) upon the Quirinal Hill. The ascent to the Square was made in 1536 for the entry of Charles V. The roadway on its right is quite recent. In forming it some remains of the tufa walls that protected the arx on this side were found, and can still be seen inside the iron gate. On the balustrade at the bottom of the ascent to the Capitol are two Egyptian lionesses. At the top of the ascent are two colossal statues of Castor and Pollux, found in the Ghetto, and by their side are the miscalled Trophies of Marius. They belonged to the decorations of the Nymphæum of Alexander Severus, the picturesque ruins of
- 58. which are on the Esquiline Hill, and which are represented on a coin. They were placed upon the balustrade of the Capitol, their present site, by Pope Sixtus V. Originally they formed part of the ornamentation of the Basilica Ulpia, and were erected in honour of Trajan by the Apollinarian and Valerian legions. Next to the trophies are two statues of Cæsar and Augustus Constantine; and in the same row, on the left, the stone that marked the seventh and, on the right, the stone that marked the first mile on the Via Appia. In the centre of the Square is THE EQUESTRIAN STATUE OF MARCUS AURELIUS, the finest piece of bronze work of ancient times. It now stands upon the Square of the Capitol, where it was erected by Michael Angelo in 1538. Before that, it stood at the Lateran, where it had been placed in 1187, having been taken from near the Column of Phocas in the Forum. It belongs to the canons of the Lateran, who receive yearly, in the shape of a bouquet of flowers, a peppercorn rent for it from the mayor of Rome. It is said that Michael Angelo on passing by used to say, "Gee up, cammina;" and that the horse had only to plant the raised hoof upon the ground to complete the illusion that it was a living creature. In front of us is the mayor's residence; on the left the Museum of the Capitol; and on the right the halls of the town council. These buildings were erected by Michael Angelo in 1544–1550. The residence for the senator was first erected on the top of the ruins of the Tabularium in 1389–1394 by Pope Boniface IX., but this gave place to the present edifice. The ascent from the Arch of Severus to the Square of the Capitol was anciently the Pass of the Two Groves. At the top of the pass was the Gate of Janus, the gate of the citadel, betrayed by Tarpeia. The ascent from the Forum, on our right, was the Clivus Capitolinus, a continuation of the Via Sacra. It is only at its termination that the
- 59. present road is on the site of the ancient slope, where some of the pavement may still be seen. The gate which here gave access to the arx was called the Gate of Saturn. On the right of the old museum some steps lead up to THE CHURCH OF ARA CŒLI. The nave is formed by twenty-two columns, the spoils of ancient buildings. The third one on the left has engraved upon it— A CVBICVLO AVGVSTORVM, showing that it came from the Palatine Hill. At the end of the nave are two Gothic ambones with mosaic work. The altar urn of red porphyry formerly, it is said, contained the body of Constantine's mother. This church is rendered famous as being the place where, on the 15th of October 1764, Gibbon "sat musing amidst the ruins of the Capitol, and conceived the idea of writing the 'Decline and Fall of the Roman Empire.'"
- 60. VIEW OF THE CAPITOL. View larger image. The church is the residence of the celebrated Santissimo Bambino, carved out of a tree from the Mount of Olives, and painted by S. Luke. This image is highly decorated with jewellery, and has a two- horse carriage at its disposal, with coachmen and footmen, when it pays a visit to the sick. "As thy faith, so be it unto thee." Apply at the sacristy to see it. The floor of the church is of the kind called opus-Alexandrinum, tesselated mosaic, and slab tombs of medieval period. A grand ceremony is held here on Christmas day, and at the Epiphany children recite the story of Christ. In the left transept an isolated octagonal chapel, dedicated to S. Helena, is said by the church authorities to stand on the site of an altar erected by Augustus—Ara primogeniti Dei—to commemorate the Cumæan sibyl's prophecy of the coming of the Saviour. Its present name is traceable to this altar. Some traces of Gothic can be seen in the walls and windows of this church, which stands on the site of THE TEMPLE OF JUPITER CAPITOLINUS. "It stood upon a high rock, and was 800 feet in circuit, each side containing near 200; the length does not exceed the width by quite 15 feet. For the temple that was built in the time of our fathers, upon the same foundations with the first, which was consumed by fire, is found to differ from the ancient temple in nothing but in magnificence and the richness of the materials, having three rows of columns in the south front, and two on each side. The body is divided into three temples, parallel to one another, the partition walls forming their common sides. The middle temple is dedicated to Jupiter; and on one side stands that of Juno, and on the other that of Minerva. And all three have but one pediment and one roof." (Dionysius, iv. 61. See also Tacitus, "Hist." iii. 72; Livy, i. 55; Plutarch, in "Publicola;" Tacitus, "Hist." iv. 53.)
- 61. TEMPLE OF JUPITER CAPITOLINUS. View larger image. Four different temples have been erected on this site, and now it is occupied by a Christian church. The first, built by Tarquinius Superbus, and consecrated by Horatius the consul, was burned in the civil war. The second, erected by Sylla, and consecrated by Catulus, was destroyed under Vitellius. The third, erected by Vespasian, was burned before it was consecrated. The fourth was built by Domitian. Access is now to be had to some curious vaults below the convent, which were formerly closed by the monks. Supporting these vaults are some remains of massive tufa walls—one piece in particular being about 36 feet long and 8 feet high—consisting of single blocks of stone, of which the other fragments seem to be continuations. These appear to have been built originally as substructions, and run parallel with the Via Marforio, and could not have been part of the city wall, for that is within the city of the two hills. Nibby records that tufa walls remain under the stairs leading up to the Ara Cœli Church. We think them to be part of the foundations of the celebrated Temple of Jupiter Capitolinus. We may mention that among the rubbish contained in the vaults of the convent are two slender columns of Pentelic marble. May not these have belonged to the temple? The strongest evidence of the position of the Temple of Jupiter "supremely good and great" is pictorial. We have it represented on the relief in the Palazzo dei Conservatori which formed part of the Arch of Marcus Aurelius. That emperor is there, after a victory, offering sacrifice upon the Capitoline Hill; and in the background is a representation of the Temple of Jupiter Capitolinus: it has three doors,
- 62. and the figures of Minerva, Jupiter, and Juno. This is to the spectator's left, and faces south, as we are told the temple faced. This relief is further corroborated by another in the Louvre, in the background of which is likewise a representation of a temple of the Corinthian order, facing the same way and to the left of the spectator, and having over the door the words Iovi Capitolinus. Upon a relief in the Capitol Museum, another building appears upon a lower level, ornamented with pilasters, having Doric capitals. This building corresponds with the front of the Tabularium towards the Capitol. To the right of the Palazzo dei Conservatori (New Museum) a road, through a gate, leads to the German Embassy. In the garden Bunsen found the remains of the Temple of Jupiter Feretrius, which have lately been covered in; but a fine piece of the wall of the Temple of Juno may yet be seen. By applying at the Embassy, permission will be given to enter the garden. TEMPLE OF JUPITER FERETRIUS (The Trophy-Bearer). The first temple built in Rome by Romulus, to receive the spoils captured from Acron, King of Cænina. "After the procession and sacrifice, Romulus built a small temple, on the top of the Capitoline Hill, to Jupiter, whom the Romans call Feretrius. For the ancient traces of it still remain, of which the longest sides are less than fifteen feet" (Dionysius, ii. 34. See Livy, i. 10). It was enlarged A.U.C. 121 (Livy, i. 33); and was repaired by Augustus on the advice of Atticus (Nepos. See Livy, iv. 20). Opposite the gate leading into the garden we can look over the parapet, down the scarped rock, to the base beneath, which is reached from below by taking the Via Tor dei Specchi on the right, looking towards the Capitol, and the Vicolo Rupe Tarpeia on the left.
- 63. TARPEIAN ROCK. View larger image. It was here that the terrible scene described in Hawthorne's "Transformation" took place. The road leads to the New German Archæological Institute. It was about here that the messenger from Veii got into the citadel, and where the Gauls tried to do the same, when the sacred geese in Juno's temple awoke the garrison. The two bronze "geese" shown in the Hall of the Conservators are ducks. Passing on under the archway, turn to the left; at a little distance the Via Monte Tarpeia turns off to the right—follow this; at the end, the house facing us is built up against the point of the hill used for the public executions. THE TARPEIAN ROCK. After the name of the hill was changed for the last time, one part, we are told, retained the name of the Tarpeian Rock, from being the burial-place of Tarpeia, and the spot from which the traitors were hurled off in sight of the people assembled in the Forum. The house in front of us is built upon a ledge of the rock below, and has upon it the following inscription:— "Hinc ad Tarpeiam sedem, et Capitolia ducit, Aurea nunc, olim, silvestribus horrida dumis." Virgil, Æn. viii. 347. GREGORIUS XIII. PONT. MAX. VIAM TARPEIAM APERINT HIER. ALTERIUS AEDILIS SECUNDO } CURABANT PAULUS BUBALUS AEDILIS SEXTO } ANNO DOMINI MDLXXXI.
- 64. "The quæstors led the man [Spurius Cassius] to the top of the precipice that commands the Forum, and in the presence of all the citizens threw him down from the rock. For this was the established punishment at that time among the Romans for those who were condemned to die"—A.U.C. 269—(Dionysius, viii. 78). If we look back up the street we came down, the height will be seen in the garden above us. It must be remembered that the top of the hill has been levelled, and the valley below filled in thirty feet; allowing for this there would have been a fall of upwards of 160 feet. The steps on our left formed the third ancient approach to the arx, the Centum Gradus, up which the Vitellians climbed when they took the citadel. On the site of the garden above stood CAMILLUS'S TEMPLES TO CONCORD AND JUNO. The first Temple of Concord of which we have any notice was that dedicated by Camillus, A.U.C. 388. "When the dictator was one day sitting on the tribunal in the Forum, the people called out to drag him from his seat; but he led off the patricians to the senate house. Previous to his entering it he turned towards the Capitol [this shows that the senate house was not on the Capitol, as some would have us believe; for if so, he would not have turned towards the Capitol before entering the senate house— he would have already faced it], and besought the gods to put a happy end to the present disturbances, vowing to build a temple to Concord when the tumult should be appeased.... Next day they assembled and voted that the temple which Camillus had vowed to Concord should, on account of this great event, be built upon a spot viewing from a height the Forum and place of assembly" (Plutarch, in "Camillus"). Ovid, speaking of the same temple ("Fasti," i. 640), says: "Fair Concord, the succeeding day places thee in a snow-white shrine, near where elevated Moneta raises her steps on high: now with ease wilt thou look down upon the Latin crowd. Now have the august hands of Cæsar restored thee,"—referring to its rebuilding by
- 65. Tiberius, A.D. 11. From both these authors we learn that it had a commanding prospect, and Ovid adds that it was near the Temple of Moneta, which was likewise founded by Camillus, A.U.C. 411, as we learn from Livy (vii. 28, and vi. 20. See Plutarch). "The site chosen was that spot in the Citadel where the house of Manlius had stood." The site of the Temple of Concord was on the Tarpeian Rock, at the top of the Centum Gradus, and Camillus's Temple of Moneta was near it. Livy (xxvi. 23) says: "In A.U.C. 542, at the Temple of Concord, a statue of Victory, which stood on the summit of the roof, being struck by lightning, and shaken at its base, fell and stuck among the ensigns of the goddess which were on the pediment." This temple, with a statue of Victory upon the summit, is represented on a coin of Tiberius, who restored it. Under the wall, on our left, which supports the garden, some blocks of tufa, in situ, are the remains of the Temple of Concord, and the wall in the garden of the German Embassy is part of the Temple of Juno. Passing down the street on our right, a left half-turn will bring us to the old entrance of THE TABULARIUM. (Public Record Office.) Open every day from 10 till 3; fee, half lira. We have now to speak of a building, the vast remains of which impress us with the grandeur of the later republic. In the year of the city 675 (B.C. 78) a building was erected against the Capitoline Hill, and facing the Forum, to contain the public records, which were engraved on bronze plates. Before that time they had been kept in various temples.
- 66. "A decree was made by the senate that the records should be kept in the Temple of Ceres with the public ædiles"—A.U.C. 306—(Livy, iii. 55). "Treaties (such as between Pyrrhus and Rome) were then usual, and the ædiles had them in their keeping in the Temple of Jupiter Capitolinus, engraved on plates of copper" (Polybius, iii.). That this was the usual way of keeping the records we learn from the same author, who saw and copied those which "Hannibal left at Lacinium—engraved tablets or records on copper of the events of his stay in Italy." "The censors went up immediately to the Temple of Liberty, where they sealed the books of the public records, shut up the office, and dismissed the clerks, affirming that they should do no kind of public business until the judgment of the people was passed on them"— A.U.C. 686—(Livy, xliii. 16). We have no mention in classic history as to when this building was erected, but fortunately an inscription has been handed down to us, in which Quintus Lutatius Catulus (who dedicated the temple to Jupiter Capitolinus) is expressly named, not only as the founder of the Tabularium, but also of the substructions, the most difficult portion of the whole, and which claim our fullest admiration. Q . LVTATIVS . Q. F. Q. N. CATVLVS . COS . SVBSTRVCTIONEM . ET . TABVLARIVM . EX . SEN . SENT . FACIENDVM . COERAVIT . EADEMQVE . PROBAVIT . The remains form the substructions of the present Capitol, or senator's residence, consisting of a massive wall of Gabii stone 240 feet long and 37 feet high, supporting the portico on the side of the Forum, which consisted of a series of arches, 23 feet by 15 feet, ornamented with sixteen Doric columns. Below this portico or arcade are a series of small chambers, with windows looking into the Forum, opening out of one another, approached by a short flight of steps, and probably used to store the records. At the back of the
- 67. arcade are a series of large vaulted rooms or offices. At one end a grand flight of steps (repaired) leads up into what has been a grand arcade on the side of the Area Capitolina: its piers now partly sustain the modern building. At the farther end of this arcade is a flight of steep travertine steps, sixty-seven in number, leading down into the Forum, the exit to which has been blocked up by the Temple of Vespasian being built against the entrance. This building must have presented a grand front to the Forum in the olden time, though now it only sustains the buildings of Michael Angelo. In 1389–1394, Pope Boniface IX. first erected on the Capitoline Hill, on the ruins of the Tabularium, a residence for the senator and his assessors. The prospect was altered so that what was the front became the back, and it faced on to what was anciently the Area Capitolina, now the Piazza del Campidoglio, instead of the Forum. The north side wall seems to have been cut down when the present edifice was erected, as outside the present wall are the remains of the ancient one; thus it was somewhat longer than we now see it. In the sort of vestibule which gives admittance to the chambers under the portico are remains of stairs, evidently leading up to some chambers above the portico. These were probably not very lofty, so that the view of the temples on the hill was not shut out from the Forum, or perhaps they only led up to the flat roof above the arcade. These old remains have been used as a prison and as a salt store, which latter has eaten the stone away in a curious manner. It is now used as a museum of fragments. The arches of the portico were filled in when the great master utilized it. Although we know an arch is as strong as a wall, it is feared to open them, and one only has been so treated. Suetonius tells us: "Vespasian undertook to restore the three thousand tablets of brass which had been destroyed in the fire which consumed the Capitol; searching in all quarters for copies of those curious and ancient records, in which were contained the decrees of
- 68. the senate almost from the building of the city, as well as the acts of the people relative to alliances, treaties, and privileges granted to any person" (Vespasian, viii.). Pliny (xxxiv. 21) says: "It is upon tablets of brass that our public enactments are engraved." From the Tabularium a new iron stair leads up to THE TOWER OF THE CAPITOL, whence a fine view of Rome and its environs can be enjoyed, standing, as it were, between ancient and medieval Rome. It is the best position for study in the world. From this height the huge mass of the Colosseum appears elegant and light. The famous Seven Hills may be made out, notwithstanding the alteration in the soil: on the left is the Quirinal, beyond that the Viminal, and beyond that the Esquiline; to the extreme right is the Aventine; before us is the Palatine, with the Cœlian beyond it; whilst we occupy the Capitoline. The contemplation of the city, however, produces the effect of a vast and solid reading of history. Each of the great representations of the city, always and differently mistress of the world, seems to have chosen its respective quarter—the Rome of the kings and emperors is spread out on the Palatine, Esquiline, and Quirinal; republican Rome occupies the Capitol and Aventine; whilst Christian Rome, isolated and solitary, reigns on the Cœlian and Vatican eminences. THE SEVEN HILLS OF ROME. The Palatine, which has ever had the preference, whether so-called from the people Palantes, or Palatini, or from the bleating and strolling of cattle, in Latin, balare and palare, or from Pales, the pastoral goddess, or from the burying-place of Pallas, is disputed amongst authors. It was on this hill that Romulus, according to
- 69. popular tradition, laid the foundations of the city, in a quadrangular form. Here Romulus and Tullus Hostilius kept their courts, as did afterwards Augustus, and all the succeeding emperors, on which account the word Palatium came to signify a royal seat (Rosin, "Antiq." i. 4). The Aventine derives its name from Aventinus, an Alban king (Varro, "De Ling. Lat." iv.), or from the river Avens (ibid.), or from Avibus, from the birds which used to fly thither in great flocks from the Tiber (ibid.). It was also called Murcius, from Murcia, the goddess of sleep, who had a temple here (Sextus Pompeius, Festus). Also Collis Dianæ, from the Temple of Diana (Martial). Likewise Remonius, from Remus, who wished the city to be commenced here, and who was buried here (Plutarch, in "Romulus"). This hill was added by Ancus Martius ("Eutropius," i.). The Capitoline, formerly Saturn, then Tarpeian, took its name from Tarpeia, a Roman virgin, who betrayed the city to the Sabines at this point (Plutarch, in "Romulus"). It was also called Mons Saturni and Saturnius, in honour of Saturn, who is reported to have lived here, and was the titular deity of this part of the city. It was afterwards called Capitoline, from the head of a man found here when digging the foundations of the famous Temple of Jupiter. It was added to the city when the Sabines were permitted by Romulus to incorporate themselves with the Romans (Dionysius). The Quirinal was either so called from the Temple of Quirinus, another name of Romulus, or from the Curetes, a people that removed hither with Tatius from Cures, a Sabine city (Sextus Pompeius, Festus). It afterwards changed its name to Caballus, from two marble horses, each having a man holding it, which are still standing, and were the works of Phidias and Praxiteles ("Fabricii Roma," iii.), made to represent Alexander the Great and Bucephalus, and presented to Nero by Tiridates, king of Armenia. Numa added this hill to the city (Dionysius, ii.).
- 70. The Esquiline was anciently called Cispius and Oppius ("Fabricii Roma," 3). The name Esquilinus was varied for the easier pronunciation from Exquilinus, a corruption of Excubinus, ab Excubiis, from the watch that Romulus kept there ("Propert." ii. 8). It was taken in by Servius Tullius, who had his palace here (Livy, i. 44). The Viminal derives its name from Vimina, signifying osiers, which grew here in large quantities. This hill was added by Servius Tullius (Dionysius, iv.). The Cœlian owes its name to Cœlius or Cœles, a famous Tuscan general, who encamped here when he came to assist the Romans against the Sabines (Varro, "De Ling. Lat." iv.). The other names by which it was sometimes known were Querculanus or Querquetulanus, and Augustus: the first, on account of its growth of oaks; and the second, because the Emperor Tiberius built on it after a fire (Tacit. "Ann." iv.; Suet. in "Tib." xlviii.). One part was called Cœliolus, and Minor Cœliolus ("Fabricii Roma," 3). Livy (i. 30) and Dionysius (iii.) attribute the taking of it into the city to Tullus Hostilius, but Strabo ("Georg." v.) to Ancus Martius. Whilst on the subject of the hills of Rome, three others are equally famous. The Janiculum, or Janicularis, so called either from an old town of the same name, said to have been built by Janus, or because Janus dwelt and was buried here (Ovid, "F." i. 246), or because it was a janua, a sort of gate to the Romans, whence they issued out upon the Tuscans (Festus). Its yellow sand gave it the name of Mons Aureus, corrupted into Montorius ("Fabricii Roma," i. 3). From an epigram of Martial, we may observe that it is the fittest place to take one's standing for a full prospect of the city (Martial, "Epig." iv. 64). It is famous for the sepulchres of Numa and Statius the poet ("Fabricii Roma," i. 3), and in more recent times as the grave of Tasso, and the spot where tradition holds that S. Peter was executed.
- 71. The Vatican owes its name to the vates, or prophets, who used to give their answers here, or from the god Vaticanus or Vagitanus (Festus). Formerly celebrated for the Gardens and Circus of Nero, the scene of the Christian martyrdoms, and in our time for S. Peter's and the Vatican. It was enclosed in the time of Aurelian, but was considered as very unhealthy (Tacitus, "H." ii. 93). The Pincio (Collis Hortulorum, or Hortorum) took its name from the gardens of Sallust adjoining it (Rosin, i. 2). It was afterwards called Pincius, from the Pincii, a noble family who had their seat here (ibid.). Aurelian first enclosed it (ibid.). The Capitol tower is crowned by a statue of Roma; and the great bell formerly announced, by a strange contrast, the death of the Pope and the opening of the Carnival. Passing up into the square, in facing the Capitol, on the right, is the PALAZZO DEI CONSERVATORI. (New Capitoline Museum.) Open every day. Fee, half lira. The principal objects in the Courtyard are, right:— 1. Statue of Julius Cæsar; the only authentic portrait of him. 2, 4, 9. Colossal fragments, found near the Basilica of Constantine. Supposed to have belonged to the statue of Apollo brought from Pontus by Lucullus. Square base, which contained the bones of Agrippina the elder. 11. Lion attacking a horse. Found in the river Almo, outside Porta S. Paolo. 12, 14. Captive Kings. 13. Large seated statue of Roma.
- 72. 15. Colossal bronze head of a colossal statue of Apollo, found near the Colosseum. Reliefs of figures representing provinces; and reliefs of military trophies, recently found in the Piazza di Pietra. 28. Statue of the Emperor Augustus. 30. Modern rostral column, with ancient inscription. (See page 26.) STAIRCASE AND LANDING. 36. Base Capitolina, an altar dedicated to Hadrian, whose bust it now supports, by the inspectors of the streets. On the sides are engraved the names of the magistrates who presided over the streets, which are named, of five of the fourteen regions into which Rome was divided. It has afforded much useful information to archæologists. 41. Alto-relief which formed part of the Arch of Antoninus Pius, found in the Piazza Sciarra, which spanned the Corso, and was destroyed in 1527. 42, 43, 44. Alto-reliefs, part of the Arch of Marcus Aurelius, which stood at the Via della Vita, in the Corso, and was pulled down in 1665. 45. Curious bas-relief, representing Mettus Curtius, on horseback, floundering in the marsh where is now the Forum. Found near the Church of S. Maria Liberatrice. 49, 50. Alto-reliefs from an arch which stood in the Corso in honour of Antoninus Pius. At the top of the stairs on this floor are several rooms. On passing the turnstile keep straight on. The authorities number these rooms in the reverse way to ours.
- 74. PLAN OF THE PALAZZO DEI CONSERVATORI. NEW CAPITOLINE MUSEUM. View larger image. First Room contains a collection of majolica from the Cini family. Second Room.—The vault is by Caracci. On the right of the door are S. Luke; S. Alexio, by Romanelli; the Virgin, by Andrea Allovisi, called L'Ingegno, pupil of Perugino; S. Cecilia, by Romanelli; S. Mark. On the left are S. John, S. Albertorn, and S. Eustachio, by Romanelli; S. Matthew.
- 75. Third Room, turn left.—Frescoes of the Punic wars by Bonfigli. Fourth Room.—Frescoes from the wars of Scipio, and tapestries from the hospital of S. Michael. Right, the Boys of Falerii scourging their Schoolmaster, B.C. 392 (Livy, v. 27); the Vestal Tuccia, B.C. 144 (Dionysius, ii. 69); Romulus and Remus; busts of Italian patriots. Fifth Room.—Garibaldi Museum. Frescoes of the school of Zuccari, representing games in the Circus Maximus, etc. There is a bust in rosso-antico called Appius Claudius, a bronze bust of Michael Angelo, and other busts. Two ducks in bronze are pointed out as the geese which saved the Capitol. Between them is a curious bronze vase, evidently a female portrait. Copy of Raphael's Holy Family. Sixth Room.—On the wall of this room are preserved the Fasti Consulares, dating from B.C. 481 to the end of the Republic. These fragments were found in the Forum, and faced the podium of the Temple-Tomb of Cæsar. The frescoes are by Benedetto Bonfigli. Seventh Room.—Frescoes: Triumph of Marius, and Defeat of the Cimbri, by Daniele da Volterra. Near the door is a relief, representing the Temple at Jerusalem; and in front of it a team of oxen drawing on a car the molten sea (1 Kings vii. 23; 2 Chron. iv. 2). Eighth Room.—Scenes of the Roman Republic, by Lauretti. Ninth Room.—Frescoes from the history of the kings, by Arpino. Passing through the rooms of the Fasti, from 1540 A.D., we enter the Hall of Busts, comprising statesmen, poets, painters, authors, sculptors, all noted in Italian history. At the end is a monument to Canova. A door on the right opens into the FIRST HALL OF BRONZES. (For numbers, see plan.)
- 76. 1, 2. Cases of small bronze articles found at various times. 3. A bronze biga, or two-horse chariot, with reliefs depicting scenes from the circus; restored upon a wooden frame, and given by Signor A. Castellani. 4. A bisellium, or chair of state. 8. Lectica, or sedan chair. "These infirmities caused him [Claudius] to be carried in a close chair, which no Roman had ever used before; and from thence have the emperors and the rest of us consular men taken the custom of using chairs of that sort, for neither Augustus nor Tiberius used anything but small litters, which are still in fashion for the women" (Dion Cassius). 9, 10. Shelves containing household utensils, &c. 11. Fragments of columns of Bigio marble. ROOM OF COINS. The beautiful alabaster pavement of this room was found, as now fixed, upon the Esquiline Hill, on Christmas eve, 1874. It formed part of the House of the Larmæ, where the statues were found. The coins formed part of the Campana Collection, and are of great value. The small case of gems is worth looking into; it contains some fragments not unlike the Portland vase, white reliefs on a blue ground. We now enter the new OCTAGONAL HALL. (The order is liable to alteration, as objects are constantly being added.) This museum is formed of the remains found in the excavations of the municipality since Rome was made the capital of united Italy. The new circular hall, designed by Signor Vespignani, presents a light and elegant effect. Amongst the most important subjects placed in the new hall, we may mention No. 2, the monument of Quintus Sulpicius Maximus, found in 1870 in the Old Porta Salaria. The inscription states that he died at the early age of thirteen years,
- 77. five months, and twelve days. He carried off the honours for composing Greek verse against fifty-two competitors. The poem is engraved on the pilasters. The subject is—The arguments used by Jove in reproving Phœbus for intrusting his chariot to Phaeton. Africa's deserts and the negroes' black skins are ascribed to the careless driving of Phaeton on that occasion. No. 5. Venus. 23. Mercury. 11. A bust of Faustina the elder. 13. A youth anointing himself. 14 and 16. Tritons. 15. A half statue of the Emperor Commodus as Hercules, beautifully executed in fine marble, with the lion's skin over his head and knotted upon his chest: in his right hand is the club. A bracket of marble, ornamented at its end with a celestial globe, rested on the pedestal, which formed a shield, a band running round the centre with the signs of the zodiac. This bracket is supported by two kneeling figures, holding cornucopias containing fruit. One is in good preservation; the fragments of the other were also found. 17. Plotina, wife of Trajan. 18. Apollo. 19. Bacchus, with a satyr on a leopard at his side. 21. Sarcophagus of the Calydonian boar hunt. Polyhymnia. 24. Terpsichore. 26. A beautiful nude statue of a young girl or nymph leaving the bath, of Parian marble, standing with sandalled feet by a pedestal, which supports her robe, the left hand fastening up the hair. 28, 29. Two magistrates about to start the racers by dropping a handkerchief. They represent L. A. A. Symmachus, prefect of Rome, A.D. 365, and his son; and are unique. The father was found in one hundred and eighty pieces, and the son in ninety pieces, which have been carefully put together. 31. Colossal statue. 33. Fortune. Apollo with the Lyre. Relief, forging the Shield of Minerva. 38, 42. Athletes starting for the Race. 40a. A Cow. 44. Manlia Scantilla. Marsyas bound to the tree; the finest statue in the collection, found in 1879. 48. Didia Clara. 49a. A Roman General; a striking statue. 8. The Earth; a sitting statuette in a niche found in the Roman Cemetery. 9. A Baccante. In the inner circle.—A magnificent marble vase, found upon the Esquiline, called by the Greeks a Rhyton: it is the work of Pontios, an Athenian sculptor. A vase with figures in relief. The infant Hercules
- 78. found at the Cemetery of S. Lorenzo. Another vase. The Muse of Astronomy. Exit. 74, 75. Hercules taming the Horses: part of a group found in many fragments, and very skilfully put together. Seated statue of a girl. 133. Minerva. 130. A statue of Silenus, which was formerly a fountain. A youth carrying a pig for sacrifice. Cupid playing with a tortoise. 123. Boy with a puppy. 81. Statuette of Venus. 81a. A Sleeping Cupid. 124. A large stone shield sculptured with the acanthus leaf. 90. Mithras slaying the Bull. 117, 105, 106. Reliefs relating to the worship of the Persian sun-god Mithras, recently found on the Esquiline Hill. Crossing the Hall of Busts, by Canova's Monument, we enter the TERRA-COTTA ROOM, composed of remains found chiefly in the excavations in building the new quarter of Rome upon the Esquiline Hill. The principal objects are:—A coffin containing skulls; a large jar containing a leaden case, in which is enclosed a beautiful alabaster urn; a large and varied collection of Roman lamps, glass, and terra-cotta; also glass in various forms, and for windows, pieces of fresco, &c. A door on the left leads into the SECOND HALL OF BRONZES. In the centre of the first room is the celebrated bronze wolf of the Capitol (1), thus alluded to by Virgil ("Æn." viii. 630):— "By the wolf were laid the martial twins, Intrepid on her swelling dugs they hung: The foster-dam lolled out her fawning tongue: They sucked secure, while, bending back her head, She licked their tender limbs, and formed them as they fed." Cicero (in "Catiline" iii. 8), mentions this object as a small gilt figure of Romulus sucking the teat of a wolf, which was struck by lightning,
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