Python编程：科学计算实用指南

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"Python_scripting_for_computational_science_v2" 本书《Python Scripting for Computational Science》第二版，由Hans Petter Langtangen撰写，是关于如何利用Python进行科学计算的一本优秀教程。作者同时在Simula Research Laboratory和奥斯陆大学的计算机科学系任职。相较于第一版，第二版进行了大量更新、重组和改进，包括更正错误、增加新的内容、改进示例以及更新软件工具，这得益于全球众多热心读者的反馈和贡献。在第二版的改动中，最显著的提升体现在以下几个方面： 1. **引入更多Python基础**：在第二章的初步示例中，读者将更早地接触到Numerical Python数组，即NumPy库的基础知识。此外，书中还介绍了如何使用IPython shell进行交互式计算，利用IPython和Pdb进行脚本调试，以及如何将单一的脚本转化为可复用的模块。这些新增章节（如2.2.5、2.2.6和2.5.3）使得初学者能更快地掌握Python在科学计算中的应用。 2. **扩展数值计算部分**：第四章的数值计算内容得到了大幅扩展，特别是章节4.3.5、4.3.7、4.3.8和4.4。这部分深入探讨了数值方法和算法，如线性代数、微积分和数值积分等，使读者能够处理更复杂的科学问题。 3. **优化第八章内容**：第八章也进行了许多较小的修改，可能涉及数据可视化、数据分析或科学编程的最佳实践，以适应Python生态系统的新发展和技术进步。这本书对想要利用Python进行科学计算的学习者来说是一份宝贵的资源。它不仅涵盖了Python语言的基础，还包括了在科学计算领域常用的数据结构、算法和工具。通过实例和练习，读者可以逐步提高解决问题的能力，并学习如何有效地利用Python进行科学研究。此外，书中强调了代码的可读性和可维护性，这对于任何编程项目都至关重要。结合IPython和相关的科学计算库，如NumPy、SciPy和Matplotlib等，读者能够构建出强大的计算解决方案。总而言之，《Python Scripting for Computational Science》第二版是一本全面而实用的教材，适合从初学者到有一定经验的科研工作者阅读，旨在帮助他们掌握使用Python进行高效计算的技巧和最佳实践。

XVIII Table of Contents

11.1.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525

11.2 Event Bindings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528

11.2.1 Binding Events to Functions with Arguments . . . . . . . 528

11.2.2 A Text Widget with Tailored Keyboard Bindings . . . 530

11.2.3 A Fancy List Widget . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533

11.3 Animated Graphics with Canvas Widgets . . . . . . . . . . . . . . . . . 537

11.3.1 The First Canvas Encounter . . . . . . . . . . . . . . . . . . . . . . 538

11.3.2 Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539

11.3.3 The Mathematical Model Class . . . . . . . . . . . . . . . . . . . 541

11.3.4 The Planet Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543

11.3.5 Drawing and Moving Planets . . . . . . . . . . . . . . . . . . . . . 545

11.3.6 Dragging Planets to New Positions . . . . . . . . . . . . . . . . 547

11.3.7 Using Pmw’s Scrolled Canvas Widget . . . . . . . . . . . . . . 550

11.4 Simulation and Visualization Scripts . . . . . . . . . . . . . . . . . . . . . 552

11.4.1 Restructuring the Script . . . . . . . . . . . . . . . . . . . . . . . . . 553

11.4.2 Representing a Parameter by a Class . . . . . . . . . . . . . . 555

11.4.3 Improved Command-Line Script . . . . . . . . . . . . . . . . . . 569

11.4.4 Improved GUI Script . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570

11.4.5 Improved CGI Script . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571

11.4.6 Parameters with Physical Dimensions . . . . . . . . . . . . . 572

11.4.7 Adding a Curve Plot Area . . . . . . . . . . . . . . . . . . . . . . . 574

11.4.8 Automatic Generation of Scripts . . . . . . . . . . . . . . . . . . 576

11.4.9 Applications of the Tools . . . . . . . . . . . . . . . . . . . . . . . . 577

11.4.10 Allowing Physical Units in Input Files . . . . . . . . . . . . . 582

11.4.11 Converting Input Files to GUIs . . . . . . . . . . . . . . . . . . . 587

12 Tools and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591

12.1 Running Series of Computer Experiments . . . . . . . . . . . . . . . . . 591

12.1.1 Multiple Values of Input Parameters . . . . . . . . . . . . . . 592

12.1.2 Implementation Details . . . . . . . . . . . . . . . . . . . . . . . . . . 595

12.1.3 Further Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600

12.2 Tools for Representing Functions . . . . . . . . . . . . . . . . . . . . . . . . . 604

12.2.1 Functions Deﬁned by String Formulas . . . . . . . . . . . . . 604

12.2.2 A Uniﬁed Interface to Functions . . . . . . . . . . . . . . . . . . 609

12.2.3 Interactive Drawing of Functions . . . . . . . . . . . . . . . . . . 615

12.2.4 A Notebook for Selecting Functions . . . . . . . . . . . . . . . 619

12.3 Solving Partial Diﬀerential Equations . . . . . . . . . . . . . . . . . . . . . 626

12.3.1 Numerical Methods for 1D Wave Equations . . . . . . . . 627

12.3.2 Implementations of 1D Wave Equations . . . . . . . . . . . . 630

12.3.3 Classes for Solving 1D Wave Equations . . . . . . . . . . . . 637

12.3.4 A Problem Solving Environment . . . . . . . . . . . . . . . . . . 643

12.3.5 Numerical Methods for 2D Wave Equations . . . . . . . . 649

12.3.6 Implementations of 2D Wave Equations . . . . . . . . . . . . 652

12.3.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661

Table of Contents XIX

A Setting up the Required Software Environment . . . 663

A.1 Installation on Unix Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663

A.1.1 A Suggested Directory Structure . . . . . . . . . . . . . . . . . . 663

A.1.2 Setting Some Environment Variables . . . . . . . . . . . . . . 664

A.1.3 Installing Tcl/Tk and Additional Modules . . . . . . . . . 665

A.1.4 Installing Python . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666

A.1.5 Installing Python Modules . . . . . . . . . . . . . . . . . . . . . . . 668

A.1.6 Installing Gnuplot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671

A.1.7 Installing SWIG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672

A.1.8 Summary of Environment Variables . . . . . . . . . . . . . . . 672

A.1.9 Testing the Installation of Scripting Utilities . . . . . . . . 673

A.2 Installation on Windows Systems . . . . . . . . . . . . . . . . . . . . . . . . 673

B Elements of Software Engineering . . . . . . . . . . . . . . . . . . . 679

B.1 Building and Using Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679

B.1.1 Single-File Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679

B.1.2 Multi-File Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683

B.1.3 Debugging and Troubleshooting . . . . . . . . . . . . . . . . . . . 684

B.2 Tools for Documenting Python Software . . . . . . . . . . . . . . . . . . 686

B.2.1 Doc Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686

B.2.2 Tools for Automatic Documentation . . . . . . . . . . . . . . . 688

B.3 Coding Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692

B.3.1 Style Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692

B.3.2 Pythonic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . 696

B.4 Veriﬁcation of Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701

B.4.1 Automating Regression Tests . . . . . . . . . . . . . . . . . . . . . 701

B.4.2 Implementing a Tool for Regression Tests . . . . . . . . . . 705

B.4.3 Writing a Test Script . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709

B.4.4 Verifying Output from Numerical Computations . . . . 710

B.4.5 Automatic Doc String Testing . . . . . . . . . . . . . . . . . . . . 714

B.4.6 Unit Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716

B.5 Version Control Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . 718

B.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727

List of Exercises

Exercise 2.1 Become familiar with the electronic documentation . . . . . 31

Exercise 2.2 Extend Exercise 2.1 with a loop . . . . . . . . . . . . . . . . . . . . . 43

Exercise 2.3 Find ﬁve errors in a script . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Exercise 2.4 Basic use of control structures . . . . . . . . . . . . . . . . . . . . . . . 43

Exercise 2.5 Test for speciﬁc exceptions . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Exercise 2.6 Use standard input/output instead of ﬁles . . . . . . . . . . . . . 45

Exercise 2.7 Read streams of (x, y) pairs from the command line . . . . 45

Exercise 2.8 Sum columns in a ﬁle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Exercise 2.9 Estimate the chance of an event in a dice game . . . . . . . . 46

Exercise 2.10 Determine if you win or loose a hazard game . . . . . . . . . . 46

Exercise 2.11 Generate an HTML report from the simviz1.py script . . 55

Exercise 2.12 Generate a L

X report from the simviz1.py script . . . . 56

Exercise 2.13 Compute time step values in the simviz1.py script . . . . . 57

Exercise 2.14 Use Matlab for curve plotting in the simviz1.py script . . 57

Exercise 2.15 Combine curves from two simulations in one plot . . . . . . . 61

Exercise 2.16 Combine two-column data ﬁles to a multi-column ﬁle . . . 71

Exercise 2.17 Read/write Excel data ﬁles in Python . . . . . . . . . . . . . . . . 72

Exercise 3.1 Write format speciﬁcations in printf-style . . . . . . . . . . . . . 105

Exercise 3.2 Write your own function for joining strings . . . . . . . . . . . . 106

Exercise 3.3 Write an improved function for joining strings . . . . . . . . . 106

Exercise 3.4 Never modify a list you are iterating on . . . . . . . . . . . . . . . 106

Exercise 3.5 Make a specialized sort function . . . . . . . . . . . . . . . . . . . . . 107

Exercise 3.6 Check if your system has a speciﬁc program . . . . . . . . . . . 108

Exercise 3.7 Find the paths to a collection of programs . . . . . . . . . . . . 108

Exercise 3.8 Use Exercise 3.7 to improve the simviz1.py script . . . . . . 108

Exercise 3.9 Use Exercise 3.7 to improve the loop4simviz2.py script . 108

Exercise 3.10 Find the version number of a utility . . . . . . . . . . . . . . . . . . 109

Exercise 3.11 Automate execution of a family of similar commands . . . 125

Exercise 3.12 Remove temporary ﬁles in a directory tree . . . . . . . . . . . . 125

Exercise 3.13 Find old and large ﬁles in a directory tree . . . . . . . . . . . . . 126

Exercise 3.14 Remove redundant ﬁles in a directory tree . . . . . . . . . . . . 126

Exercise 3.15 Annotate a ﬁlename with the current date . . . . . . . . . . . . 127

Exercise 3.16 Automatic backup of recently modiﬁed ﬁles . . . . . . . . . . . 127

Exercise 3.17 Search for a text in ﬁles with certain extensions . . . . . . . . 128

Exercise 3.18 Search directories for plots and make HTML report . . . . 128

Exercise 3.19 Fix Unix/Windows Line Ends . . . . . . . . . . . . . . . . . . . . . . . 129

Exercise 4.1 Matrix-vector multiply with NumPy arrays. . . . . . . . . . . . 140

Exercise 4.2 Work with slicing and matrix multiplication . . . . . . . . . . . 140

Exercise 4.3 Assignment and in-place NumPy array modiﬁcations . . . 140

Exercise 4.4 Vectorized constant function . . . . . . . . . . . . . . . . . . . . . . . . 146

XXII List of Exercises

Exercise 4.5 Vectorize a numerical integration rule . . . . . . . . . . . . . . . . 146

Exercise 4.6 Vectorize a formula containing an if condition . . . . . . . . . 146

Exercise 4.7 Slicing of two-dimensional arrays . . . . . . . . . . . . . . . . . . . . . 146

Exercise 4.8 Implement Exercise 2.9 using NumPy arrays . . . . . . . . . . 163

Exercise 4.9 Implement Exercise 2.10 using NumPy arrays . . . . . . . . . 163

Exercise 4.10 Replace lists by NumPy arrays in convert2.py . . . . . . . . . 164

Exercise 4.11 Use the Gnuplot module in the simviz1.py script . . . . . . . 164

Exercise 4.12 Extension of Exercise 2.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

Exercise 4.13 NumPy arrays and binary ﬁles . . . . . . . . . . . . . . . . . . . . . . . 164

Exercise 4.14 One-dimensional Monte Carlo integration . . . . . . . . . . . . . 164

Exercise 4.15 Higher-dimensional Monte Carlo integration . . . . . . . . . . . 165

Exercise 4.16 Load data ﬁle into NumPy array and visualize . . . . . . . . . 166

Exercise 4.17 Analyze trends in the data from Exercise 4.16 . . . . . . . . . 166

Exercise 4.18 Evaluate a function over a 3D grid . . . . . . . . . . . . . . . . . . . 167

Exercise 4.19 Evaluate a function over a plane or line in a 3D grid . . . . 167

Exercise 5.1 Implement a numerical integration rule in F77 . . . . . . . . . 205

Exercise 5.2 Implement a numerical integration rule in C . . . . . . . . . . . 206

Exercise 5.3 Implement a numerical integration rule in C++ . . . . . . . . 206

Exercise 6.1 Modify the Scientiﬁc Hello World GUI . . . . . . . . . . . . . . . . 240

Exercise 6.2 Change the layout of the GUI in Exercise 6.1 . . . . . . . . . . 241

Exercise 6.3 Control a layout with the grid geometry manager . . . . . . 241

Exercise 6.4 Make a demo of Newton’s method . . . . . . . . . . . . . . . . . . . 242

Exercise 6.5 Program with Pmw.EntryField in hwGUI10.py . . . . . . . . . . . 248

Exercise 6.6 Program with Pmw.EntryField in simvizGUI2.py . . . . . . . . 248

Exercise 6.7 Replace Tkinter variables by set/get-like functions . . . . . 249

Exercise 6.8 Use simviz1.py as a module in simvizGUI2.py . . . . . . . . . . 249

Exercise 6.9 Apply Matlab for visualization in simvizGUI2.py . . . . . . . 249

Exercise 6.10 Program with Pmw.OptionMenu in simvizGUI2.py . . . . . . . . 282

Exercise 6.11 Study the nonlinear motion of a pendulum . . . . . . . . . . . . 283

Exercise 6.12 Add error handling with an associated message box . . . . 284

Exercise 6.13 Add a message bar to a balloon help . . . . . . . . . . . . . . . . . 284

Exercise 6.14 Select a ﬁle from a list and perform an action . . . . . . . . . . 284

Exercise 6.15 Make a GUI for ﬁnding and selecting font names . . . . . . . 285

Exercise 6.16 Launch a GUI when command-line options are missing . 285

Exercise 6.17 Write a GUI for Exercise 3.14 . . . . . . . . . . . . . . . . . . . . . . . 286

Exercise 6.18 Write a GUI for selecting ﬁles to be plotted . . . . . . . . . . . 286

Exercise 6.19 Write an easy-to-use GUI generator . . . . . . . . . . . . . . . . . . 286

Exercise 7.1 Write a CGI debugging tool . . . . . . . . . . . . . . . . . . . . . . . . . 310

Exercise 7.2 Make a Web calculator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

Exercise 7.3 Make a Web application for registering participants . . . . 311

Exercise 7.4 Make a Web application for numerical experiments . . . . . 311

Exercise 7.5 Become a “nobody” user on a Web server . . . . . . . . . . . . . 312

Exercise 8.1 Use the getopt/optparse module in simviz1.py . . . . . . . . 318

Exercise 8.2 Store command-line options in a dictionary . . . . . . . . . . . . 319

Exercise 8.3 Turn ﬁles with commands into Python variables . . . . . . . 319

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