Python科学编程入门(1st版)：智能交互多媒体系统与服务研讨会论文集

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"A Primer on Scientific Programming with Python(1st Edition)" 是一本关于科学编程的入门书籍，由Hans Petter Langtangen编写，主要针对使用Python进行计算科学和工程领域的编程。这本书由Springer出版社出版，包含了在多媒体处理与服务导向计算领域的最新研究。在科学编程领域，Python是一种广泛使用的语言，因为它具有易读性强、语法简洁以及丰富的库支持，尤其适合于数值计算和数据科学。本书介绍了如何利用Python进行科学计算，涵盖了从基础到进阶的编程概念，可能包括但不限于变量、控制结构（如循环和条件语句）、函数、类、模块以及错误和异常处理。书中的内容可能涉及以下几个方面： 1. **基础编程概念**：解释Python的基本语法，如数据类型（整数、浮点数、字符串、列表、元组、字典等）、输入输出、流程控制等。 2. **数值计算**：介绍NumPy库，用于处理大型多维数组和矩阵，以及相关的数值运算，如线性代数、傅里叶变换和随机数生成。 3. **科学图形**：可能涵盖Matplotlib库，教授如何创建高质量的2D和3D图形，这对于数据可视化和科学研究至关重要。 4. **符号计算**：可能涉及SymPy库，该库允许进行符号数学运算，如求解方程、积分、微分等。 5. **文件操作**：教授如何读写文件，以及处理CSV、JSON等常见数据格式，这对于数据分析和数据存储是必要的。 6. **科学应用**：书中可能包含使用Python解决特定科学问题的实际示例，例如模拟物理现象、生物信息学分析或气候建模。 7. **高级主题**：可能涵盖面向对象编程、并发编程、并行计算，以及如何利用Python的包管理工具（如pip）和虚拟环境（如venv或conda）来组织项目。 8. **软件开发实践**：可能讨论代码版本控制（如Git）、测试、文档编写（如Sphinx）和代码调试技巧，这些都是科学研究中不可或缺的技能。 9. **案例研究**：通过实际的案例研究，展示如何将这些编程和计算方法应用于解决复杂问题。这本书特别适合于研究人员、教授和研究生，他们可以在多媒体处理和交互式服务开发等领域找到有价值的信息。通过学习，读者将能够利用Python的强大功能，开发出高效且用户友好的智能多媒体系统和服务。

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xvi Contents

9.4.1 MathematicalProblem ...................... 508

9.4.2 NumericalMethods ......................... 510

9.4.3 The ODE Solver Class Hierarchy . . . . . . . . . . . . . 511

9.4.4 The Backward Euler Method . . . . . . . . . . . . . . . . . 515

9.4.5 Veriﬁcation ................................ 518

9.4.6 Application 1:



= u ........................ 518

9.4.7 Application 2: The Logistic Equation . . . . . . . . . . 519

9.4.8 Application 3: An Oscillating System . . . . . . . . . . 521

9.4.9 Application 4: The Trajectory of a Ball . . . . . . . . 523

9.5 Class Hierarchy for Geometric Shapes . . . . . . . . . . . . . . . 525

9.5.1 UsingtheClassHierarchy.................... 526

9.5.2 Overall Design of the Class Hierarchy . . . . . . . . . 527

9.5.3 TheDrawingTool .......................... 529

9.5.4 Implementation of Shape Classes . . . . . . . . . . . . . 530

9.5.5 Scaling, Translating, and Rotating a Figure . . . . 534

9.6 Summary ........................................ 538

9.6.1 Chapter Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538

9.6.2 Summarizing Example: Input Data Reader . . . . . 540

9.7 Exercises......................................... 546

A Discrete Calculus .................................. 573

A.1 DiscreteFunctions ................................ 573

A.1.1 TheSine Function .......................... 574

A.1.2 Interpolation............................... 576

A.1.3 Evaluating the Approximation . . . . . . . . . . . . . . . . 576

A.1.4 Generalization.............................. 577

A.2 Diﬀerentiation Becomes Finite Diﬀerences . . . . . . . . . . . . 579

A.2.1 Diﬀerentiating the Sine Function. . . . . . . . . . . . . . 580

A.2.2 DiﬀerencesonaMesh ....................... 580

A.2.3 Generalization.............................. 582

A.3 IntegrationBecomes Summation .................... 583

A.3.1 Dividing into Subintervals . . . . . . . . . . . . . . . . . . . 584

A.3.2 Integration on Subintervals . . . . . . . . . . . . . . . . . . 585

A.3.3 Adding the Subintervals . . . . . . . . . . . . . . . . . . . . . 586

A.3.4 Generalization.............................. 587

A.4 TaylorSeries ..................................... 589

A.4.1 Approximating Functions Close to One Point. . . 589

A.4.2 Approximating the Exponential Function . . . . . . 589

A.4.3 More Accurate Expansions . . . . . . . . . . . . . . . . . . . 590

A.4.4 Accuracy oftheApproximation............... 592

A.4.5 DerivativesRevisited........................ 594

A.4.6 More Accurate Diﬀerence Approximations . . . . . 595

A.4.7 Second-Order Derivatives . . . . . . . . . . . . . . . . . . . . 597

A.5 Exercises......................................... 599

Contents xvii

B Diﬀerential Equations ............................. 605

B.1 The SimplestCase ................................ 606

B.2 Exponential Growth............................... 608

B.3 LogisticGrowth................................... 612

B.4 A General Ordinary Diﬀerential Equation . . . . . . . . . . . . 614

B.5 A Simple Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615

B.6 A Model for the SpreadofaDisease................. 619

B.7 Exercises......................................... 621

C A Complete Project ............................... 625

C.1 About the Problem: Motion and Forces in Physics . . . . . 626

C.1.1 ThePhysicalProblem....................... 626

C.1.2 The Computational Algorithm . . . . . . . . . . . . . . . 628

C.1.3 Derivation of the Mathematical Model . . . . . . . . . 628

C.1.4 Derivationof the Algorithm.................. 631

C.2 ProgramDevelopmentand Testing .................. 632

C.2.1 Implementation............................. 632

C.2.2 CallbackFunctionality....................... 635

C.2.3 Making a Module........................... 636

C.2.4 Veriﬁcation ................................ 637

C.3 Visualization ..................................... 639

C.3.1 Simultaneous Computation and Plotting . . . . . . . 639

C.3.2 Some Applications .......................... 642

C.3.3 Remark on Choosing

Δt ..................... 643

C.3.4 Comparing Several Quantities in Subplots . . . . . 644

C.3.5 Comparing Approximate and Exact Solutions . . 645

C.3.6 Evolution of the Error as

Δt Decreases ........ 646

C.4 Exercises......................................... 649

D Debugging ......................................... 651

D.1 Using a Debugger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651

D.2 Howto Debug .................................... 653

D.2.1 A Recipe for Program Writing and Debugging . . 654

D.2.2 Application oftheRecipe.................... 656

E Technical Topics ................................... 669

E.1 Diﬀerent Ways of Running Python Programs . . . . . . . . . 669

E.1.1 Executing Python Programs in IPython . . . . . . . 669

E.1.2 Executing Python Programs on Unix . . . . . . . . . . 669

E.1.3 Executing Python Programs on Windows . . . . . . 671

E.1.4 Executing Python Programs on Macintosh . . . . . 673

E.1.5 Making a Complete Stand-Alone Executable . . . 673

E.2 IntegerandFloatDivision.......................... 673

E.3 Visualizing aProgramwith Lumpy.................. 674

E.4 Doing Operating System Tasks in Python . . . . . . . . . . . . 675

E.5 Variable Number of Function Arguments . . . . . . . . . . . . . 678

List of Exercises

Exercise1.1 Compute1+1 ............................... 42

Exercise 1.2 Write a “Hello, World!” program . . . . . . . . . . . . . . . 43

Exercise 1.3 Convert from meters to British length units . . . . . 43

Exercise 1.4 Compute the mass of various substances . . . . . . . . 43

Exercise 1.5 Compute the growth of money in a bank . . . . . . . . 43

Exercise1.6 Find error(s)inaprogram .................... 43

Exercise1.7 Type inprogram text ........................ 43

Exercise 1.8 Type in programs and debug them . . . . . . . . . . . . . 44

Exercise1.9 EvaluateaGaussianfunction.................. 44

Exercise 1.10 Compute the air resistance on a football . . . . . . . . 45

Exercise1.11 Deﬁne objectsinIPython..................... 45

Exercise 1.12 Howto cooktheperfect egg................... 46

Exercise 1.13 Evaluate a function deﬁned by a sum . . . . . . . . . . . 46

Exercise 1.14 Derive the trajectoryofaball ................. 47

Exercise1.15 Finderrorsin the codingof formulas ........... 48

Exercise1.16 Finderrorsin Pythonstatements .............. 48

Exercise 1.17 Find errors in the coding of a formula . . . . . . . . . . 49

Exercise 2.1 Make a Fahrenheit–Celsius conversion table . . . . . 99

Exercise2.2 Generateodd numbers ....................... 99

Exercise2.3 Storeoddnumbersinalist ................... 100

Exercise 2.4 Generate odd numbers by the range function . . . . 100

Exercise 2.5 Simulate operations on lists by hand . . . . . . . . . . . 100

Exercise 2.6 Make a table of values from formula (1.1) . . . . . . . 100

Exercise 2.7 Store values from formula (1.1) in lists. . . . . . . . . . 100

Exercise2.8 Workwith alist ............................. 100

Exercise 2.9 Generate equally spaced coordinates . . . . . . . . . . . 100

Exercise 2.10 Use a list comprehension to solve Exer. 2.9 . . . . . . 101

Exercise 2.11 Store data from Exer. 2.7 in a nested list . . . . . . . 101

Exercise2.12 Computeamathematicalsum................. 101

Exercise 2.13 Simulate a program by hand . . . . . . . . . . . . . . . . . . 101

xix

xx List of Exercises

Exercise2.14 Use aforloop inExer.2.12 ................... 102

Exercise 2.15 Index a nested lists . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Exercise 2.16 Construct a double for loop over a nested list . . . . 102

Exercise 2.17 Compute the area of an arbitrary triangle . . . . . . . 102

Exercise 2.18 Compute the length of a path . . . . . . . . . . . . . . . . . 102

Exercise 2.19 Approximate

pi .............................. 103

Exercise 2.20 Write a Fahrenheit-Celsius conversion table . . . . . 103

Exercise 2.21 Convert nested list comprehensions to nested

standard loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Exercise 2.22 Write a Fahrenheit–Celsius conversion function . . 104

Exercise 2.23 Writesomesimplefunctions................... 104

Exercise 2.24 Write the program in Exer. 2.12 as a function . . . 104

Exercise 2.25 Implement a Gaussian function . . . . . . . . . . . . . . . . 104

Exercise 2.26 Find the max and min values of a function . . . . . . 104

Exercise 2.27 Explore the Python Library Reference . . . . . . . . . . 105

Exercise 2.28 Make a function of the formula in Exer. 1.12 . . . . 105

Exercise 2.29 Write a function for numerical diﬀerentiation . . . . 105

Exercise 2.30 Write a function for numerical integration. . . . . . . 105

Exercise 2.31 Improve the formula in Exer. 2.30 . . . . . . . . . . . . . . 106

Exercise 2.32 Compute a polynomial via a product . . . . . . . . . . . 106

Exercise 2.33 Implement the factorial function . . . . . . . . . . . . . . . 106

Exercise 2.34 Compute velocity and acceleration from position

data;onedimension.......................... 107

Exercise 2.35 Compute velocity and acceleration from position

data;two dimensions......................... 107

Exercise 2.36 Express a step function as a Python function . . . . 107

Exercise 2.37 Rewrite a mathematical function . . . . . . . . . . . . . . . 108

Exercise 2.38 Make a table for approximations of

cos x ........ 108

Exercise 2.39 Implement Exer. 1.13 with a loop . . . . . . . . . . . . . . 109

Exercise 2.40 Determine the type of objects . . . . . . . . . . . . . . . . . 109

Exercise 2.41 Implement the sum function. . . . . . . . . . . . . . . . . . . 109

Exercise 2.42 Find the max/min elements in a list . . . . . . . . . . . . 110

Exercise 2.43 Demonstrate list functionality . . . . . . . . . . . . . . . . . 110

Exercise 2.44 Write a sort function for a list of 4-tuples . . . . . . . 110

Exercise2.45 Findprimenumbers.......................... 111

Exercise 2.46 Condense the program in Exer. 2.14 . . . . . . . . . . . . 111

Exercise 2.47 Values of boolean expressions . . . . . . . . . . . . . . . . . . 112

Exercise 2.48 Explore round-oﬀ errors from a large number of

inverseoperations............................ 112

Exercise 2.49 Explore what zero can be on a computer . . . . . . . . 112

Exercise 2.50 Resolve a problem with a function . . . . . . . . . . . . . 113

Exercise 2.51 Compare two real numbers on a computer . . . . . . 113

Exercise 2.52 Use None in keyword arguments . . . . . . . . . . . . . . . 114

Exercise 2.53 Improve the program from Ch. 2.4.2. . . . . . . . . . . . 114

Exercise2.54 Interpret acode ............................. 114

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