SciPy实战：解决数值与科学计算问题的高效指南

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"《学习SciPy进行数值与科学计算实用教程》是一本面向Python用户的专业指南，作者是Francisco J. Blanco-Silva。本书旨在提供一个快速、准确且易于理解的方法，通过SciPy库解决各种复杂的数值和科学计算问题。SciPy是Python科学计算生态系统的基石，它扩展了Python的基础功能，支持线性代数、优化、统计分析、信号处理和图像处理等领域。该教程内容涵盖了SciPy的基本概念和高级应用，包括但不限于： 1. **入门介绍**：引导读者了解SciPy的核心模块和其在科学计算中的作用，以及如何与NumPy等其他Python库配合使用。 2. **数值分析**：讲解如何利用SciPy进行数值积分、微分方程求解、插值和特殊函数计算等，确保计算的精确性。 3. **优化技术**：介绍最优化算法，如梯度下降、拟牛顿法和线性规划，用于求解复杂函数的极值问题。 4. **统计与概率**：涵盖描述性统计、假设检验、随机数生成以及分布函数，帮助读者处理数据集和构建统计模型。 5. **信号处理**：教授如何使用SciPy进行滤波、频谱分析和时域分析，以处理时间序列数据。 6. **图像处理**：涉及图像的读取、操作（如变换、分割）和分析，为机器视觉和计算机视觉任务提供支持。 7. **实际项目案例**：通过实战项目演示如何将学到的知识应用于实际问题，提升读者的实践能力。版权信息强调，未经出版商书面许可，书中内容不得复制或传播。尽管作者和Packt Publishing已尽最大努力确保信息的准确性，但书中提供的所有信息均不带任何担保，也不承担因本书内容导致的直接或间接损失的责任。《学习SciPy进行数值与科学计算实用教程》是一本深入浅出的教材，适合科研人员、工程师和数据分析人员，无论他们是初学者还是寻求提高现有技能的专家，都能从中获益匪浅。"

Introduction to SciPy

There is no denying that the labor of scientists in the 21st century is so much easier

than in previous generations. This is, among other reasons, because we have

reinvented discovery into Networked Science; members of any scientic community

with similar goals gather in large interdisciplinary teams and cooperate together

to achieve complex mission-oriented goals. This new paradigm on the approach to

research is also reected in the computational resources employed by researchers.

These are not restricted any more to a single piece of commercial software,

created and maintained by a lone company, but libraries of code that sit on top

of programming languages. The same professionals, who require fast and robust

computational tools for their everyday work, get together and create these libraries

in an open-source philosophy, in such a way that the resources are thoroughly

tested, and improvements occur at faster pace than any commercial product

could ever offer.

This book presents the most robust programming environment till date – a

system based on two libraries of the computer language Python: NumPy and SciPy.

In the following sections we wish to guide you on the usage of this system, through

examples of state-of-the-art research in different branches of science and engineering.

What is SciPy?

The ideal programming environment for computational mathematics is one that

enjoys the following characteristics:

• It must be based on a computer language that allows the user to work

quickly, and integrate many systems effectively. Ideally, the underlying

computer language should run on all different platforms (Windows,

Mac OS X, Linux, Unix, iOS, Android, and so on.). This is key to fostering

cooperation among scientists with different resources, as well as accessibility.

Introduction to SciPy

[ 6 ]

• It must contain a powerful set of libraries that allow the acquisition, storing,

and handling of big datasets in a simple and effective way. This is key to

allowing simulation and the employment of numerical computations at

large scale.

• Smooth integration with other computer languages, as well as

third-party software.

• Besides the usual running of compiled code, the programming

environment should allow the possibility of interactive sessions,

as well as scripting capabilities, for quick experimentation.

• Different coding paradigms should be supported; imperative,

object-oriented, or functional coding styles should all be available to the user.

• It should be an open-source software; the user should be allowed to access

the raw code of the libraries, and modify the basic algorithms if so desired.

With commercial software, the inclusion of the improved algorithms is

applied at the discretion of the seller, and it usually comes at a cost of the

user. In the open-source universe, someone in the community usually

performs these improvements, as they are published—at no cost.

• The set of applications should not be restricted to mere numerical

computations; it should be powerful enough to allow symbolic

computations as well.

Among the best-known environments for numerical computations used by

the scientic community, we have the powerful MATLAB® and Scilab® systems

(although both of them are commercial, expensive, and do not allow any tampering

with the code). Maple® and Mathematica® are more geared towards symbolic

computation, although they can match many of the numerical computations from

MATLAB®. As the previous two, these are also commercial, expensive, and closed

to modications. A decent alternative to MATLAB®, based on similar mathematical

engine, is the GNU Octave system. Most of the MATLAB® code is easily portable

in Octave. It also has the advantage of being open source. Unfortunately, the

underlying programming environment is not very user friendly. It is also

restricted to numerical computations.

Chapter 1

[ 7 ]

The one environment that combines the best of all worlds is indeed the combination

of Python with the NumPy and SciPy libraries. The rst property that attracts the

user to Python is, without a doubt, its code readability. The syntax is extremely

clear and expressive. It has the advantage of supporting code written in different

paradigms – object oriented, functional, or old school imperative. It allows the

compilation of code for running standalone executable programs, but it can also be

used interactively, or as a scripting language. This is a great advantage if the user

needs to develop tools for symbolic computation. Python has been used in this sense

as the basis of a rm competitor to Maple® and Mathematica®: the open-source

mathematics software Sage (System for Algebra and Geometry Experimentation).

NumPy is an open-source extension to Python that adds support for

multidimensional arrays of large sizes. This support allows the desired

acquisition, storage, and complex manipulation of data mentioned previously.

NumPy alone is a great tool to solve many numerical computations.

On top of NumPy, we have yet another open-source library, SciPy. This library

contains algorithms and mathematical tools to manipulate NumPy objects, with

very denite scientic and engineering objectives.

The combination of Python, NumPy, and SciPy (which henceforth should

be coined "SciPy" for brevity) has been the environment of choice of many

applied mathematicians for years; we work on a daily basis with both the pure

mathematicians and with the hard-core engineers. One of the challenges of this

trade is to bring to a single workstation the scientic production of professionals

with different visions, techniques, tools, and software. SciPy is the perfect solution

for coordinating everything together in a smooth, reliable, and coherent way.

Any day of the week, we are required to produce scripts in which, for example,

there are combinations of experiments written and performed in SciPy itself, C/C++,

Fortran, or MATLAB®. We often receive extremely large amounts of data from some

signal acquisition devices. From all this heterogeneous material, we employ Python

to retrieve the data, manipulate and, once nished with the analysis, produce high-

quality documentation with professional-looking diagrams and visualization aids.

SciPy allows performing all these tasks with ease.

Chapter 1

[ 9 ]

PythonMath and Sage Math bring Python coding to iOS devices. Sage Math allows

importing NumPy and SciPy.

We shall not go into detail about the installation of Python on your system, since

we already assume familiarity with this language. In case of doubt, we advise

browsing the excellent book Expert Python Programming: Best practices for designing,

coding, and distributing your Python software, Tarek Ziadé, Packt Publishing, where

detailed explanations are given for installing any of the different implementations

on different systems. It is usually a good idea to follow the directions given on the

ofcial Python website, as well. We will also assume familiarity with carrying out

interactive sessions in Python, as well as writing standalone scripts.

The latest libraries for both NumPy and SciPy can be downloaded from the ofcial

SciPy site,

scipy.org/Download. They both require a Python Version 2.4 or newer,

so we should be in good shape at this point. We may choose to do the download

from sourceforge (sourceforge.net/projects/scipy), or from Git repositories

(for instance, the superpack from fonnesbeck.github.com/ScipySuperpack).

It is also possible in some systems to use pre-packaged executable bundles that

simplify the process. We will show here how to download and install in the

most common cases.

For instance, in Mac OS X, if

macports is installed, the process could not be easier.

Open a terminal as superuser and, at the prompt (%), issue the following command:

% port search scipy

This presents a list of all ports that either install SciPy or use SciPy as a requirement.

On that list, the one we require for Python 2.7 is the py27-scipy port. We install it

(again as a superuser) by issuing the following command at prompt:

% port install py27-scipy

A few minutes later, the libraries are properly installed and ready to use. Note

how macports also installs all needed requirements for us (including the NumPy

libraries) without any extra effort from our part.

Under any other Unix/Linux system, if either no ports are available or if the user

prefers to install from the packages downloaded from either sourceforge or Git,

it is enough to perform the following steps:

1. Unzip the NumPy and SciPy packages following the recommendation

of the ofcial pages. This creates two folders, one for each library.

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