MATLAB交互式计算实验室：用户指南

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"MATLAB Users' Guide.pdf - MATLAB 学习资料" MATLAB 是一个由 Cleve Moler 创建的交互式计算机程序，它主要用于矩阵运算，为用户提供了方便的计算实验室环境。这款工具特别强调对矩阵操作的支持，整合了 LINPACK 和 EISPACK 项目开发的矩阵软件。MATLAB 用 Fortran 语言编写，能够在任何允许交互执行 Fortran 程序的操作系统上轻易安装。本书《MATLAB Users’ Guide》包含了以下主要章节： 1. **Introduction**：介绍部分向读者概述了 MATLAB 的基本概念和功能，解释了它作为一个交互式计算平台如何支持矩阵运算。 2. **Elementary operations**：这一章详细介绍了 MATLAB 中的基本操作，如矩阵的创建、基本算术运算（加、减、乘、除）、指数与对数运算等。 3. **Rows, columns and submatrices**：讨论了如何处理矩阵的行、列以及子矩阵，包括选择、提取和修改特定部分的矩阵。 4. **FOR, WHILE and IF**：这部分讲解了 MATLAB 中的控制流结构，包括 FOR 循环、WHILE 循环和 IF 条件语句，用于实现条件判断和循环控制。 5. **Commands, text, files and macros**：介绍 MATLAB 的命令使用、文本处理、文件操作以及宏命令，这些是进行数据输入输出和程序组织的关键。 6. **Partial differential equation example**：通过一个实例展示了如何使用 MATLAB 解决偏微分方程，这在科学计算中是非常常见的一类问题。 7. **Eigenvalues sensitivity example**：讲解了如何利用 MATLAB 分析矩阵特征值的敏感性，这对于稳定性分析和系统动力学研究至关重要。 8. **Syntax diagrams**：提供 MATLAB 语法的图表，帮助用户理解和记忆语法规则。 9. **The parser-interpreter**：深入到 MATLAB 的解析器-解释器机制，解释了代码如何被解析和执行。 10. **The numerical algorithms**：介绍 MATLAB 实现的数值算法，包括线性代数、优化、积分、微分等领域的算法。 11. **FLOP and CHOP**：FLOP（Floating Point Operations）和 CHOP（舍入误差处理）是数值计算中的关键概念，这一章会涉及它们在 MATLAB 中的应用。 12. **Communicating with other programs**：探讨了 MATLAB 如何与其他程序进行接口通信，例如导入和导出数据，以及与其他编程语言的互操作性。 13. **Acknowledgement**：对参与 MATLAB 开发和提供支持的个人或团队表示感谢。 14. **References**：引用了相关的文献和技术资料，为用户进一步学习提供参考。 15. **Appendix. The HELP document**：附录中包含了 MATLAB 的帮助文档，是学习和解决问题的重要资源。 16. **Update to MATLAB Users’ Guide, May, 1981**：1981年5月的更新内容，可能包含了新功能、改进和修复。通过这个指南，读者可以全面了解 MATLAB 的核心功能和使用方法，无论是初学者还是有经验的用户，都能从中受益，提升在数值计算、数据分析和建模方面的能力。

for i = 1:n, for j = 1:n, A(i,j) = 1/(i+j-1);

generates the Hilbert matrix.

for j = 2:n-1, for i = j:n-1, ...

A(i,j) = 0; end; A(j,j) = j; end; A

changes all but the ”outer edge” of the lower triangle and then prints the ﬁnal matrix.

for h = 1.0: -0.1: -1.0, (<h, cos(pi*h)>)

prints a table of cosines.

<X,D> = EIG(A); for v = X, v, A*v

displays eigenvectors, one at a time.

The WHILE clause allows statements to be repeated an indeﬁnite number of times. The general

form is

WHILE expr relop expr, statement,..., statement, END

where relop is =, ¡, ¿, ¡=, ¿=, or ¡¿ (not equal) . The statements are repeatedly executed as long

as the indicated comparison between the real parts of the ﬁrst components of the two expressions

is true. Here are two examples. (Exercise for the reader: What do these segments do?)

eps = 1;

while 1 + eps > 1, eps = eps/2;

eps = 2*eps

E = 0*A; F = E + EYE; n = 1;

while NORM(E+F-E,1) > 0, E = E + F; F = A*F/n; n = n + 1;

The IF clause allows conditional execution of statements. The general form is

IF expr relop expr, statement, ..., statement,

ELSE statement, ..., statement

The ﬁrst group of statements are executed if the relation is true and the second group are executed

if the relation is false. The ELSE and the statements following it may be omitted. For example,

if abs(i-j) = 2, A(i,j) = 0;

5 Commands, text, ﬁles and macros.

MATLAB has several commands which control the output format and the overall execution of the

system.

The HELP command allows on-line access to short portions of text describing various opera-

tions, functions and special characters. The entire HELP document is reproduced in an appendix.

Results are usually printed in a scaled ﬁxed point format that shows 4 or 5 signiﬁcant ﬁgures.

The commands SHORT, LONG, SHORT E, LONG E and LONG Z alter the output format, but

do not alter the precision of the computations or the internal storage.

The WHO, WHAT and WHY commands provide information about the functions and variables

that are currently deﬁned.

The CLEAR command erases all variables, except EPS, FLOP, RAND and EYE. The statement

A = ¡¿ indicates that a ”0 by 0” matrix is to be stored in A. This causes A to be erased so that its

storage can be used for other variables.

The RETURN and EXIT commands cause return to the underlying operating system through

the Fortran RETURN statement.

MATLAB has a limited facility for handling text. Any string of characters delineated by quotes

(with two quotes used to allow one quote within the string) is saved as a vector of integer values

with ’1’ = 1, ’A’ = 10, ’ ’ = 36, etc. (The complete list is in the appendix under CHAR.) For

example

’2*A + 3’ is the same as <2 43 10 36 41 36 3>

It is possible, though seldom very meaningful, to use such strings in matrix operations. More

frequently, the text is used as a special argument to various functions.

NORM(A,’inf’) computes the infinity norm of A .

DISPLAY(T) prints the text stored in T .

EXEC(’file’) obtains MATLAB input from an external file.

SAVE(’file’) stores all the current variables in a file.

LOAD(’file’) retrieves all the variables from a file.

PRINT(’file’,X) prints X on a file.

DIARY(’file’) makes a copy of the complete MATLAB session.

The text can also be used in a limited string substitution macro facility. If a variable, say T,

contains the source text for a MATLAB statement or expression, then the construction

> T <

causes T to be executed or evaluated. For example

T = ’2*A + 3’;

S = ’B = >T< + 5’

A = 4;

> S <

produces

B =

16.

Some other examples are given under MACRO in the appendix. This facility is useful for fairly

short statements and expressions. More complicated MATLAB ”programs” should use the EXEC

facility.

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