Matlab 7 - Function Reference Volume 1 A - E.pdf

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M ATLAB ®
The Language of Technical Computing
Function Reference
Volume 1: A - E
Version 7
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MATLAB Function Reference Volume 1: A - E
COPYRIGHT 1984 - 2004 by The MathWorks, Inc.
The software described in this document is furnished under a license agreement. The software may be used
or copied only under the terms of the license agreement. No part of this manual may be photocopied or repro-
duced in any form without prior written consent from The MathWorks, Inc.
FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by,
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Printing History: December 1996 First printing
For MATLAB 5.0 (Release 8)
June 1997
Online only
Revised for MATLAB 5.1 (Release 9)
October 1997
Online only
Revised for MATLAB 5.2 (Release 10)
January 1999
Online only
Revised for MATLAB 5.3 (Release 11
June 1999
Second printing
For MATLAB 5.3 (Release 11)
June 2001
Online only Revised for MATLAB 6.1 (Release 12.1)
July 2002
Online only
Revised for 6.5 (Release 13)
June 2004
Online only
Revised for 7.0 (Release 14)
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Contents
1
Functions — Categorical List
Desktop Tools and Development Environment . . . . . . . . . . 1-2
Startup and Shutdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2
Command Window and History . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
Help for Using MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
Workspace, Search Path, and File Operations . . . . . . . . . . . . . 1-3
Workspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4
Search Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4
File Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4
Programming Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Editing and Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Performance Improvement and
Tuning Tools and Techniques . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Source Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
Publishing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7
Arrays and Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8
Basic Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8
Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8
Operations and Manipulation . . . . . . . . . . . . . . . . . . . . . . . . 1-9
Elementary Matrices and Arrays . . . . . . . . . . . . . . . . . . . . . 1-10
Specialized Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-10
Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-10
Matrix Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11
Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11
Eigenvalues and Singular Values . . . . . . . . . . . . . . . . . . . . 1-11
Matrix Logarithms and Exponentials . . . . . . . . . . . . . . . . . 1-12
Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-12
Elementary Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-12
Trigonometric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-13
Exponential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14
Complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14
Rounding and Remainder . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14
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Discrete Math (e.g., Prime Factors) . . . . . . . . . . . . . . . . . . . 1-15
Data Analysis and Fourier Transforms . . . . . . . . . . . . . . . . . . 1-15
Basic Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15
Finite Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15
Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-16
Filtering and Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-16
Fourier Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-16
Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-16
Interpolation and Computational Geometry . . . . . . . . . . . . . . 1-17
Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-17
Delaunay Triangulation and Tessellation . . . . . . . . . . . . . . 1-17
Convex Hull . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-18
Voronoi Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-18
Domain Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-18
Coordinate System Conversion . . . . . . . . . . . . . . . . . . . . . . . . . 1-18
Cartesian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-18
Nonlinear Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . 1-18
Ordinary Differential Equations (IVP) . . . . . . . . . . . . . . . . . 1-19
Delay Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . 1-19
Boundary Value Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-19
Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . . 1-19
Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-19
Numerical Integration (Quadrature) . . . . . . . . . . . . . . . . . . 1-20
Specialized Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-20
Sparse Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-20
Elementary Sparse Matrices . . . . . . . . . . . . . . . . . . . . . . . . . 1-21
Full to Sparse Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-21
Working with Sparse Matrices . . . . . . . . . . . . . . . . . . . . . . . 1-21
Reordering Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-21
Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-21
Linear Equations (Iterative Methods) . . . . . . . . . . . . . . . . . 1-22
Tree Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-22
Math Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-22
Programming and Data Types . . . . . . . . . . . . . . . . . . . . . . . . . 1-23
Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-23
Numeric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-24
Characters and Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-24
Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-26
Cell Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-26
ii
Contents
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Data Type Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-27
Determine Data Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-28
Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-28
Array Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-28
Basic Array Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-29
Array Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-29
Elementary Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-30
Operators and Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-30
Special Characters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-30
Arithmetic Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-31
Bit-wise Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-31
Relational Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-31
Logical Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-32
Set Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-32
Date and Time Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 1-32
Programming in MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-33
M-File Functions and Scripts . . . . . . . . . . . . . . . . . . . . . . . . 1-33
Evaluation of Expressions and Functions . . . . . . . . . . . . . . 1-34
Timer Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-34
Variables and Functions in Memory . . . . . . . . . . . . . . . . . . 1-34
Control Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-35
Function Handles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-35
Object-Oriented Programming . . . . . . . . . . . . . . . . . . . . . . . 1-35
Error Handling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-36
MEX Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-37
File I/O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-38
Filename Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-38
Opening, Loading, Saving Files . . . . . . . . . . . . . . . . . . . . . . . . 1-39
Low-Level File I/O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-39
Text Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-39
XML Documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-39
Spreadsheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-40
Microsoft Excel Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-40
Lotus123 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-40
Scientific Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-40
Common Data Format (CDF) . . . . . . . . . . . . . . . . . . . . . . . . 1-40
Flexible Image Transport System . . . . . . . . . . . . . . . . . . . . . 1-40
Hierarchical Data Format (HDF) . . . . . . . . . . . . . . . . . . . . . 1-40
Band-Interleaved Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-40
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