MATLAB 7 Function Reference: P - Zfaculty.jsd.claremont.edu/jhigdon/phys100/matlab... ·...

MATLAB® 7Function Reference: P - Z

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Revision HistoryDecember 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)September 2006 Online only Revised for 7.3 (Release 2006b)March 2007 Online only Revised for 7.4 (Release 2007a)September 2007 Online only Revised for Version 7.5 (Release 2007b)March 2008 Online only Revised for Version 7.6 (Release 2008a)October 2008 Online only Revised for Version 7.7 (Release 2008b)March 2009 Online only Revised for Version 7.8 (Release 2009a)

Contents

Function Reference1

Desktop Tools and Development Environment . . . . . . . 1-3Startup and Shutdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3Command Window and History . . . . . . . . . . . . . . . . . . . . . . 1-4Help for Using MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5Workspace, Search Path, and File Operations . . . . . . . . . . 1-6Programming Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11

Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-13Arrays and Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-20Elementary Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-24Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-28Interpolation and Computational Geometry . . . . . . . . . . . . 1-29Cartesian Coordinate System Conversion . . . . . . . . . . . . . . 1-32Nonlinear Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . 1-33Specialized Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-36Sparse Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-37Math Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-41

Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-43Basic Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-43Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-43Filtering and Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-44Interpolation and Regression . . . . . . . . . . . . . . . . . . . . . . . . 1-44Fourier Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-45Derivatives and Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-45Time Series Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-46Time Series Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-49

Programming and Data Types . . . . . . . . . . . . . . . . . . . . . . 1-51Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-51Data Type Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-59Operators and Special Characters . . . . . . . . . . . . . . . . . . . . 1-61Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-64

v

Bit-Wise Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-67Logical Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-67Relational Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-68Set Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-68Date and Time Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 1-69Programming in MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . 1-69

Object-Oriented Programming . . . . . . . . . . . . . . . . . . . . . . 1-77Classes and Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-77Handle Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-78Events and Listeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-79Meta-Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-79

File I/O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-81File Name Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-81File Opening, Loading, and Saving . . . . . . . . . . . . . . . . . . . 1-82Memory Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-82Low-Level File I/O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-82Text Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-83XML Documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-84Spreadsheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-84Scientific Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-85Audio and Audio/Video . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-88Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-90Internet Exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-91

Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-93Basic Plots and Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-93Plotting Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-94Annotating Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-94Specialized Plotting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-95Bit-Mapped Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-99Printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-99Handle Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-100

3-D Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-104Surface and Mesh Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-104View Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-106Lighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-108Transparency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-108Volume Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-108

vi Contents

GUI Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-110Predefined Dialog Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-110User Interface Deployment . . . . . . . . . . . . . . . . . . . . . . . . . . 1-111User Interface Development . . . . . . . . . . . . . . . . . . . . . . . . . 1-111User Interface Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-112Objects from Callbacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-113GUI Utilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-113Program Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-114

External Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-115Shared Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-115Java . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-116.NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-117Component Object Model and ActiveX . . . . . . . . . . . . . . . . . 1-117Web Services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-120Serial Port Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-120

Alphabetical List

2

Index

vii

viii Contents

1

Function Reference

Desktop Tools and DevelopmentEnvironment (p. 1-3)

Startup, Command Window, help,editing and debugging, tuning, othergeneral functions

Mathematics (p. 1-13) Arrays and matrices, linear algebra,other areas of mathematics

Data Analysis (p. 1-43) Basic data operations, descriptivestatistics, covariance and correlation,filtering and convolution, numericalderivatives and integrals, Fouriertransforms, time series analysis

Programming and Data Types(p. 1-51)

Function/expression evaluation,program control, function handles,object oriented programming, errorhandling, operators, data types,dates and times, timers

Object-Oriented Programming(p. 1-77)

Functions for working with classesand objects

File I/O (p. 1-81) General and low-level file I/O, plusspecific file formats, like audio,spreadsheet, HDF, images

Graphics (p. 1-93) Line plots, annotating graphs,specialized plots, images, printing,Handle Graphics

3-D Visualization (p. 1-104) Surface and mesh plots, view control,lighting and transparency, volumevisualization

1 Function Reference

GUI Development (p. 1-110) GUIDE, programming graphicaluser interfaces

External Interfaces (p. 1-115) Interfaces to shared librariess,Java, .NET, COM and ActiveX, Webservices, and serial port devices, andC and Fortran routines

1-2

Desktop Tools and Development Environment


Startup and Shutdown (p. 1-3) Startup and shutdown options,preferences

Command Window and History(p. 1-4)

Control Command Window andHistory, enter statements and runfunctions

Help for Using MATLAB (p. 1-5) Command line help, onlinedocumentation in the Help browser,demos

Workspace, Search Path, and FileOperations (p. 1-6)

Work with files, MATLAB searchpath, manage variables

Programming Tools (p. 1-8) Edit and debug M-files, improveperformance, source control, publishresults

System (p. 1-11) Identify current computer, license,product version, and more

Startup and Shutdown

exit Terminate MATLAB® program(same as quit)

finish Termination M-file for MATLABprogram

matlab (UNIX) Start MATLAB program (UNIX®platforms)

matlab (Windows) Start MATLAB program (Windows®platforms)

matlabrc Startup M-file for MATLAB programprefdir Directory containing preferences,

history, and layout filespreferences Open Preferences dialog boxquit Terminate MATLAB program

1-3


startup Startup M-file for user-definedoptions

userpath View or change user portion ofsearch path

Command Window and History

clc Clear Command Windowcommandhistory Open Command History window, or

select it if already opencommandwindow Open Command Window, or select

it if already opendiary Save session to filedos Execute DOS command and return

resultformat Set display format for outputhome Move cursor to upper-left corner of

Command Windowmatlabcolon (matlab:) Run specified function via hyperlinkmore Control paged output for Command

Windowperl Call Perl script using appropriate

operating system executablesystem Execute operating system command

and return resultunix Execute UNIX command and return

result

1-4


Help for Using MATLAB

builddocsearchdb Build searchable documentationdatabase

demo Access product demos via Helpbrowser

doc Reference page in Help browserdocsearch Open Help browser and search for

specified termechodemo Run M-file demo step-by-step in

Command Windowhelp Help for functions in Command

Windowhelpbrowser Open Help browser to access all

online documentation and demoshelpwin Provide access to M-file help for all

functionsinfo Information about contacting The

MathWorkslookfor Search for keyword in all help

entriesplayshow Run M-file demo (deprecated; use

echodemo instead)support Open MathWorks Technical Support

Web pagewhatsnew Release Notes for MathWorks™

products

1-5


Workspace, Search Path, and File Operations

Workspace (p. 1-6) Manage variablesSearch Path (p. 1-6) View and change MATLAB search

pathFile Operations (p. 1-7) View and change files and directories

Workspace

assignin Assign value to variable in specifiedworkspace

clear Remove items from workspace,freeing up system memory

evalin Execute MATLAB expression inspecified workspace

exist Check existence of variable, function,directory, or Java™ programminglanguage class

openvar Open workspace variable in VariableEditor or other graphical editing tool

pack Consolidate workspace memoryuiimport Open Import Wizard to import datawhich Locate functions and fileswho, whos List variables in workspaceworkspace Open Workspace browser to manage

workspace

Search Path

addpath Add directories to search pathgenpath Generate path string

1-6


partialpath Partial pathname descriptionpath View or change search pathpath2rc Save current search path to

pathdef.m filepathsep Path separator for current platformpathtool Open Set Path dialog box to view

and change search pathrestoredefaultpath Restore default search pathrmpath Remove directories from search pathsavepath Save current search pathuserpath View or change user portion of

search path

File OperationsSee also “File I/O” on page 1-81 functions.

cd Change working directorycopyfile Copy file or directorydelete Remove files or graphics objectsdir Directory listingexist Check existence of variable, function,

directory, or Java programminglanguage class

fileattrib Set or get attributes of file ordirectory

filebrowser Open Current Directory browser, orselect it if already open

isdir Determine whether input is directorylookfor Search for keyword in all help

entries

1-7


ls Directory contentsmatlabroot Root directorymkdir Make new directorymovefile Move file or directorypwd Identify current directoryrecycle Set option to move deleted files to

recycle folderrehash Refresh function and file system

path cachesrmdir Remove directorytoolboxdir Root directory for specified toolboxtype Display contents of filevisdiff Compare two text files, MAT-Files,

or binary fileswhat List MATLAB files in current

directorywhich Locate functions and files

Programming Tools

M-File Editing and Debugging(p. 1-9)

Edit and debug M-files

M-File Performance (p. 1-9) Improve performance and findpotential problems in M-files

Source Control (p. 1-10) Interface MATLAB with sourcecontrol system

Publishing (p. 1-10) Publish M-file code and results

1-8


M-File Editing and Debugging

clipboard Copy and paste strings to and fromsystem clipboard

datatipinfo Produce short description of inputvariable

dbclear Clear breakpointsdbcont Resume executiondbdown Reverse workspace shift performed

by dbup, while in debug modedbquit Quit debug modedbstack Function call stackdbstatus List all breakpointsdbstep Execute one or more lines from

current breakpointdbstop Set breakpointsdbtype List M-file with line numbersdbup Shift current workspace to

workspace of caller, while indebug mode

debug List M-file debugging functionsedit Edit or create M-filekeyboard Input from keyboard

M-File Performance

bench MATLAB benchmarkmlint Check M-files for possible problemsmlintrpt Run mlint for file or directory,

reporting results in browserpack Consolidate workspace memory

1-9


profile Profile execution time for functionprofsave Save profile report in HTML formatrehash Refresh function and file system

path cachessparse Create sparse matrixzeros Create array of all zeros

Source Control

checkin Check files into source controlsystem (UNIX platforms)

checkout Check files out of source controlsystem (UNIX platforms)

cmopts Name of source control systemcustomverctrl Allow custom source control system

(UNIX platforms)undocheckout Undo previous checkout from source

control system (UNIX platforms)verctrl Source control actions (Windows

platforms)

Publishing

grabcode MATLAB code from M-filespublished to HTML

notebook Open M-book in Microsoft® Wordsoftware (on Microsoft Windowsplatforms)

publish Publish M-file containing cells,saving output to file of specified type

snapnow Force snapshot of image for inclusionin published document

1-10


System

Operating System Interface (p. 1-11) Exchange operating systeminformation and commands withMATLAB

MATLAB Version and License(p. 1-12)

Information about MATLAB versionand license

Operating System Interface

clipboard Copy and paste strings to and fromsystem clipboard

computer Information about computer onwhich MATLAB software is running

dos Execute DOS command and returnresult

getenv Environment variablehostid Server host identification numbermaxNumCompThreads Control maximum number of

computational threadsperl Call Perl script using appropriate

operating system executablesetenv Set environment variablesystem Execute operating system command

and return resultunix Execute UNIX command and return

resultwinqueryreg Item from Windows registry

1-11


MATLAB Version and License

ismac Determine if version is for Mac OS®X platform

ispc Determine if version is for Windows(PC) platform

isstudent Determine if version is StudentVersion

isunix Determine if version is for UNIXplatform

javachk Generate error message based onSun™ Java feature support

license Return license number or performlicensing task

prefdir Directory containing preferences,history, and layout files

usejava Determine whether Sun Java featureis supported in MATLAB software

ver Version information for MathWorksproducts

verLessThan Compare toolbox version to specifiedversion string

version Version number for MATLAB

1-12

Mathematics

Mathematics

Arrays and Matrices (p. 1-14) Basic array operators andoperations, creation of elementaryand specialized arrays and matrices

Linear Algebra (p. 1-20) Matrix analysis, linear equations,eigenvalues, singular values,logarithms, exponentials,factorization

Elementary Math (p. 1-24) Trigonometry, exponentials andlogarithms, complex values,rounding, remainders, discrete math

Polynomials (p. 1-28) Multiplication, division, evaluation,roots, derivatives, integration,eigenvalue problem, curve fitting,partial fraction expansion

Interpolation and ComputationalGeometry (p. 1-29)

Interpolation, Delaunaytriangulation and tessellation,convex hulls, Voronoi diagrams,domain generation

Cartesian Coordinate SystemConversion (p. 1-32)

Conversions between Cartesian andpolar or spherical coordinates

Nonlinear Numerical Methods(p. 1-33)

Differential equations, optimization,integration

Specialized Math (p. 1-36) Airy, Bessel, Jacobi, Legendre, beta,elliptic, error, exponential integral,gamma functions

Sparse Matrices (p. 1-37) Elementary sparse matrices,operations, reordering algorithms,linear algebra, iterative methods,tree operations

Math Constants (p. 1-41) Pi, imaginary unit, infinity,Not-a-Number, largest and smallestpositive floating point numbers,floating point relative accuracy

1-13


Arrays and Matrices

Basic Information (p. 1-14) Display array contents, get arrayinformation, determine array type

Operators (p. 1-15) Arithmetic operatorsElementary Matrices and Arrays(p. 1-16)

Create elementary arrays of differenttypes, generate arrays for plotting,array indexing, etc.

Array Operations (p. 1-17) Operate on array content, applyfunction to each array element, findcumulative product or sum, etc.

Array Manipulation (p. 1-18) Create, sort, rotate, permute,reshape, and shift array contents

Specialized Matrices (p. 1-19) Create Hadamard, Companion,Hankel, Vandermonde, Pascalmatrices, etc.

Basic Information

disp Display text or arraydisplay Display text or array (overloaded

method)isempty Determine whether array is emptyisequal Test arrays for equalityisequalwithequalnans Test arrays for equality, treating

NaNs as equalisfinite Array elements that are finiteisfloat Determine whether input is

floating-point arrayisinf Array elements that are infiniteisinteger Determine whether input is integer

array

1-14

Mathematics

islogical Determine whether input is logicalarray

isnan Array elements that are NaNisnumeric Determine whether input is numeric

arrayisscalar Determine whether input is scalarissparse Determine whether input is sparseisvector Determine whether input is vectorlength Length of vectormax Largest elements in arraymin Smallest elements in arrayndims Number of array dimensionsnumel Number of elements in array or

subscripted array expressionsize Array dimensions

Operators

+ Addition+ Unary plus- Subtraction- Unary minus* Matrix multiplication^ Matrix power\ Backslash or left matrix divide/ Slash or right matrix divide’ Transpose.’ Nonconjugated transpose.* Array multiplication (element-wise)

1-15


.^ Array power (element-wise)

.\ Left array divide (element-wise)

./ Right array divide (element-wise)

Elementary Matrices and Arrays

blkdiag Construct block diagonal matrixfrom input arguments

create (RandStream) Create random number streamsdiag Diagonal matrices and diagonals of

matrixeye Identity matrixfreqspace Frequency spacing for frequency

responseget (RandStream) Random stream propertiesgetDefaultStream (RandStream) Default random number streamind2sub Subscripts from linear indexlinspace Generate linearly spaced vectorslist (RandStream) Random number generator

algorithmslogspace Generate logarithmically spaced

vectorsmeshgrid Generate X and Y arrays for 3-D plotsndgrid Generate arrays for N-D functions

and interpolationones Create array of all onesrand Uniformly distributed

pseudorandom numbersrand (RandStream) Uniformly distributed random

numbers

1-16

Mathematics

randi Uniformly distributedpseudorandom integers

randi (RandStream) Uniformly distributedpseudorandom integers

randn Normally distributed pseudorandomnumbers

randn (RandStream) Normally distributed pseudorandomnumbers

randperm (RandStream)RandStream Random number streamRandStream (RandStream) Random number streamset (RandStream) Set random stream propertysetDefaultStream (RandStream) Set default random number streamsub2ind Single index from subscriptszeros Create array of all zeros

Array Operations

See “Linear Algebra” on page 1-20 and “Elementary Math” on page 1-24 forother array operations.

accumarray Construct array with accumulationarrayfun Apply function to each element of

arraybsxfun Apply element-by-element binary

operation to two arrays withsingleton expansion enabled

cast Cast variable to different data typecross Vector cross productcumprod Cumulative productcumsum Cumulative sum

1-17


dot Vector dot productidivide Integer division with rounding

optionkron Kronecker tensor productprod Product of array elementssum Sum of array elementstril Lower triangular part of matrixtriu Upper triangular part of matrix

Array Manipulation

blkdiag Construct block diagonal matrixfrom input arguments

cat Concatenate arrays along specifieddimension

circshift Shift array circularlydiag Diagonal matrices and diagonals of

matrixend Terminate block of code, or indicate

last array indexflipdim Flip array along specified dimensionfliplr Flip matrix left to rightflipud Flip matrix up to downhorzcat Concatenate arrays horizontallyinline Construct inline objectipermute Inverse permute dimensions of N-D

arraypermute Rearrange dimensions of N-D arrayrepmat Replicate and tile arrayreshape Reshape array

1-18

Mathematics

rot90 Rotate matrix 90 degreesshiftdim Shift dimensionssort Sort array elements in ascending or

descending ordersortrows Sort rows in ascending ordersqueeze Remove singleton dimensionsvectorize Vectorize expressionvertcat Concatenate arrays vertically

Specialized Matrices

compan Companion matrixgallery Test matriceshadamard Hadamard matrixhankel Hankel matrixhilb Hilbert matrixinvhilb Inverse of Hilbert matrixmagic Magic squarepascal Pascal matrixrosser Classic symmetric eigenvalue test

problemtoeplitz Toeplitz matrixvander Vandermonde matrixwilkinson Wilkinson’s eigenvalue test matrix

1-19


Linear Algebra

Matrix Analysis (p. 1-20) Compute norm, rank, determinant,condition number, etc.

Linear Equations (p. 1-21) Solve linear systems, leastsquares, LU factorization, Choleskyfactorization, etc.

Eigenvalues and Singular Values(p. 1-22)

Eigenvalues, eigenvectors, Schurdecomposition, Hessenburgmatrices, etc.

Matrix Logarithms and Exponentials(p. 1-23)

Matrix logarithms, exponentials,square root

Factorization (p. 1-23) Cholesky, LU, and QR factorizations,diagonal forms, singular valuedecomposition

Matrix Analysis

cond Condition number with respect toinversion

condeig Condition number with respect toeigenvalues

det Matrix determinantnorm Vector and matrix normsnormest 2-norm estimatenull Null spaceorth Range space of matrixrank Rank of matrixrcond Matrix reciprocal condition number

estimaterref Reduced row echelon form

1-20

Mathematics

subspace Angle between two subspacestrace Sum of diagonal elements

Linear Equations

chol Cholesky factorizationcholinc Sparse incomplete Cholesky and

Cholesky-Infinity factorizationscond Condition number with respect to

inversioncondest 1-norm condition number estimatefunm Evaluate general matrix functionilu Sparse incomplete LU factorizationinv Matrix inverselinsolve Solve linear system of equationslscov Least-squares solution in presence

of known covariancelsqnonneg Solve nonnegative least-squares

constraints problemlu LU matrix factorizationluinc Sparse incomplete LU factorizationpinv Moore-Penrose pseudoinverse of

matrixqr Orthogonal-triangular

decompositionrcond Matrix reciprocal condition number

estimate

1-21


Eigenvalues and Singular Values

balance Diagonal scaling to improveeigenvalue accuracy

cdf2rdf Convert complex diagonal form toreal block diagonal form

condeig Condition number with respect toeigenvalues

eig Eigenvalues and eigenvectorseigs Largest eigenvalues and

eigenvectors of matrixgsvd Generalized singular value

decompositionhess Hessenberg form of matrixordeig Eigenvalues of quasitriangular

matricesordqz Reorder eigenvalues in QZ

factorizationordschur Reorder eigenvalues in Schur

factorizationpoly Polynomial with specified rootspolyeig Polynomial eigenvalue problemrsf2csf Convert real Schur form to complex

Schur formschur Schur decompositionsqrtm Matrix square rootss2tf Convert state-space filter parameters

to transfer function formsvd Singular value decompositionsvds Find singular values and vectors

1-22

Mathematics

Matrix Logarithms and Exponentials

expm Matrix exponentiallogm Matrix logarithmsqrtm Matrix square root

Factorization

balance Diagonal scaling to improveeigenvalue accuracy

cdf2rdf Convert complex diagonal form toreal block diagonal form

chol Cholesky factorizationcholinc Sparse incomplete Cholesky and

Cholesky-Infinity factorizationscholupdate Rank 1 update to Cholesky

factorizationgsvd Generalized singular value

decompositionilu Sparse incomplete LU factorizationlu LU matrix factorizationluinc Sparse incomplete LU factorizationplanerot Givens plane rotationqr Orthogonal-triangular

decompositionqrdelete Remove column or row from QR

factorizationqrinsert Insert column or row into QR

factorizationqrupdate

1-23


qz QZ factorization for generalizedeigenvalues

rsf2csf Convert real Schur form to complexSchur form

svd Singular value decomposition

Elementary Math

Trigonometric (p. 1-24) Trigonometric functions with resultsin radians or degrees

Exponential (p. 1-26) Exponential, logarithm, power, androot functions

Complex (p. 1-26) Numbers with real and imaginarycomponents, phase angles

Rounding and Remainder (p. 1-27) Rounding, modulus, and remainderDiscrete Math (p. 1-27) Prime factors, factorials,

permutations, rational fractions,least common multiple, greatestcommon divisor

Trigonometric

acos Inverse cosine; result in radiansacosd Inverse cosine; result in degreesacosh Inverse hyperbolic cosineacot Inverse cotangent; result in radiansacotd Inverse cotangent; result in degreesacoth Inverse hyperbolic cotangentacsc Inverse cosecant; result in radiansacscd Inverse cosecant; result in degreesacsch Inverse hyperbolic cosecant

1-24

Mathematics

asec Inverse secant; result in radiansasecd Inverse secant; result in degreesasech Inverse hyperbolic secantasin Inverse sine; result in radiansasind Inverse sine; result in degreesasinh Inverse hyperbolic sineatan Inverse tangent; result in radiansatan2 Four-quadrant inverse tangentatand Inverse tangent; result in degreesatanh Inverse hyperbolic tangentcos Cosine of argument in radianscosd Cosine of argument in degreescosh Hyperbolic cosinecot Cotangent of argument in radianscotd Cotangent of argument in degreescoth Hyperbolic cotangentcsc Cosecant of argument in radianscscd Cosecant of argument in degreescsch Hyperbolic cosecanthypot Square root of sum of squaressec Secant of argument in radianssecd Secant of argument in degreessech Hyperbolic secantsin Sine of argument in radianssind Sine of argument in degreessinh Hyperbolic sine of argument in

radianstan Tangent of argument in radians

1-25


tand Tangent of argument in degreestanh Hyperbolic tangent

Exponential

exp Exponentialexpm1 Compute exp(x)-1 accurately for

small values of xlog Natural logarithmlog10 Common (base 10) logarithmlog1p Compute log(1+x) accurately for

small values of xlog2 Base 2 logarithm and dissect

floating-point numbers intoexponent and mantissa

nextpow2 Next higher power of 2nthroot Real nth root of real numberspow2 Base 2 power and scale floating-point

numbersreallog Natural logarithm for nonnegative

real arraysrealpow Array power for real-only outputrealsqrt Square root for nonnegative real

arrayssqrt Square root

Complex

abs Absolute value and complexmagnitude

angle Phase angle

1-26

Mathematics

complex Construct complex data from realand imaginary components

conj Complex conjugatecplxpair Sort complex numbers into complex

conjugate pairsi Imaginary unitimag Imaginary part of complex numberisreal Check if input is real arrayj Imaginary unitreal Real part of complex numbersign Signum functionunwrap Correct phase angles to produce

smoother phase plots

Rounding and Remainder

ceil Round toward positive infinityfix Round toward zerofloor Round toward negative infinityidivide Integer division with rounding

optionmod Modulus after divisionrem Remainder after divisionround Round to nearest integer

Discrete Math

factor Prime factorsfactorial Factorial functiongcd Greatest common divisor

1-27


isprime Array elements that are primenumbers

lcm Least common multiplenchoosek Binomial coefficient or all

combinationsperms All possible permutationsprimes Generate list of prime numbersrat, rats Rational fraction approximation

Polynomials

conv Convolution and polynomialmultiplication

deconv Deconvolution and polynomialdivision

poly Polynomial with specified rootspolyder Polynomial derivativepolyeig Polynomial eigenvalue problempolyfit Polynomial curve fittingpolyint Integrate polynomial analyticallypolyval Polynomial evaluationpolyvalm Matrix polynomial evaluationresidue Convert between partial fraction

expansion and polynomialcoefficients

roots Polynomial roots

1-28

Mathematics

Interpolation and Computational Geometry

Interpolation (p. 1-29) Data interpolation, data gridding,polynomial evaluation, nearest pointsearch

Delaunay Triangulation andTessellation (p. 1-30)

Delaunay triangulation andtessellation, triangular surface andmesh plots

Convex Hull (p. 1-32) Plot convex hull, plotting functionsVoronoi Diagrams (p. 1-32) Plot Voronoi diagram, patch graphics

object, plotting functionsDomain Generation (p. 1-32) Generate arrays for 3-D plots, or for

N-D functions and interpolation

Interpolation

dsearch Search Delaunay triangulation fornearest point

dsearchn N-D nearest point searchgriddata Data griddinggriddata3 Data gridding and hypersurface

fitting for 3-D datagriddatan Data gridding and hypersurface

fitting (dimension >= 2)interp1 1-D data interpolation (table lookup)interp1q Quick 1-D linear interpolationinterp2 2-D data interpolation (table lookup)interp3 3-D data interpolation (table lookup)interpft 1-D interpolation using FFT methodinterpn N-D data interpolation (table lookup)meshgrid Generate X and Y arrays for 3-D plots

1-29


mkpp Make piecewise polynomialndgrid Generate arrays for N-D functions

and interpolationpadecoef Padé approximation of time delayspchip Piecewise Cubic Hermite

Interpolating Polynomial (PCHIP)ppval Evaluate piecewise polynomialspline Cubic spline data interpolationtsearchn N-D closest simplex searchunmkpp Piecewise polynomial details

Delaunay Triangulation and Tessellation

baryToCart (TriRep) Converts point coordinates frombarycentric to Cartesian

cartToBary (TriRep) Convert point coordinates fromcartesian to barycentric

circumcenters (TriRep) Circumcenters of specified simplicesconvexHull (DelaunayTri) Convex hulldelaunay Delaunay triangulationdelaunay3 3-D Delaunay tessellationdelaunayn N-D Delaunay tessellationDelaunayTri Contruct Delaunay triangulationDelaunayTri Delaunay triangulation in 2-D and

3-Ddsearch Search Delaunay triangulation for

nearest pointdsearchn N-D nearest point searchedgeAttachments (TriRep) Simplices attached to specified edgesedges (TriRep) Triangulation edges

1-30

Mathematics

faceNormals (TriRep) Unit normals to specified trianglesfeatureEdges (TriRep) Sharp edges of surface triangulationfreeBoundary (TriRep) Facets referenced by only one

simplexincenters (TriRep) Incenters of specified simplicesinOutStatus (DelaunayTri) Status of triangles in 2-D constrained

Delaunay triangulationisEdge (TriRep) Test if vertices are joined by edgenearestNeighbor (DelaunayTri) Point closest to specified locationneighbors (TriRep) Simplex neighbor informationpointLocation (DelaunayTri) Simplex containing specified locationsize (TriRep) Size of triangulation matrixtetramesh Tetrahedron mesh plottrimesh Triangular mesh plottriplot 2-D triangular plotTriRep Triangulation representationTriRep Triangulation representationTriScatteredInterp Interpolate scattered dataTriScatteredInterptrisurf Triangular surface plottsearch Search for enclosing Delaunay

triangletsearchn N-D closest simplex searchvertexAttachments (TriRep) Return simplices attached to

specified verticesvoronoiDiagram (DelaunayTri) Voronoi diagram

1-31


Convex Hull

convhull Convex hullconvhulln N-D convex hullpatch Create patch graphics objectplot 2-D line plottrisurf Triangular surface plot

Voronoi Diagrams

dsearch Search Delaunay triangulation fornearest point

patch Create patch graphics objectplot 2-D line plotvoronoi Voronoi diagramvoronoin N-D Voronoi diagram

Domain Generation

meshgrid Generate X and Y arrays for 3-D plotsndgrid Generate arrays for N-D functions

and interpolation

Cartesian Coordinate System Conversion

cart2pol Transform Cartesian coordinates topolar or cylindrical

cart2sph Transform Cartesian coordinates tospherical

1-32

Mathematics

pol2cart Transform polar or cylindricalcoordinates to Cartesian

sph2cart Transform spherical coordinates toCartesian

Nonlinear Numerical Methods

Ordinary Differential Equations(p. 1-33)

Solve stiff and nonstiff differentialequations, define the problem, setsolver options, evaluate solution

Delay Differential Equations(p. 1-34)

Solve delay differential equationswith constant and general delays,set solver options, evaluate solution

Boundary Value Problems (p. 1-35) Solve boundary value problems forordinary differential equations, setsolver options, evaluate solution

Partial Differential Equations(p. 1-35)

Solve initial-boundary valueproblems for parabolic-elliptic PDEs,evaluate solution

Optimization (p. 1-35) Find minimum of single andmultivariable functions, solvenonnegative least-squares constraintproblem

Numerical Integration (Quadrature)(p. 1-36)

Evaluate Simpson, Lobatto, andvectorized quadratures, evaluatedouble and triple integrals

Ordinary Differential Equations

decic Compute consistent initial conditionsfor ode15i

deval Evaluate solution of differentialequation problem

1-33


ode15i Solve fully implicit differentialequations, variable order method

ode23, ode45, ode113, ode15s,ode23s, ode23t, ode23tb

Solve initial value problems forordinary differential equations

odefile Define differential equation problemfor ordinary differential equationsolvers

odeget Ordinary differential equationoptions parameters

odeset Create or alter options structurefor ordinary differential equationsolvers

odextend Extend solution of initial valueproblem for ordinary differentialequation

Delay Differential Equations

dde23 Solve delay differential equations(DDEs) with constant delays

ddeget Extract properties from delaydifferential equations optionsstructure

ddesd Solve delay differential equations(DDEs) with general delays

ddeset Create or alter delay differentialequations options structure

deval Evaluate solution of differentialequation problem

1-34

Mathematics

Boundary Value Problems

bvp4c Solve boundary value problems forordinary differential equations

bvp5c Solve boundary value problems forordinary differential equations

bvpget Extract properties from optionsstructure created with bvpset

bvpinit Form initial guess for bvp4cbvpset Create or alter options structure of

boundary value problembvpxtend Form guess structure for extending

boundary value solutionsdeval Evaluate solution of differential

equation problem

Partial Differential Equations

pdepe Solve initial-boundary valueproblems for parabolic-elliptic PDEsin 1-D

pdeval Evaluate numerical solution of PDEusing output of pdepe

Optimization

fminbnd Find minimum of single-variablefunction on fixed interval

fminsearch Find minimum of unconstrainedmultivariable function usingderivative-free method

fzero Find root of continuous function ofone variable

1-35


lsqnonneg Solve nonnegative least-squaresconstraints problem

optimget Optimization options valuesoptimset Create or edit optimization options

structure

Numerical Integration (Quadrature)

dblquad Numerically evaluate doubleintegral over a rectangle

quad Numerically evaluate integral,adaptive Simpson quadrature

quad2d Numerically evaluate doubleintegral over planar region

quadgk Numerically evaluate integral,adaptive Gauss-Kronrod quadrature

quadl Numerically evaluate integral,adaptive Lobatto quadrature

quadv Vectorized quadraturetriplequad Numerically evaluate triple integral

Specialized Math

airy Airy functionsbesselh Bessel function of third kind (Hankel

function)besseli Modified Bessel function of first kindbesselj Bessel function of first kindbesselk Modified Bessel function of second

kindbessely Bessel function of second kind

1-36

Mathematics

beta Beta functionbetainc Incomplete beta functionbetaincinv Beta inverse cumulative distribution

functionbetaln Logarithm of beta functionellipj Jacobi elliptic functionsellipke Complete elliptic integrals of first

and second kinderf, erfc, erfcx, erfinv, erfcinv Error functionsexpint Exponential integralgamma, gammainc, gammaln Gamma functionsgammaincinv Inverse incomplete gamma functionlegendre Associated Legendre functionspsi Psi (polygamma) function

Sparse Matrices

Elementary Sparse Matrices(p. 1-38)

Create random and nonrandomsparse matrices

Full to Sparse Conversion (p. 1-38) Convert full matrix to sparse, sparsematrix to full

Sparse Matrix Manipulation (p. 1-39) Test matrix for sparseness, getinformation on sparse matrix,allocate sparse matrix, applyfunction to nonzero elements,visualize sparsity pattern

Reordering Algorithms (p. 1-39) Random, column, minimum degree,Dulmage-Mendelsohn, and reverseCuthill-McKee permutations

1-37


Linear Algebra (p. 1-40) Compute norms, eigenvalues,factorizations, least squares,structural rank

Linear Equations (IterativeMethods) (p. 1-40)

Methods for conjugate andbiconjugate gradients, residuals,lower quartile

Tree Operations (p. 1-41) Elimination trees, tree plotting,factorization analysis

Elementary Sparse Matrices

spdiags Extract and create sparse band anddiagonal matrices

speye Sparse identity matrixsprand Sparse uniformly distributed

random matrixsprandn Sparse normally distributed random

matrixsprandsym Sparse symmetric random matrix

Full to Sparse Conversion

find Find indices and values of nonzeroelements

full Convert sparse matrix to full matrixsparse Create sparse matrixspconvert Import matrix from sparse matrix

external format

1-38

Mathematics

Sparse Matrix Manipulation

issparse Determine whether input is sparsennz Number of nonzero matrix elementsnonzeros Nonzero matrix elementsnzmax Amount of storage allocated for

nonzero matrix elementsspalloc Allocate space for sparse matrixspfun Apply function to nonzero sparse

matrix elementsspones Replace nonzero sparse matrix

elements with onesspparms Set parameters for sparse matrix

routinesspy Visualize sparsity pattern

Reordering Algorithms

amd Approximate minimum degreepermutation

colamd Column approximate minimumdegree permutation

colperm Sparse column permutation basedon nonzero count

dmperm Dulmage-Mendelsohn decompositionldl Block LDL’ factorization for

Hermitian indefinite matricesrandperm Random permutationsymamd Symmetric approximate minimum

degree permutationsymrcm Sparse reverse Cuthill-McKee

ordering

1-39


Linear Algebra

cholinc Sparse incomplete Cholesky andCholesky-Infinity factorizations

condest 1-norm condition number estimateeigs Largest eigenvalues and

eigenvectors of matrixilu Sparse incomplete LU factorizationluinc Sparse incomplete LU factorizationnormest 2-norm estimatespaugment Form least squares augmented

systemsprank Structural ranksvds Find singular values and vectors

Linear Equations (Iterative Methods)

bicg Biconjugate gradients methodbicgstab Biconjugate gradients stabilized

methodbicgstabl Biconjugate gradients stabilized (l)

methodcgs Conjugate gradients squared methodgmres Generalized minimum residual

method (with restarts)lsqr LSQR methodminres Minimum residual methodpcg Preconditioned conjugate gradients

methodqmr Quasi-minimal residual method

1-40

Mathematics

symmlq Symmetric LQ methodtfqmr Transpose-free quasi-minimal

residual method

Tree Operations

etree Elimination treeetreeplot Plot elimination treegplot Plot nodes and links representing

adjacency matrixsymbfact Symbolic factorization analysistreelayout Lay out tree or foresttreeplot Plot picture of treeunmesh Convert edge matrix to coordinate

and Laplacian matrices

Math Constants

eps Floating-point relative accuracyi Imaginary unitInf Infinityintmax Largest value of specified integer

typeintmin Smallest value of specified integer

typej Imaginary unitNaN Not-a-Numberpi Ratio of circle’s circumference to its

diameter, π

1-41


realmax Largest positive floating-pointnumber

realmin Smallest positive normalizedfloating-point number

1-42

Data Analysis

Data Analysis

Basic Operations (p. 1-43) Sums, products, sortingDescriptive Statistics (p. 1-43) Statistical summaries of dataFiltering and Convolution (p. 1-44) Data preprocessingInterpolation and Regression(p. 1-44)

Data fitting

Fourier Transforms (p. 1-45) Frequency content of dataDerivatives and Integrals (p. 1-45) Data rates and accumulationsTime Series Objects (p. 1-46) Methods for timeseries objectsTime Series Collections (p. 1-49) Methods for tscollection objects

Basic Operations

brush Interactively mark, delete, modify,and save observations in graphs

cumprod Cumulative productcumsum Cumulative sumlinkdata Automatically update graphs when

variables changeprod Product of array elementssort Sort array elements in ascending or

descending ordersortrows Sort rows in ascending ordersum Sum of array elements

Descriptive Statistics

corrcoef Correlation coefficientscov Covariance matrix

1-43


max Largest elements in arraymean Average or mean value of arraymedian Median value of arraymin Smallest elements in arraymode Most frequent values in arraystd Standard deviationvar Variance

Filtering and Convolution

conv Convolution and polynomialmultiplication

conv2 2-D convolutionconvn N-D convolutiondeconv Deconvolution and polynomial

divisiondetrend Remove linear trendsfilter 1-D digital filterfilter2 2-D digital filter

Interpolation and Regression

interp1 1-D data interpolation (table lookup)interp2 2-D data interpolation (table lookup)interp3 3-D data interpolation (table lookup)interpn N-D data interpolation (table lookup)mldivide \, mrdivide / Left or right matrix divisionpolyfit Polynomial curve fittingpolyval Polynomial evaluation

1-44

Data Analysis

Fourier Transforms

abs Absolute value and complexmagnitude

angle Phase anglecplxpair Sort complex numbers into complex

conjugate pairsfft Discrete Fourier transformfft2 2-D discrete Fourier transformfftn N-D discrete Fourier transformfftshift Shift zero-frequency component to

center of spectrumfftw Interface to FFTW library run-time

algorithm tuning controlifft Inverse discrete Fourier transformifft2 2-D inverse discrete Fourier

transformifftn N-D inverse discrete Fourier

transformifftshift Inverse FFT shiftnextpow2 Next higher power of 2unwrap Correct phase angles to produce

smoother phase plots

Derivatives and Integrals

cumtrapz Cumulative trapezoidal numericalintegration

del2 Discrete Laplaciandiff Differences and approximate

derivatives

1-45


gradient Numerical gradientpolyder Polynomial derivativepolyint Integrate polynomial analyticallytrapz Trapezoidal numerical integration

Time Series Objects

Utilities (p. 1-46) Combine timeseries objects,query and set timeseries objectproperties, plot timeseries objects

Data Manipulation (p. 1-47) Add or delete data, manipulatetimeseries objects

Event Data (p. 1-48) Add or delete events, create newtimeseries objects based on eventdata

Descriptive Statistics (p. 1-48) Descriptive statistics for timeseriesobjects

Utilities

get (timeseries) Query timeseries object propertyvalues

getdatasamplesize Size of data sample in timeseriesobject

getqualitydesc Data quality descriptionsisempty (timeseries) Determine whether timeseries

object is emptylength (timeseries) Length of time vectorplot (timeseries) Plot time seriesset (timeseries) Set properties of timeseries objectsize (timeseries) Size of timeseries object

1-46

Data Analysis

timeseries Create timeseries objecttsdata.event Construct event object for

timeseries objecttsprops Help on timeseries object

propertieststool Open Time Series Tools GUI

Data Manipulation

addsample Add data sample to timeseriesobject

ctranspose (timeseries) Transpose timeseries objectdelsample Remove sample from timeseries

objectdetrend (timeseries) Subtract mean or best-fit line and all

NaNs from time seriesfilter (timeseries) Shape frequency content of time

seriesgetabstime (timeseries) Extract date-string time vector into

cell arraygetinterpmethod Interpolation method for timeseries

objectgetsampleusingtime (timeseries) Extract data samples into new

timeseries objectidealfilter (timeseries) Apply ideal (noncausal) filter to

timeseries objectresample (timeseries) Select or interpolate timeseries

data using new time vectorsetabstime (timeseries) Set times of timeseries object as

date stringssetinterpmethod Set default interpolation method for

timeseries object

1-47


synchronize Synchronize and resample twotimeseries objects using commontime vector

transpose (timeseries) Transpose timeseries objectvertcat (timeseries) Vertical concatenation of

timeseries objects

Event Data

addevent Add event to timeseries objectdelevent Remove tsdata.event objects from

timeseries objectgettsafteratevent New timeseries object with samples

occurring at or after eventgettsafterevent New timeseries object with samples

occurring after eventgettsatevent New timeseries object with samples

occurring at eventgettsbeforeatevent New timeseries object with samples

occurring before or at eventgettsbeforeevent New timeseries object with samples

occurring before eventgettsbetweenevents New timeseries object with samples

occurring between events

Descriptive Statistics

iqr (timeseries) Interquartile range of timeseriesdata

max (timeseries) Maximum value of timeseries datamean (timeseries) Mean value of timeseries datamedian (timeseries) Median value of timeseries data

1-48

Data Analysis

min (timeseries) Minimum value of timeseries datastd (timeseries) Standard deviation of timeseries

datasum (timeseries) Sum of timeseries datavar (timeseries) Variance of timeseries data

Time Series Collections

Utilities (p. 1-49) Query and set tscollection objectproperties, plot tscollectionobjects

Data Manipulation (p. 1-50) Add or delete data, manipulatetscollection objects

Utilities

get (tscollection) Query tscollection object propertyvalues

isempty (tscollection) Determine whether tscollectionobject is empty

length (tscollection) Length of time vectorplot (timeseries) Plot time seriesset (tscollection) Set properties of tscollection

objectsize (tscollection) Size of tscollection objecttscollection Create tscollection objecttstool Open Time Series Tools GUI

1-49


Data Manipulation

addsampletocollection Add sample to tscollection objectaddts Add timeseries object to

tscollection objectdelsamplefromcollection Remove sample from tscollection

objectgetabstime (tscollection) Extract date-string time vector into

cell arraygetsampleusingtime (tscollection) Extract data samples into new

tscollection objectgettimeseriesnames Cell array of names of timeseries

objects in tscollection objecthorzcat (tscollection) Horizontal concatenation for

tscollection objectsremovets Remove timeseries objects from

tscollection objectresample (tscollection) Select or interpolate data in

tscollection using new time vectorsetabstime (tscollection) Set times of tscollection object as

date stringssettimeseriesnames Change name of timeseries object

in tscollectionvertcat (tscollection) Vertical concatenation for

tscollection objects

1-50

Programming and Data Types


Data Types (p. 1-51) Numeric, character, structures, cellarrays, and data type conversion

Data Type Conversion (p. 1-59) Convert one numeric type to another,numeric to string, string to numeric,structure to cell array, etc.

Operators and Special Characters(p. 1-61)

Arithmetic, relational, and logicaloperators, and special characters

Strings (p. 1-64) Create, identify, manipulate, parse,evaluate, and compare strings

Bit-Wise Operations (p. 1-67) Perform set, shift, and, or, compare,etc. on specific bit fields

Logical Operations (p. 1-67) Evaluate conditions, testing for trueor false

Relational Operations (p. 1-68) Compare values for equality, greaterthan, less than, etc.

Set Operations (p. 1-68) Find set members, unions,intersections, etc.

Date and Time Operations (p. 1-69) Obtain information about dates andtimes

Programming in MATLAB (p. 1-69) M-files, function/expressionevaluation, program control,function handles, object orientedprogramming, error handling

Data Types

Numeric Types (p. 1-52) Integer and floating-point dataCharacters and Strings (p. 1-53) Characters and arrays of charactersStructures (p. 1-54) Data of varying types and sizes

stored in fields of a structure

1-51


Cell Arrays (p. 1-55) Data of varying types and sizesstored in cells of array

Function Handles (p. 1-56) Invoke a function indirectly viahandle

Java Classes and Objects (p. 1-56) Access Java classes throughMATLAB interface

Data Type Identification (p. 1-58) Determine data type of a variable

Numeric Types

arrayfun Apply function to each element ofarray

cast Cast variable to different data typecat Concatenate arrays along specified

dimensionclass Create object or return class of objectfind Find indices and values of nonzero

elementsintmax Largest value of specified integer

typeintmin Smallest value of specified integer

typeintwarning Control state of integer warningsipermute Inverse permute dimensions of N-D

arrayisa Determine whether input is object

of given classisequal Test arrays for equalityisequalwithequalnans Test arrays for equality, treating

NaNs as equalisfinite Array elements that are finite

1-52


isinf Array elements that are infiniteisnan Array elements that are NaNisnumeric Determine whether input is numeric

arrayisreal Check if input is real arrayisscalar Determine whether input is scalarisvector Determine whether input is vectorpermute Rearrange dimensions of N-D arrayrealmax Largest positive floating-point

numberrealmin Smallest positive normalized

floating-point numberreshape Reshape arraysqueeze Remove singleton dimensionszeros Create array of all zeros

Characters and Strings

See “Strings” on page 1-64 for all string-related functions.

cellstr Create cell array of strings fromcharacter array

char Convert to character array (string)eval Execute string containing MATLAB

expressionfindstr Find string within another, longer

stringisstr Determine whether input is

character arrayregexp, regexpi Match regular expressionsprintf Write formatted data to string

1-53


sscanf Read formatted data from stringstrcat Concatenate strings horizontallystrcmp, strcmpi Compare stringsstrings String handlingstrjust Justify character arraystrmatch Find possible matches for stringstrread Read formatted data from stringstrrep Find and replace substringstrtrim Remove leading and trailing white

space from stringstrvcat Concatenate strings vertically

Structures

arrayfun Apply function to each element ofarray

cell2struct Convert cell array to structure arrayclass Create object or return class of objectdeal Distribute inputs to outputsfieldnames Field names of structure, or public

fields of objectgetfield Field of structure arrayisa Determine whether input is object

of given classisequal Test arrays for equalityisfield Determine whether input is

structure array fieldisscalar Determine whether input is scalarisstruct Determine whether input is

structure array

1-54


isvector Determine whether input is vectororderfields Order fields of structure arrayrmfield Remove fields from structuresetfield Set value of structure array fieldstruct Create structure arraystruct2cell Convert structure to cell arraystructfun Apply function to each field of scalar

structure

Cell Arrays

cell Construct cell arraycell2mat Convert cell array of matrices to

single matrixcell2struct Convert cell array to structure arraycelldisp Cell array contentscellfun Apply function to each cell in cell

arraycellplot Graphically display structure of cell

arraycellstr Create cell array of strings from

character arrayclass Create object or return class of objectdeal Distribute inputs to outputsisa Determine whether input is object

of given classiscell Determine whether input is cell

arrayiscellstr Determine whether input is cell

array of strings

1-55


isequal Test arrays for equalityisscalar Determine whether input is scalarisvector Determine whether input is vectormat2cell Divide matrix into cell array of

matricesnum2cell Convert numeric array to cell arraystruct2cell Convert structure to cell array

Function Handles

class Create object or return class of objectfeval Evaluate functionfunc2str Construct function name string from

function handlefunctions Information about function handlefunction_handle (@) Handle used in calling functions

indirectlyisa Determine whether input is object

of given classisequal Test arrays for equalitystr2func Construct function handle from

function name string

Java Classes and Objects

cell Construct cell arrayclass Create object or return class of objectclear Remove items from workspace,

freeing up system memorydepfun List dependencies of M-file or P-file

1-56


exist Check existence of variable, function,directory, or Java programminglanguage class

fieldnames Field names of structure, or publicfields of object

im2java Convert image to Java imageimport Add package or class to current

import listinmem Names of M-files, MEX-files, Sun

Java classes in memoryisa Determine whether input is object

of given classisjava Determine whether input is Sun

Java objectjavaaddpath Add entries to dynamic Sun Java

class pathjavaArray Construct Sun Java arrayjavachk Generate error message based on

Sun Java feature supportjavaclasspath Get and set Sun Java class pathjavaMethod Call Sun Java methodjavaMethodEDT Call Sun Java method from Event

Dispatch Thread (EDT)javaObject Construct Sun Java objectjavaObjectEDT Construct Sun Java object on Event

Dispatch Thread (EDT)javarmpath Remove entries from dynamic Sun

Java class pathmethods Information on class methodsmethodsview Information on class methods in

separate window

1-57


usejava Determine whether Sun Java featureis supported in MATLAB software

which Locate functions and files

Data Type Identification

is* Detect stateisa Determine whether input is object

of given classiscell Determine whether input is cell

arrayiscellstr Determine whether input is cell

array of stringsischar Determine whether item is character

arrayisfield Determine whether input is

structure array fieldisfloat Determine whether input is

floating-point arrayisinteger Determine whether input is integer

arrayisjava Determine whether input is Sun

Java objectislogical Determine whether input is logical

arrayisnumeric Determine whether input is numeric

arrayisobject Determine if input is MATLAB

objectisreal Check if input is real arrayisstr Determine whether input is

character array

1-58


isstruct Determine whether input isstructure array

validateattributes Check validity of arraywho, whos List variables in workspace

Data Type Conversion

Numeric (p. 1-59) Convert data of one numeric type toanother numeric type

String to Numeric (p. 1-60) Convert characters to numericequivalent

Numeric to String (p. 1-60) Convert numeric to characterequivalent

Other Conversions (p. 1-61) Convert to structure, cell array,function handle, etc.

Numeric

cast Cast variable to different data typedouble Convert to double precisionint8, int16, int32, int64 Convert to signed integersingle Convert to single precisiontypecast Convert data types without changing

underlying datauint8, uint16, uint32, uint64 Convert to unsigned integer

1-59


String to Numeric

base2dec Convert base N number string todecimal number

bin2dec Convert binary number string todecimal number

cast Cast variable to different data typehex2dec Convert hexadecimal number string

to decimal numberhex2num Convert hexadecimal number string

to double-precision numberstr2double Convert string to double-precision

valuestr2num Convert string to numberunicode2native Convert Unicode® characters to

numeric bytes

Numeric to String

cast Cast variable to different data typechar Convert to character array (string)dec2base Convert decimal to base N number

in stringdec2bin Convert decimal to binary number

in stringdec2hex Convert decimal to hexadecimal

number in stringint2str Convert integer to stringmat2str Convert matrix to stringnative2unicode Convert numeric bytes to Unicode

charactersnum2str Convert number to string

1-60


Other Conversions

cell2mat Convert cell array of matrices tosingle matrix

cell2struct Convert cell array to structure arraydatestr Convert date and time to string

formatfunc2str Construct function name string from

function handlelogical Convert numeric values to logicalmat2cell Divide matrix into cell array of

matricesnum2cell Convert numeric array to cell arraynum2hex Convert singles and doubles to

IEEE® hexadecimal stringsstr2func Construct function handle from

function name stringstr2mat Form blank-padded character matrix

from stringsstruct2cell Convert structure to cell array

Operators and Special Characters

Arithmetic Operators (p. 1-62) Plus, minus, power, left and rightdivide, transpose, etc.

Relational Operators (p. 1-62) Equal to, greater than, less than orequal to, etc.

Logical Operators (p. 1-62) Element-wise and short circuit and,or, not

Special Characters (p. 1-63) Array constructors, linecontinuation, comments, etc.

1-61


Arithmetic Operators

+ Plus- Minus. Decimal point= Assignment* Matrix multiplication/ Matrix right division\ Matrix left division^ Matrix power’ Matrix transpose.* Array multiplication (element-wise)./ Array right division (element-wise).\ Array left division (element-wise).^ Array power (element-wise).’ Array transpose

Relational Operators

< Less than Greater than>= Greater than or equal to== Equal to~= Not equal to

Logical OperatorsSee also “Logical Operations” on page 1-67 for functions like xor, all, any, etc.

1-62


&& Logical AND|| Logical OR& Logical AND for arrays| Logical OR for arrays~ Logical NOT

Special Characters

: Create vectors, subscript arrays, specify for-loop iterations( ) Pass function arguments, prioritize operators[ ] Construct array, concatenate elements, specify multiple

outputs from function{ } Construct cell array, index into cell array. Insert decimal point, define structure field, reference methods

of object.( ) Reference dynamic field of structure.. Reference parent directory

... Continue statement to next line, Separate rows of array, separate function input/output

arguments, separate commands; Separate columns of array, suppress output from current

command% Insert comment line into code

%{ %} Insert block of comments into code! Issue command to operating system’ ’ Construct character array@ Construct function handle, reference class directory

1-63


Strings

Description of Strings in MATLAB(p. 1-64)

Basics of string handling inMATLAB

String Creation (p. 1-64) Create strings, cell arrays of strings,concatenate strings together

String Identification (p. 1-65) Identify characteristics of stringsString Manipulation (p. 1-65) Convert case, strip blanks, replace

charactersString Parsing (p. 1-66) Formatted read, regular expressions,

locate substringsString Evaluation (p. 1-66) Evaluate stated expression in stringString Comparison (p. 1-66) Compare contents of strings

Description of Strings in MATLAB

strings String handling

String Creation

blanks Create string of blank characterscellstr Create cell array of strings from

character arraychar Convert to character array (string)sprintf Write formatted data to stringstrcat Concatenate strings horizontallystrvcat Concatenate strings vertically

1-64


String Identification

class Create object or return class of objectisa Determine whether input is object

of given classiscellstr Determine whether input is cell

array of stringsischar Determine whether item is character

arrayisletter Array elements that are alphabetic

lettersisscalar Determine whether input is scalarisspace Array elements that are space

charactersisstrprop Determine whether string is of

specified categoryisvector Determine whether input is vectorvalidatestring Check validity of text string

String Manipulation

deblank Strip trailing blanks from end ofstring

lower Convert string to lowercasestrjust Justify character arraystrrep Find and replace substringstrtrim Remove leading and trailing white

space from stringupper Convert string to uppercase

1-65


String Parsing

findstr Find string within another, longerstring

regexp, regexpi Match regular expressionregexprep Replace string using regular

expressionregexptranslate Translate string into regular

expressionsscanf Read formatted data from stringstrfind Find one string within anotherstrread Read formatted data from stringstrtok Selected parts of string

String Evaluation

eval Execute string containing MATLABexpression

evalc Evaluate MATLAB expression withcapture


String Comparison

strcmp, strcmpi Compare stringsstrmatch Find possible matches for stringstrncmp, strncmpi Compare first n characters of strings

1-66


Bit-Wise Operations

bitand Bitwise ANDbitcmp Bitwise complementbitget Bit at specified positionbitmax Maximum double-precision

floating-point integerbitor Bitwise ORbitset Set bit at specified positionbitshift Shift bits specified number of placesbitxor Bitwise XORswapbytes Swap byte ordering

Logical Operations

all Determine whether all arrayelements are nonzero

and Find logical AND of array or scalarinputs

any Determine whether any arrayelements are nonzero

false Logical 0 (false)find Find indices and values of nonzero

elementsisa Determine whether input is object

of given classiskeyword Determine whether input is

MATLAB keywordisvarname Determine whether input is valid

variable namelogical Convert numeric values to logical

1-67


not Find logical NOT of array or scalarinput

or Find logical OR of array or scalarinputs

true Logical 1 (true)xor Logical exclusive-OR

See “Operators and Special Characters” on page 1-61 for logical operators.

Relational Operations

eq Test for equalityge Test for greater than or equal togt Test for greater thanle Test for less than or equal tolt Test for less thanne Test for inequality

See “Operators and Special Characters” on page 1-61 for relational operators.

Set Operations

intersect Find set intersection of two vectorsismember Array elements that are members

of setissorted Determine whether set elements are

in sorted ordersetdiff Find set difference of two vectorssetxor Find set exclusive OR of two vectors

1-68


union Find set union of two vectorsunique Find unique elements of vector

Date and Time Operations

addtodate Modify date number by fieldcalendar Calendar for specified monthclock Current time as date vectorcputime Elapsed CPU timedate Current date stringdatenum Convert date and time to serial date

numberdatestr Convert date and time to string

formatdatevec Convert date and time to vector of

componentseomday Last day of monthetime Time elapsed between date vectorsnow Current date and timeweekday Day of week

Programming in MATLAB

M-Files and Scripts (p. 1-70) Declare functions, handlearguments, identify dependencies,etc.

Evaluation (p. 1-71) Evaluate expression in string, applyfunction to array, run script file, etc.

Timer (p. 1-72) Schedule execution of MATLABcommands

1-69


Variables and Functions in Memory(p. 1-73)

List files in memory, clear M-filesin memory, assign to variable innondefault workspace, refreshcaches

Control Flow (p. 1-74) if-then-else, for loops, switch-case,try-catch

Error Handling (p. 1-75) Generate warnings and errors, testfor and catch errors, retrieve mostrecent error message

MEX Programming (p. 1-76) Compile MEX function from C orFortran code, list MEX-files inmemory, debug MEX-files

M-Files and Scripts

addOptional (inputParser) Add optional argument toinputParser schema

addParamValue (inputParser) Add parameter-value argument toinputParser schema

addRequired (inputParser) Add required argument toinputParser schema

createCopy (inputParser) Create copy of inputParser objectdepdir List dependent directories of M-file

or P-filedepfun List dependencies of M-file or P-fileecho Echo M-files during executionend Terminate block of code, or indicate

last array indexfunction Declare M-file functioninput Request user inputinputname Variable name of function inputinputParser Construct input parser object

1-70


mfilename Name of currently running M-filenamelengthmax Maximum identifier lengthnargchk Validate number of input argumentsnargin, nargout Number of function argumentsnargoutchk Validate number of output

argumentsparse (inputParser) Parse and validate named inputspcode Create protected M-file (P-file)script Script M-file descriptionsyntax Two ways to call MATLAB functionsvarargin Variable length input argument listvarargout Variable length output argument list

Evaluation

ans Most recent answerarrayfun Apply function to each element of

arrayassert Generate error when condition is

violatedbuiltin Execute built-in function from

overloaded methodcellfun Apply function to each cell in cell

arrayecho Echo M-files during executioneval Execute string containing MATLAB

expressionevalc Evaluate MATLAB expression with

capture

1-71



feval Evaluate functioniskeyword Determine whether input is

MATLAB keywordisvarname Determine whether input is valid

variable namepause Halt execution temporarilyrun Run script that is not on current

pathscript Script M-file descriptionstructfun Apply function to each field of scalar

structuresymvar Determine symbolic variables in

expressiontic, toc Measure performance using

stopwatch timer

Timer

delete (timer) Remove timer object from memorydisp (timer) Information about timer objectget (timer) Timer object propertiesisvalid (timer) Determine whether timer object is

validset (timer) Configure or display timer object

propertiesstart Start timer(s) runningstartat Start timer(s) running at specified

timestop Stop timer(s)

1-72


timer Construct timer objecttimerfind Find timer objectstimerfindall Find timer objects, including

invisible objectswait Wait until timer stops running

Variables and Functions in Memory

ans Most recent answerassignin Assign value to variable in specified

workspacedatatipinfo Produce short description of input

variablegenvarname Construct valid variable name from

stringglobal Declare global variablesinmem Names of M-files, MEX-files, Sun

Java classes in memoryisglobal Determine whether input is global

variablememory Display memory informationmislocked Determine whether M-file or

MEX-file cannot be cleared frommemory

mlock Prevent clearing M-file or MEX-filefrom memory

munlock Allow clearing M-file or MEX-filefrom memory

namelengthmax Maximum identifier lengthpack Consolidate workspace memory

1-73


persistent Define persistent variablerehash Refresh function and file system

path caches

Control Flow

break Terminate execution of for or whileloop

case Execute block of code if condition istrue

catch Specify how to respond to error intry statement

continue Pass control to next iteration of foror while loop

else Execute statements if condition isfalse

elseif Execute statements if additionalcondition is true

end Terminate block of code, or indicatelast array index

error Display message and abort functionfor Execute block of code specified

number of timesif Execute statements if condition is

trueotherwise Default part of switch statementparfor Parallel for-loopreturn Return to invoking functionswitch Switch among several cases, based

on expression

1-74


try Attempt to execute block of code, andcatch errors

while Repeatedly execute statements whilecondition is true

Error Handling

addCause (MException) Append MException objectsassert Generate error when condition is

violatedcatch Specify how to respond to error in

try statementdisp (MException) Display MException objecteq (MException) Compare MException objects for

equalityerror Display message and abort functionferror Query MATLAB software about

errors in file input or outputgetReport (MException) Get error message for exceptionintwarning Control state of integer warningsisequal (MException) Compare MException objects for

equalitylast (MException) Last uncaught exceptionlasterr Last error messagelasterror Last error message and related

informationlastwarn Last warning messageMException Construct MException objectne (MException) Compare MException objects for

inequalityrethrow Reissue error

1-75


rethrow (MException) Reissue existing exceptionthrow (MException) Terminate function and issue

exceptiontry Attempt to execute block of code, and

catch errorswarning Warning message

MEX Programming

dbmex Enable MEX-file debugging (onUNIX platforms)

inmem Names of M-files, MEX-files, SunJava classes in memory

mex Compile MEX-function from C/ C++or Fortran source code

mex.getCompilerConfigurations Get compiler configurationinformation for building MEX-files

mexext Binary MEX-file name extension

1-76

Object-Oriented Programming


Classes and Objects (p. 1-77) Get information about classes andobjects

Handle Classes (p. 1-78) Define and use handle classesEvents and Listeners (p. 1-79) Define and use events and listenersMeta-Classes (p. 1-79) Access information about classes

without requiring instances

Classes and Objects

class Create object or return class of objectclassdef Class definition key wordsfieldnames Field names of structure, or public

fields of objectimport Add package or class to current

import listinferiorto Specify inferior class relationshipisa Determine whether input is object

of given classisobject Determine if input is MATLAB

objectloadobj Modify how load function loads

objectsmethods Information on class methodsmethodsview Information on class methods in

separate windowproperties Display class property namessaveobj Modify how save function saves

objectssubsasgn Subscripted assignment for objects

1-77


subsindex Subscripted indexing using object asindex

subsref Subscripted reference for objectssubstruct Create structure argument for

subsasgn or subsrefsuperiorto Establish superior class relationship

Handle Classes

addlistener (handle) Create event listeneraddprop (dynamicprops) Add dynamic propertydelete (handle) Handle object destructor functiondynamicprops Abstract class used to derive handle

class with dynamic propertiesfindobj (handle) Find objects matching specified

conditionsfindprop (handle) Find meta.property object

associated with property nameget (hgsetget) Query property values of handle

objects derived from hgsetget classgetdisp (hgsetget) Override to change command

window displayhandle Abstract class for deriving handle

classeshgsetget Abstract class used to derive handle

class with set and get methodsisvalid (handle) Is object valid handle class objectnotify (handle) Notify listeners that event is

occurringrelationaloperators (handle) Equality and sorting of handle

objects

1-78


set (hgsetget) Assign property values to handleobjects derived from hgsetget class

setdisp (hgsetget) Override to change commandwindow display

Events and Listeners

addlistener (handle) Create event listenerevent.EventData Base class for all data objects passed

to event listenersevent.listener Class defining listener objectsevent.PropertyEvent Listener for property eventsevent.proplistener Define listener object for property

eventsevents Display class event namesnotify (handle) Notify listeners that event is

occurring

Meta-Classes

meta.class meta.class class describesMATLAB classes

meta.class.fromName Return meta.class object associatedwith named class

meta.DynamicProperty meta.DynamicProperty classdescribes dynamic property ofMATLAB object

meta.event meta.event class describesMATLAB class events

meta.method meta.method class describesMATLAB class methods

1-79


meta.package meta.package class describesMATLAB packages

meta.package.fromName Return meta.package object forspecified package

meta.package.getAllPackages Get all top-level packagesmeta.property meta.property class describes

MATLAB class propertiesmetaclass Return meta.class object

1-80

File I/O

File I/O

File Name Construction (p. 1-81) Get path, directory, filenameinformation; construct filenames

File Opening, Loading, and Saving(p. 1-82)

Open files; transfer data betweenfiles and MATLAB workspace

Memory Mapping (p. 1-82) Access file data via memory mapusing MATLAB array indexing

Low-Level File I/O (p. 1-82) Low-level operations that use a fileidentifier

Text Files (p. 1-83) Delimited or formatted I/O to textfiles

XML Documents (p. 1-84) Documents written in ExtensibleMarkup Language

Spreadsheets (p. 1-84) Excel and Lotus 1-2-3 filesScientific Data (p. 1-85) CDF, FITS, HDF formatsAudio and Audio/Video (p. 1-88) General audio functions;

SparcStation, WAVE, AVI filesImages (p. 1-90) Graphics filesInternet Exchange (p. 1-91) URL, FTP, zip, tar, and e-mail

To see a listing of file formats that are readable from MATLAB, go to fileformats.

File Name Construction

filemarker Character to separate file name andinternal function name

fileparts Parts of file name and pathfilesep Directory separator for current

platformfullfile Build full filename from parts

1-81


tempdir Name of system’s temporarydirectory

tempname Unique name for temporary file

File Opening, Loading, and Saving

daqread Read Data Acquisition Toolbox™(.daq) file

importdata Load data from disk fileload Load workspace variables from diskopen Open files based on extensionsave Save workspace variables to diskuiimport Open Import Wizard to import datawinopen Open file in appropriate application

(Windows)

Memory Mapping

disp (memmapfile) Information about memmapfileobject

get (memmapfile) Memmapfile object propertiesmemmapfile Construct memmapfile object

Low-Level File I/O

fclose Close one or more open filesfeof Test for end-of-fileferror Query MATLAB software about

errors in file input or output

1-82

File I/O

fgetl Read line from file, discardingnewline characters

fgets Read line from file, keeping newlinecharacters

fopen Open file, or obtain informationabout open files

fprintf Write formatted data to filefread Read binary data from filefrewind Move file position indicator to

beginning of open filefscanf Read formatted data from a text filefseek Set file position indicatorftell File position indicatorfwrite Write binary data to file

Text Files

csvread Read comma-separated value filecsvwrite Write comma-separated value filedlmread Read ASCII-delimited file of numeric

data into matrixdlmwrite Write matrix to ASCII-delimited filefileread Return contents of file as string

vectortextread Read data from text file; write to

multiple outputstextscan Read formatted data from text file

or string

1-83


XML Documents

xmlread Parse XML document and returnDocument Object Model node

xmlwrite Serialize XML Document ObjectModel node

xslt Transform XML document usingXSLT engine

Spreadsheets

Microsoft Excel (p. 1-84) Read and write Microsoft Excelspreadsheet

Lotus 1-2-3 (p. 1-84) Read and write Lotus WK1spreadsheet

Microsoft Excel

xlsfinfo Determine whether file contains aMicrosoft® Excel® spreadsheet

xlsread Read Microsoft Excel spreadsheetfile

xlswrite Write Microsoft Excel spreadsheetfile

Lotus 1-2-3

wk1finfo Determine whether file contains1-2-3 WK1 worksheet

wk1read Read Lotus 1-2-3 WK1 spreadsheetfile into matrix

wk1write Write matrix to Lotus 1-2-3 WK1spreadsheet file

1-84

File I/O

Scientific Data

Common Data Format (p. 1-85) Work with CDF filesNetwork Common Data Form(p. 1-85)

Work with netCDF files

Flexible Image Transport System(p. 1-87)

Work with FITS files

Hierarchical Data Format (p. 1-87) Work with HDF filesBand-Interleaved Data (p. 1-88) Work with band-interleaved files

Common Data Format

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