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# 19. Reference

There are many MATLAB features which cannot be included in these introductory notes. Listed below are some of the MATLAB functions and operators available, grouped by subject area. [Source: MATLAB User's Guide, version 3.5] Use the on-line help facility or consult the User's Guide for more detailed information on the functions.

There are many functions beyond these. There exist, in particular, several "toolboxes" of functions for specific areas; included among such are signal processing, control systems, robust-control, system identification, optimization, splines, chemometrics, mu-analysis and synthesis, state-space identification, and neural networks. [The toolboxes, which are optional, may not be installed on your system.] These can be explored via the command help.

[Note: Some of the following tables require a tables-aware browser, such as Netscape 1.1N or later. - Ed.]

 help help facility demo run demonstrations who list variables in memory what list M-files on disk size row and column dimensions length vector length clear clear workspace computer type of computer ^C local abort exit exit MATLAB quit same as exit

Matrix Operators Array Operators
 + addition - subtraction * multiplication / division \ left division ^ power ' conjugate transpose
 + addition - subtraction .* multiplication ./ division .\ left division .^ power .' transpose

Relational and Logical Operators
 < less than <= less than or equal > greater than >= greater than or equal == equal ~= not equal
 & and | or ~ not

Special Characters
 = assignment statement [ used to form vectors and matrices ] see [ ( arithmetic expression precedence ) see ( . decimal point ... continue statement to next line , separate subscripts and function arguments ; end rows, suppress printing % comments : subscripting, vector generation ! execute operating system command

Special Values
 ans answer when expression not assigned eps floating point precision pi 3.14159... i, j sqrt(-1) inf infinity NaN Not-a-Number clock wall clock date date flops floating point operation count nargin number of function input arguments nargout number of function output arguments

Disk Files
 chdir change current directory delete delete file diary diary of the session dir directory of files on disk load load variables from file save save variables to file type list function or file what show M-files on disk fprintf write to a file pack compact memory via save

Special Matrices
 compan companion diag diagonal eye identity gallery esoteric hadamard Hadamard hankel Hankel hilb Hilbert invhilb inverse Hilbert linspace linearly spaced vectors logspace logarithmically spaced vectors magic magic square meshdom domain for mesh points ones constant pascal Pascal rand random elements toeplitz Toeplitz vander Vandermonde zeros zero

Matrix Manipulation
 rot90 rotation fliplr flip matrix left-to-right flipud flip matrix up-to-down diag diagonal matrices tril lower triangular part triu upper triangular part reshape reshape .' transpose : convert matrix to single column; A(:)

Relational and Logical Functions
 any logical conditions all logical conditions find find array indices of logical values isnan detect NaNs finite detect infinities isempty detect empty matrices isstr detect string variables strcmp compare string variables

Control Flow
 if conditionally execute statements elseif used with if else used with if end terminate if, for, while for repeat statements a number of times while do while break break out of for and while loops return return from functions pause pause until key pressed

Programming and M-Files
 input get numbers from keyboard keyboard call keyboard as M-file error display error message function define function eval interpret text in variables feval evaluate function given by string echo enable command echoing exist check if variables exist casesen set case sensitivity global define global variables startup startup M-file getenv get environment string menu select item from menu etime elapsed time

Text and Strings
 abs convert string to ASCII values eval evaluate text macro num2str convert number to string int2str convert integer to string setstr set flag indicating matrix is a string sprintf convert number to string isstr detect string variables strcomp compare string variables hex2num convert hex string to number

Command Window
 clc clear command screen home move cursor home format set output display format disp display matrix or text fprintf print formatted number echo enable command echoing

Graph Paper
 plot linear X-Y plot loglog loglog X-Y plot semilogx semi-log X-Y plot semilogy semi-log X-Y plot polar polar plot mesh 3-dimensional mesh surface contour contour plot meshdom domain for mesh plots bar bar charts stairs stairstep graph errorbar add error bars

Graph Annotation
 title plot title xlabel x-axis label ylabel y-axis label grid draw grid lines text arbitrarily position text gtext mouse-positioned text ginput graphics input

Graph Window Control
 axis manual axis scaling hold hold plot on screen shg show graph window clg clear graph window subplot split graph window

Graph Window Hardcopy
 print send graph to printer prtsc screen dump meta graphics metafile

Elementary Math Functions
 abs absolute value or complex magnitude angle phase angle sqrt square root real real part imag imaginary part conj complex conjugate round round to nearest integer fix round toward zero floor round toward $-\infty$ ceil round toward $\infty$ sign signum function rem remainder exp exponential base e log natural logarithm log10 log base 10

Trigonometric Functions
 sin sine cos cosine tan tangent asin arcsine acos arccosine atan arctangent atan2 four quadrant arctangent sinh hyperbolic sine cosh hyperbolic cosine tanh hyperbolic tangent asinh hyperbolic arcsine acosh hyperbolic arccosine atanh hyperbolic arctangent

Special Functions
 bessel bessel function gamma gamma function rat rational approximation erf error function inverf inverse error function ellipk complete elliptic integral of first kind ellipj Jacobian elliptic integral

Decompositions and Factorizations
 balance balanced form backsub backsubstitution cdf2rdf convert complex-diagonal to real-diagonal chol Cholesky factorization eig eigenvalues and eigenvectors hess Hessenberg form inv inverse lu factors from Gaussian elimination nnls nonnegative least squares null null space orth orthogonalization pinv pseudoinverse qr orthogonal-triangular decomposition qz QZ algorithm rref reduced row echelon form schur Schur decomposition svd singular value decomposition

Matrix Conditioning
 cond condition number in 2-norm norm 1-norm,2-norm,F-norm,$\infty$-norm rank rank rcond condition estimate (reciprocal)

Elementary Matrix Functions
 expm matrix exponential logm matrix logarithm sqrtm matrix square root funm arbitrary matrix function poly characteristic polynomial det determinant trace trace kron Kronecker tensor product

Polynomials
 poly characteristic polynomial roots polynomial roots---companion matrix method roots1 polynomial roots---Laguerre's method polyval polynomial evaluation polyvalm matrix polynomial evaluation conv multiplication deconv division residue partial-fraction expansion polyfit polynomial curve fitting

Column-wise Data Analysis
 max maximum value min minimum value mean mean value median median value std standard deviation sort sorting sum sum of elements prod product of elements cumsum cumulative sum of elements cumprod cumulative product of elements diff approximate derivatives hist histograms corrcoef correlation coefficients cov covariance matrix cplxpair reorder into complex pairs

Signal Processing
 abs complex magnitude angle phase angle conv convolution corrcoef correlation coefficients cov covariance deconv deconvolution fft radix-2 fast Fourier transform fft2 two-dimensional FFT ifft inverse fast Fourier transform ifft2 inverse 2-D FFT fftshift FFT rearrangement

Numerical Integration
 quad numerical function integration quad8 numerical function integration

Differential Equation Solution
 ode23 2nd/3rd order Runge-Kutta method ode45 4th/5th order Runge-Kutta-Fehlberg method

Nonlinear Equations and Optimization
 fmin minimum of a function of one variable fmins minimum of a multivariable function fsolve solution of a system of nonlinear equations (zeros of a multivariable function) fzero zero of a function of one variable

Interpolation
 spline cubic spline table1 1-D table look-up table2 2-D table look-up