MATLAB Quick Reference MATLAB 2007b Starting MATLAB matlab start interactive MATLAB session Stopping MATLAB quit or exit exit MATLAB Ctrl-C stop current command and return to

top-level prompt. Getting Help help list all commands and built-in variables help cmd briefly describes the command based on t

header of the m-file. he

apital

ay.

, t) compare strings. The strings must be

imit imit Specify a range of values

in ents

trings and Comm

ence of

aracter.

ex Expressicts the elements of a matrix, where

g:

A{selection}

Selected Built-inInf, NaNA M ng value

t explicitly assigned

lookfor str search for command based on str. Command-Line Cursor Motion ↑ scroll up through the command history. ↓ scroll down through the command history. HOME go to the start of a command line. END go to the end of the command line. Ctrl-← move backward a word. Ctrl-→ move forward a word. TAB complete a command or variable name. Shell Commands cd dir change the working directory to dir pwd print the working directory ls print the directory listing getenv(string) returns the value of the named

environment variable. [status,result]=system(cmd) executes

arbitrary shell command string, cmd, and returns the status and the result of the string.

Matrices

Square brackets delimit literal matrices. Commas separate elements on the same row. Semicolons separate rows. Commas may be replaced by spaces, and semicolons may be replaced by one or more newlines. Elements of a matrix may be arbitrary expressions, assuming all the dimensions agree. Generic matrices will denoted as a cletter, for example, A. A vector, which is, either a row or column matrix will be denoted by a lower case letter, for example, x. [x, y, ... ] enter a row vector. [x; y; ... ] enter a column vector. [w, x; y, z ] enter a 2-by-2 matrix.

Multi-dimensional Arrays Multi-dimensional arrays may be created with the

cat or reshape commands from two-dimensional submatrices. squeeze(A) remove the singleton dimensions of the

array. ndims(A) returns the number of dimensions in the

array. Cells and Structures F.field = ... set a field of a structure. F{idx} = ... set an element of a cell array. cellfun(F, c) apply a function to elements of cell arrfieldnames(F) returns the fields of a structure. Strings strcmp (s

identical for it to return true. strcat (s, t, ...) concatenate strings Ranges base:lbase:incr:l

beginn g with base with no elemgreater than limit. If it is omitted, the default value of incr is 1. Negative increments are permitted.

on Escape Sequences SA string constant consists of a sequ

characters enclosed in single-quote marks. \\ a literal backslash.

e ch\’ a literal single-quot\n newline, ASCII code 10.

e 9. \t horizontal tab, ASCII cod nd ons IA(selection)sele

selection can be any of the followin1) “2,3” selects the entry located at the 2nd row and 3rd column of the matrix; 2) “2” selects the second entry of a vector; 3) “a:b,2” selects the values in rows between a and b and the second column; 4) “:,2” selects all the values in the secondcolumn; 5) “4:end,2” selects all the values in the second column and in rows starting at the 4th row and continuing to the end.

selects the elements of a cell array, where selection can be any of the following: 1) “2,3” selects the entry located at the 2nd

row and 3rd column of the matrix; 2) “2” selects the second entry of a vector; 3) “a:b,2” selects the values in rows between a and b and the second column; 4) “:,2” selects all the values in the second column; 5) “4:end,2” selects all the values in the second column and in rows starting at the 4th row and going to the end.

Functions IEEE infinity, NaN

issiNans last result noeps machine precision pi π

i or j 1− realmax maximum representable value rea ilmin m nimum representable value

x)= e ndexed

ments. y.

i

ltiplication

, this is

Assignment Expressions

xpr var = e assign expression to variable. var (id xpr assign expression to i

variable. var (idx) = [] delete the indexed ele

var {idx} = expr assign elements of a cell arra

emenArithmetic and Incr t Operators x+y addition x–y subtract on x*y matrix multiplication

ux.*y element by element mx/y matrix right division x./y element by element right division X\y left division. For a full-rank system

equal to 1X y− . For non-full-rank systems, res this is equivalent to the least-squa

solution, ( ) 1T TX X X y−

.

power operator element b wer operator negation

x^y x.^y y element po-x

tranx’ complex conjugate transpose x.’ spose

Comparison and Boolean Operators These operators work on an element-by

basi ments are always evaluated. -element

al to y.

usual ons are and y

e can rted to scalars using the

able of easing e.

ent separators

co

vision

T

cute commands ge vector is

hed. This is MATLAB’s FOR loop. xecutes

break

ndit cutes true.

ed.

ition n is

.

try; body;

Defining Functiist);

d outputs ist

or a

Function Handl@func @(var1, ...

nonymous function handles take opy of the variables in the current

func2str (h

error (messel.

lear pattern clear variables matching the given pattern string

ether str exists.

A are nonzero.

ices of the nonzero elements

umns

ns

he maximum value in each of the

an n-by-n diagonal matrix.

m) an n-by-m matrix of zeros.

m) es. [x,y]=size(A) e size of A, where x is the

er of

ts in A.

expm (A) atrix onential of A. - computes the -norm of the matrix, .

omputes the QR-factorisation of A.

f

dimen

s. Both argux < y true if x is less than y. x <= y x true if is less than or equal to y. x == y true if x is equal to y.

or equx >= y true if x is greater thanx > y true if x is greater than y.

y. x~=y true if x is not equal tox & y true if both x and y are true.

y is true. x | y true if at least one of x or ~bool true if bool is false.

Note: if x and y are scalars than the comparis performed. If x is a vector or matrix

l the criterion.is a scalar, then all entries must be fulfi Short-circuit Boolean Operators

Operators evaluate left-to-right. Operands are only evaluated if necessary, stopping once overall truth valube determined. Operands are conveall function. x && y true if both x and y are true. x || y true if at least one of x or y is true.

PrecedOperator ence T MATLAB operators, in order of incr

precedenc; , statem= assignment, groups left to right || && logical OR and AND | & element-wise OR and AND < <= == >= > != relational operators : lon + - addition and subtraction */\ .* ./ .\ multiplication and di’ .’ transpose - ! unary minus, logical NO

xponent^ .^ e iation

rol StatemeCont nts efor i =range; commands; end; Ex

until the last entry of the ranreac

while (condition); commands; end; Ecommands until the condition is false. Thisis MATLAB’s WHILE loop. exits the innermost loop

return return to the calling function. if (condition); commands; end;

executes the commands if the condition is true.

if (co ion); commands1; else;execommands2; end;

commands1 if the condition is Otherwise, commands2 is execut

if (condition1); commands1; elseif (condition2); commands2;…; else; commandsE; end executes commands1 if the first cond

itiois true. Otherwise, the second condtested and if true commands2 is executedThis can be continued, with the final conditions ending in an “else” and then thecommandsE will be executed if none of the conditions are satisfied. catch; cleanup; end; executes the body. If the body fails, the code in clean-up is executed.

ons tList]=fctName(argLfunction [oufunction-body; return; defines a function, called fctName,

ch has inputs argList anwhioutList. Both outList and argLcan be empty, contain a single variable, contain a list of variables separated bycomma.

es defines a function handle to func. ) expr defines an anonymous function handle. Aa cworkspace.

str2func (str) creates a function handle from astring. andle) returns a string representation of afunction handle.

...)handle (arg1, evaluates a function handle.

feval (func, args) evaluates a function handle or string by passing the remaining

func. args to

Miscellaneous Functions eval(str) evaluates a string, str, as a command.

age) prints the error message and returns to top lev

c

exist(str) checks whrem(x, y) finds the remainder of x divided by y. Basic Matrix Manipulations

urns throws(A) ret e number of rows in A. columns(A) return the number of columns in A. all(A) checks if all the elements of any(A) checks if any of the elements in A are

nonzero. find(A) returns the ind

of A. sum(A) sums the elements in each of the col

of A. prod(A) finds the product of the elements of A. min(A) finds the minimum value in each colum

of A. max(A) finds t

columns of A. diag(n) creates eye(n) creates an n-by-n identity matrix.

, ones(n creates an n-by-m matrix of ones. zeros(n, m) creates rand(n, creates an n-by-m matrix of random valu

Determines thnumber of rows, and y is the numbcolumns in A.

length(A) Returns the total number of elemen Linear Algebra chol(A) Cholesky factorisation of A. det(A) computes the determinant of matrix, A. eig(A) computes the eigenvalues of A.

computes the m expinv(A) or A^ 1 inverts a square matrix, A. norm(A, p) p Aqr(A) crank(A) finds the rank of matrix A. svd(A) finds the singular value decomposition o

A. cross(x,y) Determines the cross product for two

3- sional vectors, x and y.

Signal Processing usfft(a) computes the Fast Fourier Transform ing

)

a and b

b.

t) h

will

plot3(x,y,,z,format) plots a 3-D graph using

string, which can be omitted, describes how ata will be plotted. Linear axes are

surf(x,y,z) x is

t

loglog(x,y, have a

le. hist(x) title(string)

ylabel(stri

plots t

FFTW. ifft(a) computes the inverse FFT using FFTW. freqz(args) computes the finite impulse response (FIR

filter frequency response. filter(a,b,x) computes the filtered data based

on the filter transfer functions (which are given as polynomials in decreasing powers of z or z-1) and the original data, x.

conv(a,b) finds the convolution of 2 vectors a and

Plotting Functions plot(x,y,forma plots a 2-D graph using the data as

the point (x, y). The format string, whiccan be omitted, describes how the databe plotted. Linear axes are used.

the data as the point (x, y, z). The format

the dused. Creates a 3-dimensional graph, wherethe data for the x-axis, y is the data for they-axis, and z is the data for the z-axis.

fplot(‘function’,[l,u]) Plots a function over the range [l, u], where l is the lower poinand u is the upper point of the region, so that it appears correctly.

semilogx(x,y,format) plots a 2-D graph similar to plot, except that the scale for the x-axis is logarithmic.

plots a 2-D graph simsemilogy(x,y,format) ilar to plot, except that the scale for the y-axis is logarithmic. format) plots a 2-D graph similarto plot, except that both axeslogarithmic scaplots a histogram of the data.

sets the plot title. xlabel(string) sets the x-axis label.

ng) sets the y-axis label. sets the zzlabel(string) -axis label

legend(array) sets the legend. The data in array is a cell array containing an entry for each of the data.

plays grid on dis grids on a plot.

grid off removes grids from a plot. hold on holds the current plot.

. hold off stops holding the current plotsubplot(r,c,w), plot() creates an array of

with r rows and c columns, with the currenplot being located at point w, which is an integer given by ( )1d dr c cw = − + , where

he matrix.

es

d is the desired position in t

Table 1: Common Plot Formatting Codforformat meaning mat meaning

b blue g green r red w white c cyan m magenta y yellow k black . point o (letter) circle x cross, + x-mark + * star, ✴ s square

d di amond, ◇ v ▽

^ △ < ◁

> ▻ p ☆ h h exagram - solid : dotted -. dash-dot -- dashed

on TeX Codes

TeX Table 2: Comm

TeX Display Display^ sup cript su ipt ers _ bscr{} gro ing \a ha up lp α

\beta β \g amma γ \d a \t ta elt δ he θ

\la da mb λ \mu μ \pi π \ o rh ρ

\sigma σ \tau τ \phi χ \chi \psi ψ \ omega ω \ circ ° \it italics \rm Roman \partial ∂

\nabla \pm  \infty ∞ \bf b  old

Equati DEs, an uadratu

ore info ation abo the op s and required meters f hese func refer to nuals or more inv MATLA ummariesfsolv solv onlinea raic

odeID solv linear ary dif al equa ns. ID is a the fo g tags: 23, , 15s, 23t, 2

unctionum

tion can be an M-file. a

e value

feval(‘Mfil

as

s lies in the

the name of the

Polynomials Polynom

coefficients in decontaining the co e referred to as p aconv(p, q)

deconv(p, q

ynomial from the co-efficient

r,

putes the value of the polynomial, X.

of the polynomial, r. osition

o OFor mns, d Q

rmor t

e

re ut all tion

para tions maolved B s . e() s n r algeb equations.

() es nontio113

ordinn f

ferentillowin3tb. s.

y o23s,

quad() integrates nonlinear ffminsearch(‘f’,xo) Calculates the minim

of the function, f,based on an initial guess, xo. The funcThe output from the function must be scalar. Thus, a vector funtion can be converted to a scalar by taking the normal of the function. However, the values should

e thhave a similar magnitude or elsay not obtained m be very accurate.

fzero(‘f’,xo) Determines a zero of the function f based on the initial guess xo. The function can be an M-file. ename’,x1,x2,…,xn) or feval(handlef, x1,x2,…,xn) Evaluates an M-file using the variables given after the file name. There must be many variables as is necessary. The difference between the two form

nner ima n which the function is presented. In the first case, the actual name of the M-file is known, while in the second

handlefvariable, , stores thefunction.

ials are stored as a vector consisting of the creasing powers of x. The vectors efficients of the generic polynomials will bnd q. computes the convolution of 2 polynomials. ) computes the deconvolution of 2 polynomials (long division of a by b). create a polr=poly(p) vector.

polyval(r, x) computes the value of the polynomial, at a vector value of x.

polyvalm(r, X) comr, for a matrix (or set) of values

roots(r) finds the roots residue(p, q) finds the partial fraction decomp

of the ratio p / q.

C-style Input and Output fid=fopen(name, mode) open a file in mode

located at name and stores its identification in fid.

fclose(fid closes the file with identification fid. )

n by fid. The string contains the text and formatting desired, while variables is a vector containing the

ormatted. s

fgetl(fid) le with

ftell(fid)

frewind(fid)

a files s file).

’)s e,

erical data in A and all text data in B.

ple kernel. The symb he

al

b) “positipositive, t

c) “negati be negative, t

d) “unreal the variable to include complex numbers.

hen s.

disp

di

vp

ble2’Replaces all

ly

r

solve(f) Statistics corrcoef(x,

median(a)

un (p p,

p,df)Calculates the inverse t-distribution at a bili degrees

nt =regress(b,a multiple

form Ax = b rs:

contains the 100(1-alpha)% confidence intervals for the coefficients; res a vector that contains

residuals; resint a vector for residual

at

s.

Ci=nlparci( s the

ue of

[y,delta]=n

Copyright ©2009

fprintf(fid, string,variables) sends formatted output to the file with identification give

data to be fsprintf(fid, string, variables) send

formatted output to a string reads a line of text from the fiidentification, fid.

fgets(fid, len) reads len characters from the file with identification, fid. returns the file pointer position for the given file identification number, fid. moves the file pointer to the beginning of the file with the given file identification

su

number, fid. fread(fid, size, prec) reads binary datfwrite(fid, size, prec) writes binary data filefeof(fid) returns if the pointer is at EOF (end of Other Input and Output functions save filename var1,var2,... saves variables

(var1, var2,…) in the file called, filename.

load filename loads the variables stored in the given file.

[A B] = xlsread(‘filename’,’sheetname Reads an Excel file, ‘filename’, takethe data from the given spreadsheet nam‘sheetname’, and then stores all num

Symbolic Math

Matlab can perform symbol math using the Maolic variables are declared as using t

ms var1 var2 conditionsyntax “>>sy ”, where condition is any of the following:

real is limits tha) “ ” th e variable to only be in the redomain, that is, ∈R .

ve” this limits the variable to only be hat is, ≥0.

ve” this limits the variable to only hat is, ≤0. ” this undoes any of the above 3 statements

and allowsGenerally, the same function can be used for symbolic math as for numerical math. The following are special functions: simplify(expression) simplifies a given

expression. It should be run more tonce in order to truly simplify the result

pretty(expression) lays the results in a nice format.

gits(n) sets the precision for the evaluation of asymbolic expression to n-digits.

a(expression) evaluates an expression to the speficied precision.

bs(expression,{‘variable1’,’varia}, {value1,value2}) instance of variable1 with value1, which can be another variable and so on.

calc of thejacobian(v, [x y z]) ulates the Jacobianvector function, v, which is entered as a column vector, and the independent

d variables, x, y, and z. It should be notethat the vector function need not be directa function of the variables desired. The chain rule will, if necessary, be applied.

diff(f,’variableWRT’,n) calculates the nth ordederivative of the function, f, with respect to the variable variableWRT.

int(f,’variable’,a,b) integrates symbolically the function, f, with respect to the variable, variable and determines the exact value ofthe integral from a to b.

dsolve(f) Solves algebraically the differential equation, f. Algebraically solves the equation, f.

y) computes the correlation coefficient for the data.

cov(x, y) computes the covariance. mean(a) determines the mean value.

determines the median value. std(a) determines the standard deviation. var(a) determines the variance.

Statistical Toolbox The following f ctions require the statistical toolbox.Z=norminv )Calculates the Z-score for probability

which lies between 0 and 1. X=tinv(

proba ty, p, given the number ofof freedom, df. ,res,resint,stats[coeff,Ci ]A,alpha) Computes linear regression model of the and returns the following parametecoeff a vector of the estimated coefficients; Cint vector that

the analysis; stats a vector with the following entries: R2-statistic assuming ththe model contains a constant term; the F-statistic for the full model; p-value for the full model; and the estimated error variance.

[beta,r,J] = nlinfit(x,y,’FUN’,beta0) Performs non-linear regression. The x-datais given as x, while the y-data is given as y. The function, FUN that is to be fitted must be written as an M-file that takes 3 arguments: x, y, and the coefficient valueThe function should allow matrix evaluation. The initial guess is given as beta0. beta contains the estimated coefficients, r contains the residuals, and Jis the Jacobian evaluated at final calculation. beta,r,J,alpha) Calculate100(1-alpha)% confidence intervals for the coefficients, beta, given the residuals,r, and the Jacobian, J. The default valalpha is 0.05. lpredci(‘Fun’, x, beta,r,J) Calculates the 100(1-alpha)% predictionconfidence intervals for the non-linear function, Fun, given x, the estimated coefficients, beta, the residuals, r, the Jacobian, J. The function returns the predicted y-values, y, and the half-widthlengths, delta. Yuri Shardt. All rights reserved.