MATLAB – A brief Introduction !Rohit PathakSatyadhar Joshi

(Kindly Cite this work as: Satyadhar Joshi, Rohit Pathak; Online document Available at http: www.nanotechbiz.org; July 2009)

www.nanotechbiz.org

Contents What is MATLAB? Overview Elementary Mathematics Programming I/O M-Files

Basics of M-File Function and Script Files M-File Programming

Graphics 2D Plots 3D Plots

What is MATLAB ?

• It stands for MATrix LABoratory

•A set of Software comprising▫A Very High Level 4th Generation Language▫Computation Tools▫Visualization Tools▫Simulation Tools▫Integrated Development Environment

MATLAB’s System

• Language: arrays and matrices, control flow, I/O, data structures, user-defined functions and scripts

• Working Environment: editing, variable management, importing and exporting data, debugging, profiling

• Graphics system: 2D and 3D data visualization, animation and custom GUI development

• Mathematical Functions: basic (sum, sin,…) to advanced (fft, inv, Bessel functions, …)

• API: can use MATLAB with C, Fortran, and Java, in either direction

Parts of MATLAB

•Developed Environment•Programming Language•Graphics•Toolboxes•Application Program Interface

MATLAB’s Appeal• Interactive code development proceeds

incrementally; excellent development and rapid prototyping environment

•Basic data element is the auto-indexed array•This allows quick solutions to problems that

can be formulated in vector or matrix form•Powerful GUI tools•Large collection of toolboxes: collections of

topic-related MATLAB functions that extend the core functionality significantly

MATLAB Toolboxes• Math and Analysis

▫ Optimization▫ Requirements

Management Interface▫ Statistics▫ Neural Network▫ Symbolic/Extended Math▫ Partial Differential

Equations▫ PLS Toolbox▫ Mapping▫ Spline

• Data Acquisition and Import▫ Data Acquisition▫ Instrument Control▫ Excel Link▫ Portable Graph Object

• Signal & Image Processing▫ Signal Processing▫ Image Processing▫ Communications ▫ Frequency Domain System

Identification▫ Higher-Order Spectral

Analysis▫ System Identification▫ Wavelet▫ Filter Design

• Control Design ▫ Control System▫ Fuzzy Logic▫ Robust Control▫ μ-Analysis and Synthesis▫ Model Predictive Control

MATLAB’s Important Windows• Command Window: where you enter commands• Command History: running history of commands

which is preserved across MATLAB sessions• Current directory: Default is $matlabroot/work• Workspace: GUI for viewing, loading and saving

MATLAB variables• Array Editor: GUI for viewing and/or modifying

contents of MATLAB variables (openvar varname or double-click the array’s name in the Workspace)

• Editor/Debugger: text editor, debugger; editor works with file types in addition to .m (MATLAB “m-files”)

The MATLAB’s main interface window called the MATLAB desktop. It consist of Workspace, Command Window, Command History, Current Directory window, and the start button to just get you started.

The Editor Window is used to edit source files and other files such as .m files etc.

MATLAB’s help is very sophisticated. It provides help topics and tutorials on nearly every topic. There is a help for every function available in MATLAB.

Getting Help using Command Window

▫ >> help▫ HELP topics:▫ ▫ matlab\general - General purpose commands.▫ matlab\ops - Operators and special characters.▫ matlab\lang - Programming language constructs.▫ matlab\elmat - Elementary matrices and matrix manipulation.▫ matlab\elfun - Elementary math functions.▫ matlab\specfun - Specialized math functions.▫ matlab\matfun - Matrix functions - numerical linear algebra.▫ matlab\datafun - Data analysis and Fourier transforms.▫ matlab\polyfun - Interpolation and polynomials.▫ matlab\funfun - Function functions and ODE solvers.▫ matlab\sparfun - Sparse matrices.▫ matlab\scribe - Annotation and Plot Editing.▫ matlab\graph2d - Two dimensional graphs.▫ matlab\graph3d - Three dimensional graphs.▫ matlab\specgraph - Specialized graphs.▫ matlab\graphics - Handle Graphics.▫ …etc...

Command Line Help – Topic Help

▫ >> help matfun▫ Matrix functions - numerical linear algebra.▫ ▫ Matrix analysis.▫ norm - Matrix or vector norm.▫ normest - Estimate the matrix 2-norm.▫ rank - Matrix rank.▫ det - Determinant.▫ trace - Sum of diagonal elements.▫ null - Null space.▫ orth - Orthogonalization.▫ rref - Reduced row echelon form.▫ subspace - Angle between two subspaces.▫ …

Command Line Help – Function Help

▫ >> help det▫ DET Determinant.▫ DET(X) is the determinant of the square matrix X.▫ ▫ Use COND instead of DET to test for matrix▫ singularity.▫ ▫ See also cond.▫ ▫ Overloaded functions or methods (ones with the same▫ name in other directories)▫ help laurmat/det.m▫ ▫ Reference page in Help browser▫ doc det

Keyword’s Search in Help Entries

▫ >> lookfor who▫ newton.m: % inputs: 'x' is the number whose square

root we seek▫ testNewton.m: % inputs: 'x' is the number whose

square root we seek▫ WHO List current variables.▫ WHOS List current variables, long form. ▫ TIMESTWO S-function whose output is two times its

input.

▫ >> whos▫ Name Size Bytes Class Attributes▫ ans 1x1 8 double ▫ fid 1x1 8 double ▫ i 1x1 8 double

Variables Basics▫>> 16 + 24▫ans =▫ 40

▫>> product = 16 * 23.24▫product =▫ 371.84

▫>> product = 16 *555.24;▫>> product▫product =▫ 8883.8

Variable Basics▫ >> clear▫ >> product = 2 * 3^3;▫ >> comp_sum = (2 + 3i) + (2 - 3i);▫ >> show_i = i^2;▫ >> save three_things▫ >> clear▫ >> load three_things▫ >> who▫ Your variables are:▫ comp_sum product show_i ▫ >> product▫ product =▫ 54▫ >> show_i▫ show_i =▫ -1

MATLAB Data Types Basics• The basic data type used in MATLAB is the double

precision array

• No declarations needed: MATLAB automatically allocates required memory

• Resize arrays dynamically

• To reuse a variable name, simply use it in the left hand side

• of an assignment statement

• MATLAB displays results in scientific notation▫ Use File/Preferences and/or format function to change default▫ short (5 digits), long (16 digits)

Variables Basics• Variable names are case sensitive and over-written when re-

used

• Basic variable class: Auto-Indexed Array• Allows use of entire arrays (scalar, 1-D, 2-D, etc…) as operands• Vectorization: Always use array operands to get best

performance (see next slide)

• Terminology: “scalar” (1 x 1 array), “vector” (1 x N array), “matrix” (M x N array)

• Special variables/functions: ans, pi, eps, inf, NaN, i, nargin, nargout, varargin, varargout, ...

• Commands who (terse output) and whos (verbose output) show variables in Workspace

Multi-Dimensional Arrays▫ >> r = randn(2,3,4) % create a 3 dimensional array

filled with▫ normally distributed random

numbers▫ r(:,:,1) =▫ -0.6918 1.2540 -1.4410▫ 0.8580 -1.5937 0.5711▫ r(:,:,2) =▫ -0.3999 0.8156 1.2902▫ 0.6900 0.7119 0.6686▫ r(:,:,3) =▫ 1.1908 -0.0198 -1.6041▫ -1.2025 -0.1567 0.2573▫ r(:,:,4) =▫ -1.0565 -0.8051 0.2193▫ 1.4151 0.5287 -0.9219

Strings▫ >> hi = ' hello';▫ >> class = 'MATLAB';▫ >> hi▫ hi =▫ hello▫ >> class▫ class =▫ MATLAB▫ >> greetings = [hi class]▫ greetings =▫ helloMATLAB▫ >> vgreetings = [hi;class]▫ vgreetings =▫ hello▫ MATLAB

Diagonal Elements of Matrix▫ >> durer▫ durer =▫ 16 3 2 13▫ 5 10 11 8▫ 9 6 7 12▫ 4 15 14 1

▫ >> diag(durer) % diag plucks out the diagonal elements▫ ans =▫ 16▫ 10▫ 7▫ 1

▫ >> sum(diag(durer))▫ ans =▫ 34

Other Diagonal using Flip Left-Right

▫ >> durer▫ durer =▫ 16 3 2 13▫ 5 10 11 8▫ 9 6 7 12▫ 4 15 14 1

▫ >> fliplr(durer) % “flip left-right”▫ ans =▫ 13 2 3 16▫ 8 11 10 5▫ 12 7 6 9▫ 1 14 15 4▫ >> sum(diag(fliplr(durer)))▫ ans =▫ 34

Accessing Elements using Sub-Scripting

▫ >> durer▫ durer =▫ 16 3 2 13▫ 5 10 11 8▫ 9 6 7 12▫ 4 15 14 1

▫ >> diag_sum = durer(1,1) + durer(2,2) + durer(3,3)▫ diag_sum =▫ 33▫ >> durer(4,4) = pi▫ durer =▫ 16.0000 3.0000 2.0000 13.0000▫ 5.0000 10.0000 11.0000 8.0000▫ 9.0000 6.0000 7.0000 12.0000▫ 4.0000 15.0000 14.0000 3.1416

The colon operator▫>> 1:5 % use the colon operator to create row

vectors▫ans =▫ 1 2 3 4 5

▫>> 1:0.9:6 % you can vary the increment (0.9 in this case)

▫ans =▫ 1.0000 1.9000 2.8000 3.7000 4.6000

5.5000

The last element is always less than or equal to the upper limit

Scripts and Functions• Scripts do not accept input arguments, nor do they

produce output arguments. Scripts are simply MATLAB commands written into a file. They operate on the existing workspace.

• Functions accept input arguments and produce output variables. All internal variables are local to the function and commands operate on the function workspace.

• A file containing a script or function is called an m-file• If duplicate functions (names) exist, the first in the

search path (from path command) is executed.

Function - Example▫ function [a b c] = myfun(x, y)▫ b = x * y; a = 100; c = x.^2;

▫ >> myfun(2,3) % called with zero outputs▫ ans =▫ 100▫ >> u = myfun(2,3) % called with one output▫ u = ▫ 100▫ >> [u v w] = myfun(2,3) % called with all outputs▫ u =▫ 100▫ v =▫ 6▫ w =▫ 4

Syntax of Function• If the m-file name and function name differ, the

file name takes precedence

• Function names must begin with a letter

• First line must contain function followed by the most general calling syntax

• Statements after initial contiguous comments (help lines) are the body of the function

• Terminates on the last line or a return statement

If-Else Statement▫>> A = 2; B = 3;▫>> if A > B▫ 'A is bigger'▫ elseif A < B▫ 'B is bigger'▫ elseif A == B▫ 'A equals B'▫ else▫ error('Something odd is happening')▫ end▫ans =▫B is bigger

Switch Statement▫ >> n = 8▫ n =▫ 8▫ >> switch(rem(n,3))▫ case 0▫ m = 'no remainder'▫ case 1▫ m = ‘the remainder is one'▫ case 2▫ m = ‘the remainder is two'▫ otherwise▫ error('not possible')▫ end▫ m =▫ the remainder is two

For Loop▫>> for i = 2:5▫ for j = 3:6▫ a(i,j) = (i + j)^2▫ end▫ end▫>> a▫a =▫ 0 0 0 0 0 0▫ 0 0 25 36 49 64▫ 0 0 36 49 64 81▫ 0 0 49 64 81 100▫ 0 0 64 81 100 121

While Loop▫>> b = 4; a = 2.1; count = 0;▫>> while b - a > 0.01▫ a = a + 0.001;▫ count = count + 1;▫ end▫>> count▫count =▫ 1891

Loading and Saving Workspace• MATLAB can load and save data in .MAT format

• .MAT files are binary files that can be transferred across platforms; as much accuracy as possible is preserved.

• Load: load filename OR A = load(‘filename’)▫ loads all the variables in the specified file (the default

name is MATLAB.MAT)

• Save: save filename variables▫ saves the specified variables (all variables by default) in

the specified file (the default name is MATLAB.MAT)

Low-Level File I/O• File Opening and Closing

▫ fclose: Close one or more open files ▫ fopen: Open a file or obtain information about open files

• Unformatted I/O▫ fread: Read binary data from file ▫ fwrite: Write binary data to a file

• Formatted I/O▫ fgetl: Return the next line of a file as a string

without line terminator(s) ▫ fgets: Return the next line of a file as a string with line▫ terminator(s) ▫ fprintf: Write formatted data to file ▫ fscanf: Read formatted data from file

Low-Level File I/O• File Positioning

▫ feof: Test for end-of-file ▫ ferror: Query MATLAB about errors in file

input or output ▫ frewind: Rewind an open file ▫ fseek: Set file position indicator ▫ ftell: Get file position indicator

• • String Conversion

▫ sprintf: Write formatted data to a string ▫ sscanf: Read string under format control

Example•fid = fopen(‘filename’, ‘permission’);

•status = fclose(fid);

•fscanf: [A, count] = fscanf(fid,format,size);

• fprintf: count = fprintf(fid, format, A,...);

• fscanf and fprintf are similar to C version but vectorized

Format Specifiers• Specifier Description• %c Single character• %d Decimal notation (signed)• %e Exponential notation• %f Fixed-point notation• %g The more compact of %e or %f• %o Octal notation (unsigned)• %s String of characters• %u Decimal notation (unsigned)• %x Hexadecimal notation• etc.

Other I/O Commands• fgetl: line = fgetl(fid);

▫ reads next line from file without line terminator

• fgets: line = fgets(fid);▫ reads next line from file with line terminator

• textread: [A,B,C,...] = textread('filename','format',N)▫ reads N lines of formatted text from file filename

• sscanf: A = sscanf(s, format, size);▫ reads string under format control

• sprintf: s = sprintf(format, A);▫ writes formatted data to a string

Read and Write

•[data, count] = fread(fid, num, precision);

•count = fwrite(fid, data, precision);

•fread and fwrite are vectorized

File Pointer Commands• feof: tf = feof(fid);

▫ tests for end of file

• fseek: status = fseek(fid, offset, origin);▫ sets the file position

• ftell: position = ftell(fid);▫ gets the file position

• frewind: frewind(fid);▫ rewinds the file

• ferror: message = ferror(fid);▫ inquire about file I/O status

Structures• Multidimensional MATLAB arrays• Access elements using textual field

designators• Create structures by using periods (.):

▫ >> class.name = ‘MATLAB’;▫ >> class.day1 = ‘2/27/07’;▫ >> class.day2 = ‘2/28/07’;▫ >> class▫ class =▫ name: ‘MATLAB’▫ day1: ‘2/27/07’▫ day2: ‘2/28/07’

Using Structures• Structures are like arrays• Fields can be added one at a time:

▫ >> class(2).name = ‘MPI’;▫ >> class(2).day1 = ‘TBA’;▫ >> class(2).day2 = ‘TBA’;

• Can also use a single statement:

▫ >> class(2) = struct(‘name’,‘MPI’,...▫ ‘day1’,‘TBA’,‘day2’,‘TBA’)

Using Structures

•Consider the simple structure

▫ >> exam.name = ‘Jim Kirk’;▫ >> exam.score = 79;▫ >> exam(2).name = ‘Janice Lester’;▫ >> exam(2).score = 89;▫ >> [exam.score]▫ ans =▫ 79 89

Using Structures

•Can also create a cell array using curly braces:

▫ >> {exam.name}▫ ans = ▫ 'Jim Kirk' 'Janice Lester'

The MAX and MIN functions • [Y,I] = MAX(X) returns the indices of the maximum values in vector

I. If the values along the first non-singleton dimension contain more than one maximal element, the index of the first one is returned.

▫ >> max(rpm_raw)▫ ans =▫ 1115 1120 1043

▫ >> max(max(rpm_raw))▫ ans =▫ 1120

▫ >> [y,i] = max(rpm_raw)▫ y =▫ 1115 1120 1043▫ i =▫ 8 2 17

MIN Function▫ >> min(rpm_raw)▫ ans =▫ 1053 1053 961

▫ >> min(min(rpm_raw))▫ ans =▫ 961

▫ >> [y,i] = min(rpm_raw)▫ y =▫ 1053 1053 961▫ i =▫ 22 1 22

Median, Covariance and Standard Deviation• The median is used to calculate median, cov for covariance, std

for standard deviation, var for variance

▫ >> median(rpm_raw) % median along each column▫ ans =▫ 1080 1083.5 1004▫ >> cov(rpm_raw) % covariance of the data▫ ans =▫ 306.4 -34.76 32.192▫ -34.76 244.9 -165.21▫ 32.192 -165.21 356.25▫ >> std(rpm_raw) % standard deviation along each column▫ ans =▫ 17.504 15.649 18.875▫ >> var(rpm_raw) % variance is the square of std▫ ans =▫ 306.4 244.9 356.25

Polynomial Equation• The equationin MATLAB is represented as

▫ >> p = [1 -6 -72 -27]▫ p =▫ 1 -6 -72 -27

▫ >> roots(p)▫ ans =▫ 12.1229▫ -5.7345▫ -0.3884

Using Symbolic Computation Toolbox•syms or sym is used to declare symbols

▫>> syms x y▫>> y = x^4 + x^2 + (x*2) + 87 ▫y = ▫x^4 + x^2 + 2*x + 87

▫>> subs(y, x, 10)▫ans =▫ 10207

Differentiation and Integration• The diff and int functions are used to differentiate

and integrate respectively

▫ >> syms x y▫ >> y = x^2 + x + 1 ▫ y = ▫ x^2 + x + 1▫ ▫ >> differentiation = diff(y, x) ▫ differentiation = ▫ 2*x + 1▫ ▫ >> integration = int(y, x) ▫ integration = ▫ (x*(2*x^2 + 3*x + 6))/6

>> x = [0:pi/100:pi];>> y = sin(x);>> plot(x,y), title('Simple

Plot')

>> z = cos(x);>> plot(x,y,'g.',x,z,'b-.'),

title('More Complicated')

>> t = 0:pi/25:pi; >> [x,y,z] =

cylinder(4*cos(t)); >> subplot(2,1,1) >> contour(y) >> subplot(2,1,2) >> mesh(x,y,z) >> xlabel('x') >> ylabel('this is the y

axis') >> text(1,-2,0.5,... '\it{Note the gap!}')

Used to display multiple plots in the same figure window

subplot(m,n,i) subdivides the window into m-by-n subregions (subplots) and makes the ith subplot active for the current plot

>> subplot(2,3,1)>> plot(t, sin(t), 'r:square')>> axis([-Inf,Inf,-Inf,Inf])

>> subplot(2,3,3)>> plot(t, cos(t), 'g')>> axis([-Inf,Inf,-1,1])

>> subplot(2,3,5)>> plot(t, sin(t).*cos(t),

'b-.')>> axis([-Inf,Inf,-Inf,Inf])

mesh(Z) generates a wireframe view of matrix Z, where Z(i,j) define the height of a surface over the rectangular x-y grid

>> figure(2);>> [X,Y] = meshgrid(-

16:1.0:16);>> Z = sqrt(X.^2 + Y.^2

+ 5000);>> mesh(Z)

surf(Z) generates a colored faceted 3-D view of the surface.By default, the faces are quadrilaterals, each of constant color, with black mesh linesThe shading command allows you to control the view

>> figure(2);>> [X,Y] = meshgrid(-

16:1.0:16);>> Z = sqrt(X.^2 + Y.^2 +

5000);>> surf(Z)

>> shading flat

>> shading interp

>> colormap hot

>> colormap gray

>> colormap cool

>> colormap pink

Use to create, display, and label isolines determined by one or more matrices

contour(Z) generates isolines from values given by a matrix Z and displays it in 2-D

Use to create, display, and label isolines determined by one or more matrices

contour3(Z) generates isolines from values given by a matrix Z and displays it in 3-D

Reading Images• MATLAB can read images of various formats

including • BMP, HDF, JPEG, PCX, TIFF, XWD• Use function imread to read image files• imread reads indexed, intensity, and

truecolor images• Images are read into a uint8 matrix of

appropriate size• imread automatically determines the format

of the image based on information in the header

• You can specify a format as an optional second argument

Reading Image - Example▫>> Crusader = imread(’Crusader.jpg');▫>> image(Crusader)▫>> whos Crusader▫ Name Size Bytes Class▫ Crusader 186x250x3 139500 uint8 array▫ Grand total is 139500 elements using

139500 bytes

Writing Images• MATLAB can write images of various formats

including the following• BMP, HDF, JPEG, PCX, TIFF, XWD• Use function imwrite to write image files• imwrite writes indexed, intensity, and truecolor

images• Images are written as a uint8 matrix (converted

if necessary) of appropriate size along with colormaps (if necessary) and headers

• imwrite determines the format from extension of filename. You can specify an optional format if extension is absent or to force a particular format

Writing Images - Example▫>> Abrams = imread(‘Abrams.jpg');▫>> image(Abrams)▫>> whos Abrams▫ Name Size Bytes Class▫ Abrams 511x640x3 981120 uint8 array▫Grand total is 981120 elements using 981120

bytes▫>> % Write out tank as gray image▫>> AbramsGray = rgb2gray(Abrams);▫>> colormap gray;▫>> image(AbramsGray)▫>> imwrite(AbramsGray, gray, 'Abrams.bmp');

MEX Basics• MEX stands for MATLAB EXecutable • MEX files are C and FORTRAN programs that

are callable from MATLAB after compiling• Why?

▫Pre-existing C/FORTRAN programs can be called from MATLAB without rewriting codes in MATLAB

▫Computations that do not run fast enough in MATLAB, such as for loops, can be coded in C or FORTRAN for efficient implementation.

▫Access to hardware such as A/D, D/A converters, GPIB hardware, serial/parallel port, etc.

Using MEX

1. Prepare the C or Fortran MEX program according to MATLAB external interfacing rules

2. Compile the C or FORTRAN MEX program using MATLAB command “mex”

3. mex in turn makes use of external C or FORTRAN compilers

4. Call the compiled MEX function in the same way as calling any MATLAB function

Changing MATLAB’s Startup behavior•Customize MATLAB’s start-up behavior•Create startup.m file and place in:$matlabroot\work

•My startup.m file:▫addpath e:\download\MatlabMPI\src▫addpath e:\download\MatlabMPI\examples▫addpath .\MatMPI▫format short g▫format compact

MATLAB’s path• The addpath command adds directories to the MATLAB

search path. The specified directories are added to the beginning of the search path.

• rmpath is used to remove paths from the search path

▫ >> addpath('c:\');▫ >> matlabpath

▫ MATLABPATH▫ c:\▫ E:\MATLAB\R2006b\work▫ E:\MATLAB\R2006b\work\f_funcs▫ E:\MATLAB\R2006b\work\na_funcs▫ E:\MATLAB\R2006b\work\na_scripts▫ E:\MATLAB\R2006b\toolbox\matlab\general▫ E:\MATLAB\R2006b\toolbox\matlab\ops

Some common commands• ls / dir provide a directory listing of the current

directory

▫ >> ls▫ . .. sample.m ▫ >>

• pwd shows the current directory

▫ >> pwd▫ ans =▫ e:\Program Files\MATLAB\R2006b\work▫ >>

Some common commands• The system command can be used to run OS

commands• On Unix systems, the unix command can be used

as well• On DOS systems, the corresponding command is

dos

▫ >> dos('date')▫ The current date is: Thu 01/04/2007 ▫ Enter the new date: (mm-dd-yy) ▫ ▫ ans =▫ 0

Links of Online MATLAB Resources• www.mathworks.com/• www.mathtools.net/MATLAB• www.math.utah.edu/lab/ms/matlab/matlab.html• web.mit.edu/afs/athena.mit.edu/software/

matlab/• www/home.html• www.utexas.edu/its/rc/tutorials/matlab/• www.math.ufl.edu/help/matlab-tutorial/• www.indiana.edu/~statmath/math/matlab/

links.html• www-h.eng.cam.ac.uk/help/tpl/programs/

matlab.html

Thanking YouRohit PathakSatyadhar JoshiSalman AhmedRipudaman Singh

www.nanotechbiz.org