University:
Boston University
Course:
CAS MA 511 | Introduction to Analysis I
Academic year:

2019
Views:

97

Pages:

20
Author:

Clint W.

INTRODUCTION TO MATLAB Introduction to MATLAB 2  It is an interactive, integrated, environment • for numerical/symbolic, scientific computations and other apps. • shorter program development and debugging time than traditional • • • • programming languages such as FORTRAN and C. slower (compared with FORTRAN or C) because it is interpreted. automatic memory management; no need to declare arrays. intuitive, easy to use. compact notations. Introduction to MATLAB  Latest version is MATLAB 2014a  For Windows: double click MATLAB icon  For Linux clusters: scc1% matlab  Either case spawns a MATLAB window with >> prompt. >> >> >> >> >> >> >> >> doc >> >> 3 Introduction to MATLAB 4  Variables  case sensitive, NAME and Name are 2 distinct names. • variable begins with a , A2z or a2z • can be a mix of letters, digits, and underscores ( vector_A) [] () , @ # $& ^ • reserved characters: % = + – ~ ; : ! • up to 63 characters (no reserved characters) • Commands/Functions/scripts • performs specific tasks; same naming rules apply  File names command files should be named with a suffix of ".m", . An m-file typically contains a sequence of MATLAB commands that will be executed in order • An m-file may also contain other m-files • A file may also be just data (strings, numbers • 5 Introduction to MATLAB , • Some characters are • • • • • by for various purposes. Some as arithmetic or matrix operators: =, +, , *, / , \ and others are used to perform a multitude of operations. Reserved characters cannot be used in variable or function names. They may have multiple uses. >> >> >> a= 3 >> >> >> >> >> d= 6 Introduction to MATLAB • >> x= 1 3 5 7 • >> y= 3 4 5 1 4 2 5 3 6 • >> X= • >> ans = 6 9 6 Introduction to MATLAB >> >> >> x= 1 2 3 >> ans = 2 >> ans = 6 3 7 Introduction to MATLAB • >> Volume in drive C has no label. Volume Serial Number is 6860-EA46 Directory of C:\Program Files\MATLAB704\work 01/31/2007 10:56 AM . 01/31/2007 10:56 AM .. 06/13/2006 12:09 PM 12 foo.exe 06/13/2006 08:57 AM 77 mkcopy.m • >> total 0 -rw-r--r-- 1 kadin scv 0 Jan 19 15:53 file1.m -rw-r--r-- 1 kadin scv 0 Jan 19 15:53 file2.m -rw-r--r-- 1 kadin scv 0 Jan 19 15:53 file3.m >> 8 9 Introduction to MATLAB >> >> >> 5 7 9 >> A= 1 4 2 5 3 6 >> B= 1 4 2 5 3 6 Other ways to create B ? (hint: with & directly) Introduction to MATLAB >> C= 14 32 32 77 1 16 4 25 >> D= 9 36 >> E= 1 1 1 1 1 1 >> Your variables are: A B C D E a b d 10 11 Introduction to MATLAB >> Name A B C D E a b c >> >> Name A >> Size 2x3 3x2 2x2 2x3 2x3 1x3 1x3 1x3 Size 2x3 Bytes 48 48 32 48 48 24 24 24 Class double double double double double double double double Bytes Class 24 single Attributes Introduction to MATLAB Utilities to initialize or define arrays: Trigonometric and hyperbolic functions : These utilities can be used on scalar or vector inputs >> 12 Introduction to MATLAB Scalar operation . . . for j=1:3 % column index for i=1:3 % row index a(i,j) = rand; % a(i,j) = random number b(i,j) = 0; % b(i,j) = 0 if a(i,j) > 0.5 % unless . . . b(i,j) = 2; end end end Equivalent vector operations . . . A = rand(3); % A is a 3x3 random number double array B = zeros(3); % Initialize B as a 3x3 array of zeroes B(A > 0.5) = 2; % for all A(i,j) > 0.5, set B(i,j) to 2 13 Introduction to MATLAB 14 A cell array is a special array of arrays. Each element of the cell array may point to a scalar, an array, or another cell array. >> >> >> >> C= [2x2 double] [2x1 double] >> ans = 1 3 4 2 >> Related utilities: [1x3 double] {1x1 cell} ‘This is a string.‘ [] Introduction to MATLAB Ideal layout for grouping arrays that are related. >> name(1).last = ‘Smith’; name(2).last = ‘Hess’; >> name(1).first = ‘Mary’; name(2).first = ‘Robert’; >> name(1).sex = ‘female’; name(2).sex = ‘male’; >> name(1).age = 45; name(2).age = 50; >> name(2) ans = last: 'Hess' first: 'Robert' sex: 'male' age: 50 Alternative style: >> name = struct(‘last’,{Smith’,’Hess’}, ‘first’,{Mary’,’Robert’},… (‘sex’,{female’,’male’}, ‘age’,{45,50}); Related utilities: 15 Introduction to MATLAB 16 There are many types of files in MATLAB. Only script-, function-, and mat-files are covered here: 1.script m-files (.m) -- group of commands; reside in base workspace 2.function m-files (.m) -- memory access controlled; parameters passed as input, output arguments; reside in own workspace and 3.mat files (.mat) -- binary (or text) files handled with 4.mex files (.mex) -- runs C/FORTRAN codes from m-file 5.eng files (.eng) -- runs m-file from C/FORTRAN code 6.C codes (.c) – C codes generated by MATLAB compiler 7.P codes (.p) – converted m-files to hide source for security Introduction to MATLAB 17 If you have a group of commands that are expected to be executed repeatedly, it is convenient to save them in a file . . . >> edit mytrig.m % enter commands in editor window Select File/Save to save it as mytrig.m A script m-file shares same memory space from which it was invoked. Define x, then use it in mytrig.m (mytrig can “see” x): >> >> a = 0.5000 b = 0.8660 Script works as if sequentially inserting the commands in mytrig.m at the >> Introduction to MATLAB • Declared with the key word 18 , with optional output parameters on the left and optional input on the right of =. All other parameters within function reside in function’s own workspace; deleted upon exiting the function. Use MATLAB editor to create file: >> edit average.m • Keep file name the same as function name to avoid confusions • May be called from a script or another function • >> a= 2 >> Introduction to MATLAB 19 Scripts • Pros: - convenient; script’s variables are in same workspace as caller’s • Cons: - slow; script commands loaded and interpreted each time used - risks of variable name conflict inside & outside of script Functions • Pros: • Scope of function’s variables is confined to within function. No worry for name conflict with those outside of function. • What comes in and goes out are tightly controlled which helps when debugging becomes necessary. • Compiled the first time it is used; runs faster subsequent times. • Easily be deployed in another project. • Auto cleaning of temporary variables. • Cons: • I/O are highly regulated, if the function requires many pre-defined variables, it is cumbersome to pass in and out of the function – a script m-file is more convenient. Introduction to MATLAB >> >> >> >> >> >> >> >> >> >> >> >> >> >> >> >> 20 % creates a special matrix; handy for testing matrix of (0) zeros(n,m) % creates ones(n,m) % creates matrix of (1) rand(n,m) % creates matrix of random numbers repmat(a,n,m replicates by rows and columns diag(M) % extracts the diagonals of a matrix M ) help elmat % list all elementary matrix operations ( or abs(x); % absolute value of exp(x); % to the x-th power fix(x); % rounds x to integer towards 0 log10(x); % common logarithm of x to the base 10 rem(x,y); % remainder of x/y mod(x, y); % modulus after division – unsigned rem sqrt(x); % square root of x sin(x); % sine of x; x in radians acoth(x) % inversion hyperbolic cotangent of x