Introduction to MATLAB Programming

Transcription

1 Introduction to MATLAB Programming Arun A. Balakrishnan Asst. Professor Dept. of AE&I, RSET

2 Overview 1 Overview 2 Introduction 3 Getting Started 4 Basics of Programming

3 Overview 1 Overview 2 Introduction 3 Getting Started 4 Basics of Programming

4 Overview 1 Overview 2 Introduction 3 Getting Started 4 Basics of Programming

5 Overview 1 Overview 2 Introduction 3 Getting Started 4 Basics of Programming

6 What is MATLAB? numerical computing environment and fourth-generation programming language Developed by MathWorks matrix laboratory MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, Java, and Fortran. Applications signal and image processing communication control design financial modeling and analysis

7 History Cleve Moler, University of New Mexico, started developing MATLAB in the late 1970s Cleve Moler, Jack Little and Steve Bangert rewrote MATLAB in C and founded MathWorks in 1984 to continue its development. Version Release Matlab Matlab Matlab MATLAB (R2011a) clevescorner/dec04.html

8 Founders Figure: Cleve Moler Figure: Jack Little

9 Key Features High-level language for technical computing Development environment for managing code, files, and data Interactive tools for iterative exploration, design, and problem solving Mathematical functions for linear algebra, statistics, Fourier analysis, filtering, optimization, and numerical integration 2-D and 3-D graphics functions for visualizing data Tools for building custom graphical user interfaces Functions for integrating MATLAB based algorithms with external applications and languages, such as C, C++, Fortran, Java, COM, and Microsoft Excel

10 Getting Started

11 How to RUN...

12 Can you find?...

13 Customization File Preferences Allows you personalize your MATLAB experience

14 Making Folders Use folders to keep your programs organized To make a new folder, click the Browse button next to Current Directory Click the Make New Folder button, and change the name of the folder. Do NOT use spaces in folder names In the MATLAB folder, make a new folder Highlight the folder you just made and click OK The current directory is now the folder you just created You can also make an existing folder the current directory

15 Matlab as a Calculator To familiarize Various in-built functions Priorities Workspace

16 Arithmetic Operators (+ - * / ˆ) These are used in conjunction with brackets: ( ). Example : 2 + 3/4* /(4*5) Priorities: 1 quantities in brackets 2 powers 2 + 3ˆ = 11 3 * /, working left to right (3*4/5=12/5) 4 + -, working left to right (3+4-5=7-5) Examples : i) -2ˆ3+9 ii) 2/3*3 iii) 3*2/3 iv) 3*4-5ˆ2*2-3 v) (2/3ˆ2*5)*(3-4ˆ3)ˆ2 vi) 3*(3*4-2*5ˆ2-3)

17 Built-In Functions Trigonometric Functions : sin, cos, tan arguments should be in radians Examples : 5*cos(pi/4), 5*sin(pi/4) inverse functions are called asin, acos, atan Examples : acos(1), asin(1) Other Elementary Functions : sqrt, exp, log, log10 round(1.4), floor(3.3), ceil(4.23) angle(3+2*i); abs(1+i);

18 Basics of Programming To familiarize Initialization of Variables Types : Scalars and Vectors Arrays : Row vectors Column Vectors Matrix of numbers Cell arrays

19 Variables MATLAB is a weakly typed language No need to initialize variables! x = 3.35 MATLAB supports various data types, the most often used are y = bit double (default) z = a 16-bit char Most variables you ll deal with will be arrays or matrices of type double or char

20 Naming variables To create a variable, simply assign a value to a name: var1 = 5.38 c = 1.3*45-2*a mystring = hello world Variable names first character must be a LETTER after that, any combination of letters, numbers and CASE SENSITIVE! (var1 is different from Var1)

21 Built-in variables 1 i and j can be used to indicate complex numbers 1 2 pi has the value (π) 3 ans stores the last unassigned value (like on a calculator) 4 Inf and -Inf are positive and negative infinity 5 NaN represents Not a Number 6 If you wish to do arithmetic with complex numbers,both i and j have the value 1 unless you change them

22 Scalars Constants and variables Constants pre-defined like i, pi, Inf, etc User defined Amp=10 Variables- Values is changing in programme Can assign result of operation to any variable c=a+b Scope of variables Useful functions save and load

23 save/clear/load Use save to save variables to a file save myfile a b saves variables a and b to the file myfile.mat myfile.mat file in the current directory Use clear to remove variables from environment clear a b look at workspace, the variables a and b are gone Use load to load variable bindings into the environment load myfile look at workspace, the variables a and b are back Can do the same for entire variables save myfile; clear all; load myfile;

24 Exercise: Scalars 1 Make the following variables a = 10 b = 2.5x10 23 c = 2 + 3i, where i is the imaginary number d = e j2π/3, where j is the imaginary number and e is Euler s number (use exp, pi) 2 Verify that e ix = cos(x) + i sin(x) for a few values of x. Exercise is not complete!!go to next slide

25 Exercise: Scalars Using the variables created in previous slide, calculate x, y, and z x = e (a 15)/6 y = ( a + 21 b) π z = log(re[(c + d)(c d)] sin(aπ/3)) cc hint : use real, conj, log

26 Command Line Help help : The most important function for learning MATLAB on your own Type help log help elfun more on help elfun doc : To get a nicer version of help with examples and easy-to-read descriptions Type doc sin lookfor hyperbolic who : MATLAB replies with the variables in your workspace what : MATLAB replies with the current directory and MATLAB files in the directory

27 Arrays Like other programming languages, arrays are an important part of MATLAB Two types of arrays Matrix of numbers Cell array of objects (more advanced data structure)

28 Row Vectors Row vector: comma or space separated values between brackets row = [ ]; row = [1, 2, 5.4, -6.6]; row = [1 2, 5.4, -6.6]; Spaces can be vitally important : v2 = [3+ 4 5] v3 = [3 +4 5] You can check the variables in workspace

29 Column vectors Column vector: semicolon separated values between brackets column = [4;2;7;4]; Elements can be result of an operation v = [ 1; 3; sqrt(5)] u = [ 1; 3; x+y; zˆ2] Check the variables in workspace

30 Exercise: Vectors Do the following 5 things: Create the variable r as a row vector with values Create the variable c as a column vector with values Save these two variables to file varex clear the workspace load the two variables you just created

31 Matrices Make matrices like vectors a=[1,2;3,4] Concatenating concatenating vectors or matrices (dimension matters)

32 Matrix Manipulations Main attraction of MATLAB Operations on matrix data (SIGNALS, INFORMATIONS) All functions can be applicable to matrices Multiplication and Divisions need more attention Very simple in-built function to do tedious works c=[ ] s=sum(c) s=prod(c) Indexing Elements is very simple!!!

33 size & length Use the variables in the previous exercise.. You can tell the difference between a row and a column vector by: Looking in the workspace Displaying the variable in the command window Using the size function To get a vector s length, use the length function length of a vector? max(size(x))

34 Transpose The transpose operators turns a column vector into a row vector and vice versa a = [ ] transpose(a) Can use dot-apostrophe as short-cut a. The apostrophe gives the Hermitian-transpose, i.e. transposes and conjugates of all complex numbers a = [1+j 2+3j] a a. For vectors of real numbers. and give same result

35 Addition and Subtraction Addition and subtraction are element-wise; sizes must match (unless one is a scalar): The following would give an error r=[1 2 3], c=[1 3] rc=r+c but, a=row+2; Can sum up or multiply elements of vector s=sum(row); p=prod(row);

36 Element-Wise Functions All the functions that work on scalars also work on vectors t = [1 2 3]; f = exp(t); is the same as f = [exp(1) exp(2) exp(3)]; If in doubt, check a function s help file to see if it handles vectors elementwise Operators (* / ˆ ) have two modes of operation element-wise standard

37 Operators: element-wise: dot To do element-wise operations, use the dot. BOTH dimensions must match (unless one is scalar)! a=[1 2 3];b=[4;2;1]; a.*b, a./b, a.ˆ b all errors a.*b, a./b, a.ˆ (b ) all valid

38 Operators (* / ˆ ) : standard Multiplication can be done in a standard way or element-wise Standard multiplication (*) is either a dot-product or an outer-product Standard exponentiation (ˆ ) implicitly uses * Can only be done on square matrices or scalars

39 Exercise: Vector Operations 1 Find the dot product between a = i + j + k and b = i 2j + k 2 Multiply the same two vectors element-wise 3 Calculate the natural log of each element of the resulting vector 4 Find the magnitude of the 3-D vector x = 2i + 3j + 4k hint: x = ax 2 + ay 2 + az 2 5 Calculate the distance between the two points, A(2, 1, 5) and B( 1, 4, 3), in Cartesian co-ordinate system

40 Automatic Initialization Initialize a vector of ones, zeros, or random numbers General Syntax var=function(m,n,p,...) o=ones(1,10) row vector with 10 elements, all 1 z=zeros(23,1) column vector with 23 elements, all 0 r=rand(1,45) row vector with 45 elements (uniform [0,1]) x=[ ] diag(x) diagonal matrix with as the diagonal elements

41 Automatic Initialization linspace r=linspace(a,b) row vector with 100 elements uniformly from [A,B] r=linspace(a,b,n) row vector with N elements uniformly from [A,B] colon : operator r=m:n row vector starts at M, increment by 1, ends at or before N r=m:inc:n row vector starts at M, increment by Inc, ends at or before N

42 Exercise : Automatic Initialization Find the sum of the first 20 natural numbers. Find the sum of the first 20 even numbers. Create a row vector, x with 100 equally spaced samples of [0, 2π] Create a row vector, y with 100 samples of sin(θ) in the [0, 2π] Create a row vector, z with 100 samples of cos(θ) in the [0, 2π]

43 Vector Indexing MATLAB indexing starts with 1, not 0 a(n) returns the n th element The index argument can be a vector. In this case, each element is looked up individually, and returned as a vector of the same size as the index vector.

44 Matrix Indexing Matrices can be indexed in two ways using subscripts(row, column) using linear indices(as if matrix is a vector)

45 Matrix Indexing Picking submatrices A = rand(5) % shorthand for 5x5 matrix A(1:3,1:2) % specify contiguous submatrix A([1 5 3], [1 4]) Picking particular row/column A(:,3) % all rows and 3 rd column A(2,:) % 2 rd row and all column

46 Matrix Indexing MATLAB contains functions to help you find desired values within a vector or matrix vec = [ ] To get the minimum value and its index: [minval,minind] = min(vec); max works the same way To find any the indices of specific values or ranges ind = find(vec == 9); ind = find(vec > 2 & vec < 6); find expressions can be very complex To convert between subscripts and indices, use ind2sub, and sub2ind. Look up helpto see how to use them.