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Introduction to matlab
 

Introduction to matlab

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    Introduction to matlab Introduction to matlab Presentation Transcript

    • An Introduction to MATLABSantosh K Venu 1
    • What is MATLAB?• MATLAB – MATrix LABoratory: MATLAB is a program for doing numerical computation. It was originally designed for solving linear algebra type problems using matrices. It’s name is derived from MATrix LABoratory. – MATLAB has since been expanded and now has built-in functions for solving problems requiring data analysis, signal processing, optimization, and several other types of scientific computations. It also contains functions for 2-D and 3-D graphics and animation. 2
    • • Stands for MATrix LABoratory• Interpreted language• Scientific programming environment• Very good tool for the manipulation of matrices• Great visualisation capabilities• Loads of built-in functions• Easy to learn and simple to use 3
    • MATLAB Overview• Strengths of MATLAB• Weaknesses of MATLAB 4
    • Strengths of MATLAB• MATLAB is relatively easy to learn• MATLAB code is optimized to be relatively quick when performing matrix operations• MATLAB may behave like a calculator or as a programming language• MATLAB is interpreted, errors are easier to fix 5
    • Weaknesses of MATLAB• MATLAB is NOT a general purpose programming language• MATLAB is an interpreted language (making it for the most part slower than a compiled language such as C, C++)• MATLAB is designed for scientific computation and is not suitable for some things (such as design an interface) 6
    • Matlab Desktop• Command Window – type commands• Workspace – view program variables – clear to clear • clear all: removes all variables, globals, functions and MEX links • clc: clear command window – double click on a variable to see it in the Array Editor• Command History – view past commands• Launch Pad – access help, tools, demos and documentation 7
    • Matlab Desktop - con’t Launch Pad Workspace CurrentDIrectory Command Window History 8
    • How to Resume Default Desktop 9
    • Matlab Help• Different ways to find information – help – help general, help mean, sqrt... – helpdesk - an html document with links to further information 10
    • Matlab Help - con’t 11
    • Matlab Help - con’t 12
    • Command window• The MATLAB environment is command oriented somewhat like UNIX. A prompt (>>) appears on the screen and a MATLAB statement can be entered. When the <ENTER> key is pressed, the statement is executed, and another prompt appears.• If a statement is terminated with a semicolon ( ; ), no results will be displayed. Otherwise results will appear before the next prompt. » a=5; » b=a/2 b= 2.5000 » 13
    • MATLAB Special Variablesans Default variable name for resultspi Value of inf InfinityNaN Not a number e.g. 0/0i and j i = j = square root of minus one: (-1) (imaginary number) e.g. sqrt(-1) ans= 0 + 1.0000irealmin The smallest usable positive real numberrealmax The largest usable positive real number 14
    • Variables• No need for types. i.e., int a; double b; float c;• All variables are created with double precision unless specified and they are matrices. Example: >>x=5; >>x1=2;• After these statements, the variables are 1x1 matrices with double precision
    • Working with Matrices and Arrays• Since Matlab makes extensive use of matrices, the best way for you to get started with MATLAB is to learn how to handle matrices. – Separate the elements of a row with blanks or commas. – Use a semicolon ; to indicate the end of each row. – Surround the entire list of elements with square brackets, [ ]. A = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1]
    • MATLAB displays the matrix you just entered: A= 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1• Once you have entered the matrix, it is automatically remembered in the MATLAB workspace. You can simply refer to it as A.• Keep in mind, variable names are case-sensitive
    • Manipulating Matrices A= 16 3 2 13 5 10 11 8• Access elements of a matrix 9 6 7 12>>A(1,2) 4 15 14 1ans=3 indices of matrix element(s)• Remember Matrix(row,column)• Naming convention Matrix variables start with a capital letter while vectors or scalar variables start with a simple letter 18
    • MATLAB Relational Operators• MATLAB supports six relational operators. Less Than < Less Than or Equal <= Greater Than > Greater Than or Equal >= Equal To == Not Equal To ~= 19
    • MATLAB Logical Operators• MATLAB supports three logical operators. not ~ % highest precedence and & % equal precedence with or or | % equal precedence with and 20
    • MATLAB Matrices• MATLAB treats all variables as matrices. For our purposes a matrix can be thought of as an array, in fact, that is how it is stored.• Vectors are special forms of matrices and contain only one row OR one column.• Scalars (1,1)are matrices with only one row AND one column 21
    • MATLAB Matrices• A matrix with only one row AND one column is a scalar. A scalar can be created in MATLAB as follows:» a=23a= 23 22
    • MATLAB Matrices• A matrix with only one row is called a row vector. A row vector can be created in MATLAB as follows (note the commas):» rowvec = [12 , 14 , 63] or rowvec = [12 14 63]rowvec = 12 14 63 23
    • MATLAB Matrices• A matrix with only one column is called a column vector. A column vector can be created in MATLAB as follows (note the semicolons):» colvec = [13 ; 45 ; -2]colvec = 13 45 -2 24
    • MATLAB Matrices• A matrix can be created in MATLAB as follows (note the commas AND semicolons):» matrix = [1 , 2 , 3 ; 4 , 5 ,6 ; 7 , 8 , 9]matrix = 1 2 3 4 5 6 7 8 9 25
    • Extracting a Sub-Matrix• A portion of a matrix can be extracted and stored in a smaller matrix by specifying the names of both matrices, the rows and columns. The syntax is: sub_matrix = matrix ( r1 : r2 , c1 : c2 ) ; where r1 and r2 specify the beginning and ending rows and c1 and c2 specify the beginning and ending columns to be extracted to make the new matrix. 26
    • MATLAB Matrices• A column vector can be • Here we extract column 2 of extracted from a matrix. As the matrix and make a an example we create a column vector: matrix below:» matrix=[1,2,3;4,5,6;7,8,9] » col_two=matrix( : , 2)matrix = col_two = 1 2 3 2 4 5 6 5 7 8 9 8 27
    • MATLAB Matrices• A row vector can be extracted • Here we extract row 2 of the from a matrix. As an example matrix and make a row vector. we create a matrix below: Note that the 2:2 specifies the second row and the 1:3» matrix=[1,2,3;4,5,6;7,8,9] specifies which columns of the row.matrix = » rowvec=matrix(2 : 2 , 1 : 3) 1 2 3 4 5 6 rowvec = 7 8 9 4 5 6 28
    • Matrices transpose• a vector x = [1 2 5 1] x = 1 2 5 1• transpose y = x’ y = 1 2 5 1 29
    • Scalar - Matrix Addition» a=3;» b=[1, 2, 3;4, 5, 6]b= 1 2 3 4 5 6» c= b+a % Add a to each element of bc= 4 5 6 7 8 9 30
    • Scalar - Matrix Subtraction» a=3;» b=[1, 2, 3;4, 5, 6]b= 1 2 3 4 5 6» c = b - a %Subtract a from each element of bc= -2 -1 0 1 2 3 31
    • Scalar - Matrix Multiplication» a=3;» b=[1, 2, 3; 4, 5, 6]b= 1 2 3 4 5 6» c = a * b % Multiply each element of b by ac= 3 6 9 12 15 18 32
    • Scalar - Matrix Division» a=3;» b=[1, 2, 3; 4, 5, 6]b= 1 2 3 4 5 6» c = b / a % Divide each element of b by ac= 0.3333 0.6667 1.0000 1.3333 1.6667 2.0000 33
    • Math & Assignment OperatorsPower ^ or .^ a^b or a.^bMultiplication * or .* a*b or a.*bDivision / or ./ a/b or a./b - (unary) + (unary) Addition + a+b Subtraction - a-b Assignment = a=b (assign b to a) 34
    • Other operators[ ] concatenation x = [ zeros(1,3) ones(1,2) ] x = 0 0 0 1 1( ) subscription x = [ 1 3 5 7 9] x = 1 3 5 7 9 y = x(2) y = 3 y = x(2:4) y = 3 5 7 35
    • The : operator• VERY important operator in Matlab• Means ‘to’>> 1:10ans = 1 2 3 4 5 6 7 8 9 10>> 1:2:10 Try the followingans = >> x=0:pi/12:2*pi; >> y=sin(x) 1 3 5 7 9Introduction to Matlab 36Sumitha Balasuriya
    • • Length• Max• Mean• Median• Min• Prod• Size• Var• Sum• Det• Rank• Eig• sort/flipr 37
    • Matlab Graphicsx = 0:pi/100:2*pi;y = sin(x);plot(x,y)xlabel(x = 0:2pi)ylabel(Sine of x)title(Plot of the Sine Function) 38
    • Multiple Graphst = 0:pi/100:2*pi;y1=sin(t);y2=sin(t+pi/2);plot(t,y1,t,y2)grid on 39
    • • Plotting Multiple Data Sets in One Graph – Multiple x-y pair arguments create multiple graphs with a single call to plot. For example: x = 0:pi/100:2*pi; y = sin(x); y2 = sin(x-.25); y3 = sin(x-.5); plot(x,y,x,y2,x,y3)
    • Multiple Plotst = 0:pi/100:2*pi;y1=sin(t);y2=sin(t+pi/2);subplot(2,2,1)plot(t,y1)subplot(2,2,2)plot(t,y2) 41
    • Graph Functions (summary)• plot linear plot• stem discrete plot• grid add grid lines• xlabel add X-axis label• ylabel add Y-axis label• title add graph title• subplot divide figure window• figure create new figure window• pause wait for user response 42
    • Some Useful MATLAB commands• who List known variables• whos List known variables plus their size• help >> help sqrt Help on using sqrt• lookfor >> lookfor sqrt Search for keyword sqrt in on MATLABPATH.• what >> what (directory) List MATLAB files in directory• clear Clear all variables from work space• clear x y Clear variables x and y from work space• clc Clear the command window 43
    • Flow Control• if• for• while• break• ….
    • Control Structures Some Dummy Examples• If Statement Syntax if ((a>3) & (b==5)) Some Matlab Commands;if (Condition_1) end Matlab Commands if (a<3)elseif (Condition_2) Some Matlab Commands; elseif (b~=5) Matlab Commands Some Matlab Commands;elseif (Condition_3) end Matlab Commands if (a<3)else Some Matlab Commands; Matlab Commands else Some Matlab Commands;end end
    • Control Structures Some Dummy Examples for i=1:100• For loop syntax end Some Matlab Commands; for j=1:3:200for i=Index_Array Some Matlab Commands; Matlab Commands endend for m=13:-0.2:-21 Some Matlab Commands; end for k=[0.1 0.3 -13 12 7 -9.3] Some Matlab Commands; end
    • Control Structures• While Loop Syntax Dummy Examplewhile (condition) while ((a>3) & (b==5)) Matlab Commands Some Matlab Commands;end end
    • Classification of flow%|-------------------------------------|This function classifies a flow |according to the values of the Reynolds (Re) and Mach (Ma). |Re <= 2000, laminar flow2000 < Re <= 5000, transitional flowRe > 5000, turbulent flowMa < 1, sub-sonic flowMa = 1, sonic flowMa > 1, super-sonic flow%|-------------------------------------| 48
    • Vector FunctionConsider now a vector function f(x) = [f1(x1,x2,x3) f2(x1,x2,x3)f3(x1,x2,x3)]T, where x =[x1,x2,x3]T (The symbol []T indicates the transpose of a matrix).Specifically,f1(x1,x2,x3) = x1 cos(x2) + x2 cos(x1) + x3f2(x1,x2,x3) = x1x2 + x2x3 + x3x1f3(x1,x2,x3) = x12 + 2x1x2x3 + x32A function to evaluate the vector function f(x) is shown below. 49
    • Summation%Check if m or n are matricesif length(n)>1 | length(m)>1 thenerror(sum2 - n,m must be scalar values)abortend%Calculate summation if n and m are scalarsS = 0; %initialize sumfor i = 1:n %sweep by index ifor j = 1:m %sweep by index jS = S + 1/((i+j)^2+1);endend 50
    • Thank U 51