Introduction To MATLAB Prof. Muhammad Saeed Mathematical Modeling and Simulation

Basic Features MATLAB Windows 1.Command ( << ) 2.Command History 3.Workspace 4.Current Directory 5.Editor 6.Profiler 7.Help Simple Math in Command Window 1.Operators: +, -, *, /, \, ^ 2.Variables: ans, pi, inf, NaN, i, j, realmin, realmax, ……, user-defined 2 Mathematical Modeling and Simulation

3.Precision: significant digits and formats a)format short, format short eand format short g b)format long, format long e, format long g c)format hex d)format bank e)format + 4.Complex numbers a)imag(), real(), abs() and angle() Display and Help 1.who, whos, clear, clear a*, clear –regexp, clc, disp, ver, version, diary, commands 2.Comments in MATLAB (%) 3.Ellipses ( … ) and ; at the end of commands 4.Built-in Functions and Help using fx, start and Help 3 Mathematical Modeling and Simulation

Arrays and Matrices 1.Initialization: i.Row Matrix: a=[1,2,3,4], [ ], [1:1:4] or [1:4] a=1:2:20, b=1:10,(1:1:10), (1:7) ii.Column Matrix: a=[1;2;3;4] iii.3x3 Matrix: d3=[1,2,3;4,5,6;7,8,9], [1 2 3;4 5 6;7,8,9], [1:3;4:6;7:9], [1:exp(1.4567):100], angle=[0:pi/10:pi] iv.sine=sin(angle) v. d=[a b], d=[a b;b a] or d=[a b b], c(:)=1.5 vi. x=(0:0.1:2)*pi, linspace(0,2*pi,21), logspace(0, 3, 5) vii. ones(n, m), ones(n), zeros(n), zeros(n, m), eye(n), eye(n, m), rand(n), rand(n, m), randn(n), randn(n, m), randi(10,5), randperm(n), diag([ ]), diag(a), diag(a, n), diag(a,-n) 4 Mathematical Modeling and Simulation

2.Operations: i.a(2), a(2:6), a(3:end), a(12:-1:5), a(3:1:9), a([ ]) ii.Transpose : a., [1:5], (0:0.1:1) iii.Conjugate Transpose : a iv.Maths: 3*(a-1), a*2, 3\a, a/3, a+4, a+b, a*b, a.*b, a./b, a^2, a.^2, 2./a v.Extraction: a=b([2 3],[1 3 4]), a=b(:,1:3) 3.Special Functions: sort(a), sort(a,ascend), sort(a,descend), sort(a,1), sort(a,2), sortrows(a), sortrows(a,1), sortrows(a,[1 3]), sortrows(a,-2), find(a>7), find(a, k), find(a, k, first), find(a, k,last), max(a), min(a), flipud(a), fliplr(a), rot90(a), rot90(a,2), triu(a). tril(a), ……………….. continued 5 Mathematical Modeling and Simulation ….. Arrays and Matrices

66 Mathematical Modeling and Simulation repmat(a,1,4),repmat(a, 2, 2), repmat(pi,size(a)), repmat(pi, 2, 3), reshape(a, 4, 3), reshape(1:10, 2, 5) numel(a), length(a), size(a), size(a,1), size(a,2), ndims(a), prod(a), prod(a,1), prod(a,2), dot(a,b), cross(a,b), sub2ind(size(a),3,5), ind2sub(size(a),15), sum(a), diag(diag(a)), blkdiag(a,b,c), ….. Arrays and Matrices

4.Data Types: declaration, conversion and display int8, uint8……. Int64, uint64, char, double, single, inf, NaN, ones(n,m,uint32), cast(a,int16), class(a), realmax(type), realmin(type), intmin, intmax, num2str, int2str, mat2str, str2double, str2num, strmatch(…, str), regexp, regexpi sprintf(…..), fprintf(….. ) 5.Operators: +, -, *, /, \, ^, =,, =, ==, ~=,,.,.*,./,.^,.\ &, |, ~, &&, || 7 Mathematical Modeling and Simulation ….. Arrays and Matrices

88 Mathematical Modeling and Simulation Basic Matrix Functions 1.rank(a) 2.inv(A) 3.A\y, solves set of linear equations, A is a matrix and y is a vector 4.det(A) 5.eig(A), [v d]=eig(A) calculates eigen values and eigen vectors 6.trace(A) 10.sp=sparse(A), 11. full(sp) 12. or(a,b) 13. xor(a,b)

99 Mathematical Modeling and Simulation M-File Scripts 1.Specific Functions used in M-Files: echo, disp, input, keyboard, pause, pause(n), waitforbuttonpress 2.All functions and control statements of MATLAB can be used in script files. 3.Extension is m ( file.m ) 4.M-File directly runs on the command line ( >>) as simple statements do. It is evaluated in MATLAB workspace.

10 Mathematical Modeling and Simulation 1.Function name must be identical to M-File name. 2.Function start with function keyword and ends with end keyword 3.1 st line in M-File must be the function declaration 4.The error and warning functions in the M-File are like sprintf 5.Script file called in a function is evaluated in function workspace 6.Subfunctions are called from the 1 st functions body 7.Help for subfunction can be displayed by >>helpwin func/subfunc 8.Functions can have zero input or zero output arguments. 9.Functions can be called with fewer input and output arguments than are specified in the function definition but not with more arguments than specified. M-File Functions

11 Mathematical Modeling and Simulation ……….. M-File Functions 10.Function arguments can be determined by two variables: nargin and nargout. 11.The first set of contiguous comment lines after the function declaration are the help text for the function 12.The return statement is not necessary. 13.Script file called in a function is evaluated in function WS 14.Unlimited number of input and output arguments by specifying varargin as the last argument and varargout for output arguments. 15.pcode command compiles the function 16.Functions can be nested. 17. One-Lineinline functions can be defined as in C (by #define) 18.Anonymous functions are defined by handles. 19. Handles of MATLAB functions can also be created

12 Mathematical Modeling and Simulation Set Functions 1.isequal(a, b), compares as a whole 2.unique(a), removes duplications 3.ismember(a,b), ismember(a,xyz), element by element 4.union(a,b), must be rows or columns 5.intersect(a,b) 6.diff(a) Base Conversion Functions 1.dec2bin(x), bin2dec(x) 2.dec2hex(x), hex2dec(x) 3.dec2base(x, base), base2dec(x, base) Precision Functions digits(n), vpa(pi), vpa(x, d), vpa(pi)

13 Mathematical Modeling and Simulation Data Analysis 1.mean(a), for a 2D matrix each rows s mean will be calculated. 2.mean(a,1), row values are averaged 3.mean(a,2), column values are averaged 4.median(a) 4.std(a), standard deviation 5.var(a), Variance 5.cov(a), covariance 6.corrcoef(a), correlation coefficient 7.diff(a), rows are subtracted 8.min(a) 9.max(a) 10.cumsum(a) 11.cumprod(a)

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