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Mastering Matlab Programming: Functions, Controls, and Tricks

Explore Matlab programming principles, functions, control statements, and tips. From setting paths to creating M-files, learn to optimize your Matlab environment. Dive into core functionalities, toolboxes, and constructing M-files. Understand flow control, user-defined functions, and Matrix operations. Discover the power of script files, display code, and use the help command. Differentiate scripts and functions based on their usage. Explore flow control with selection and repetition using if-elseif-else and loops. Immerse in creating animations, solving equations, and conditional repetitions in Matlab. Enhance your Matlab skills today!

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Mastering Matlab Programming: Functions, Controls, and Tricks

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  1. Today’s Lecture • Matlab programming • Programming environment and search path • M-file scripts and functions • Flow control statements • Function functions • Programming tricks and tips

  2. Matlab environment • Matlab construction • Core functionality as compiled C-code, m-files • Additional functionality in toolboxes (m-files) • Today: Matlab programming (construct own m-files) Contr. Syst. Sig. Proc User defined Core m-files C-kernel

  3. The programming environment • The working directory is controlled by • >> dir • >> cd catalogue • >> pwd • The path variable defines where matlab searches for m-files • >> path • >> addpath • >> pathtool • >> which function

  4. The programming environment • Matlab can’t tell if identifier is variable or function • >> z=theta; • Matlab searches for identifier in the following order 1. variable in current workspace 2. built-in variable 3. built-in m-file 4. m-file in current directory 5. m-file on search path • Note: m-files can be located in current directory, or in path

  5. Matrix Indexing

  6. Matrix Functions • sort - For matrices, SORT(X) sorts each column of X in ascending order. • sortrows - SORTROWS(X,COL) sorts the matrix based on the columns specified in the vector COL. • rand(m, n) • randn(m, n) • reshape

  7. Script files • Script-files contain a sequence of Matlab commands factscript.m %FACTSCRIPT – Compute n-factorial, n!=1*2*...*n y = prod(1:n); • Executed by typing its name • >> factscript • Operates on variables in global workspace • Variablen must exist in workspace • Variable yis created (or over-written) • Use comment lines (starting with %) to document file!

  8. Displaying code and getting help • To list code, use type command • >> type factscript • The help command displays first consecutive comment lines • >> help factscript

  9. Functions • Functions describe subprograms • Take inputs, generate outputs • Have local variables (invisible in global workspace) • [output_arguments]= function_name(input_arguments) • % Comment lines • <function body> factfun.m function [z]=factfun(n)% FACTFUN – Compute factorial% Z=FACTFUN(N) z = prod(1:n); • >> y=factfun(10);

  10. Scripts or function: when use what? • Functions • Take inputs, generate outputs, have internal variables • Solve general problem for arbitrary parameters • Scripts • Operate on global workspace • Document work, design experiment or test • Solve a very specific problem once • HW: all problems will require you to write functions facttest.m % FACTTEST – Test factfun N=50;y=factfun(N);

  11. Flow control - selection • The if-elseif-else construction if <logical expression> <commands> elseif <logical expression> <commands> else <commands> end if height>170 disp(’tall’) elseif height<150 disp(’small’) else disp(’average’) end

  12. Logical expressions • Relational operators (compare arrays of same sizes) • == (equal to) ~= (not equal) < (less than) <= (less than or equal to)> (greater than) >= (greater than or equal to) • Logical operators (combinations of relational operators) • & (and)| (or)~ (not) • Logical functionsxorisemptyanyall if (x>=0) & (x<=10) disp(‘x is in range [0,10]’) else disp(‘x is out of range’) end

  13. Flow control - repetition • Repeats a code segment a fixed number of times for index=<vector> <statements> end The <statements> are executed repeatedly.At each iteration, the variable index is assigneda new value from <vector>. for k=1:12 kfac=prod(1:k); disp([num2str(k),’ ‘,num2str(kfac)])end

  14. Example – selection and repetition fact.m function y=fact(n)% FACT – Display factorials of integers 1..n if nargin < 1 error(’No input argument assigned’) elseif n < 0 error(’Input must be non-negative’) elseif abs(n-round(n)) > eps error(’Input must be an integer’) end for k=1:n kfac=prod(1:k); disp([num2str(k),’ ’,num2str(kfac)]) y(k)=kfac; end;

  15. Repetition: Animation demo • The function movie replays a sequence of captured frames • Construct a movie to animate the peaks function Z = peaks; surf(Z); axis tight set(gca,'nextplot','replacechildren'); % Record the movie for j = 1:20 surf(sin(2*pi*j/20)*Z,Z) F(j) = getframe; end % Play the movie ten times movie(F,10) peaksmovie.m

  16. Flow control – conditional repetition • while-loops while <logical expression> <statements> end <statements> are executed repeatedly as long as the <logical expression> evaluates to true k=1; while prod(1:k)~=Inf, k=k+1; end disp([‘Largest factorial in Matlab:’,num2str(k-1)]);

  17. Flow control – conditional repetition • Solutions to nonlinear equations • can be found using Newton’s method • Task: write a function that finds a solution to • Given , iterate maxit times or until

  18. Flow control – conditional repetition newton.m • >> [x,n]=newton(0,1e-3,10) function [x,n] = newton(x0,tol,maxit) % NEWTON – Newton’s method for solving equations % [x,n] = NEWTON(x0,tol,maxit) x = x0; n = 0; done=0; while ~done, n = n + 1; x_new = x - (exp(-x)-sin(x))/(-exp(-x)-cos(x)); done=(n>=maxit) | ( abs(x_new-x)<tol ); x=x_new; end

  19. Function functions • Do we need to re-write newton.m for every new function? • No! General purpose functions take other m-files as input. • >> help feval • >> [f,f_prime]=feval(’myfun’,0); myfun.m function [f,f_prime] = myfun(x) % MYFUN– Evaluate f(x) = exp(x)-sin(x) % and its first derivative % [f,f_prime] = myfun(x) f=exp(-x)-sin(x); f_prime=-exp(-x)-cos(x);

  20. Function functions • Can update newton.m • >> [x,n]=newtonf(’myfun’,0,1e-3,10) newtonf.m function [x,n] = newtonf(fname,x0,tol,maxit) % NEWTON – Newton’s method for solving equations % [x,n] = NEWTON(fname,x0,tol,maxit) x = x0; n = 0; done=0; while ~done, n = n + 1; [f,f_prime]=feval(fname,x); x_new = x – f/f_prime; done=(n>maxit) | ( abs(x_new-x)<tol ); x=x_new; end

  21. Function functions in Matlab • Heavily used: integration, differentiation, optimization, … • >> help ode45 • Find the solution to the ordinary differential equation myodefun.m function x_dot = myodefun(t,x) % MYODEFUN – Define RHS of ODE x_dot(1,1)=x(2); x_dot(2,1)=-x(1)+0.1*(1-x(1)^2)*x(2); >> ode45(‘myodefun’,[0 10],[1;-10]);

  22. MATLAB Math & Assignment Operators • Power ^ or .^ a^b or a.^b • Multiplication * or .* a*b or a.*b • Division / or ./ a/b or a./b • or \ or .\ b\a or b.\a • NOTE: 56/8 = 8\56 • - (unary) + (unary) • Addition + a + b • Subtraction - a - b • Assignment = a = b (assign b to a)

  23. Other MATLAB symbols • >> prompt • . . . continue statement on next line • , separate statements and data • % start comment which ends at • end of line • ; (1) suppress output • (2) used as a row separator in a matrix • : specify range

  24. Programming tips and tricks • Programming style has huge influence on program speed! slow.m tic; X=-250:0.1:250; for ii=1:length(x) if x(ii)>=0, s(ii)=sqrt(x(ii)); else s(ii)=0; end; end; toc fast.m tic x=-250:0.1:250; s=sqrt(x); s(x<0)=0; toc; • Loops are slow: Replace loops by vector operations! • Memory allocation takes a lot of time: Pre-allocate memory! • Use profile to find code bottlenecks!

  25. Summary • User-defined functionality in m-files • Stored in current directory, or on search path • Script-files vs. functions • Functions have local variables, • Scripts operate on global workspace • Writing m-files • Header (function definition), comments, program body • Have inputs, generate outputs, use internal variables • Flow control: ”if...elseif...if”, ”for”, ”while” • General-purpose functions: use functions as inputs • Programming style and speed • Vectorization, memory allocation, profiler

  26. Advanced Matlab Programming • Functions • Can have variable number of inputs and outputs(see: nargin, nargout, varargin, varargout) • Can have internal functions • Data types: more than just arrays and strings: • Structures • Cell arrays • File handling • Supports most C-commands for file I/O (fprintf,…)

  27. Advanced Matlab Programming • Object-orientation • Object: “structure” + methods • Creation, encapsulation, inheritage, aggregation • Graphical user interfaces • Based on “handle” concept for graphics • Menus, buttons, slides, and interactive graphics • Interfacing other codes • Can call compiled C/C++ (“mex”), Java and ActiveX

  28. Advanced Matlab Programming • FMINSEARCH Multidimensional unconstrained nonlinear minimization (Nelder-Mead). • X = FMINSEARCH(FUN,X0) starts at X0 and attempts to find a local minimizer • X of the function FUN. FUN is a function handle. FUN accepts input X and • returns a scalar function value F evaluated at X. X0 can be a scalar, vector or matrix.

  29. Advanced Matlab Programming • Here myfun is an M-file • Call FMINSEARCH myfun1.m function f = myfun(x,c) f = x(1)^2 + c*x(2)^2; c = 1.5; % define parameter first x = fminsearch(@(x) myfun1(x,c),[0.3;1])

  30. Debugger • Use matlab built-in editor • Set breakpoint • Drop some “;” • Add keyboard command in the program (return and click enter to return) • Sprintf - Write formatted data to string • >> dbstop if error • >> dbstatus • Check each function work space • Display call stack • Step-by-step execution

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