Tutorial on Matlab Basics EECS 639 August 31, 2016

Tutorial on Matlab Basics EECS 639 August 31, 2016

Matlab Basics To start Matlab: Select MATLAB on the menu (if using Windows). Type “matlab” on the command line (if using Linux).

Getting Help and Looking Up Functions To get help on a function type “help function name”, e.g., “help plot”. To find a topic, type “lookfor topic”, e.g., “lookfor matrix”

Matlab’s Workspace who, whos – current workspace vars. save – save workspace vars to *.mat file. load – load variables from *.mat file. clear all – clear workspace vars. close all – close all figures clc – clear screen clf – clear figure

Basic Commands % used to denote a comment ; suppresses display of value (when placed at end of a statement) . continues the statement on next line eps machine epsilon inf infinity NaN not-a number, e.g., 0/0.

Numbers To change format of numbers: format long, format short, etc. See “help format”. Mathematical functions: sqrt(x), exp(x), cos(x), sin(x), sum(x), etc. Operations: , -, *, / Constants: pi, exp(1), etc.

Arrays and Matrices v [-2 3 0 4.5 -1.5]; % length 5 row vector. v v’; % transposes v. v(1); % first element of v. v(2:4); % entries 2-4 of v. v([3,5]); % returns entries 3 & 5. v [4:-1:2]; % same as v [4 3 2]; a 1:3; b 2:3; c [a b]; c [1 2 3 2 3];

Arrays and Matrices (2) x linspace(-pi,pi,10); % creates 10 linearly-spaced elements from –pi to pi. logspace is similar. A [1 2 3; 4 5 6]; % creates 2x3 matrix A(1,2) % the element in row 1, column 2. A(:,2) % the second column. A(2,:) % the second row.

Arrays and Matrices (3) A B, A-B, 2*A, A*B% matrix addition, matrix subtraction, scalar multiplication, matrix multiplication A.*B % element-by-element mult. A’ % transpose of A (complexconjugate transpose) det(A) % determinant of A

Creating special matrices diag(v) diag(A) eye(n) zeros(m,n) ones(m,n) % change a vector v to a diagonal matrix. % get diagonal of A. % identity matrix of size n. % m-by-n zero matrix. % m*n matrix with all ones.

Logical Conditions , , , , , (not equal), (not) & (element-wise logical and), (or) find(‘condition’) – Return indices of A’s elements that satisfies the condition. Example: A [7 6 5; 4 3 2]; find (‘A 3’); -- returns 5.

Solving Linear Equations A [1 2 3; 2 5 3; 1 0 8]; b [2; 1; 0]; x inv(A)*b; % solves Ax b if A is invertible. (Note: This is a BAD way to solve the equations!!! It’s unstable and inefficient.) x A\b; % solves Ax b. (Note: This way is better, but we’ll learn how to program methods to solve Ax b.) Do NOT use either of these commands in your codes!

More matrix/vector operations length(v) % determine length of vector. size(A) % determine size of matrix. rank(A) % determine rank of matrix. norm(A), norm(A,1), norm(A,inf) % determine 2-norm, 1-norm, and infinity-norm of A. norm(v) % compute vector 2-norm.

For loops x 0; for i 1:2:5 x x i; end % start at 1, increment by 2 % end with 5. This computes x 0 1 3 5 9.

While loops x 7; while (x 0) x x-2; end; This computes x 7-2-2-2-2 -1.

If statements if (x 3) disp(‘The value of x is 3.’); elseif (x 5) disp(‘The value of x is 5.’); else disp(‘The value of x is not 3 or 5.’); end;

Switch statement switch face case {1} disp(‘Rolled a 1’); case {2} disp(‘Rolled a 2’); otherwise disp(‘Rolled a number 3’); end NOTE: Unlike C, ONLY the SWITCH statement between the matching case and the next case, otherwise, or end are executed. (So breaks are unnecessary.)

Break statements break – terminates execution of for and while loops. For nested loops, it exits the innermost loop only.

Vectorization Because Matlab is an interpreted language, i.e., it is not compiled before execution, loops run slowly. Vectorized code runs faster in Matlab. Example: x [1 2 3]; for i 1:3 Vectorized: x(i) x(i) 5; VS. x x 5; end;

Graphics x linspace(-1,1,10); y sin(x); plot(x,y); % plots y vs. x. plot(x,y,’k-’); % plots a black line of y vs. x. hold on; % put several plots in the same figure window. figure; % open new figure window.

Graphics (2) subplot(m,n,1) % Makes an mxn array for plots. Will place plot in 1st position. X Here m 2 and n 3.

Graphics (3) plot3(x,y,z) % plot 2D function. mesh(x ax,y ax,z mat) – surface plot. contour(z mat) – contour plot of z. axis([xmin xmax ymin ymax]) – change axes title(‘My title’); - add title to figure; xlabel, ylabel – label axes. legend – add key to figure.

Examples of Matlab Plots

Examples of Matlab Plots

Examples of Matlab Plots

File Input/Output fid fopen(‘in.dat’,’rt’); % open text file for reading. v fscanf(fid,’%lg’,10); % read 10 doubles from the text file. fclose(fid); % close the file. help textread; % formatted read. help fprintf; % formatted write.

Example Data File Sally Type1 12.34 45 Yes Joe Type2 23.54 60 No Bill Type1 34.90 12 No

Read Entire Dataset fid fopen(‘mydata.dat’, ‘r’); % open file for reading. % Read-in data from mydata.dat. [names,types,x,y,answer] textread(fid,’%s%s%f%d%s’); fclose(fid); % close file.

Read Partial Dataset fid fopen(‘mydata.dat’, ‘r’); % open file for reading. % Read-in first column of data from mydata.dat. [names] textread(fid,’%s %*s %*f %*d %*s’); fclose(fid); % close file.

Read 1 Line of Data fid fopen(‘mydata.dat’, ‘r’); % open file % for reading. % Read-in one line of data corresponding % to Joe’s entry. [name,type,x,y,answer] textread(fid,’%s%s %f%d%s’,1, ’headerlines’,1); fclose(fid); % close file.

Writing formatted data. % open file for writing. fid fopen(‘out.txt’,’w’); % Write out Joe’s info to file. fprintf(fid,’%s %s %f %d %s\ n’,name,type,x,y,answer); fclose(fid); % close the file.

Keeping a record To keep a record of your session, use the diary command: diary filename x 3 diary off This will keep a diary called filename showing the value of x (your work for this session).

Timing Use tic, toc to determine the running time of an algorithm as follows: tic commands toc This will give the elapsed time.

Scripts and Functions Two kinds of M-files: - Scripts, which do not accept input arguments or return output arguments. They operate on data in the workspace. - Functions, which can accept input arguments and return output arguments. Internal variables are local to the function.

M-file functions function [area,circum] circle(r) % [area, circum] circle(r) returns the % area and circumference of a circle % with radius r. area pi*r 2; circum 2*pi*r; Save function in circle.m.

M-file scripts r 7; [area,circum] circle(r); % call our circle function. disp([‘The area of a circle having radius ‘ num2str(r) ‘ is ‘ num2str(area)]); Save the file as myscript.m.

Tutorial sources http://docplayer.net/15715694-Introduction -to-matlab-basics-reference-from-azerniko v-sergei-mesergei-tx-technion-ac-il.html Tutorial by Azernikov Sergei.

Interactive Example (1) Write a Matlab program to compute the following sum 1/i2, for i 1, 2, , 10 two different ways: 1. 1/1 1/4 1/100 2. 1/100 1/81 1/1.

Solution % Forward summation forwardsum 0; for i 1:10 forwardsum forwardsum 1/(i 2); end; % Backward summation backwardsum 0; for i 10:-1:1 backwardsum backwardsum 1/(i 2); end;

Interactive Example (2) Write a Matlab function to multiply two n-by-n matrices A and B. (Do not use built-in functions.)

Solution function [C] matrix multiply(A,B,n) C zeros(n,n); for i 1:n Can this code be written so that it for j 1:n runs faster? for k 1:n C(i,j) C(i,j) A(i,k)*B(k,j); end; end; Hint: Use vectorization. end;

Solution Script to use for testing: n 10; A rand(n,n); B rand(n,n); C matrix multiply(A,B,n);