matlab tutorial with separate function description and handson learning

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 (complex- conjugate transpose) • det(A) % determinant of A

Creating special matrices • diag(v) % change a vector v to a diagonal matrix. • diag(A) % get diagonal of A. • eye(n) % identity matrix of size n. • zeros(m,n) % m-by-n zero matrix. • ones(m,n) % 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 = Ab; % 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 % start at 1, increment by 2 x = x+i; % end with 5. end 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.

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 for j=1:n for k=1:n C(i,j) = C(i,j) + A(i,k)*B(k,j); end; end; end; Can this code be written so that it runs faster? Hint: Use vectorization.

Solution • Script to use for testing: n = 10; A = rand(n,n); B = rand(n,n); C = matrix_multiply(A,B,n);

matlab tutorial with separate function description and handson learning

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