Getting started with MATLAB You can work through this tutorial in the computer classes over the first 2 weeks, or in your own time. The Farber and Goldfarb computer classrooms have working Matlab, but it can be downloaded with your UNET id onto your laptop, as Brandeis has a site license. See: https://sites.google.com/a/brandeis.edu/matlab/student-computers and open the file within that page: matlab_insructions.pdf Be sure to click Academic Use (not Student Use ) when asked How will you use the Matlab software? Introduction to Matlab This course is adapted from MIT, Stanford, U Delaware Matlab crash courses. I have used the documents written by Stefan Roth and Tobin Driscoll besides the Matlab online tutorial. Azadeh Samadani 01/10/2007 Adapted more for BIOL135b and NBIO136b by Paul Miller 01/10/2009 Useful links: The Getting Started with MATLAB manual is a very good place to get a more gentle and thorough introduction: http://www.mathworks.com/access/helpdesk/help/techdoc/learn_matlab/ http://www.mathworks.com/academia/student_center/tutorials/ Basics: If you type in a valid expression and press Enter, MATLAB will immediately execute it and return the result, just like a calculator. >> 2+2 ans = 4 >> 4ˆ2 ans = 16 >> 1/0 Warning: Divide by zero. ans = Inf Notice the special expression here: Inf for. Another special value is NaN, which stands for not a number. NaN is used to express an undefined value. For example, >> Inf/Inf ans = NaN 5 2 * Challenge: Calculate the following statements:! =. Here are a few other demonstration statements. Anything after a sign is a comment. x = rand(2,2); ; means "don t print out result" s = Hello world ; single quotes enclose a string 1+
t = 1 + 2 + 3 +... 4 + 5 + 6...... means continue a line Here are a few useful commands: who cd pwd dir ls gives you your variables Change current working directory. Show (print) current working directory. List directory. List directory. * Type why in your command window Creating matrices and vectors A = [1 2; 3 4]; B = [1,2; 3,4]; N = 5 v = [1 0 0] v = [1; 2; 3] v = v' v = 1:0.5:3 v = pi*[-4:4]/4 v = [] Creates a 2x2 matrix The simplest way to create a matrix is to list its entries in square brackets. The ";" symbol separates rows; the (optional) "," separates columns. A scalar A row vector A column vector Transpose a vector (row to column or column to row) A vector filled in a specified range: [start:stepsize:end], brackets are optional Empty vector Creating special matrices 1ST parameter is ROWS, 2ND parameter is COLS m = zeros(2, 3) v = ones(1, 3) m = eye(3) v = rand(3, 1) m = zeros(3) Creates a 2x3 matrix of zeros Creates a 1x3 matrix (row vector)of ones Identity matrix (3x3) Randomly filled 3x1 matrix (column vector); see also randn Creates a 3x3 matrix (!) of zeros * Challenge: Create a 3x1 matrix with random elements between 0 and 5. (Hint: >>doc rand) Challenge: Find the row-wise sum of the elements of A. Find the column-wise product of the elements of A. (Hint: >>doc sum) Indexing vectors and matrices Warning: Indices always start at 1 and *NOT* at 0! v = [1 2 3]; v(3) Access a vector element
m = [1 2 3 4; 5 6 7 8; 9 10 11 12; 13 14 15 16] m(1, 3) Access a matrix element matrix(row #, COLUMN #) m(2, :) Access a whole matrix row (2nd row) m(:, 1) Access a whole matrix column(1 st column) m(1, 1:3) Access elements 1 through 3 of the 1 st row m(2:3, 2) Access elements 2 through 3 of the 2nd column m(2:end, 3) Keyword "end" accesses the remainder of a column or row m = [1 2 3; 4 5 6] size(m) Returns the size of a matrix size(m, 1) Number of rows size(m, 2) Number of columns m1 = zeros(size(m)) Create a new matrix with the size of m *Challenge: Create a 5x3 matrix with random elements and access the (3x2) elements on the lower right hand corner. (Hint: >>help end) Remember to check the help system often! It is really easy! If you know the command that you want to obtain some info about it is as easy as typing help command where command is the command that you are interested in. Simple operations and the dot modifier a = [1 2 3 4]'; A column vector 2 * a Scalar multiplication a / 4 Scalar division b = [5 6 7 8]'; Another column vector a + b Vector addition a - b Vector subtraction a.^ 2 Element-wise squaring (note the ".") a.* b Element-wise multiplication (note the ".") a./ b Element-wise division (note the ".") * Challenge: Define two arbitrary vectors A and B with same dimensions. Calculate A*B, A.*B and A*B? What is the answer to A/B and A./B? Which operations do not make sense? Vector operations Built-in Matlab functions that operate on vectors sum(a) mean(a) std(a) max(a) min(a) Sum of vector elements Mean of vector elements Standard deviation Maximum Minimum * Challenge: Without using a for loop, calculate the sum of all prime numbers less than 100. (Hint:>>help isprime) If a matrix is given, then these functions will operate on each column of the matrix and return a row vector as result
a = [1 2 3; 4 5 6] mean(a) max(a) max(max(a)) A matrix Mean of each column Max of each column Obtaining the max of a matrix Graphics (2D plotting) x = [0 1 2 3 4]; plot(x); pause plot(x, 2*x); axis([0 4 0 8]); figure; x = pi*[-24:24]/24; plot(x, sin(x)); xlabel('radians'); ylabel('sin value'); title('dummy'); figure; subplot(1, 2, 1); plot(x, sin(x)); axis square; subplot(1, 2, 2); plot(x, 2*cos(x)); axis square; figure; plot(x, sin(x)); hold on; plot(x, 2*cos(x), '--'); legend('sin', 'cos'); hold off; figure; m = rand(64,64); imagesc(m) colormap gray; axis image; axis off; Basic plotting Plot x versus its index values Wait for key press Plot 2*x versus x Adjust visible rectangle Open new figure Assign label for x-axis Assign label for y-axis Assign plot title Multiple functions in separate graphs (see "help subplot") Make visible area square Multiple functions in single graph '--' chooses different line pattern Assigns names to each plot Stop putting multiple figures in current graph Plot matrix as image Choose gray level colormap Show pixel coordinates as axes Remove axes You may zoom in to particular portions of a plot by clicking on the magnifying glass icon in the figure and drawing a rectangle. * Challenge: Plot functions x (blue squares and line), x^2 (red circles and line) and x^1/2 (green diamonds and line) between (0,2) on the same plot. Let s do Exercise 1! Creating scripts and functions using m-files Matlab scripts are files with ".m" extension containing Matlab commands. Variables in a script file are global and will change the value of variables of the same name in the environment of the current Matlab session. A script with name "script1.m" can be invoked by typing "script1" in the command window.
* Challenge: Create a script called myfirstscript.m to prints out today s date. (Hint: >>help date) Functions are also m-files. The first line in a function file must be of this form: function [out_1,..., out_m] = myfunction(in_1,..., in_n) The function name should be the same as that of the file (i.e. function "myfunction" should be saved in file "myfunction.m"). Have a look at myfunction.m for examples. a = [1 2 3 4]; b = myfunction(2 * a) >>a Global variable a Call myfunction which has local variable a function y = myfunction(x) Function of one argument with one return value a = [-2-1 0 1]; Have a global variable of the same name y = a + x; >>help myfunction Functions are executed using local workspaces: there is no risk of conflicts with the variables in the main workspace. At the end of a function execution only the output arguments will be visible in the main workspace. If we create a file named f.m in the current working directory with this code f.m function y = f(x, a) Returns the square of the first argument times the second y = a * x ^ 2; Then, from the command window we can just evaluate the function f(3, 4) ans = 36 In the command window type: >>help f * Challenge: Define a new function called stat.m that calculates the mean and standard deviation of a vector x. * Challenge: Define a new function called bellcurve.m that creates 10000 normally distributed random numbers with mean 3 and standard deviation 2. Make a histogram to verify the bell curve. (Hint:>> help randn and >>help hist) Syntax of flow control statements (for, while and if expressions) for VARIABLE = EXPR STATEMENT... STATEMENT end
EXPR is a vector here, e.g. 1:10 or -1:0.5:1 or [1 4 7] Example for loop to calculate 100 terms of the Fibonacci numbers, where each successive term is the sum of the two prior terms: Fibonacci.m clear clear all variables from the computer s memory Fib_seq(1) = 0; first two terms are defined as 1 and 1 Fib_seq(2) = 1; for i = 3:100 Fib_seq(i) = Fib_seq(i-1)+Fib_seq(i-2); end Fib_seq(1:10) plot(fib_seq) prints out the first ten terms for interest plots all 100 terms while EXPRESSION STATEMENTS end Example while loop for the Fibonacci numbers is almost (but not quite) identical: Fibonacci_while.m clear clear all variables from the computer s memory Fib_seq(1) = 0; first two terms are defined as 1 and 1 Fib_seq(2) = 1; i = 2; while( i < 100) i = i+1; Fib_seq(i) = Fib_seq(i-1)+Fib_seq(i-2); end Fib_seq(1:10) plot(fib_seq) prints out the first ten terms for interest plots all 100 terms if EXPRESSION STATEMENTS elseif EXPRESSION STATEMENTS else STATEMENTS end (elseif and else clauses are optional, the "end" is required) EXPRESSIONs are usually made of relational clauses, e.g. a < b The operators are <, >, <=, >=, ==, ~=
The following example code combines a for loop with an if expression to sum the multiples of 3 that are less than 100, and separately sum the nonmultiples: multiple_nonmultiple_sum.m sums multiples and nonmultiples of 3: sum_multiples = 0; sum_nonmultiples = 0; initialize sums to zero before accumulation for i = 1:99 all numbers less than 100 end if ( mod(i,3) == 0 ) if remainder is zero when dividing by 3 sum_multiples = sum_multiples + i; else sum_nonmultiples = sum_nonmultiples + i; end sum_multiples sum_nonmultiples * Challenge: Write a function that takes two variables and prints a statement indicating whether the first variable is smaller, larger, or equal to the second variable. * Challenge: Write a function that calculates! 3 2 ( n + n ) 200 0 More operations useful for HW Now you can perform some simple operations. Now let's implement a toy excercise that is somewhat similar to the homework. Suppose you want to write some code that tells you whenever some function, say a sinewave, has the value of 0.5 or greater. Off the top of my head, I can think of two basic ways to implement this: using a 'for' loop (the slow way), or using a few carefully chosen Matlab expressions. Both are fine for this course. First, let's look at a toy 'for' loop, and then we'll implement the procedure above using a 'for' loop. Type the following: for A=[1 2 3 4 5], A, end; for A=a, A, end; for A=1:5, A, end; All of these 'for' loops do the same thing. The variable A steps through the matrix [1 2 3 4 5], and inside the loop we have asked Matlab to display the value of A. We have defined the matrix [1 2 3 4 5] three different ways: explicitly, using our variable a as before, and a new way, using the colon operator. The colon operator allows you to define a vector as running from a beginning value to an ending value, and optionally using a step different from 1. Try this below:
A=1:5 A=5:-1:1 A=0:0.1:1 Now you should have a good grasp of the colon operator. Let's solve the problem we introduced at the beginning of the section with a 'for' loop and plot the result. T=0:0.01:10; define T to be a vector running between 0 and 10 in steps of 0.01 sw = []; define sw to be an empty vector th=[]; define an empty vector for determining if we are exceeding threshold or not for t=t, for each value of T sw(end+1) = sin(2*pi*t); set next value of sw to be the sine of 2*pi*t th(end+1) = sw(end)>0.5; add either a 1 or a 0 to th end; now let's plot figure(1); subplot(2,1,1); plot(t,sw); axis([t(1) T(end) -1.5 1.5]); subplot(2,1,2); plot(t,th); axis([t(1) T(end) -0.5 1.5]); set the axis so it looks prettier Here we've introduced two new operations. One is the idea of creating an empty vector and adding to it. If you want to see this more closely, type 'A=[], A(end+1)=1, A(end+1)=1,'. We've also introduced the comment syntax: any text on a line following a '' will not be treated as code. This will help you remind yourself what you have written, and will help the TAs grade your homework. Now let's do this same function in a way that takes advantage of Matlab's matrix style. First, let's use the 'clear' command to clear some of our old variables: clear T sw th T=0:0.01:10; sw=sin(2*pi*t); this does all values of T at once th = sw>0.5; this does all entries of sw at once now let's plot figure(1); subplot(2,1,1); plot(t,sw); axis([t(1) T(end) -1.5 1.5]); subplot(2,1,2); plot(t,th); axis([t(1) T(end) -0.5 1.5]); set the axis so it looks prettier So hopefully now you are begining to understand how Matlab's language can allow you to briefly perform some complicated manipulations. If you were doing actual homework, you would want to title these plots and label the y and x axes.