Introduction To Matlab Class 4

1. Introduction To MatlabClass 4 Instructors: Hristiyan (Chris) Kourtev and Xiaotao Su, PhD Double click the matlab icon When prompted click “Skip”

2. Managing data • To manage basic numerical data we use matrices • our_data = [1, 4, 10.59, 12; 2, 9, 18.76, 5; 3, 7, 1.13, 2]; Trial 1 Trial 2 Trial 3 Trial Number Response2 (perhaps the response time) Response3 Response1

3. our_data = [1, 4, 10.59, 12; 2, 9, 18.76, 5; 3, 7, 1.13, 2]; • To set the 4th row (4th trial) data: our_data(4, :) = [4, 7, 2.93, 3] • or we could our_data(5, 1) = 5; our_data(5, 2) = 1; our_data(5, 3) = 2.10; our_data(5, 4) = 9; • To get this 4th row data • trial_data = our_data(4, :) : gets or sets all elementsfrom row or column

4. disp('I am thinking of a number between'); disp([' 1 and ', num2str(highest_number)]); response = input('What is it?'); stop_time = GetSecs; response_time = stop_time - start_time; is_correct = (response==random_num); if(is_correct) disp('Right!'); else disp(['Wrong! The correct answer was ', ... num2str(random_num)]); end disp('Press any key to continue'); pause disp('--------'); %record data guessing_game_data(t, :) =... [t, response_time, response, ... random_num, is_correct ]; end %guessing_game.m %test to see if subject is psychic clear all; %settings num_trials = 5; highest_number = 3; %get info subject_name = input('What is your name?', 's'); for t = 1:num_trials %trial set up random_num = ceil(rand*highest_number); %perform experiment start_time = GetSecs;

5. disp('I am thinking of a number between'); disp([' 1 and ', num2str(highest_number)]); response = input('What is it?'); stop_time = GetSecs; response_time = stop_time - start_time; is_correct = (response==random_num); if(is_correct) disp('Right!'); else disp(['Wrong! The correct answer was ', ... num2str(random_num)]); end disp('Press any key to continue'); pause disp('--------'); %record data guessing_game_data(t, :) =... [t, response_time, response, ... random_num, is_correct ]; end Task 1: Write this section of the program Hint: input without ‘s’ is a good way To get numeric responses from The subject %guessing_game.m %test to see if subject is psychic clear all; %settings num_trials = 5; highest_number = 3; %get info subject_name = input('What is your name?', 's'); for t = 1:num_trials %trial set up random_num = ceil(rand*highest_number); %perform experiment start_time = GetSecs;

6. disp('I am thinking of a number between'); disp([' 1 and ', num2str(highest_number)]); response = input('What is it?'); stop_time = GetSecs; response_time = stop_time - start_time; is_correct = (response==random_num); if(is_correct) disp('Right!'); else disp(['Wrong! The correct answer was ', ... num2str(random_num)]); end disp('Press any key to continue'); pause disp('--------'); %record data guessing_game_data(t, :) =... [t, response_time, response, ... random_num, is_correct ]; end %guessing_game.m %test to see if subject is psychic clear all; %settings num_trials = 5; highest_number = 3; %get info subject_name = input('What is your name?', 's'); for t = 1:num_trials %trial set up random_num = ceil(rand*highest_number); %perform experiment start_time = GetSecs;

7. disp('I am thinking of a number between'); disp([' 1 and ', num2str(highest_number)]); response = input('What is it?'); stop_time = GetSecs; response_time = stop_time - start_time; is_correct = (response==random_num); if(is_correct) disp('Right!'); else disp(['Wrong! The correct answer was ', ... num2str(random_num)]); end disp('Press any key to continue'); pause disp('--------'); %record data guessing_game_data(t, :) =... [t, response_time, response, ... random_num, is_correct ]; end %guessing_game.m %test to see if subject is psychic clear all; %settings num_trials = 5; highest_number = 3; %get info subject_name = input('What is your name?', 's'); for t = 1:num_trials %trial set up random_num = ceil(rand*highest_number); %perform experiment start_time = GetSecs;

8. CSV format • Stands for “Comma separated value” • It is a simple text file for data storage • Each data item is delimited (separated) by a comma • Each data row is delimited by a return character

9. Notepad example • Start->run • notepad 1, 4, 9.3 1, 9, 100 4, 0, 12 Save as test.csv Double click -> opens in excel

10. csvwrite • saves a 2d matrix as a csv file • csvwrite(FILENAME, MATRIX_VAR) • my_matrix = [3, 5; 1, 2]; • csvwrite(‘my_data.csv’, my_matrix);

11. disp('I am thinking of a number between'); disp([' 1 and ', num2str(highest_number)]); response = input('What is it?'); stop_time = GetSecs; response_time = stop_time - start_time; is_correct = (response==random_num); if(is_correct) disp('Right!'); else disp(['Wrong! The correct answer was ', ... num2str(random_num)]); end disp('Press any key to continue'); pause disp('--------'); %record data guessing_game_data(t, :) =... [t, response_time, response, ... random_num, is_correct ]; end %guessing_game.m %test to see if subject is psychic clear all; %settings num_trials = 5; highest_number = 3; %get info subject_name = input('What is your name?', 's'); for t = 1:num_trials %trial set up random_num = ceil(rand*highest_number); %perform experiment start_time = GetSecs; %data_storage csvwrite([subject_name, '.csv'], … guessing_game_data);

12. csvread • clear all; • my_matrix = csvread(‘my_data.csv’); • can be used to load parameters at the beginning of a program • can be used to load data to analyze through matlab

13. cell arrays • this_is_a_matrix_and_a_vector = [5, 3, 9, 3] • and_so_is_this = [‘hello’]; • which_is_the_same_as = [‘h’, ‘e’, ‘l’, ‘l’, ‘o’];

14. cell arrays • cell array provides a storage mechanism for dissimilar kinds of data • they are like a matrix where each element is any other data type example_cell_array = {‘cat’, 3, [5, 9]; ‘zebra’, [10, 3; 9, 5], ‘dog’};

15. a = example_cell_array{2, 3} • example_cell_array{2, 1} = a • example_cell_array{2, 2}(2, 1)

16. cell2csv • Works just like csvwrite • Will only work with “simple” cell arrays • no numeric vectors or matrices • data = {‘trial number’, ‘time’, ‘color’, ‘response’; 1, 5.99, ‘blue’, 3; 2, 4, ‘green’, 2; 3, 55, ‘yellow’, 2} • cell2csv(‘somefile.csv’, data); !Note: cell2csv is not a built in Matlab function. Download it here:http://ruccs.rutgers.edu/matlab_course/materials/summer_2010/class_7/cell2csv.m

17. important note • to add one data element to a cell array • data{5, 3} = 'yellow’ • curly braces • To add one row of data • data(5, :) = {4, 2.93, ‘yellow’, 4} • parenthesis • data(trial+1, :) = {trial, time, color, response}

18. Creating a vector of numbers • This is similar to the way you create an iteration for a “for” loop • x = (0:20) ----> x = [0, 1, … 20] • x = (0.1:0.1:1) ---> x = [0.1, 0.2, … , 1.0] • x = (0:2:20) ----> x = [0, 2, 4, … 20] • x = (0:2:20)’ ---> vertical vector like the previous one

19. discrete distributions and selecting segments • you can use something like x=(0:20) to specify a discrete distribution of 21 different possibilities • to select the first 6 elements you could sayy = x(1:6) ---> y would be [0, 1 … 5] • Or to select the last 4 elements • y = x(end-3:end) ---> y would be [17, 18, 19, 20]

20. y = binopdf(x(1:6), 5, .8) • used to generate a binomial distribution function the case in which one flips a weighted coin • .8 probability of getting heads • there are 6 possibilities (0 heads, 1 head… 5 heads • y gives the probability of each of these outcomes This function requires the stats toolbox

21. Plotting • Subplot will create a figure window for plotting • subplot (2, 1, 2) will say we are going to create a (2 row, 1 column, …) figure. The last number specifies that we are currently going to write in the second element of this figure. • plot(y) will create a graph on currently chosen section of the figure (specified by the third parameter in subplot)

22. setting up the plot • xlim([1 5]) %sets the limits of the x axis • bar(y) %will use a bar graph • ylabel(‘Probability of n’) • xlabel(‘N’) • title(‘Discrete distributions should be plotted as histograms’)

23. more then one figure? • figure %opens a new figure window • All new subplots will go to the new figure • subplot(2, 1, 1) • bar(y) • xlim([1 21]) %we want 21 possibilities

24. more then one graph on a plot • hold on %tells matlab to keep the previous graph and draw a new one on top • stairs(cumsum(y), ‘r’) • cumsum(y) <--- each value is the sum of previous values of y • ‘r’ makes the graph line red • stairs will plot it as a staircase • hold off % now any future graph additions will clear previous graphs on this plot • legend(‘distribution’, ‘cumsum’)

25. ezplot Easy-to-use function plotter • ezplot(fun) plots the expression fun(x) over the default domain -2pi < x < 2pi. • This example plots the implicitly defined function x2 - y4 = 0 over the domain [-2pi, 2pi]:ezplot('x^2-y^4') • You can specify a different domain by passing in a second argument to ezplot, in this case -6<x<6 and -2<y<1:eq='y - sin(x) + 1/2';  ezplot(eq,[-6,6,-2,1])

26. Solving Equations Using Matlab (symbolic toolbox) • http://people.clarkson.edu/~wwilcox/ES100/eqsolve.htm • The present tutorial deals exclusively with numerical methods of solving algebraic and trigonometric equations, both single and several simultaneously, both linear and non-linear.  • Analytical solutions can be obtained using the methods described in the symbolic tutorial.   When both symbolic and numerical methods work, sometimes one is simpler and sometimes the other.

27. Solving Equations Using Matlab (examples) • “fzero” command - finds the value of x for f(x) = 0. e.g. For equation  sin2(x) e-x/2 – 1 = 0x = fzero('sin(x)^2*exp(-x/2)-1', -1) • Using “solve” to solve linear and quadratic equations:e.g. For equation y = x2 – 1, or y = 5x - 4solve(‘x^2-1’);solve(‘5*x – 4’); • And many more types of equations. Just read the tutorial and the help page for “solve”, “dsolve”, “fsolve”, “fzero”, etc.