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

2. Optional Presentation Title Unit Name 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 Response 1 Response 2 (perhaps the response time) Response 3 Trial Number

3. Optional Presentation Title Unit Name 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 elements from row or column

4. Optional Presentation Title Unit Name %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; 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

5. Optional Presentation Title Unit Name %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; 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

6. Optional Presentation Title Unit Name %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; 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

7. Optional Presentation Title Unit Name %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; 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

8. Optional Presentation Title Unit Name 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. Optional Presentation Title Unit Name 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. Optional Presentation Title Unit Name 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. Optional Presentation Title Unit Name %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; 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 %data_storage csvwrite([subject_name, '.csv'], … guessing_game_data);

12. Optional Presentation Title Unit Name 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. Optional Presentation Title Unit Name 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. Optional Presentation Title Unit Name 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’}; ‘cat’3 ‘zebra’‘dog’ 59 103 95

15. Optional Presentation Title Unit Name a = example_cell_array{2, 3} example_cell_array{2, 1} = a example_cell_array{2, 2}(2, 1) ‘cat’3 ‘zebra’‘dog’ 59 103 95

16. Optional Presentation Title Unit Name 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 http://ruccs.rutgers.edu/matlab_course/materials/summer_2010/class _7/cell2csv.m

17. Optional Presentation Title Unit Name 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. Optional Presentation Title Unit Name 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. Optional Presentation Title Unit Name 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 say y = 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. Optional Presentation Title Unit Name 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. Optional Presentation Title Unit Name 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. Optional Presentation Title Unit Name 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. Optional Presentation Title Unit Name 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. Optional Presentation Title Unit Name 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. Optional Presentation Title Unit Name 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 x 2 - y 4 = 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. Optional Presentation Title Unit Name 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.symbolic tutorial

27. Optional Presentation Title Unit Name Solving Equations Using Matlab (examples) “fzero” command - finds the value of x for f(x) = 0. e.g. For equation sin 2 (x) e -x/2 – 1 = 0 x = fzero('sin(x)^2*exp(-x/2)-1', -1) Using “solve” to solve linear and quadratic equations: e.g. For equation y = x 2 – 1, or y = 5x - 4 solve(‘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.