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Introduction To MatlabClass 4
Instructors: Hristiyan (Chris) Kourtev
and Xiaotao Su, PhD
Double click the matlab icon
When prompted click “Skip”
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
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
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
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
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
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
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
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
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);
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);
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
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’];
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’
5 9
10 3
9 5
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’
5 9
10 3
9 5
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
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}
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
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 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]
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
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)
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’)
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
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’)
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 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])
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.
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 sin2(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 = x2 – 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.