introduction to matlab class 4 instructors: hristiyan (chris) kourtev and xiaotao su, phd double...

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


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


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


Unit Name

%guessing_game.m


clear all;

%settings

num_trials = 5;

highest_number = 3;

%get info



%trial set up


%perform experiment








if(is_correct)

disp('Right!');

else



end


pause

disp('--------');

%record data




end

Task 1:

Write this section of the program

Hint:

input without ‘s’ is a good way

To get numeric responses from

The subject


Unit Name

%guessing_game.m


clear all;

%settings

num_trials = 5;

highest_number = 3;

%get info



%trial set up


%perform experiment








if(is_correct)

disp('Right!');

else



end


pause

disp('--------');

%record data




end


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


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


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);


Unit Name

%guessing_game.m


clear all;

%settings

num_trials = 5;

highest_number = 3;

%get info



%trial set up


%perform experiment








if(is_correct)

disp('Right!');

else



end


pause

disp('--------');

%record data




end

%data_storage

csvwrite([subject_name, '.csv'], …

guessing_game_data);


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


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’];


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


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


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


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}


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


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]


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


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)


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’)


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


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’)


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])


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.


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.

introduction to matlab class 4 instructors: hristiyan (chris) kourtev and xiaotao su, phd double...

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